The 506 Programs

Every cell of the 16 × 16 × 16 gates-of-gates grid is a lambda term, λp.λq.λa.λb. G (X p q) (Y p q) a b. Reducing all 4,096 of them gives 506 different normal forms, each behaving like one of the 16 gates. Here is every one, as a Tromp diagram and in eight notations. Numbers #1–506 match the Gates of Gates page.

Where it comes from maps, for each program, the cells that reduce to it: all 16 squares, laid out 4 × 4 as on the Gates of Gates page, with each marked cell coloured for the chosen quarter (one truth-table row). Coloured means the program is TRUE on that row, grey means FALSE.

Short form drops brackets by convention. Fully bracketed shows every application.

De Bruijn replaces names with “how many λs up”. Tromp binary writes that in bits: 00 = λ, 01 = apply, n ones and a zero = variable n.

Polish puts @ (apply) and λx before their parts; reverse Polish puts them after.

SKI uses no variables at all: S, K and I combined. JavaScript is arrow functions, runnable as written.

0 FALSE 0000 · 63 programs · 680 cells

#1FALSE · 0000396 cellslambda16.txt

Lambda, short form: λpqab.b
Lambda, fully bracketed: λp.(λq.(λa.(λb.b)))
De Bruijn: λλλλ1
Tromp binary: 0000000010 (10 bits)
Polish (prefix): λp λq λa λb b
Reverse Polish: b λb λa λq λp
SKI combinators: K(K(KI))
JavaScript: p => q => a => b => b

Where it comes from

FALSE ×256 · q∧¬p ×17 · AND ×17 · Q ×16 · p∧¬q ×17 · XOR ×2 · P ×16 · OR ×1 · NOR ×17 · ¬P ×16 · XNOR ×2 · p→q ×1 · ¬Q ×16 · NAND ×1 · q→p ×1

#2FALSE · 000016 cellse.g. q∧¬p(q∧¬p, FALSE)

Lambda, short form: λpqab.p b (q b b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) b)))))
De Bruijn: λλλλ((4 1) ((3 1) 1))
Tromp binary: 0000000001011111010010111101010 (31 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b b
Reverse Polish: p b @ q b @ b @ @ λb λa λq λp
SKI combinators: S(K(S(KK)))(S(S(KS)(S(KK)S))(K(SS(KI))))
JavaScript: p => q => a => b => p(b)(q(b)(b))

Where it comes from

q∧¬p ×4 · AND ×4 · p∧¬q ×4 · NOR ×4

#3FALSE · 000016 cellse.g. q∧¬p(AND, FALSE)

Lambda, short form: λpqab.p (q b b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) b)) b))))
De Bruijn: λλλλ((4 ((3 1) 1)) 1)
Tromp binary: 0000000001011111001011110101010 (31 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b b b
Reverse Polish: p q b @ b @ @ b @ λb λa λq λp
SKI combinators: S(K(S(KK)))(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(K(SS(KI))))))(K(KI)))
JavaScript: p => q => a => b => p(q(b)(b))(b)

Where it comes from

q∧¬p ×4 · AND ×4 · p∧¬q ×4 · NOR ×4

#4FALSE · 00008 cellse.g. q∧¬p(Q, FALSE)

Lambda, short form: λpqab.q b b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) b))))
De Bruijn: λλλλ((3 1) 1)
Tromp binary: 00000000010111101010 (20 bits)
Polish (prefix): λp λq λa λb @ @ q b b
Reverse Polish: q b @ b @ λb λa λq λp
SKI combinators: K(S(KK)(SS(KI)))
JavaScript: p => q => a => b => q(b)(b)

Where it comes from

q∧¬p ×2 · AND ×2 · p∧¬q ×2 · NOR ×2

#6FALSE · 00008 cellse.g. q∧¬p(P, FALSE)

Lambda, short form: λpqab.p b b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) b))))
De Bruijn: λλλλ((4 1) 1)
Tromp binary: 000000000101111101010 (21 bits)
Polish (prefix): λp λq λa λb @ @ p b b
Reverse Polish: p b @ b @ λb λa λq λp
SKI combinators: S(KK)(S(KK)(SS(KI)))
JavaScript: p => q => a => b => p(b)(b)

Where it comes from

q∧¬p ×2 · AND ×2 · p∧¬q ×2 · NOR ×2

#5FALSE · 00008 cellse.g. q∧¬p(XOR, FALSE)

Lambda, short form: λpqab.p (q b b) (q b b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) b)) ((q b) b)))))
De Bruijn: λλλλ((4 ((3 1) 1)) ((3 1) 1))
Tromp binary: 00000000010111110010111101010010111101010 (41 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b b @ @ q b b
Reverse Polish: p q b @ b @ @ q b @ b @ @ λb λa λq λp
SKI combinators: S(K(S(KK)))(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(K(SS(KI))))))(K(SS(KI))))
JavaScript: p => q => a => b => p(q(b)(b))(q(b)(b))

Where it comes from

q∧¬p ×2 · AND ×2 · p∧¬q ×2 · NOR ×2

#40FALSE · 00004 cellse.g. q∧¬p(Q, Q)

Lambda, short form: λpqab.q b (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((q a) b)))))
De Bruijn: λλλλ((3 1) ((3 2) 1))
Tromp binary: 0000000001011110100101111011010 (31 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ q a b
Reverse Polish: q b @ q a @ b @ @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(KK)S))I)
JavaScript: p => q => a => b => q(b)(q(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#86FALSE · 00004 cellse.g. q∧¬p(P, P)

Lambda, short form: λpqab.p b (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p a) b)))))
De Bruijn: λλλλ((4 1) ((4 2) 1))
Tromp binary: 000000000101111101001011111011010 (33 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p a b
Reverse Polish: p b @ p a @ b @ @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(KK)S))I)
JavaScript: p => q => a => b => p(b)(p(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#134FALSE · 00004 cellse.g. q∧¬p(¬P, ¬P)

Lambda, short form: λpqab.p (p b a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) b))))
De Bruijn: λλλλ((4 ((4 1) 2)) 1)
Tromp binary: 000000000101111100101111101011010 (33 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a b
Reverse Polish: p p b @ a @ @ b @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI)))
JavaScript: p => q => a => b => p(p(b)(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#180FALSE · 00004 cellse.g. q∧¬p(¬Q, ¬Q)

Lambda, short form: λpqab.q (q b a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((q b) a)) b))))
De Bruijn: λλλλ((3 ((3 1) 2)) 1)
Tromp binary: 0000000001011110010111101011010 (31 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ q b a b
Reverse Polish: q q b @ a @ @ b @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI)))
JavaScript: p => q => a => b => q(q(b)(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#10FALSE · 00004 cellse.g. q∧¬p(Q, q∧¬p)

Lambda, short form: λpqab.q b (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p b) ((q a) b))))))
De Bruijn: λλλλ((3 1) ((4 1) ((3 2) 1)))
Tromp binary: 000000000101111010010111110100101111011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p b @ @ q a b
Reverse Polish: q b @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => q(b)(p(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#16FALSE · 00004 cellse.g. q∧¬p(¬P, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) b))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) 1)
Tromp binary: 0000000001011111001011111010010111101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b b
Reverse Polish: p p b @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#25FALSE · 00004 cellse.g. q∧¬p(Q, AND)

Lambda, short form: λpqab.q b (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((3 1) ((4 ((3 2) 1)) 1))
Tromp binary: 000000000101111010010111110010111101101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p @ @ q a b b
Reverse Polish: q b @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => q(b)(p(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#28FALSE · 00004 cellse.g. q∧¬p(P, AND)

Lambda, short form: λpqab.p b (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 1) ((4 ((3 2) 1)) 1))
Tromp binary: 0000000001011111010010111110010111101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p @ @ q a b b
Reverse Polish: p b @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(p(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#43FALSE · 00004 cellse.g. q∧¬p(OR, Q)

Lambda, short form: λpqab.p b (q b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((q a) b))))))
De Bruijn: λλλλ((4 1) ((3 1) ((3 2) 1)))
Tromp binary: 000000000101111101001011110100101111011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ q a b
Reverse Polish: p b @ q b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))I))
JavaScript: p => q => a => b => p(b)(q(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#46FALSE · 00004 cellse.g. q∧¬p(p→q, Q)

Lambda, short form: λpqab.p (q b (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((q a) b))) b))))
De Bruijn: λλλλ((4 ((3 1) ((3 2) 1))) 1)
Tromp binary: 000000000101111100101111010010111101101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ q a b b
Reverse Polish: p q b @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))I))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#56FALSE · 00004 cellse.g. q∧¬p(P, p∧¬q)

Lambda, short form: λpqab.p b (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 1) ((4 ((3 1) 2)) 1))
Tromp binary: 0000000001011111010010111110010111101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p @ @ q b a b
Reverse Polish: p b @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(p(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#62FALSE · 00004 cellse.g. q∧¬p(¬Q, p∧¬q)

Lambda, short form: λpqab.q (p (q b a) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) b)) b))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) 1)) 1)
Tromp binary: 000000000101111001011111001011110101101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a b b
Reverse Polish: q p q b @ a @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(q(b)(a))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#87FALSE · 00004 cellse.g. q∧¬p(OR, P)

Lambda, short form: λpqab.p b (q b (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p a) b))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 2) 1)))
Tromp binary: 0000000001011111010010111101001011111011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p a b
Reverse Polish: p b @ q b @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))K)
JavaScript: p => q => a => b => p(b)(q(b)(p(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#94FALSE · 00004 cellse.g. q∧¬p(q→p, P)

Lambda, short form: λpqab.p b (q (p a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p a) b)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 2) 1)) 1))
Tromp binary: 0000000001011111010010111100101111101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p a b b
Reverse Polish: p b @ q p a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#119FALSE · 00004 cellse.g. q∧¬p(¬P, NOR)

Lambda, short form: λpqab.p (p b (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) b))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) 1)
Tromp binary: 0000000001011111001011111010010111101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a b
Reverse Polish: p p b @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#122FALSE · 00004 cellse.g. q∧¬p(¬Q, NOR)

Lambda, short form: λpqab.q (p b (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) ((q b) a))) b))))
De Bruijn: λλλλ((3 ((4 1) ((3 1) 2))) 1)
Tromp binary: 000000000101111001011111010010111101011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b @ @ q b a b
Reverse Polish: q p b @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(b)(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#136FALSE · 00004 cellse.g. q∧¬p(p→q, ¬P)

Lambda, short form: λpqab.p (q b (p b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) a))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) 2))) 1)
Tromp binary: 0000000001011111001011110100101111101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b a b
Reverse Polish: p q b @ p b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#138FALSE · 00004 cellse.g. q∧¬p(NAND, ¬P)

Lambda, short form: λpqab.p (q (p b a) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) 1)) 1)
Tromp binary: 0000000001011111001011110010111110101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a b b
Reverse Polish: p q p b @ a @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(b)(a))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#181FALSE · 00004 cellse.g. q∧¬p(NAND, ¬Q)

Lambda, short form: λpqab.p (q (q b a) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) 1)) 1)
Tromp binary: 000000000101111100101111001011110101101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a b b
Reverse Polish: p q q b @ a @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(q(b)(a))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#182FALSE · 00004 cellse.g. q∧¬p(q→p, ¬Q)

Lambda, short form: λpqab.p b (q (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((q b) a)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((3 1) 2)) 1))
Tromp binary: 000000000101111101001011110010111101011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ q b a b
Reverse Polish: p b @ q q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI))))
JavaScript: p => q => a => b => p(b)(q(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#244FALSE · 00004 cellse.g. XOR(Q, Q)

Lambda, short form: λpqab.q (q b a) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((q b) a)) ((q a) b)))))
De Bruijn: λλλλ((3 ((3 1) 2)) ((3 2) 1))
Tromp binary: 000000000101111001011110101100101111011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ q b a @ @ q a b
Reverse Polish: q q b @ a @ @ q a @ b @ @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I)
JavaScript: p => q => a => b => q(q(b)(a))(q(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#287FALSE · 00004 cellse.g. XOR(P, P)

Lambda, short form: λpqab.p (p b a) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((p a) b)))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((4 2) 1))
Tromp binary: 000000000101111100101111101011001011111011010 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ p a b
Reverse Polish: p p b @ a @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I)
JavaScript: p => q => a => b => p(p(b)(a))(p(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#14FALSE · 00004 cellse.g. q∧¬p(OR, q∧¬p)

Lambda, short form: λpqab.p b (q b (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 1) ((3 2) 1))))
Tromp binary: 00000000010111110100101111010010111110100101111011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p b @ @ q a b
Reverse Polish: p b @ q b @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(b)(q(b)(p(b)(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#18FALSE · 00004 cellse.g. q∧¬p(p→q, q∧¬p)

Lambda, short form: λpqab.p (q b (p b (q a b))) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) ((q a) b)))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) ((3 2) 1)))) 1)
Tromp binary: 00000000010111110010111101001011111010010111101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b @ @ q a b b
Reverse Polish: p q b @ p b @ q a @ b @ @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S)))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(b)(q(a)(b))))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#20FALSE · 00004 cellse.g. q∧¬p(NAND, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) 1)) 1)
Tromp binary: 00000000010111110010111100101111101001011110110101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b b b
Reverse Polish: p q p b @ q a @ b @ @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#29FALSE · 00004 cellse.g. q∧¬p(OR, AND)

Lambda, short form: λpqab.p b (q b (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 ((3 2) 1)) 1)))
Tromp binary: 00000000010111110100101111010010111110010111101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p @ @ q a b b
Reverse Polish: p b @ q b @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(b)(q(b)(p(q(a)(b))(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#33FALSE · 00004 cellse.g. q∧¬p(p→q, AND)

Lambda, short form: λpqab.p (q b (p (q a b) b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) b))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) 1))) 1)
Tromp binary: 00000000010111110010111101001011111001011110110101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b b b
Reverse Polish: p q b @ p q a @ b @ @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#36FALSE · 00004 cellse.g. q∧¬p(q→p, AND)

Lambda, short form: λpqab.p b (q (p (q a b) b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p ((q a) b)) b)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 ((3 2) 1)) 1)) 1))
Tromp binary: 00000000010111110100101111001011111001011110110101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p @ @ q a b b b
Reverse Polish: p b @ q p q a @ b @ @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(q(a)(b))(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#57FALSE · 00004 cellse.g. q∧¬p(OR, p∧¬q)

Lambda, short form: λpqab.p b (q b (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 ((3 1) 2)) 1)))
Tromp binary: 00000000010111110100101111010010111110010111101011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p @ @ q b a b
Reverse Polish: p b @ q b @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(b)(q(b)(p(q(b)(a))(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#63FALSE · 00004 cellse.g. q∧¬p(NAND, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) 1)) 1)
Tromp binary: 00000000010111110010111100101111100101111010110101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b b b
Reverse Polish: p q p q b @ a @ @ b @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#64FALSE · 00004 cellse.g. q∧¬p(q→p, p∧¬q)

Lambda, short form: λpqab.p b (q (p (q b a) b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p ((q b) a)) b)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 ((3 1) 2)) 1)) 1))
Tromp binary: 00000000010111110100101111001011111001011110101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p @ @ q b a b b
Reverse Polish: p b @ q p q b @ a @ @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(q(b)(a))(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#102FALSE · 00004 cellse.g. q∧¬p(OR, OR)

Lambda, short form: λpqab.p b (q b (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 2) ((3 2) 1))))
Tromp binary: 000000000101111101001011110100101111101100101111011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p a @ @ q a b
Reverse Polish: p b @ q b @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(b)(q(b)(p(a)(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#121FALSE · 00004 cellse.g. q∧¬p(p→q, NOR)

Lambda, short form: λpqab.p (q b (p b (q b a))) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) ((q b) a)))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) ((3 1) 2)))) 1)
Tromp binary: 00000000010111110010111101001011111010010111101011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b @ @ q b a b
Reverse Polish: p q b @ p b @ q b @ a @ @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(b)(q(b)(a))))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#123FALSE · 00004 cellse.g. q∧¬p(NAND, NOR)

Lambda, short form: λpqab.p (q (p b (q b a)) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) 1)) 1)
Tromp binary: 00000000010111110010111100101111101001011110101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a b b
Reverse Polish: p q p b @ q b @ a @ @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#124FALSE · 00004 cellse.g. q∧¬p(q→p, NOR)

Lambda, short form: λpqab.p b (q (p b (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p b) ((q b) a))) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 1) ((3 1) 2))) 1))
Tromp binary: 00000000010111110100101111001011111010010111101011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p b @ @ q b a b
Reverse Polish: p b @ q p b @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(b)(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#166FALSE · 00004 cellse.g. q∧¬p(p→q, p→q)

Lambda, short form: λpqab.p (q b (p (q a b) a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) a))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) 2))) 1)
Tromp binary: 000000000101111100101111010010111110010111101101011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b a b
Reverse Polish: p q b @ p q a @ b @ @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#196FALSE · 00004 cellse.g. q∧¬p(NAND, NAND)

Lambda, short form: λpqab.p (q (p (q b a) a) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) 1)) 1)
Tromp binary: 000000000101111100101111001011111001011110101101101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a b b
Reverse Polish: p q p q b @ a @ @ a @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#212FALSE · 00004 cellse.g. q∧¬p(q→p, q→p)

Lambda, short form: λpqab.p b (q (p a (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p a) ((q b) a))) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 2) ((3 1) 2))) 1))
Tromp binary: 000000000101111101001011110010111110110010111101011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p a @ @ q b a b
Reverse Polish: p b @ q p a @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(a)(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#72FALSE · 00004 cellse.g. q∧¬p(OR, XOR)

Lambda, short form: λpqab.p b (q b (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 0000000001011111010010111101001011111001011110101100101111011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p b @ q b @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(b)(q(b)(p(q(b)(a))(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#78FALSE · 00004 cellse.g. q∧¬p(NAND, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1)) 1)
Tromp binary: 0000000001011111001011110010111110010111101011001011110110101010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b b b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#151FALSE · 00004 cellse.g. q∧¬p(p→q, XNOR)

Lambda, short form: λpqab.p (q b (p (q a b) (q b a))) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) ((q b) a)))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) ((3 1) 2)))) 1)
Tromp binary: 0000000001011111001011110100101111100101111011010010111101011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b @ @ q b a b
Reverse Polish: p q b @ p q a @ b @ @ q b @ a @ @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(q(b)(a))))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#154FALSE · 00004 cellse.g. q∧¬p(q→p, XNOR)

Lambda, short form: λpqab.p b (q (p (q a b) (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p ((q a) b)) ((q b) a))) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1))
Tromp binary: 0000000001011111010010111100101111100101111011010010111101011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p @ @ q a b @ @ q b a b
Reverse Polish: p b @ q p q a @ b @ @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(q(a)(b))(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#8FALSE · 00004 cellse.g. q∧¬p(q∧¬p, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (q b (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((q b) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((3 1) ((4 1) ((3 2) 1))))
Tromp binary: 000000000101111100101111101001011110110100101111010010111110100101111011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ q b @ @ p b @ @ q a b
Reverse Polish: p p b @ q a @ b @ @ @ q b @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(q(b)(p(b)(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#24FALSE · 00004 cellse.g. q∧¬p(AND, AND)

Lambda, short form: λpqab.p (q b (p (q a b) b)) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) b))) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) 1))) ((4 ((3 2) 1)) 1))
Tromp binary: 000000000101111100101111010010111110010111101101010010111110010111101101010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b b @ @ p @ @ q a b b
Reverse Polish: p q b @ p q a @ b @ @ b @ @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(b)))(p(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#54FALSE · 00004 cellse.g. q∧¬p(p∧¬q, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) b) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) b)) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) 1)) ((4 ((3 1) 2)) 1))
Tromp binary: 000000000101111100101111001011111001011110101101010010111110010111101011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b b @ @ p @ @ q b a b
Reverse Polish: p q p q b @ a @ @ b @ @ b @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(b))(p(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#118FALSE · 00004 cellse.g. q∧¬p(NOR, NOR)

Lambda, short form: λpqab.p (p b (q b a)) (q (p b (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((q ((p b) ((q b) a))) b)))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((3 ((4 1) ((3 1) 2))) 1))
Tromp binary: 000000000101111100101111101001011110101100101111001011111010010111101011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ q @ @ p b @ @ q b a b
Reverse Polish: p p b @ q b @ a @ @ @ q p b @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(q(p(b)(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#12FALSE · 00004 cellse.g. q∧¬p(XOR, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) b) (q b (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) b)) ((q b) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) 1)) ((3 1) ((4 1) ((3 2) 1))))
Tromp binary: 0000000001011111001011110010111110100101111011010100101111010010111110100101111011010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b b @ @ q b @ @ p b @ @ q a b
Reverse Polish: p q p b @ q a @ b @ @ @ b @ @ q b @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(b))(q(b)(p(b)(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#32FALSE · 00004 cellse.g. q∧¬p(XNOR, AND)

Lambda, short form: λpqab.p (q b (p (q a b) b)) (q (p (q a b) b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) b))) ((q ((p ((q a) b)) b)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) 1))) ((3 ((4 ((3 2) 1)) 1)) 1))
Tromp binary: 0000000001011111001011110100101111100101111011010100101111001011111001011110110101010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b b @ @ q @ @ p @ @ q a b b b
Reverse Polish: p q b @ p q a @ b @ @ b @ @ @ q p q a @ b @ @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(b)))(q(p(q(a)(b))(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#55FALSE · 00004 cellse.g. q∧¬p(XOR, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) b) (q b (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) b)) ((q b) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) 1)) ((3 1) ((4 ((3 1) 2)) 1)))
Tromp binary: 0000000001011111001011110010111110010111101011010100101111010010111110010111101011010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b b @ @ q b @ @ p @ @ q b a b
Reverse Polish: p q p q b @ a @ @ b @ @ b @ @ q b @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(b))(q(b)(p(q(b)(a))(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#120FALSE · 00004 cellse.g. q∧¬p(XNOR, NOR)

Lambda, short form: λpqab.p (q b (p b (q b a))) (q (p b (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) ((q b) a)))) ((q ((p b) ((q b) a))) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) ((3 1) 2)))) ((3 ((4 1) ((3 1) 2))) 1))
Tromp binary: 0000000001011111001011110100101111101001011110101100101111001011111010010111101011010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b @ @ q b a @ @ q @ @ p b @ @ q b a b
Reverse Polish: p q b @ p b @ q b @ a @ @ @ @ q p b @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(b)(q(b)(a))))(q(p(b)(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#214FALSE · 00004 cellse.g. XOR(q∧¬p, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (q (p a (q b a)) (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((q ((p a) ((q b) a))) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1))))
Tromp binary: 00000000010111110010111110100101111011010010111100101111101100101111010110010111110100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b
Reverse Polish: p p b @ q a @ b @ @ @ q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(q(p(a)(q(b)(a)))(p(b)(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

#229FALSE · 00004 cellse.g. XOR(AND, AND)

Lambda, short form: λpqab.p (q (p (q b a) a) (p (q a b) b)) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) ((p ((q a) b)) b))) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1))) ((4 ((3 2) 1)) 1))
Tromp binary: 00000000010111110010111100101111100101111010110110010111110010111101101010010111110010111101101010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b @ @ p @ @ q a b b
Reverse Polish: p q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(p(q(a)(b))(b)))(p(q(a)(b))(b))

Where it comes from

XOR ×2 · XNOR ×2

#257FALSE · 00004 cellse.g. XOR(p∧¬q, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) (p (q a b) a)) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) ((p ((q a) b)) a))) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2))) ((4 ((3 1) 2)) 1))
Tromp binary: 00000000010111110010111100101111100101111010110100101111100101111011010110010111110010111101011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a @ @ p @ @ q b a b
Reverse Polish: p q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(p(q(a)(b))(a)))(p(q(b)(a))(b))

Where it comes from

XOR ×2 · XNOR ×2

#302FALSE · 00004 cellse.g. XOR(OR, OR)

Lambda, short form: λpqab.p (p b (q b a)) (q (p b (q b a)) (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((q ((p b) ((q b) a))) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1))))
Tromp binary: 00000000010111110010111110100101111010110010111100101111101001011110101100101111101100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b
Reverse Polish: p p b @ q b @ a @ @ @ q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(q(p(b)(q(b)(a)))(p(a)(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

#70FALSE · 00004 cellse.g. q∧¬p(XOR, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) b) (q b (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) b)) ((q b) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1)) ((3 1) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 00000000010111110010111100101111100101111010110010111101101010010111101001011111001011110101100101111011010 (107 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b b @ @ q b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ b @ @ q b @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(b))(q(b)(p(q(b)(a))(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#150FALSE · 00004 cellse.g. q∧¬p(XNOR, XNOR)

Lambda, short form: λpqab.p (q b (p (q a b) (q b a))) (q (p (q a b) (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) ((q b) a)))) ((q ((p ((q a) b)) ((q b) a))) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) ((3 1) 2)))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1))
Tromp binary: 00000000010111110010111101001011111001011110110100101111010110010111100101111100101111011010010111101011010 (107 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q a b @ @ q b a b
Reverse Polish: p q b @ p q a @ b @ @ q b @ a @ @ @ @ q p q a @ b @ @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(q(b)(a))))(q(p(q(a)(b))(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#272FALSE · 00004 cellse.g. XOR(XOR, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) (p (q a b) (q b a))) (q (p (q a b) (q b a)) (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a)))) ((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2)))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 00000000010111110010111100101111100101111010110010111101101001011111001011110110100101111010110010111100101111100101111011010010111101011001011111001011110101100101111011010 (173 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ @ q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a))))(q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

1 q AND NOT p 0010 · 32 programs · 216 cells

#7q AND NOT p · 001092 cellslambda16.txt

Lambda, short form: λpqab.p b (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q a) b)))))
De Bruijn: λλλλ((4 1) ((3 2) 1))
Tromp binary: 00000000010111110100101111011010 (32 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q a b
Reverse Polish: p b @ q a @ b @ @ λb λa λq λp
SKI combinators: S(KS)(S(KK)S)
JavaScript: p => q => a => b => p(b)(q(a)(b))

Where it comes from

q∧¬p ×3 · AND ×3 · Q ×16 · p∧¬q ×3 · XOR ×4 · P ×16 · OR ×2 · NOR ×3 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#137q AND NOT p · 00104 cellse.g. q∧¬p(¬Q, ¬P)

Lambda, short form: λpqab.q (p b a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) a)) b))))
De Bruijn: λλλλ((3 ((4 1) 2)) 1)
Tromp binary: 00000000010111100101111101011010 (32 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b a b
Reverse Polish: q p b @ a @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(b)(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#13q AND NOT p · 00104 cellse.g. q∧¬p(P, q∧¬p)

Lambda, short form: λpqab.p b (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 1) ((4 1) ((3 2) 1)))
Tromp binary: 0000000001011111010010111110100101111011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p b @ @ q a b
Reverse Polish: p b @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(b)(p(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#19q AND NOT p · 00104 cellse.g. q∧¬p(¬Q, q∧¬p)

Lambda, short form: λpqab.q (p b (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) ((q a) b))) b))))
De Bruijn: λλλλ((3 ((4 1) ((3 2) 1))) 1)
Tromp binary: 000000000101111001011111010010111101101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b @ @ q a b b
Reverse Polish: q p b @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(b)(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#49q AND NOT p · 00104 cellse.g. q∧¬p(q→p, Q)

Lambda, short form: λpqab.p b (q (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((q a) b)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((3 2) 1)) 1))
Tromp binary: 000000000101111101001011110010111101101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ q a b b
Reverse Polish: p b @ q q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI))))
JavaScript: p => q => a => b => p(b)(q(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#101q AND NOT p · 00104 cellse.g. q∧¬p(P, OR)

Lambda, short form: λpqab.p b (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 1) ((4 2) ((3 2) 1)))
Tromp binary: 00000000010111110100101111101100101111011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p a @ @ q a b
Reverse Polish: p b @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(b)(p(a)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#139q AND NOT p · 00104 cellse.g. q∧¬p(q→p, ¬P)

Lambda, short form: λpqab.p b (q (p b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p b) a)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 1) 2)) 1))
Tromp binary: 0000000001011111010010111100101111101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p b a b
Reverse Polish: p b @ q p b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#195q AND NOT p · 00104 cellse.g. q∧¬p(¬Q, NAND)

Lambda, short form: λpqab.q (p (q b a) a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) a)) b))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) 2)) 1)
Tromp binary: 0000000001011110010111110010111101011011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a a b
Reverse Polish: q p q b @ a @ @ a @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(q(b)(a))(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#21q AND NOT p · 00104 cellse.g. q∧¬p(q→p, q∧¬p)

Lambda, short form: λpqab.p b (q (p b (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p b) ((q a) b))) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 1) ((3 2) 1))) 1))
Tromp binary: 00000000010111110100101111001011111010010111101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p b @ @ q a b b
Reverse Polish: p b @ q p b @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(b)(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#39q AND NOT p · 00104 cellse.g. q∧¬p(AND, Q)

Lambda, short form: λpqab.p (q b (q a b)) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((q a) b))) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 1) ((3 2) 1))) ((3 2) 1))
Tromp binary: 00000000010111110010111101001011110110100101111011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ q a b @ @ q a b
Reverse Polish: p q b @ q a @ b @ @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))I))))))(KI)
JavaScript: p => q => a => b => p(q(b)(q(a)(b)))(q(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#71q AND NOT p · 00104 cellse.g. q∧¬p(P, XOR)

Lambda, short form: λpqab.p b (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 1) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 000000000101111101001011111001011110101100101111011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p b @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(b)(p(q(b)(a))(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#77q AND NOT p · 00104 cellse.g. q∧¬p(¬Q, XOR)

Lambda, short form: λpqab.q (p (q b a) (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) ((q a) b))) b))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1)
Tromp binary: 00000000010111100101111100101111010110010111101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a @ @ q a b b
Reverse Polish: q p q b @ a @ @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(q(b)(a))(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#109q AND NOT p · 00104 cellse.g. q∧¬p(q→p, OR)

Lambda, short form: λpqab.p b (q (p a (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p a) ((q a) b))) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 2) ((3 2) 1))) 1))
Tromp binary: 000000000101111101001011110010111110110010111101101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p a @ @ q a b b
Reverse Polish: p b @ q p a @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(a)(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#133q AND NOT p · 00104 cellse.g. q∧¬p(NOR, ¬P)

Lambda, short form: λpqab.p (p b a) (q (p b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((q ((p b) a)) b)))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((3 ((4 1) 2)) 1))
Tromp binary: 0000000001011111001011111010110010111100101111101011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ q @ @ p b a b
Reverse Polish: p p b @ a @ @ q p b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(b)(a))(q(p(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#169q AND NOT p · 00104 cellse.g. q∧¬p(q→p, p→q)

Lambda, short form: λpqab.p b (q (p (q a b) a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p ((q a) b)) a)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 ((3 2) 1)) 2)) 1))
Tromp binary: 000000000101111101001011110010111110010111101101011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p @ @ q a b a b
Reverse Polish: p b @ q p q a @ b @ @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(q(a)(b))(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#197q AND NOT p · 00104 cellse.g. q∧¬p(q→p, NAND)

Lambda, short form: λpqab.p b (q (p (q b a) a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p ((q b) a)) a)) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 ((3 1) 2)) 2)) 1))
Tromp binary: 000000000101111101001011110010111110010111101011011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p @ @ q b a a b
Reverse Polish: p b @ q p q b @ a @ @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(q(b)(a))(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#45q AND NOT p · 00104 cellse.g. q∧¬p(XNOR, Q)

Lambda, short form: λpqab.p (q b (q a b)) (q (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((q a) b))) ((q ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((3 2) 1))) ((3 ((3 2) 1)) 1))
Tromp binary: 000000000101111100101111010010111101101001011110010111101101010 (63 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ q a b @ @ q @ @ q a b b
Reverse Polish: p q b @ q a @ b @ @ @ q q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))I))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI))))
JavaScript: p => q => a => b => p(q(b)(q(a)(b)))(q(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#79q AND NOT p · 00104 cellse.g. q∧¬p(q→p, XOR)

Lambda, short form: λpqab.p b (q (p (q b a) (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q ((p ((q b) a)) ((q a) b))) b)))))
De Bruijn: λλλλ((4 1) ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1))
Tromp binary: 0000000001011111010010111100101111100101111010110010111101101010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q @ @ p @ @ q b a @ @ q a b b
Reverse Polish: p b @ q p q b @ a @ @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI))))
JavaScript: p => q => a => b => p(b)(q(p(q(b)(a))(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#135q AND NOT p · 00104 cellse.g. q∧¬p(XNOR, ¬P)

Lambda, short form: λpqab.p (q b (p b a)) (q (p b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) a))) ((q ((p b) a)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) 2))) ((3 ((4 1) 2)) 1))
Tromp binary: 00000000010111110010111101001011111010110010111100101111101011010 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b a @ @ q @ @ p b a b
Reverse Polish: p q b @ p b @ a @ @ @ q p b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(b)(a)))(q(p(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#230q AND NOT p · 00104 cellse.g. XOR(Q, AND)

Lambda, short form: λpqab.q (p (q b a) a) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) a)) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1))
Tromp binary: 00000000010111100101111100101111010110110010111110010111101101010 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b
Reverse Polish: q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => q(p(q(b)(a))(a))(p(q(a)(b))(b))

Where it comes from

XOR ×2 · XNOR ×2

#243q AND NOT p · 00104 cellse.g. XOR(AND, Q)

Lambda, short form: λpqab.p (q (q b a) (q a b)) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) ((q a) b))) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) ((3 2) 1))) ((3 2) 1))
Tromp binary: 0000000001011111001011110010111101011001011110110100101111011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a @ @ q a b @ @ q a b
Reverse Polish: p q q b @ a @ @ q a @ b @ @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I))))))(KI)
JavaScript: p => q => a => b => p(q(q(b)(a))(q(a)(b)))(q(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#288q AND NOT p · 00104 cellse.g. XOR(OR, P)

Lambda, short form: λpqab.p (p b a) (q (p b a) (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((q ((p b) a)) ((p a) b))))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((3 ((4 1) 2)) ((4 2) 1)))
Tromp binary: 0000000001011111001011111010110010111100101111101011001011111011010 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ q @ @ p b a @ @ p a b
Reverse Polish: p p b @ a @ @ q p b @ a @ @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K)
JavaScript: p => q => a => b => p(p(b)(a))(q(p(b)(a))(p(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#301q AND NOT p · 00104 cellse.g. XOR(P, OR)

Lambda, short form: λpqab.p (p b (q b a)) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1)))
Tromp binary: 000000000101111100101111101001011110101100101111101100101111011010 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ p a @ @ q a b
Reverse Polish: p p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(p(a)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#9q AND NOT p · 00104 cellse.g. q∧¬p(AND, q∧¬p)

Lambda, short form: λpqab.p (q b (p b (q a b))) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) ((q a) b)))) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) ((3 2) 1)))) ((4 1) ((3 2) 1)))
Tromp binary: 000000000101111100101111010010111110100101111011010010111110100101111011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b @ @ q a b @ @ p b @ @ q a b
Reverse Polish: p q b @ p b @ q a @ b @ @ @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S)))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(q(b)(p(b)(q(a)(b))))(p(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#11q AND NOT p · 00104 cellse.g. q∧¬p(p∧¬q, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) b) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) b)) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) 1)) ((4 1) ((3 2) 1)))
Tromp binary: 000000000101111100101111001011111010010111101101010010111110100101111011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b b @ @ p b @ @ q a b
Reverse Polish: p q p b @ q a @ b @ @ @ b @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI))))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(b))(p(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#15q AND NOT p · 00104 cellse.g. q∧¬p(NOR, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (q (p b (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((q ((p b) ((q a) b))) b)))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((3 ((4 1) ((3 2) 1))) 1))
Tromp binary: 000000000101111100101111101001011110110100101111001011111010010111101101010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ q @ @ p b @ @ q a b b
Reverse Polish: p p b @ q a @ b @ @ @ q p b @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(q(p(b)(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#310q AND NOT p · 00104 cellse.g. OR(q∧¬p, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (q a (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((q a) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((3 2) ((4 1) ((3 2) 1))))
Tromp binary: 0000000001011111001011111010010111101101001011110110010111110100101111011010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ q a @ @ p b @ @ q a b
Reverse Polish: p p b @ q a @ b @ @ @ q a @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(q(a)(p(b)(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#17q AND NOT p · 00104 cellse.g. q∧¬p(XNOR, q∧¬p)

Lambda, short form: λpqab.p (q b (p b (q a b))) (q (p b (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) ((q a) b)))) ((q ((p b) ((q a) b))) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) ((3 2) 1)))) ((3 ((4 1) ((3 2) 1))) 1))
Tromp binary: 0000000001011111001011110100101111101001011110110100101111001011111010010111101101010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b @ @ q a b @ @ q @ @ p b @ @ q a b b
Reverse Polish: p q b @ p b @ q a @ b @ @ @ @ q p b @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(KK)S)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(b)(q(a)(b))))(q(p(b)(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#165q AND NOT p · 00104 cellse.g. q∧¬p(XNOR, p→q)

Lambda, short form: λpqab.p (q b (p (q a b) a)) (q (p (q a b) a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) a))) ((q ((p ((q a) b)) a)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) 2))) ((3 ((4 ((3 2) 1)) 2)) 1))
Tromp binary: 000000000101111100101111010010111110010111101101011001011110010111110010111101101011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b a @ @ q @ @ p @ @ q a b a b
Reverse Polish: p q b @ p q a @ b @ @ a @ @ @ q p q a @ b @ @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(a)))(q(p(q(a)(b))(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#69q AND NOT p · 00104 cellse.g. q∧¬p(p∧¬q, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) b) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) b)) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1)) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110010111110010111101011001011110110101001011111001011110101100101111011010 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ b @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(b))(p(q(b)(a))(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#258q AND NOT p · 00104 cellse.g. XOR(XOR, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) (p (q a b) a)) (q (p (q a b) a) (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) ((p ((q a) b)) a))) ((q ((p ((q a) b)) a)) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2))) ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1)))
Tromp binary: 00000000010111110010111100101111100101111010110100101111100101111011010110010111100101111100101111011010110010111110010111101011010 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b
Reverse Polish: p q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ @ q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(p(q(a)(b))(a)))(q(p(q(a)(b))(a))(p(q(b)(a))(b)))

Where it comes from

XOR ×2 · XNOR ×2

#271q AND NOT p · 00104 cellse.g. XOR(p∧¬q, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) (p (q a b) (q b a))) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a)))) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2)))) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110010111110010111101011001011110110100101111100101111011010010111101011001011111001011110101100101111011010 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a))))(p(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

2 AND 1000 · 32 programs · 216 cells

#22AND · 100092 cellslambda16.txt

Lambda, short form: λpqab.p (q a b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) b))))
De Bruijn: λλλλ((4 ((3 2) 1)) 1)
Tromp binary: 00000000010111110010111101101010 (32 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b b
Reverse Polish: p q a @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(a)(b))(b)

Where it comes from

q∧¬p ×3 · AND ×3 · Q ×16 · p∧¬q ×3 · XOR ×4 · P ×16 · OR ×2 · NOR ×3 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#92AND · 10004 cellse.g. q∧¬p(¬Q, P)

Lambda, short form: λpqab.q (p a b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) b)) b))))
De Bruijn: λλλλ((3 ((4 2) 1)) 1)
Tromp binary: 00000000010111100101111101101010 (32 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a b b
Reverse Polish: q p a @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(a)(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#31AND · 10004 cellse.g. q∧¬p(¬P, AND)

Lambda, short form: λpqab.p (p (q a b) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) b))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) 1)
Tromp binary: 0000000001011111001011111001011110110101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b b
Reverse Polish: p p q a @ b @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#34AND · 10004 cellse.g. q∧¬p(¬Q, AND)

Lambda, short form: λpqab.q (p (q a b) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) b)) b))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) 1)) 1)
Tromp binary: 000000000101111001011111001011110110101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b b b
Reverse Polish: q p q a @ b @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(q(a)(b))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#48AND · 10004 cellse.g. q∧¬p(NAND, Q)

Lambda, short form: λpqab.p (q (q a b) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) 1)) 1)
Tromp binary: 000000000101111100101111001011110110101010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b b b
Reverse Polish: p q q a @ b @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(q(a)(b))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#93AND · 10004 cellse.g. q∧¬p(NAND, P)

Lambda, short form: λpqab.p (q (p a b) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) 1)) 1)
Tromp binary: 0000000001011111001011110010111110110101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b b b
Reverse Polish: p q p a @ b @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(a)(b))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#164AND · 10004 cellse.g. q∧¬p(¬P, p→q)

Lambda, short form: λpqab.p (p (q a b) a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) b))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) 1)
Tromp binary: 00000000010111110010111110010111101101011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a b
Reverse Polish: p p q a @ b @ @ a @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#210AND · 10004 cellse.g. q∧¬p(¬Q, q→p)

Lambda, short form: λpqab.q (p a (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) ((q b) a))) b))))
De Bruijn: λλλλ((3 ((4 2) ((3 1) 2))) 1)
Tromp binary: 0000000001011110010111110110010111101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a @ @ q b a b
Reverse Polish: q p a @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(a)(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#35AND · 10004 cellse.g. q∧¬p(NAND, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) 1)) 1)
Tromp binary: 00000000010111110010111100101111100101111011010101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b b b
Reverse Polish: p q p q a @ b @ @ b @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#38AND · 10004 cellse.g. q∧¬p(q∧¬p, Q)

Lambda, short form: λpqab.p (q a b) (q b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 1) ((3 2) 1)))
Tromp binary: 00000000010111110010111101101001011110100101111011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q b @ @ q a b
Reverse Polish: p q a @ b @ @ q b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))I))
JavaScript: p => q => a => b => p(q(a)(b))(q(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#84AND · 10004 cellse.g. q∧¬p(p∧¬q, P)

Lambda, short form: λpqab.p (q (p a b) b) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) b)) ((p a) b)))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) 1)) ((4 2) 1))
Tromp binary: 0000000001011111001011110010111110110101001011111011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b b @ @ p a b
Reverse Polish: p q p a @ b @ @ b @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI))))))))K
JavaScript: p => q => a => b => p(q(p(a)(b))(b))(p(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#108AND · 10004 cellse.g. q∧¬p(NAND, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) 1)) 1)
Tromp binary: 000000000101111100101111001011111011001011110110101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b b b
Reverse Polish: p q p a @ q a @ b @ @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#149AND · 10004 cellse.g. q∧¬p(¬P, XNOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) b))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) 1)
Tromp binary: 000000000101111100101111100101111011010010111101011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a b
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#152AND · 10004 cellse.g. q∧¬p(¬Q, XNOR)

Lambda, short form: λpqab.q (p (q a b) (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) ((q b) a))) b))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1)
Tromp binary: 00000000010111100101111100101111011010010111101011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b @ @ q b a b
Reverse Polish: q p q a @ b @ @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(q(a)(b))(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#168AND · 10004 cellse.g. q∧¬p(NAND, p→q)

Lambda, short form: λpqab.p (q (p (q a b) a) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) 1)) 1)
Tromp binary: 000000000101111100101111001011111001011110110101101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a b b
Reverse Polish: p q p q a @ b @ @ a @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#211AND · 10004 cellse.g. q∧¬p(NAND, q→p)

Lambda, short form: λpqab.p (q (p a (q b a)) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) 1)) 1)
Tromp binary: 000000000101111100101111001011111011001011110101101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a b b
Reverse Polish: p q p a @ q b @ a @ @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#42AND · 10004 cellse.g. q∧¬p(XOR, Q)

Lambda, short form: λpqab.p (q (q a b) b) (q b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) b)) ((q b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) 1)) ((3 1) ((3 2) 1)))
Tromp binary: 000000000101111100101111001011110110101001011110100101111011010 (63 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b b @ @ q b @ @ q a b
Reverse Polish: p q q a @ b @ @ b @ @ q b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI))))))))(K(S(S(KS)(S(KK)S))I))
JavaScript: p => q => a => b => p(q(q(a)(b))(b))(q(b)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#85AND · 10004 cellse.g. q∧¬p(XOR, P)

Lambda, short form: λpqab.p (q (p a b) b) (q b (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) b)) ((q b) ((p a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) 1)) ((3 1) ((4 2) 1)))
Tromp binary: 00000000010111110010111100101111101101010010111101001011111011010 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b b @ @ q b @ @ p a b
Reverse Polish: p q p a @ b @ @ b @ @ q b @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))K)
JavaScript: p => q => a => b => p(q(p(a)(b))(b))(q(b)(p(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#153AND · 10004 cellse.g. q∧¬p(NAND, XNOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) b)) b))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1)) 1)
Tromp binary: 0000000001011111001011110010111110010111101101001011110101101010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a b b
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#216AND · 10004 cellse.g. XOR(Q, q∧¬p)

Lambda, short form: λpqab.q (p a (q b a)) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) ((q b) a))) ((p b) ((q a) b))))))
De Bruijn: λλλλ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1)))
Tromp binary: 00000000010111100101111101100101111010110010111110100101111011010 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b
Reverse Polish: q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => q(p(a)(q(b)(a)))(p(b)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#242AND · 10004 cellse.g. XOR(q∧¬p, Q)

Lambda, short form: λpqab.p (q a b) (q (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110110100101111001011110101100101111011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q @ @ q b a @ @ q a b
Reverse Polish: p q a @ b @ @ q q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I))
JavaScript: p => q => a => b => p(q(a)(b))(q(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#259AND · 10004 cellse.g. XOR(P, p∧¬q)

Lambda, short form: λpqab.p (p (q a b) a) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1))
Tromp binary: 000000000101111100101111100101111011010110010111110010111101011010 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ p @ @ q b a b
Reverse Polish: p p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(p(q(b)(a))(b))

Where it comes from

XOR ×2 · XNOR ×2

#285AND · 10004 cellse.g. XOR(p∧¬q, P)

Lambda, short form: λpqab.p (q (p a b) (p b a)) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) ((p b) a))) ((p a) b)))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) ((4 1) 2))) ((4 2) 1))
Tromp binary: 0000000001011111001011110010111110110100101111101011001011111011010 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b @ @ p b a @ @ p a b
Reverse Polish: p q p a @ b @ @ p b @ a @ @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))K
JavaScript: p => q => a => b => p(q(p(a)(b))(p(b)(a)))(p(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#23AND · 10004 cellse.g. q∧¬p(q∧¬p, AND)

Lambda, short form: λpqab.p (p (q a b) b) (q b (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((q b) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((3 1) ((4 ((3 2) 1)) 1)))
Tromp binary: 000000000101111100101111100101111011010100101111010010111110010111101101010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ q b @ @ p @ @ q a b b
Reverse Polish: p p q a @ b @ @ b @ @ q b @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(q(b)(p(q(a)(b))(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#26AND · 10004 cellse.g. q∧¬p(p∧¬q, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) b) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) b)) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) 1)) ((4 ((3 2) 1)) 1))
Tromp binary: 000000000101111100101111001011111001011110110101010010111110010111101101010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b b @ @ p @ @ q a b b
Reverse Polish: p q p q a @ b @ @ b @ @ b @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(b))(p(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#30AND · 10004 cellse.g. q∧¬p(NOR, AND)

Lambda, short form: λpqab.p (p (q a b) b) (q (p (q a b) b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((q ((p ((q a) b)) b)) b)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((3 ((4 ((3 2) 1)) 1)) 1))
Tromp binary: 000000000101111100101111100101111011010100101111001011111001011110110101010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ q @ @ p @ @ q a b b b
Reverse Polish: p p q a @ b @ @ b @ @ q p q a @ b @ @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(q(p(q(a)(b))(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#325AND · 10004 cellse.g. OR(AND, AND)

Lambda, short form: λpqab.p (q a (p (q a b) b)) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) b))) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) 1))) ((4 ((3 2) 1)) 1))
Tromp binary: 0000000001011111001011110110010111110010111101101010010111110010111101101010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b b @ @ p @ @ q a b b
Reverse Polish: p q a @ p q a @ b @ @ b @ @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(b)))(p(q(a)(b))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#27AND · 10004 cellse.g. q∧¬p(XOR, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) b) (q b (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) b)) ((q b) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) 1)) ((3 1) ((4 ((3 2) 1)) 1)))
Tromp binary: 0000000001011111001011110010111110010111101101010100101111010010111110010111101101010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b b @ @ q b @ @ p @ @ q a b b
Reverse Polish: p q p q a @ b @ @ b @ @ b @ @ q b @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(b))(q(b)(p(q(a)(b))(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#100AND · 10004 cellse.g. q∧¬p(XOR, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) b) (q b (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) b)) ((q b) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) 1)) ((3 1) ((4 2) ((3 2) 1))))
Tromp binary: 000000000101111100101111001011111011001011110110101001011110100101111101100101111011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b b @ @ q b @ @ p a @ @ q a b
Reverse Polish: p q p a @ q a @ b @ @ @ b @ @ q b @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(b))(q(b)(p(a)(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#148AND · 10004 cellse.g. q∧¬p(NOR, XNOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (q (p (q a b) (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((q ((p ((q a) b)) ((q b) a))) b)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1))
Tromp binary: 0000000001011111001011111001011110110100101111010110010111100101111100101111011010010111101011010 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q a b @ @ q b a b
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ q p q a @ b @ @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(q(p(q(a)(b))(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#274AND · 10004 cellse.g. XOR(OR, XOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (q (p (q a b) (q b a)) (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 0000000001011111001011111001011110110100101111010110010111100101111100101111011010010111101011001011111001011110101100101111011010 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

#300AND · 10004 cellse.g. XOR(XOR, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) (p b (q b a))) (q (p b (q b a)) (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) ((p b) ((q b) a)))) ((q ((p b) ((q b) a))) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2)))) ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1))))
Tromp binary: 00000000010111110010111100101111101100101111011010010111110100101111010110010111100101111101001011110101100101111101100101111011010 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b
Reverse Polish: p q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ @ q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(p(b)(q(b)(a))))(q(p(b)(q(b)(a)))(p(a)(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

3 Q 1010 · 21 programs · 168 cells

#37Q · 101088 cellslambda16.txt

Lambda, short form: λpqab.q a b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) b))))
De Bruijn: λλλλ((3 2) 1)
Tromp binary: 000000000101111011010 (21 bits)
Polish (prefix): λp λq λa λb @ @ q a b
Reverse Polish: q a @ b @ λb λa λq λp
SKI combinators: KI
JavaScript: p => q => a => b => q(a)(b)

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×2 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#47Q · 10104 cellse.g. q∧¬p(¬Q, Q)

Lambda, short form: λpqab.q (q a b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((q a) b)) b))))
De Bruijn: λλλλ((3 ((3 2) 1)) 1)
Tromp binary: 0000000001011110010111101101010 (31 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ q a b b
Reverse Polish: q q a @ b @ @ b @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI)))
JavaScript: p => q => a => b => q(q(a)(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#340Q · 10104 cellse.g. OR(Q, Q)

Lambda, short form: λpqab.q a (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((q a) b)))))
De Bruijn: λλλλ((3 2) ((3 2) 1))
Tromp binary: 00000000010111101100101111011010 (32 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ q a b
Reverse Polish: q a @ q a @ b @ @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(KK))))I)
JavaScript: p => q => a => b => q(a)(q(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#107Q · 10104 cellse.g. q∧¬p(¬Q, OR)

Lambda, short form: λpqab.q (p a (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) ((q a) b))) b))))
De Bruijn: λλλλ((3 ((4 2) ((3 2) 1))) 1)
Tromp binary: 0000000001011110010111110110010111101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a @ @ q a b b
Reverse Polish: q p a @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(a)(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#167Q · 10104 cellse.g. q∧¬p(¬Q, p→q)

Lambda, short form: λpqab.q (p (q a b) a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) a)) b))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) 2)) 1)
Tromp binary: 0000000001011110010111110010111101101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b a b
Reverse Polish: q p q a @ b @ @ a @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI)))
JavaScript: p => q => a => b => q(p(q(a)(b))(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#312Q · 10104 cellse.g. OR(Q, q∧¬p)

Lambda, short form: λpqab.q a (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p b) ((q a) b))))))
De Bruijn: λλλλ((3 2) ((4 1) ((3 2) 1)))
Tromp binary: 0000000001011110110010111110100101111011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p b @ @ q a b
Reverse Polish: q a @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => q(a)(p(b)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#326Q · 10104 cellse.g. OR(Q, AND)

Lambda, short form: λpqab.q a (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((3 2) ((4 ((3 2) 1)) 1))
Tromp binary: 0000000001011110110010111110010111101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p @ @ q a b b
Reverse Polish: q a @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => q(a)(p(q(a)(b))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#41Q · 10104 cellse.g. q∧¬p(p∧¬q, Q)

Lambda, short form: λpqab.p (q (q a b) b) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) b)) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) 1)) ((3 2) 1))
Tromp binary: 00000000010111110010111100101111011010100101111011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b b @ @ q a b
Reverse Polish: p q q a @ b @ @ b @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI))))))))(KI)
JavaScript: p => q => a => b => p(q(q(a)(b))(b))(q(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#44Q · 10104 cellse.g. q∧¬p(NOR, Q)

Lambda, short form: λpqab.p (q a b) (q (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 ((3 2) 1)) 1))
Tromp binary: 00000000010111110010111101101001011110010111101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q @ @ q a b b
Reverse Polish: p q a @ b @ @ q q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI))))
JavaScript: p => q => a => b => p(q(a)(b))(q(q(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#338Q · 10104 cellse.g. OR(q∧¬p, Q)

Lambda, short form: λpqab.p (q a b) (q a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 2) ((3 2) 1)))
Tromp binary: 000000000101111100101111011010010111101100101111011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q a @ @ q a b
Reverse Polish: p q a @ b @ @ q a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))I))
JavaScript: p => q => a => b => p(q(a)(b))(q(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#339Q · 10104 cellse.g. OR(AND, Q)

Lambda, short form: λpqab.p (q a (q a b)) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((q a) b))) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 2) ((3 2) 1))) ((3 2) 1))
Tromp binary: 000000000101111100101111011001011110110100101111011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ q a b @ @ q a b
Reverse Polish: p q a @ q a @ b @ @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))I))))))(KI)
JavaScript: p => q => a => b => p(q(a)(q(a)(b)))(q(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#99Q · 10104 cellse.g. q∧¬p(p∧¬q, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) b) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) b)) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) 1)) ((4 2) ((3 2) 1)))
Tromp binary: 00000000010111110010111100101111101100101111011010100101111101100101111011010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b b @ @ p a @ @ q a b
Reverse Polish: p q p a @ q a @ b @ @ @ b @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(b))(p(a)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#163Q · 10104 cellse.g. q∧¬p(NOR, p→q)

Lambda, short form: λpqab.p (p (q a b) a) (q (p (q a b) a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((q ((p ((q a) b)) a)) b)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((3 ((4 ((3 2) 1)) 2)) 1))
Tromp binary: 00000000010111110010111110010111101101011001011110010111110010111101101011010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ q @ @ p @ @ q a b a b
Reverse Polish: p p q a @ b @ @ a @ @ q p q a @ b @ @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(q(p(q(a)(b))(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#311Q · 10104 cellse.g. OR(AND, q∧¬p)

Lambda, short form: λpqab.p (q a (p b (q a b))) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) ((q a) b)))) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) ((3 2) 1)))) ((4 1) ((3 2) 1)))
Tromp binary: 0000000001011111001011110110010111110100101111011010010111110100101111011010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b @ @ q a b @ @ p b @ @ q a b
Reverse Polish: p q a @ p b @ q a @ b @ @ @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S)))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(q(a)(p(b)(q(a)(b))))(p(b)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#324Q · 10104 cellse.g. OR(q∧¬p, AND)

Lambda, short form: λpqab.p (p (q a b) b) (q a (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((q a) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((3 2) ((4 ((3 2) 1)) 1)))
Tromp binary: 0000000001011111001011111001011110110101001011110110010111110010111101101010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ q a @ @ p @ @ q a b b
Reverse Polish: p p q a @ b @ @ b @ @ q a @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(q(a)(p(q(a)(b))(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#273Q · 10104 cellse.g. XOR(P, XOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 000000000101111100101111100101111011010010111101011001011111001011110101100101111011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#286Q · 10104 cellse.g. XOR(XOR, P)

Lambda, short form: λpqab.p (q (p a b) (p b a)) (q (p b a) (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) ((p b) a))) ((q ((p b) a)) ((p a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) ((4 1) 2))) ((3 ((4 1) 2)) ((4 2) 1)))
Tromp binary: 00000000010111110010111100101111101101001011111010110010111100101111101011001011111011010 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b @ @ p b a @ @ q @ @ p b a @ @ p a b
Reverse Polish: p q p a @ b @ @ p b @ a @ @ @ q p b @ a @ @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K)
JavaScript: p => q => a => b => p(q(p(a)(b))(p(b)(a)))(q(p(b)(a))(p(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#215Q · 10104 cellse.g. XOR(AND, q∧¬p)

Lambda, short form: λpqab.p (q (p a (q b a)) (p b (q a b))) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) ((p b) ((q a) b)))) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1)))) ((4 1) ((3 2) 1)))
Tromp binary: 00000000010111110010111100101111101100101111010110010111110100101111011010010111110100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b @ @ p b @ @ q a b
Reverse Polish: p q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S)))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(p(b)(q(a)(b))))(p(b)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#228Q · 10104 cellse.g. XOR(q∧¬p, AND)

Lambda, short form: λpqab.p (p (q a b) b) (q (p (q b a) a) (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((q ((p ((q b) a)) a)) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1)))
Tromp binary: 00000000010111110010111110010111101101010010111100101111100101111010110110010111110010111101101010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b
Reverse Polish: p p q a @ b @ @ b @ @ q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(q(p(q(b)(a))(a))(p(q(a)(b))(b)))

Where it comes from

XOR ×2 · XNOR ×2

#260Q · 10104 cellse.g. XOR(OR, p∧¬q)

Lambda, short form: λpqab.p (p (q a b) a) (q (p (q a b) a) (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((q ((p ((q a) b)) a)) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1)))
Tromp binary: 000000000101111100101111100101111011010110010111100101111100101111011010110010111110010111101011010 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b
Reverse Polish: p p q a @ b @ @ a @ @ q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(q(p(q(a)(b))(a))(p(q(b)(a))(b)))

Where it comes from

XOR ×2 · XNOR ×2

#299Q · 10104 cellse.g. XOR(p∧¬q, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) (p b (q b a))) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) ((p b) ((q b) a)))) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2)))) ((4 2) ((3 2) 1)))
Tromp binary: 000000000101111100101111001011111011001011110110100101111101001011110101100101111101100101111011010 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a @ @ p a @ @ q a b
Reverse Polish: p q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(p(b)(q(b)(a))))(p(a)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

4 p AND NOT q 0100 · 32 programs · 216 cells

#50p AND NOT q · 010092 cellslambda16.txt

Lambda, short form: λpqab.p (q b a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) b))))
De Bruijn: λλλλ((4 ((3 1) 2)) 1)
Tromp binary: 00000000010111110010111101011010 (32 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a b
Reverse Polish: p q b @ a @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(a))(b)

Where it comes from

q∧¬p ×3 · AND ×3 · Q ×16 · p∧¬q ×3 · XOR ×4 · P ×16 · OR ×2 · NOR ×3 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#83p AND NOT q · 01004 cellse.g. q∧¬p(Q, P)

Lambda, short form: λpqab.q b (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p a) b)))))
De Bruijn: λλλλ((3 1) ((4 2) 1))
Tromp binary: 00000000010111101001011111011010 (32 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p a b
Reverse Polish: q b @ p a @ b @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))K
JavaScript: p => q => a => b => q(b)(p(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#53p AND NOT q · 01004 cellse.g. q∧¬p(Q, p∧¬q)

Lambda, short form: λpqab.q b (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((3 1) ((4 ((3 1) 2)) 1))
Tromp binary: 000000000101111010010111110010111101011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p @ @ q b a b
Reverse Polish: q b @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => q(b)(p(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#59p AND NOT q · 01004 cellse.g. q∧¬p(¬P, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) b))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) 1)
Tromp binary: 0000000001011111001011111001011110101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b b
Reverse Polish: p p q b @ a @ @ b @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#91p AND NOT q · 01004 cellse.g. q∧¬p(p→q, P)

Lambda, short form: λpqab.p (q b (p a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) b))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) 1))) 1)
Tromp binary: 0000000001011111001011110100101111101101010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a b b
Reverse Polish: p q b @ p a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))K)))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#98p AND NOT q · 01004 cellse.g. q∧¬p(Q, OR)

Lambda, short form: λpqab.q b (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p a) ((q a) b))))))
De Bruijn: λλλλ((3 1) ((4 2) ((3 2) 1)))
Tromp binary: 0000000001011110100101111101100101111011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p a @ @ q a b
Reverse Polish: q b @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => q(b)(p(a)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#179p AND NOT q · 01004 cellse.g. q∧¬p(p→q, ¬Q)

Lambda, short form: λpqab.p (q b (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((q b) a))) b))))
De Bruijn: λλλλ((4 ((3 1) ((3 1) 2))) 1)
Tromp binary: 000000000101111100101111010010111101011010 (42 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ q b a b
Reverse Polish: p q b @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#192p AND NOT q · 01004 cellse.g. q∧¬p(¬P, NAND)

Lambda, short form: λpqab.p (p (q b a) a) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) b))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) 1)
Tromp binary: 00000000010111110010111110010111101011011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a b
Reverse Polish: p p q b @ a @ @ a @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#61p AND NOT q · 01004 cellse.g. q∧¬p(p→q, p∧¬q)

Lambda, short form: λpqab.p (q b (p (q b a) b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) b))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) 1))) 1)
Tromp binary: 00000000010111110010111101001011111001011110101101010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a b b
Reverse Polish: p q b @ p q b @ a @ @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#68p AND NOT q · 01004 cellse.g. q∧¬p(Q, XOR)

Lambda, short form: λpqab.q b (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((3 1) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 00000000010111101001011111001011110101100101111011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p @ @ q b a @ @ q a b
Reverse Polish: q b @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => q(b)(p(q(b)(a))(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#74p AND NOT q · 01004 cellse.g. q∧¬p(¬P, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) b))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) 1)
Tromp binary: 000000000101111100101111100101111010110010111101101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b b
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#82p AND NOT q · 01004 cellse.g. q∧¬p(AND, P)

Lambda, short form: λpqab.p (q b (p a b)) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) b))) ((p a) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) 1))) ((4 2) 1))
Tromp binary: 0000000001011111001011110100101111101101001011111011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a b @ @ p a b
Reverse Polish: p q b @ p a @ b @ @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))K)))))K
JavaScript: p => q => a => b => p(q(b)(p(a)(b)))(p(a)(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#106p AND NOT q · 01004 cellse.g. q∧¬p(p→q, OR)

Lambda, short form: λpqab.p (q b (p a (q a b))) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) ((q a) b)))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) ((3 2) 1)))) 1)
Tromp binary: 000000000101111100101111010010111110110010111101101010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a @ @ q a b b
Reverse Polish: p q b @ p a @ q a @ b @ @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(a)(q(a)(b))))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#177p AND NOT q · 01004 cellse.g. q∧¬p(NOR, ¬Q)

Lambda, short form: λpqab.p (q b a) (q (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 ((3 1) 2)) 1))
Tromp binary: 00000000010111110010111101011001011110010111101011010 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q @ @ q b a b
Reverse Polish: p q b @ a @ @ q q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI))))
JavaScript: p => q => a => b => p(q(b)(a))(q(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#194p AND NOT q · 01004 cellse.g. q∧¬p(p→q, NAND)

Lambda, short form: λpqab.p (q b (p (q b a) a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) a))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) 2))) 1)
Tromp binary: 000000000101111100101111010010111110010111101011011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a a b
Reverse Polish: p q b @ p q b @ a @ @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#209p AND NOT q · 01004 cellse.g. q∧¬p(p→q, q→p)

Lambda, short form: λpqab.p (q b (p a (q b a))) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) ((q b) a)))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) ((3 1) 2)))) 1)
Tromp binary: 000000000101111100101111010010111110110010111101011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a @ @ q b a b
Reverse Polish: p q b @ p a @ q b @ a @ @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(a)(q(b)(a))))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#76p AND NOT q · 01004 cellse.g. q∧¬p(p→q, XOR)

Lambda, short form: λpqab.p (q b (p (q b a) (q a b))) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) ((q a) b)))) b))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) ((3 2) 1)))) 1)
Tromp binary: 0000000001011111001011110100101111100101111010110010111101101010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a @ @ q a b b
Reverse Polish: p q b @ p q b @ a @ @ q a @ b @ @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(K(K(KI)))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(q(a)(b))))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#90p AND NOT q · 01004 cellse.g. q∧¬p(XNOR, P)

Lambda, short form: λpqab.p (q b (p a b)) (q (p a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) b))) ((q ((p a) b)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) 1))) ((3 ((4 2) 1)) 1))
Tromp binary: 00000000010111110010111101001011111011010010111100101111101101010 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a b @ @ q @ @ p a b b
Reverse Polish: p q b @ p a @ b @ @ @ q p a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(a)(b)))(q(p(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#178p AND NOT q · 01004 cellse.g. q∧¬p(XNOR, ¬Q)

Lambda, short form: λpqab.p (q b (q b a)) (q (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((q b) a))) ((q ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((3 1) 2))) ((3 ((3 1) 2)) 1))
Tromp binary: 000000000101111100101111010010111101011001011110010111101011010 (63 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ q b a @ @ q @ @ q b a b
Reverse Polish: p q b @ q b @ a @ @ @ q q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK))))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI))))
JavaScript: p => q => a => b => p(q(b)(q(b)(a)))(q(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#233p AND NOT q · 01004 cellse.g. XOR(P, AND)

Lambda, short form: λpqab.p (p (q b a) a) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1))
Tromp binary: 000000000101111100101111100101111010110110010111110010111101101010 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ p @ @ q a b b
Reverse Polish: p p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(p(q(a)(b))(b))

Where it comes from

XOR ×2 · XNOR ×2

#247p AND NOT q · 01004 cellse.g. XOR(OR, Q)

Lambda, short form: λpqab.p (q b a) (q (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110101100101111001011110101100101111011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q @ @ q b a @ @ q a b
Reverse Polish: p q b @ a @ @ q q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I))
JavaScript: p => q => a => b => p(q(b)(a))(q(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#283p AND NOT q · 01004 cellse.g. XOR(AND, P)

Lambda, short form: λpqab.p (q (p b a) (p a b)) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) ((p a) b))) ((p a) b)))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) ((4 2) 1))) ((4 2) 1))
Tromp binary: 0000000001011111001011110010111110101100101111101101001011111011010 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a @ @ p a b @ @ p a b
Reverse Polish: p q p b @ a @ @ p a @ b @ @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K)))))K
JavaScript: p => q => a => b => p(q(p(b)(a))(p(a)(b)))(p(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#298p AND NOT q · 01004 cellse.g. XOR(Q, OR)

Lambda, short form: λpqab.q (p b (q b a)) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) ((q b) a))) ((p a) ((q a) b))))))
De Bruijn: λλλλ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1)))
Tromp binary: 00000000010111100101111101001011110101100101111101100101111011010 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b
Reverse Polish: q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => q(p(b)(q(b)(a)))(p(a)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#51p AND NOT q · 01004 cellse.g. q∧¬p(q∧¬p, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (q b (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((q b) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((3 1) ((4 ((3 1) 2)) 1)))
Tromp binary: 000000000101111100101111100101111010110100101111010010111110010111101011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ q b @ @ p @ @ q b a b
Reverse Polish: p p q b @ a @ @ b @ @ q b @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(q(b)(p(q(b)(a))(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#52p AND NOT q · 01004 cellse.g. q∧¬p(AND, p∧¬q)

Lambda, short form: λpqab.p (q b (p (q b a) b)) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) b))) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) 1))) ((4 ((3 1) 2)) 1))
Tromp binary: 000000000101111100101111010010111110010111101011010010111110010111101011010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a b @ @ p @ @ q b a b
Reverse Polish: p q b @ p q b @ a @ @ b @ @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(b)))(p(q(b)(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#58p AND NOT q · 01004 cellse.g. q∧¬p(NOR, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (q (p (q b a) b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((q ((p ((q b) a)) b)) b)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((3 ((4 ((3 1) 2)) 1)) 1))
Tromp binary: 000000000101111100101111100101111010110100101111001011111001011110101101010 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ q @ @ p @ @ q b a b b
Reverse Polish: p p q b @ a @ @ b @ @ q p q b @ a @ @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(q(p(q(b)(a))(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#353p AND NOT q · 01004 cellse.g. OR(p∧¬q, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) a) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) a)) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) 2)) ((4 ((3 1) 2)) 1))
Tromp binary: 0000000001011111001011110010111110010111101011010110010111110010111101011010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b a @ @ p @ @ q b a b
Reverse Polish: p q p q b @ a @ @ b @ @ a @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(a))(p(q(b)(a))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#60p AND NOT q · 01004 cellse.g. q∧¬p(XNOR, p∧¬q)

Lambda, short form: λpqab.p (q b (p (q b a) b)) (q (p (q b a) b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) b))) ((q ((p ((q b) a)) b)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) 1))) ((3 ((4 ((3 1) 2)) 1)) 1))
Tromp binary: 0000000001011111001011110100101111100101111010110100101111001011111001011110101101010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a b @ @ q @ @ p @ @ q b a b b
Reverse Polish: p q b @ p q b @ a @ @ b @ @ @ q p q b @ a @ @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(b)))(q(p(q(b)(a))(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#208p AND NOT q · 01004 cellse.g. q∧¬p(XNOR, q→p)

Lambda, short form: λpqab.p (q b (p a (q b a))) (q (p a (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) ((q b) a)))) ((q ((p a) ((q b) a))) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) ((3 1) 2)))) ((3 ((4 2) ((3 1) 2))) 1))
Tromp binary: 000000000101111100101111010010111110110010111101011001011110010111110110010111101011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a @ @ q b a @ @ q @ @ p a @ @ q b a b
Reverse Polish: p q b @ p a @ q b @ a @ @ @ @ q p a @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(a)(q(b)(a))))(q(p(a)(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#66p AND NOT q · 01004 cellse.g. q∧¬p(q∧¬p, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (q b (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((q b) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((3 1) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 0000000001011111001011111001011110101100101111011010010111101001011111001011110101100101111011010 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ q b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ q b @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(q(b)(p(q(b)(a))(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#218p AND NOT q · 01004 cellse.g. XOR(XOR, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) (p a (q b a))) (q (p a (q b a)) (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) ((p a) ((q b) a)))) ((q ((p a) ((q b) a))) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2)))) ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1))))
Tromp binary: 00000000010111110010111100101111101001011110110100101111101100101111010110010111100101111101100101111010110010111110100101111011010 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b
Reverse Polish: p q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ @ q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(p(a)(q(b)(a))))(q(p(a)(q(b)(a)))(p(b)(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

#268p AND NOT q · 01004 cellse.g. XOR(q∧¬p, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (q (p (q a b) (q b a)) (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 0000000001011111001011111001011110101100101111011010010111100101111100101111011010010111101011001011111001011110101100101111011010 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

5 XOR 0110 · 20 programs · 168 cells

#65XOR · 011092 cellslambda16.txt

Lambda, short form: λpqab.p (q b a) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 2) 1))
Tromp binary: 0000000001011111001011110101100101111011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q b @ a @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)
JavaScript: p => q => a => b => p(q(b)(a))(q(a)(b))

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×6 · P ×16 · OR ×2 · NOR ×2 · ¬P ×16 · XNOR ×6 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#284XOR · 01104 cellse.g. XOR(Q, P)

Lambda, short form: λpqab.q (p b a) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) a)) ((p a) b)))))
De Bruijn: λλλλ((3 ((4 1) 2)) ((4 2) 1))
Tromp binary: 00000000010111100101111101011001011111011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b a @ @ p a b
Reverse Polish: q p b @ a @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K
JavaScript: p => q => a => b => q(p(b)(a))(p(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#97XOR · 01104 cellse.g. q∧¬p(AND, OR)

Lambda, short form: λpqab.p (q b (p a (q a b))) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) ((q a) b)))) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) ((3 2) 1)))) ((4 2) ((3 2) 1)))
Tromp binary: 00000000010111110010111101001011111011001011110110100101111101100101111011010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a @ @ q a b @ @ p a @ @ q a b
Reverse Polish: p q b @ p a @ q a @ b @ @ @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(q(b)(p(a)(q(a)(b))))(p(a)(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#191XOR · 01104 cellse.g. q∧¬p(NOR, NAND)

Lambda, short form: λpqab.p (p (q b a) a) (q (p (q b a) a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((q ((p ((q b) a)) a)) b)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((3 ((4 ((3 1) 2)) 2)) 1))
Tromp binary: 00000000010111110010111110010111101011011001011110010111110010111101011011010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ q @ @ p @ @ q b a a b
Reverse Polish: p p q b @ a @ @ a @ @ q p q b @ a @ @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(q(p(q(b)(a))(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#313XOR · 01104 cellse.g. OR(p∧¬q, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) a) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) a)) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) 2)) ((4 1) ((3 2) 1)))
Tromp binary: 0000000001011111001011110010111110100101111011010110010111110100101111011010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b a @ @ p b @ @ q a b
Reverse Polish: p q p b @ q a @ b @ @ @ a @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK)))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(a))(p(b)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#350XOR · 01104 cellse.g. OR(q∧¬p, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (q a (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((q a) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((3 2) ((4 ((3 1) 2)) 1)))
Tromp binary: 0000000001011111001011111001011110101101001011110110010111110010111101011010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ q a @ @ p @ @ q b a b
Reverse Polish: p p q b @ a @ @ b @ @ q a @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(q(a)(p(q(b)(a))(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#105XOR · 01104 cellse.g. q∧¬p(XNOR, OR)

Lambda, short form: λpqab.p (q b (p a (q a b))) (q (p a (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) ((q a) b)))) ((q ((p a) ((q a) b))) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) ((3 2) 1)))) ((3 ((4 2) ((3 2) 1))) 1))
Tromp binary: 000000000101111100101111010010111110110010111101101001011110010111110110010111101101010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a @ @ q a b @ @ q @ @ p a @ @ q a b b
Reverse Polish: p q b @ p a @ q a @ b @ @ @ @ q p a @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(a)(q(a)(b))))(q(p(a)(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#193XOR · 01104 cellse.g. q∧¬p(XNOR, NAND)

Lambda, short form: λpqab.p (q b (p (q b a) a)) (q (p (q b a) a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) a))) ((q ((p ((q b) a)) a)) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) 2))) ((3 ((4 ((3 1) 2)) 2)) 1))
Tromp binary: 000000000101111100101111010010111110010111101011011001011110010111110010111101011011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a a @ @ q @ @ p @ @ q b a a b
Reverse Polish: p q b @ p q b @ a @ @ a @ @ @ q p q b @ a @ @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(a)))(q(p(q(b)(a))(a))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#314XOR · 01104 cellse.g. OR(XOR, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) a) (q a (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) a)) ((q a) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) 2)) ((3 2) ((4 1) ((3 2) 1))))
Tromp binary: 000000000101111100101111001011111010010111101101011001011110110010111110100101111011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b a @ @ q a @ @ p b @ @ q a b
Reverse Polish: p q p b @ q a @ b @ @ @ a @ @ q a @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(a))(q(a)(p(b)(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#354XOR · 01104 cellse.g. OR(XOR, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) a) (q a (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) a)) ((q a) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) 2)) ((3 2) ((4 ((3 1) 2)) 1)))
Tromp binary: 000000000101111100101111001011111001011110101101011001011110110010111110010111101011010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b a @ @ q a @ @ p @ @ q b a b
Reverse Polish: p q p q b @ a @ @ b @ @ a @ @ q a @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(a))(q(a)(p(q(b)(a))(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#67XOR · 01104 cellse.g. q∧¬p(AND, XOR)

Lambda, short form: λpqab.p (q b (p (q b a) (q a b))) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) ((q a) b)))) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) ((3 2) 1)))) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110100101111100101111010110010111101101001011111001011110101100101111011010 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a @ @ q a b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q b @ p q b @ a @ @ q a @ b @ @ @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(q(a)(b))))(p(q(b)(a))(q(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#73XOR · 01104 cellse.g. q∧¬p(NOR, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (q (p (q b a) (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((q ((p ((q b) a)) ((q a) b))) b)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1))
Tromp binary: 0000000001011111001011111001011110101100101111011010010111100101111100101111010110010111101101010 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q b a @ @ q a b b
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ q p q b @ a @ @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(q(p(q(b)(a))(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#217XOR · 01104 cellse.g. XOR(p∧¬q, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) (p a (q b a))) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) ((p a) ((q b) a)))) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2)))) ((4 1) ((3 2) 1)))
Tromp binary: 00000000010111110010111100101111101001011110110100101111101100101111010110010111110100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a @ @ p b @ @ q a b
Reverse Polish: p q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(p(a)(q(b)(a))))(p(b)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#234XOR · 01104 cellse.g. XOR(OR, AND)

Lambda, short form: λpqab.p (p (q b a) a) (q (p (q b a) a) (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((q ((p ((q b) a)) a)) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1)))
Tromp binary: 000000000101111100101111100101111010110110010111100101111100101111010110110010111110010111101101010 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b
Reverse Polish: p p q b @ a @ @ a @ @ q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(q(p(q(b)(a))(a))(p(q(a)(b))(b)))

Where it comes from

XOR ×2 · XNOR ×2

#254XOR · 01104 cellse.g. XOR(q∧¬p, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (q (p (q a b) a) (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((q ((p ((q a) b)) a)) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1)))
Tromp binary: 00000000010111110010111110010111101011010010111100101111100101111011010110010111110010111101011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b
Reverse Polish: p p q b @ a @ @ b @ @ q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(q(p(q(a)(b))(a))(p(q(b)(a))(b)))

Where it comes from

XOR ×2 · XNOR ×2

#297XOR · 01104 cellse.g. XOR(AND, OR)

Lambda, short form: λpqab.p (q (p b (q b a)) (p a (q a b))) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) ((p a) ((q a) b)))) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1)))) ((4 2) ((3 2) 1)))
Tromp binary: 000000000101111100101111001011111010010111101011001011111011001011110110100101111101100101111011010 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b @ @ p a @ @ q a b
Reverse Polish: p q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(p(a)(q(a)(b))))(p(a)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#364XOR · 01104 cellse.g. OR(q∧¬p, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (q a (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((q a) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((3 2) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 00000000010111110010111110010111101011001011110110100101111011001011111001011110101100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ q a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ q a @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(q(a)(p(q(b)(a))(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#367XOR · 01104 cellse.g. OR(p∧¬q, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) a) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) a)) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2)) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 00000000010111110010111100101111100101111010110010111101101011001011111001011110101100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ a @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(a))(p(q(b)(a))(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#75XOR · 01104 cellse.g. q∧¬p(XNOR, XOR)

Lambda, short form: λpqab.p (q b (p (q b a) (q a b))) (q (p (q b a) (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) ((q a) b)))) ((q ((p ((q b) a)) ((q a) b))) b)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) ((3 2) 1)))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) 1))
Tromp binary: 00000000010111110010111101001011111001011110101100101111011010010111100101111100101111010110010111101101010 (107 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q b a @ @ q a b b
Reverse Polish: p q b @ p q b @ a @ @ q a @ b @ @ @ @ q p q b @ a @ @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(q(a)(b))))(q(p(q(b)(a))(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#368XOR · 01104 cellse.g. OR(XOR, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) a) (q a (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) a)) ((q a) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2)) ((3 2) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 0000000001011111001011110010111110010111101011001011110110101100101111011001011111001011110101100101111011010 (109 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b a @ @ q a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ a @ @ q a @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(a))(q(a)(p(q(b)(a))(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

6 P 1100 · 21 programs · 168 cells

#80P · 110088 cellslambda16.txt

Lambda, short form: λpqab.p a b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) b))))
De Bruijn: λλλλ((4 2) 1)
Tromp binary: 0000000001011111011010 (22 bits)
Polish (prefix): λp λq λa λb @ @ p a b
Reverse Polish: p a @ b @ λb λa λq λp
SKI combinators: K
JavaScript: p => q => a => b => p(a)(b)

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×2 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#89P · 11004 cellse.g. q∧¬p(¬P, P)

Lambda, short form: λpqab.p (p a b) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) b))))
De Bruijn: λλλλ((4 ((4 2) 1)) 1)
Tromp binary: 000000000101111100101111101101010 (33 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b b
Reverse Polish: p p a @ b @ @ b @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(K(KI)))
JavaScript: p => q => a => b => p(p(a)(b))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#383P · 11004 cellse.g. OR(P, P)

Lambda, short form: λpqab.p a (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p a) b)))))
De Bruijn: λλλλ((4 2) ((4 2) 1))
Tromp binary: 0000000001011111011001011111011010 (34 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p a b
Reverse Polish: p a @ p a @ b @ @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(KK))))I)
JavaScript: p => q => a => b => p(a)(p(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#104P · 11004 cellse.g. q∧¬p(¬P, OR)

Lambda, short form: λpqab.p (p a (q a b)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) b))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) 1)
Tromp binary: 00000000010111110010111110110010111101101010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b b
Reverse Polish: p p a @ q a @ b @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#207P · 11004 cellse.g. q∧¬p(¬P, q→p)

Lambda, short form: λpqab.p (p a (q b a)) b
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) b))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) 1)
Tromp binary: 00000000010111110010111110110010111101011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a b
Reverse Polish: p p a @ q b @ a @ @ @ b @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI)))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(b)

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#329P · 11004 cellse.g. OR(P, AND)

Lambda, short form: λpqab.p a (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 2) ((4 ((3 2) 1)) 1))
Tromp binary: 00000000010111110110010111110010111101101010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p @ @ q a b b
Reverse Polish: p a @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(a)(p(q(a)(b))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#355P · 11004 cellse.g. OR(P, p∧¬q)

Lambda, short form: λpqab.p a (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 2) ((4 ((3 1) 2)) 1))
Tromp binary: 00000000010111110110010111110010111101011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p @ @ q b a b
Reverse Polish: p a @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(a)(p(q(b)(a))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#81P · 11004 cellse.g. q∧¬p(q∧¬p, P)

Lambda, short form: λpqab.p (p a b) (q b (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((q b) ((p a) b))))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((3 1) ((4 2) 1)))
Tromp binary: 0000000001011111001011111011010010111101001011111011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ q b @ @ p a b
Reverse Polish: p p a @ b @ @ q b @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))))(S(K(S(S(KS)(S(KK)S))))K)
JavaScript: p => q => a => b => p(p(a)(b))(q(b)(p(a)(b)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#88P · 11004 cellse.g. q∧¬p(NOR, P)

Lambda, short form: λpqab.p (p a b) (q (p a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((q ((p a) b)) b)))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((3 ((4 2) 1)) 1))
Tromp binary: 0000000001011111001011111011010010111100101111101101010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ q @ @ p a b b
Reverse Polish: p p a @ b @ @ q p a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(a)(b))(q(p(a)(b))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#379P · 11004 cellse.g. OR(AND, P)

Lambda, short form: λpqab.p (q a (p a b)) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) b))) ((p a) b)))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) 1))) ((4 2) 1))
Tromp binary: 00000000010111110010111101100101111101101001011111011010 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a b @ @ p a b
Reverse Polish: p q a @ p a @ b @ @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K)))))K
JavaScript: p => q => a => b => p(q(a)(p(a)(b)))(p(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#381P · 11004 cellse.g. OR(p∧¬q, P)

Lambda, short form: λpqab.p (q (p a b) a) (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) a)) ((p a) b)))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) 2)) ((4 2) 1))
Tromp binary: 00000000010111110010111100101111101101011001011111011010 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b a @ @ p a b
Reverse Polish: p q p a @ b @ @ a @ @ p a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK)))))))K
JavaScript: p => q => a => b => p(q(p(a)(b))(a))(p(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#96P · 11004 cellse.g. q∧¬p(q∧¬p, OR)

Lambda, short form: λpqab.p (p a (q a b)) (q b (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((q b) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((3 1) ((4 2) ((3 2) 1))))
Tromp binary: 00000000010111110010111110110010111101101001011110100101111101100101111011010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ q b @ @ p a @ @ q a b
Reverse Polish: p p a @ q a @ b @ @ @ q b @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(K(S(S(KS)(S(KK)S))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(q(b)(p(a)(q(a)(b))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#206P · 11004 cellse.g. q∧¬p(NOR, q→p)

Lambda, short form: λpqab.p (p a (q b a)) (q (p a (q b a)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((q ((p a) ((q b) a))) b)))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((3 ((4 2) ((3 1) 2))) 1))
Tromp binary: 00000000010111110010111110110010111101011001011110010111110110010111101011010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ q @ @ p a @ @ q b a b
Reverse Polish: p p a @ q b @ a @ @ @ q p a @ q b @ a @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(q(p(a)(q(b)(a)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#327P · 11004 cellse.g. OR(p∧¬q, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) a) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) a)) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) 2)) ((4 ((3 2) 1)) 1))
Tromp binary: 0000000001011111001011110010111110010111101101010110010111110010111101101010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b a @ @ p @ @ q a b b
Reverse Polish: p q p q a @ b @ @ b @ @ a @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(a))(p(q(a)(b))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#351P · 11004 cellse.g. OR(AND, p∧¬q)

Lambda, short form: λpqab.p (q a (p (q b a) b)) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) b))) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) 1))) ((4 ((3 1) 2)) 1))
Tromp binary: 0000000001011111001011110110010111110010111101011010010111110010111101011010 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a b @ @ p @ @ q b a b
Reverse Polish: p q a @ p q b @ a @ @ b @ @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(b)))(p(q(b)(a))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#246P · 11004 cellse.g. XOR(XOR, Q)

Lambda, short form: λpqab.p (q (q a b) (q b a)) (q (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) ((q b) a))) ((q ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) ((3 1) 2))) ((3 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110010111101101001011110101100101111001011110101100101111011010 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b @ @ q b a @ @ q @ @ q b a @ @ q a b
Reverse Polish: p q q a @ b @ @ q b @ a @ @ @ q q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK))))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I))
JavaScript: p => q => a => b => p(q(q(a)(b))(q(b)(a)))(q(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#270P · 11004 cellse.g. XOR(Q, XOR)

Lambda, short form: λpqab.q (p (q a b) (q b a)) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 00000000010111100101111100101111011010010111101011001011111001011110101100101111011010 (86 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b
Reverse Polish: q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#220P · 11004 cellse.g. XOR(OR, q∧¬p)

Lambda, short form: λpqab.p (p a (q b a)) (q (p a (q b a)) (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((q ((p a) ((q b) a))) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1))))
Tromp binary: 000000000101111100101111101100101111010110010111100101111101100101111010110010111110100101111011010 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b
Reverse Polish: p p a @ q b @ a @ @ @ q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(q(p(a)(q(b)(a)))(p(b)(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

#231P · 11004 cellse.g. XOR(p∧¬q, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) (p (q b a) a)) (p (q a b) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) ((p ((q b) a)) a))) ((p ((q a) b)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2))) ((4 ((3 2) 1)) 1))
Tromp binary: 00000000010111110010111100101111100101111011010100101111100101111010110110010111110010111101101010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a @ @ p @ @ q a b b
Reverse Polish: p q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ @ p q a @ b @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(p(q(b)(a))(a)))(p(q(a)(b))(b))

Where it comes from

XOR ×2 · XNOR ×2

#255P · 11004 cellse.g. XOR(AND, p∧¬q)

Lambda, short form: λpqab.p (q (p (q a b) a) (p (q b a) b)) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) ((p ((q b) a)) b))) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1))) ((4 ((3 1) 2)) 1))
Tromp binary: 00000000010111110010111100101111100101111011010110010111110010111101011010010111110010111101011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b @ @ p @ @ q b a b
Reverse Polish: p q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(p(q(b)(a))(b)))(p(q(b)(a))(b))

Where it comes from

XOR ×2 · XNOR ×2

#296P · 11004 cellse.g. XOR(q∧¬p, OR)

Lambda, short form: λpqab.p (p a (q a b)) (q (p b (q b a)) (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((q ((p b) ((q b) a))) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1))))
Tromp binary: 000000000101111100101111101100101111011010010111100101111101001011110101100101111101100101111011010 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b
Reverse Polish: p p a @ q a @ b @ @ @ q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(q(p(b)(q(b)(a)))(p(a)(q(a)(b))))

Where it comes from

XOR ×2 · XNOR ×2

7 OR 1110 · 32 programs · 216 cells

#95OR · 111092 cellslambda16.txt

Lambda, short form: λpqab.p a (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) b)))))
De Bruijn: λλλλ((4 2) ((3 2) 1))
Tromp binary: 000000000101111101100101111011010 (33 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a b
Reverse Polish: p a @ q a @ b @ @ λb λa λq λp
SKI combinators: S(KS)(S(K(S(KS)))(S(KK)))
JavaScript: p => q => a => b => p(a)(q(a)(b))

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×3 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×3 · ¬Q ×16 · NAND ×3 · q→p ×3

#380OR · 11104 cellse.g. OR(Q, P)

Lambda, short form: λpqab.q a (p a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p a) b)))))
De Bruijn: λλλλ((3 2) ((4 2) 1))
Tromp binary: 000000000101111011001011111011010 (33 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p a b
Reverse Polish: q a @ p a @ b @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K
JavaScript: p => q => a => b => q(a)(p(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#315OR · 11104 cellse.g. OR(P, q∧¬p)

Lambda, short form: λpqab.p a (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 2) ((4 1) ((3 2) 1)))
Tromp binary: 00000000010111110110010111110100101111011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p b @ @ q a b
Reverse Polish: p a @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(a)(p(b)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#343OR · 11104 cellse.g. OR(OR, Q)

Lambda, short form: λpqab.p a (q a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((q a) b))))))
De Bruijn: λλλλ((4 2) ((3 2) ((3 2) 1)))
Tromp binary: 00000000010111110110010111101100101111011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ q a b
Reverse Polish: p a @ q a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))I))
JavaScript: p => q => a => b => p(a)(q(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#352OR · 11104 cellse.g. OR(Q, p∧¬q)

Lambda, short form: λpqab.q a (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((3 2) ((4 ((3 1) 2)) 1))
Tromp binary: 0000000001011110110010111110010111101011010 (43 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p @ @ q b a b
Reverse Polish: q a @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => q(a)(p(q(b)(a))(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#384OR · 11104 cellse.g. OR(OR, P)

Lambda, short form: λpqab.p a (q a (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p a) b))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 2) 1)))
Tromp binary: 000000000101111101100101111011001011111011010 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p a b
Reverse Polish: p a @ q a @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K)
JavaScript: p => q => a => b => p(a)(q(a)(p(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#394OR · 11104 cellse.g. OR(Q, OR)

Lambda, short form: λpqab.q a (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p a) ((q a) b))))))
De Bruijn: λλλλ((3 2) ((4 2) ((3 2) 1)))
Tromp binary: 00000000010111101100101111101100101111011010 (44 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p a @ @ q a b
Reverse Polish: q a @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => q(a)(p(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#397OR · 11104 cellse.g. OR(P, OR)

Lambda, short form: λpqab.p a (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 2) ((4 2) ((3 2) 1)))
Tromp binary: 000000000101111101100101111101100101111011010 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p a @ @ q a b
Reverse Polish: p a @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(a)(p(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#316OR · 11104 cellse.g. OR(OR, q∧¬p)

Lambda, short form: λpqab.p a (q a (p b (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p b) ((q a) b)))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 1) ((3 2) 1))))
Tromp binary: 0000000001011111011001011110110010111110100101111011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p b @ @ q a b
Reverse Polish: p a @ q a @ p b @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S)))
JavaScript: p => q => a => b => p(a)(q(a)(p(b)(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#330OR · 11104 cellse.g. OR(OR, AND)

Lambda, short form: λpqab.p a (q a (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 ((3 2) 1)) 1)))
Tromp binary: 0000000001011111011001011110110010111110010111101101010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p @ @ q a b b
Reverse Polish: p a @ q a @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(a)(q(a)(p(q(a)(b))(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#341OR · 11104 cellse.g. OR(p∧¬q, Q)

Lambda, short form: λpqab.p (q (q a b) a) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) a)) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) 2)) ((3 2) 1))
Tromp binary: 000000000101111100101111001011110110101100101111011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b a @ @ q a b
Reverse Polish: p q q a @ b @ @ a @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK)))))))(KI)
JavaScript: p => q => a => b => p(q(q(a)(b))(a))(q(a)(b))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#356OR · 11104 cellse.g. OR(OR, p∧¬q)

Lambda, short form: λpqab.p a (q a (p (q b a) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p ((q b) a)) b))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 ((3 1) 2)) 1)))
Tromp binary: 0000000001011111011001011110110010111110010111101011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p @ @ q b a b
Reverse Polish: p a @ q a @ p q b @ a @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(a)(q(a)(p(q(b)(a))(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#366OR · 11104 cellse.g. OR(Q, XOR)

Lambda, short form: λpqab.q a (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((3 2) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 000000000101111011001011111001011110101100101111011010 (54 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p @ @ q b a @ @ q a b
Reverse Polish: q a @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => q(a)(p(q(b)(a))(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#369OR · 11104 cellse.g. OR(P, XOR)

Lambda, short form: λpqab.p a (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 2) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111011001011111001011110101100101111011010 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p a @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(a)(p(q(b)(a))(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#378OR · 11104 cellse.g. OR(q∧¬p, P)

Lambda, short form: λpqab.p (p a b) (q a (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((q a) ((p a) b))))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((3 2) ((4 2) 1)))
Tromp binary: 00000000010111110010111110110100101111011001011111011010 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ q a @ @ p a b
Reverse Polish: p p a @ b @ @ q a @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K)
JavaScript: p => q => a => b => p(p(a)(b))(q(a)(p(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#398OR · 11104 cellse.g. OR(OR, OR)

Lambda, short form: λpqab.p a (q a (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 2) ((3 2) 1))))
Tromp binary: 00000000010111110110010111101100101111101100101111011010 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p a @ @ q a b
Reverse Polish: p a @ q a @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(a)(q(a)(p(a)(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#219OR · 11104 cellse.g. XOR(P, q∧¬p)

Lambda, short form: λpqab.p (p a (q b a)) (p b (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((p b) ((q a) b))))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1)))
Tromp binary: 000000000101111100101111101100101111010110010111110100101111011010 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ p b @ @ q a b
Reverse Polish: p p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(p(b)(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#245OR · 11104 cellse.g. XOR(p∧¬q, Q)

Lambda, short form: λpqab.p (q (q a b) (q b a)) (q a b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) ((q b) a))) ((q a) b)))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) ((3 1) 2))) ((3 2) 1))
Tromp binary: 0000000001011111001011110010111101101001011110101100101111011010 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b @ @ q b a @ @ q a b
Reverse Polish: p q q a @ b @ @ q b @ a @ @ @ q a @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK))))))))(KI)
JavaScript: p => q => a => b => p(q(q(a)(b))(q(b)(a)))(q(a)(b))

Where it comes from

XOR ×2 · XNOR ×2

#256OR · 11104 cellse.g. XOR(Q, p∧¬q)

Lambda, short form: λpqab.q (p (q a b) a) (p (q b a) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) a)) ((p ((q b) a)) b)))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1))
Tromp binary: 00000000010111100101111100101111011010110010111110010111101011010 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b
Reverse Polish: q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))
JavaScript: p => q => a => b => q(p(q(a)(b))(a))(p(q(b)(a))(b))

Where it comes from

XOR ×2 · XNOR ×2

#282OR · 11104 cellse.g. XOR(q∧¬p, P)

Lambda, short form: λpqab.p (p a b) (q (p b a) (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((q ((p b) a)) ((p a) b))))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((3 ((4 1) 2)) ((4 2) 1)))
Tromp binary: 0000000001011111001011111011010010111100101111101011001011111011010 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ q @ @ p b a @ @ p a b
Reverse Polish: p p a @ b @ @ q p b @ a @ @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K)
JavaScript: p => q => a => b => p(p(a)(b))(q(p(b)(a))(p(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

#342OR · 11104 cellse.g. OR(XOR, Q)

Lambda, short form: λpqab.p (q (q a b) a) (q a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) a)) ((q a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) 2)) ((3 2) ((3 2) 1)))
Tromp binary: 00000000010111110010111100101111011010110010111101100101111011010 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b a @ @ q a @ @ q a b
Reverse Polish: p q q a @ b @ @ a @ @ q a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))I))
JavaScript: p => q => a => b => p(q(q(a)(b))(a))(q(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#370OR · 11104 cellse.g. OR(OR, XOR)

Lambda, short form: λpqab.p a (q a (p (q b a) (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p ((q b) a)) ((q a) b)))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 ((3 1) 2)) ((3 2) 1))))
Tromp binary: 000000000101111101100101111011001011111001011110101100101111011010 (66 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p @ @ q b a @ @ q a b
Reverse Polish: p a @ q a @ p q b @ a @ @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))
JavaScript: p => q => a => b => p(a)(q(a)(p(q(b)(a))(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#382OR · 11104 cellse.g. OR(XOR, P)

Lambda, short form: λpqab.p (q (p a b) a) (q a (p a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) a)) ((q a) ((p a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) 2)) ((3 2) ((4 2) 1)))
Tromp binary: 0000000001011111001011110010111110110101100101111011001011111011010 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b a @ @ q a @ @ p a b
Reverse Polish: p q p a @ b @ @ a @ @ q a @ p a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K)
JavaScript: p => q => a => b => p(q(p(a)(b))(a))(q(a)(p(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#103OR · 11104 cellse.g. q∧¬p(NOR, OR)

Lambda, short form: λpqab.p (p a (q a b)) (q (p a (q a b)) b)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((q ((p a) ((q a) b))) b)))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((3 ((4 2) ((3 2) 1))) 1))
Tromp binary: 00000000010111110010111110110010111101101001011110010111110110010111101101010 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ q @ @ p a @ @ q a b b
Reverse Polish: p p a @ q a @ b @ @ @ q p a @ q a @ b @ @ @ b @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(K(KI))))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(q(p(a)(q(a)(b)))(b))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#392OR · 11104 cellse.g. OR(q∧¬p, OR)

Lambda, short form: λpqab.p (p a (q a b)) (q a (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((q a) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((3 2) ((4 2) ((3 2) 1))))
Tromp binary: 000000000101111100101111101100101111011010010111101100101111101100101111011010 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ q a @ @ p a @ @ q a b
Reverse Polish: p p a @ q a @ b @ @ @ q a @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(q(a)(p(a)(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#393OR · 11104 cellse.g. OR(AND, OR)

Lambda, short form: λpqab.p (q a (p a (q a b))) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) ((q a) b)))) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) ((3 2) 1)))) ((4 2) ((3 2) 1)))
Tromp binary: 000000000101111100101111011001011111011001011110110100101111101100101111011010 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a @ @ q a b @ @ p a @ @ q a b
Reverse Polish: p q a @ p a @ q a @ b @ @ @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(q(a)(p(a)(q(a)(b))))(p(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#395OR · 11104 cellse.g. OR(p∧¬q, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) a) (p a (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) a)) ((p a) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) 2)) ((4 2) ((3 2) 1)))
Tromp binary: 000000000101111100101111001011111011001011110110101100101111101100101111011010 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b a @ @ p a @ @ q a b
Reverse Polish: p q p a @ q a @ b @ @ @ a @ @ p a @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK)))))))(S(KS)(S(K(S(KS)))(S(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(a))(p(a)(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#328OR · 11104 cellse.g. OR(XOR, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) a) (q a (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) a)) ((q a) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) 2)) ((3 2) ((4 ((3 2) 1)) 1)))
Tromp binary: 000000000101111100101111001011111001011110110101011001011110110010111110010111101101010 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b a @ @ q a @ @ p @ @ q a b b
Reverse Polish: p q p q a @ b @ @ b @ @ a @ @ q a @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(a))(q(a)(p(q(a)(b))(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#396OR · 11104 cellse.g. OR(XOR, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) a) (q a (p a (q a b)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) a)) ((q a) ((p a) ((q a) b)))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) 2)) ((3 2) ((4 2) ((3 2) 1))))
Tromp binary: 00000000010111110010111100101111101100101111011010110010111101100101111101100101111011010 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b a @ @ q a @ @ p a @ @ q a b
Reverse Polish: p q p a @ q a @ b @ @ @ a @ @ q a @ p a @ q a @ b @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK)))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(a))(q(a)(p(a)(q(a)(b))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#365OR · 11104 cellse.g. OR(AND, XOR)

Lambda, short form: λpqab.p (q a (p (q b a) (q a b))) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) ((q a) b)))) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) ((3 2) 1)))) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 00000000010111110010111101100101111100101111010110010111101101001011111001011110101100101111011010 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a @ @ q a b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q a @ p q b @ a @ @ q a @ b @ @ @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(q(a)(b))))(p(q(b)(a))(q(a)(b)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#232OR · 11104 cellse.g. XOR(XOR, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) (p (q b a) a)) (q (p (q b a) a) (p (q a b) b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) ((p ((q b) a)) a))) ((q ((p ((q b) a)) a)) ((p ((q a) b)) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2))) ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1)))
Tromp binary: 00000000010111110010111100101111100101111011010100101111100101111010110110010111100101111100101111010110110010111110010111101101010 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b
Reverse Polish: p q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ @ q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(p(q(b)(a))(a)))(q(p(q(b)(a))(a))(p(q(a)(b))(b)))

Where it comes from

XOR ×2 · XNOR ×2

#269OR · 11104 cellse.g. XOR(AND, XOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) (p (q b a) (q a b))) (p (q b a) (q a b))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b)))) ((p ((q b) a)) ((q a) b))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1)))) ((4 ((3 1) 2)) ((3 2) 1)))
Tromp binary: 0000000001011111001011110010111110010111101101001011110101100101111100101111010110010111101101001011111001011110101100101111011010 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b @ @ p @ @ q b a @ @ q a b
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ @ p q b @ a @ @ q a @ b @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b))))(p(q(b)(a))(q(a)(b)))

Where it comes from

XOR ×2 · XNOR ×2

8 NOR 0001 · 32 programs · 216 cells

#110NOR · 000192 cellslambda16.txt

Lambda, short form: λpqab.p b (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) a)))))
De Bruijn: λλλλ((4 1) ((3 1) 2))
Tromp binary: 00000000010111110100101111010110 (32 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b a
Reverse Polish: p b @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(b)(q(b)(a))

Where it comes from

q∧¬p ×3 · AND ×3 · Q ×16 · p∧¬q ×3 · XOR ×4 · P ×16 · OR ×2 · NOR ×3 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#128NOR · 00014 cellse.g. q∧¬p(Q, ¬P)

Lambda, short form: λpqab.q b (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p b) a)))))
De Bruijn: λλλλ((3 1) ((4 1) 2))
Tromp binary: 00000000010111101001011111010110 (32 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p b a
Reverse Polish: q b @ p b @ a @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => q(b)(p(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#113NOR · 00014 cellse.g. q∧¬p(Q, NOR)

Lambda, short form: λpqab.q b (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p b) ((q b) a))))))
De Bruijn: λλλλ((3 1) ((4 1) ((3 1) 2)))
Tromp binary: 000000000101111010010111110100101111010110 (42 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p b @ @ q b a
Reverse Polish: q b @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(b)(p(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#116NOR · 00014 cellse.g. q∧¬p(P, NOR)

Lambda, short form: λpqab.p b (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 1) ((4 1) ((3 1) 2)))
Tromp binary: 0000000001011111010010111110100101111010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p b @ @ q b a
Reverse Polish: p b @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(b)(p(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#132NOR · 00014 cellse.g. q∧¬p(OR, ¬P)

Lambda, short form: λpqab.p b (q b (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p b) a))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 1) 2)))
Tromp binary: 0000000001011111010010111101001011111010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p b a
Reverse Polish: p b @ q b @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(b)(q(b)(p(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#158NOR · 00014 cellse.g. q∧¬p(Q, p→q)

Lambda, short form: λpqab.q b (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((3 1) ((4 ((3 2) 1)) 2))
Tromp binary: 0000000001011110100101111100101111011010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p @ @ q a b a
Reverse Polish: q b @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => q(b)(p(q(a)(b))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#176NOR · 00014 cellse.g. q∧¬p(OR, ¬Q)

Lambda, short form: λpqab.p b (q b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((q b) a))))))
De Bruijn: λλλλ((4 1) ((3 1) ((3 1) 2)))
Tromp binary: 000000000101111101001011110100101111010110 (42 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ q b a
Reverse Polish: p b @ q b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(b)(q(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#204NOR · 00014 cellse.g. q∧¬p(P, q→p)

Lambda, short form: λpqab.p b (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 1) ((4 2) ((3 1) 2)))
Tromp binary: 00000000010111110100101111101100101111010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p a @ @ q b a
Reverse Polish: p b @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(b)(p(a)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#117NOR · 00014 cellse.g. q∧¬p(OR, NOR)

Lambda, short form: λpqab.p b (q b (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 1) ((3 1) 2))))
Tromp binary: 00000000010111110100101111010010111110100101111010110 (53 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p b @ @ q b a
Reverse Polish: p b @ q b @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(b)(q(b)(p(b)(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#126NOR · 00014 cellse.g. q∧¬p(q∧¬p, ¬P)

Lambda, short form: λpqab.p (p b a) (q b (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((q b) ((p b) a))))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((3 1) ((4 1) 2)))
Tromp binary: 0000000001011111001011111010110010111101001011111010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ q b @ @ p b a
Reverse Polish: p p b @ a @ @ q b @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))))(S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(b)(a))(q(b)(p(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#143NOR · 00014 cellse.g. q∧¬p(Q, XNOR)

Lambda, short form: λpqab.q b (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((3 1) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 00000000010111101001011111001011110110100101111010110 (53 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p @ @ q a b @ @ q b a
Reverse Polish: q b @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(b)(p(q(a)(b))(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#146NOR · 00014 cellse.g. q∧¬p(P, XNOR)

Lambda, short form: λpqab.p b (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 1) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 000000000101111101001011111001011110110100101111010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p b @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(b)(p(q(a)(b))(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#162NOR · 00014 cellse.g. q∧¬p(OR, p→q)

Lambda, short form: λpqab.p b (q b (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 ((3 2) 1)) 2)))
Tromp binary: 000000000101111101001011110100101111100101111011010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p @ @ q a b a
Reverse Polish: p b @ q b @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(b)(q(b)(p(q(a)(b))(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#174NOR · 00014 cellse.g. q∧¬p(p∧¬q, ¬Q)

Lambda, short form: λpqab.p (q (q b a) b) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) b)) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) 1)) ((3 1) 2))
Tromp binary: 00000000010111110010111100101111010110100101111010110 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a b @ @ q b a
Reverse Polish: p q q b @ a @ @ b @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI))))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(q(b)(a))(b))(q(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#190NOR · 00014 cellse.g. q∧¬p(OR, NAND)

Lambda, short form: λpqab.p b (q b (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 ((3 1) 2)) 2)))
Tromp binary: 000000000101111101001011110100101111100101111010110110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p @ @ q b a a
Reverse Polish: p b @ q b @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(b)(q(b)(p(q(b)(a))(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#205NOR · 00014 cellse.g. q∧¬p(OR, q→p)

Lambda, short form: λpqab.p b (q b (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 2) ((3 1) 2))))
Tromp binary: 000000000101111101001011110100101111101100101111010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p a @ @ q b a
Reverse Polish: p b @ q b @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(b)(q(b)(p(a)(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#130NOR · 00014 cellse.g. q∧¬p(XOR, ¬P)

Lambda, short form: λpqab.p (q (p b a) b) (q b (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) b)) ((q b) ((p b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) 1)) ((3 1) ((4 1) 2)))
Tromp binary: 00000000010111110010111100101111101011010010111101001011111010110 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a b @ @ q b @ @ p b a
Reverse Polish: p q p b @ a @ @ b @ @ q b @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(a))(b))(q(b)(p(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#147NOR · 00014 cellse.g. q∧¬p(OR, XNOR)

Lambda, short form: λpqab.p b (q b (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((q b) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 1) ((3 1) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 0000000001011111010010111101001011111001011110110100101111010110 (64 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ q b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p b @ q b @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(b)(q(b)(p(q(a)(b))(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#175NOR · 00014 cellse.g. q∧¬p(XOR, ¬Q)

Lambda, short form: λpqab.p (q (q b a) b) (q b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) b)) ((q b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) 1)) ((3 1) ((3 1) 2)))
Tromp binary: 000000000101111100101111001011110101101001011110100101111010110 (63 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a b @ @ q b @ @ q b a
Reverse Polish: p q q b @ a @ @ b @ @ q b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(K(KI))))))))(K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(q(b)(a))(b))(q(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#222NOR · 00014 cellse.g. XOR(¬P, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2)))
Tromp binary: 000000000101111100101111101001011110110100101111101100101111010110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ p a @ @ q b a
Reverse Polish: p p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(p(a)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#250NOR · 00014 cellse.g. XOR(p→q, Q)

Lambda, short form: λpqab.p (q (q b a) (q a b)) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) ((q a) b))) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) ((3 2) 1))) ((3 1) 2))
Tromp binary: 0000000001011111001011110010111101011001011110110100101111010110 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a @ @ q a b @ @ q b a
Reverse Polish: p q q b @ a @ @ q a @ b @ @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(q(b)(a))(q(a)(b)))(q(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#265NOR · 00014 cellse.g. XOR(¬Q, p∧¬q)

Lambda, short form: λpqab.q (p (q b a) b) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) b)) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2))
Tromp binary: 00000000010111100101111100101111010110100101111100101111011010110 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a
Reverse Polish: q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => q(p(q(b)(a))(b))(p(q(a)(b))(a))

Where it comes from

XOR ×2 · XNOR ×2

#295NOR · 00014 cellse.g. XOR(q→p, P)

Lambda, short form: λpqab.p (p b a) (q (p a b) (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((q ((p a) b)) ((p b) a))))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((3 ((4 2) 1)) ((4 1) 2)))
Tromp binary: 0000000001011111001011111010110010111100101111101101001011111010110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ q @ @ p a b @ @ p b a
Reverse Polish: p p b @ a @ @ q p a @ b @ @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(b)(a))(q(p(a)(b))(p(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#111NOR · 00014 cellse.g. q∧¬p(q∧¬p, NOR)

Lambda, short form: λpqab.p (p b (q b a)) (q b (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((q b) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((3 1) ((4 1) ((3 1) 2))))
Tromp binary: 000000000101111100101111101001011110101100101111010010111110100101111010110 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ q b @ @ p b @ @ q b a
Reverse Polish: p p b @ q b @ a @ @ @ q b @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(q(b)(p(b)(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#112NOR · 00014 cellse.g. q∧¬p(AND, NOR)

Lambda, short form: λpqab.p (q b (p b (q b a))) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) ((q b) a)))) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) ((3 1) 2)))) ((4 1) ((3 1) 2)))
Tromp binary: 000000000101111100101111010010111110100101111010110010111110100101111010110 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b @ @ q b a @ @ p b @ @ q b a
Reverse Polish: p q b @ p b @ q b @ a @ @ @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(b)(p(b)(q(b)(a))))(p(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#114NOR · 00014 cellse.g. q∧¬p(p∧¬q, NOR)

Lambda, short form: λpqab.p (q (p b (q b a)) b) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) b)) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) 1)) ((4 1) ((3 1) 2)))
Tromp binary: 000000000101111100101111001011111010010111101011010010111110100101111010110 (75 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a b @ @ p b @ @ q b a
Reverse Polish: p q p b @ q b @ a @ @ @ b @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(b))(p(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#413NOR · 00014 cellse.g. OR(NOR, NOR)

Lambda, short form: λpqab.p (p b (q b a)) (q (p b (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((q ((p b) ((q b) a))) a)))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((3 ((4 1) ((3 1) 2))) 2))
Tromp binary: 0000000001011111001011111010010111101011001011110010111110100101111010110110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ q @ @ p b @ @ q b a a
Reverse Polish: p p b @ q b @ a @ @ @ q p b @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(q(p(b)(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#115NOR · 00014 cellse.g. q∧¬p(XOR, NOR)

Lambda, short form: λpqab.p (q (p b (q b a)) b) (q b (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) b)) ((q b) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) 1)) ((3 1) ((4 1) ((3 1) 2))))
Tromp binary: 0000000001011111001011110010111110100101111010110100101111010010111110100101111010110 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a b @ @ q b @ @ p b @ @ q b a
Reverse Polish: p q p b @ q b @ a @ @ @ b @ @ q b @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(b))(q(b)(p(b)(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#188NOR · 00014 cellse.g. q∧¬p(XOR, NAND)

Lambda, short form: λpqab.p (q (p (q b a) a) b) (q b (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) b)) ((q b) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) 1)) ((3 1) ((4 ((3 1) 2)) 2)))
Tromp binary: 000000000101111100101111001011111001011110101101101001011110100101111100101111010110110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a b @ @ q b @ @ p @ @ q b a a
Reverse Polish: p q p q b @ a @ @ a @ @ b @ @ q b @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(b))(q(b)(p(q(b)(a))(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#142NOR · 00014 cellse.g. q∧¬p(AND, XNOR)

Lambda, short form: λpqab.p (q b (p (q a b) (q b a))) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) ((q b) a)))) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) ((3 1) 2)))) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110100101111100101111011010010111101011001011111001011110110100101111010110 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b @ @ q b a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q b @ p q a @ b @ @ q b @ a @ @ @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(q(b)(a))))(p(q(a)(b))(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#237NOR · 00014 cellse.g. XOR(XNOR, AND)

Lambda, short form: λpqab.p (q (p (q b a) a) (p (q a b) b)) (q (p (q a b) b) (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) ((p ((q a) b)) b))) ((q ((p ((q a) b)) b)) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1))) ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2)))
Tromp binary: 00000000010111110010111100101111100101111010110110010111110010111101101010010111100101111100101111011010100101111100101111010110110 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a
Reverse Polish: p q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ @ q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(p(q(a)(b))(b)))(q(p(q(a)(b))(b))(p(q(b)(a))(a)))

Where it comes from

XOR ×2 · XNOR ×2

#280NOR · 00014 cellse.g. XOR(NAND, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) (p (q a b) (q b a))) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a)))) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2)))) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110010111110010111101011001011110110100101111100101111011010010111101011001011111001011110110100101111010110 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a))))(p(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

9 NOT P 0011 · 21 programs · 168 cells

#125NOT P · 001188 cellslambda16.txt

Lambda, short form: λpqab.p b a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) a))))
De Bruijn: λλλλ((4 1) 2)
Tromp binary: 0000000001011111010110 (22 bits)
Polish (prefix): λp λq λa λb @ @ p b a
Reverse Polish: p b @ a @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(KK)S))(KK))
JavaScript: p => q => a => b => p(b)(a)

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×2 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#131NOT P · 00114 cellse.g. q∧¬p(P, ¬P)

Lambda, short form: λpqab.p b (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p b) a)))))
De Bruijn: λλλλ((4 1) ((4 1) 2))
Tromp binary: 000000000101111101001011111010110 (33 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p b a
Reverse Polish: p b @ p b @ a @ @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(b)(p(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#428NOT P · 00114 cellse.g. OR(¬P, ¬P)

Lambda, short form: λpqab.p (p b a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) a))))
De Bruijn: λλλλ((4 ((4 1) 2)) 2)
Tromp binary: 0000000001011111001011111010110110 (34 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a a
Reverse Polish: p p b @ a @ @ a @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK))
JavaScript: p => q => a => b => p(p(b)(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#161NOT P · 00114 cellse.g. q∧¬p(P, p→q)

Lambda, short form: λpqab.p b (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 1) ((4 ((3 2) 1)) 2))
Tromp binary: 00000000010111110100101111100101111011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p @ @ q a b a
Reverse Polish: p b @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(b)(p(q(a)(b))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#189NOT P · 00114 cellse.g. q∧¬p(P, NAND)

Lambda, short form: λpqab.p b (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p b) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 1) ((4 ((3 1) 2)) 2))
Tromp binary: 00000000010111110100101111100101111010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p b @ @ p @ @ q b a a
Reverse Polish: p b @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(b)(p(q(b)(a))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#318NOT P · 00114 cellse.g. OR(¬P, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) a))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) 2)
Tromp binary: 00000000010111110010111110100101111011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b a
Reverse Polish: p p b @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#414NOT P · 00114 cellse.g. OR(¬P, NOR)

Lambda, short form: λpqab.p (p b (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) a))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) 2)
Tromp binary: 00000000010111110010111110100101111010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a a
Reverse Polish: p p b @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#127NOT P · 00114 cellse.g. q∧¬p(AND, ¬P)

Lambda, short form: λpqab.p (q b (p b a)) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p b) a))) ((p b) a)))))
De Bruijn: λλλλ((4 ((3 1) ((4 1) 2))) ((4 1) 2))
Tromp binary: 0000000001011111001011110100101111101011001011111010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p b a @ @ p b a
Reverse Polish: p q b @ p b @ a @ @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(b)(p(b)(a)))(p(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#129NOT P · 00114 cellse.g. q∧¬p(p∧¬q, ¬P)

Lambda, short form: λpqab.p (q (p b a) b) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) b)) ((p b) a)))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) 1)) ((4 1) 2))
Tromp binary: 0000000001011111001011110010111110101101001011111010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a b @ @ p b a
Reverse Polish: p q p b @ a @ @ b @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(p(b)(a))(b))(p(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#420NOT P · 00114 cellse.g. OR(q∧¬p, ¬P)

Lambda, short form: λpqab.p (p b a) (q a (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((q a) ((p b) a))))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((3 2) ((4 1) 2)))
Tromp binary: 00000000010111110010111110101100101111011001011111010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ q a @ @ p b a
Reverse Polish: p p b @ a @ @ q a @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(b)(a))(q(a)(p(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#427NOT P · 00114 cellse.g. OR(NOR, ¬P)

Lambda, short form: λpqab.p (p b a) (q (p b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) a)) ((q ((p b) a)) a)))))
De Bruijn: λλλλ((4 ((4 1) 2)) ((3 ((4 1) 2)) 2))
Tromp binary: 00000000010111110010111110101100101111001011111010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b a @ @ q @ @ p b a a
Reverse Polish: p p b @ a @ @ q p b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(p(b)(a))(q(p(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#157NOT P · 00114 cellse.g. q∧¬p(AND, p→q)

Lambda, short form: λpqab.p (q b (p (q a b) a)) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q a) b)) a))) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 2) 1)) 2))) ((4 ((3 2) 1)) 2))
Tromp binary: 00000000010111110010111101001011111001011110110101100101111100101111011010110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q a b a @ @ p @ @ q a b a
Reverse Polish: p q b @ p q a @ b @ @ a @ @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(q(b)(p(q(a)(b))(a)))(p(q(a)(b))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#187NOT P · 00114 cellse.g. q∧¬p(p∧¬q, NAND)

Lambda, short form: λpqab.p (q (p (q b a) a) b) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) b)) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) 1)) ((4 ((3 1) 2)) 2))
Tromp binary: 00000000010111110010111100101111100101111010110110100101111100101111010110110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a b @ @ p @ @ q b a a
Reverse Polish: p q p q b @ a @ @ a @ @ b @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(b))(p(q(b)(a))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#317NOT P · 00114 cellse.g. OR(NOR, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (q (p b (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((q ((p b) ((q a) b))) a)))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((3 ((4 1) ((3 2) 1))) 2))
Tromp binary: 0000000001011111001011111010010111101101001011110010111110100101111011010110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ q @ @ p b @ @ q a b a
Reverse Polish: p p b @ q a @ b @ @ @ q p b @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK)))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(q(p(b)(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#406NOT P · 00114 cellse.g. OR(q∧¬p, NOR)

Lambda, short form: λpqab.p (p b (q b a)) (q a (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((q a) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((3 2) ((4 1) ((3 1) 2))))
Tromp binary: 0000000001011111001011111010010111101011001011110110010111110100101111010110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ q a @ @ p b @ @ q b a
Reverse Polish: p p b @ q b @ a @ @ @ q a @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(q(a)(p(b)(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#249NOT P · 00114 cellse.g. XOR(XNOR, Q)

Lambda, short form: λpqab.p (q (q b a) (q a b)) (q (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) ((q a) b))) ((q ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) ((3 2) 1))) ((3 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110010111101011001011110110100101111001011110110100101111010110 (85 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a @ @ q a b @ @ q @ @ q a b @ @ q b a
Reverse Polish: p q q b @ a @ @ q a @ b @ @ @ q q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))I))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(q(b)(a))(q(a)(b)))(q(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#279NOT P · 00114 cellse.g. XOR(¬Q, XOR)

Lambda, short form: λpqab.q (p (q b a) (q a b)) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 00000000010111100101111100101111010110010111101101001011111001011110110100101111010110 (86 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#221NOT P · 00114 cellse.g. XOR(NOR, q∧¬p)

Lambda, short form: λpqab.p (p b (q a b)) (q (p b (q a b)) (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q a) b))) ((q ((p b) ((q a) b))) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 2) 1))) ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2))))
Tromp binary: 00000000010111110010111110100101111011010010111100101111101001011110110100101111101100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q a b @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a
Reverse Polish: p p b @ q a @ b @ @ @ q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(b)(q(a)(b)))(q(p(b)(q(a)(b)))(p(a)(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

#238NOT P · 00114 cellse.g. XOR(p→q, AND)

Lambda, short form: λpqab.p (q (p (q b a) a) (p (q a b) b)) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) ((p ((q a) b)) b))) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) ((4 ((3 2) 1)) 1))) ((4 ((3 1) 2)) 2))
Tromp binary: 000000000101111100101111001011111001011110101101100101111100101111011010100101111100101111010110110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a @ @ p @ @ q a b b @ @ p @ @ q b a a
Reverse Polish: p q p q b @ a @ @ a @ @ p q a @ b @ @ b @ @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(p(q(a)(b))(b)))(p(q(b)(a))(a))

Where it comes from

XOR ×2 · XNOR ×2

#266NOT P · 00114 cellse.g. XOR(NAND, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) (p (q a b) a)) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) ((p ((q a) b)) a))) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2))) ((4 ((3 2) 1)) 2))
Tromp binary: 000000000101111100101111001011111001011110101101001011111001011110110101100101111100101111011010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a @ @ p @ @ q a b a
Reverse Polish: p q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(p(q(a)(b))(a)))(p(q(a)(b))(a))

Where it comes from

XOR ×2 · XNOR ×2

#309NOT P · 00114 cellse.g. XOR(q→p, OR)

Lambda, short form: λpqab.p (p b (q b a)) (q (p a (q a b)) (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p b) ((q b) a))) ((q ((p a) ((q a) b))) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 1) ((3 1) 2))) ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2))))
Tromp binary: 00000000010111110010111110100101111010110010111100101111101100101111011010010111110100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p b @ @ q b a @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a
Reverse Polish: p p b @ q b @ a @ @ @ q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(b)(q(b)(a)))(q(p(a)(q(a)(b)))(p(b)(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

10 XNOR 1001 · 20 programs · 168 cells

#140XNOR · 100192 cellslambda16.txt

Lambda, short form: λpqab.p (q a b) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 1) 2))
Tromp binary: 0000000001011111001011110110100101111010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q a @ b @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(a)(b))(q(b)(a))

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×6 · P ×16 · OR ×2 · NOR ×2 · ¬P ×16 · XNOR ×6 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#293XNOR · 10014 cellse.g. XOR(¬Q, P)

Lambda, short form: λpqab.q (p a b) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) b)) ((p b) a)))))
De Bruijn: λλλλ((3 ((4 2) 1)) ((4 1) 2))
Tromp binary: 00000000010111100101111101101001011111010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a b @ @ p b a
Reverse Polish: q p a @ b @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => q(p(a)(b))(p(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#156XNOR · 10014 cellse.g. q∧¬p(q∧¬p, p→q)

Lambda, short form: λpqab.p (p (q a b) a) (q b (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((q b) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((3 1) ((4 ((3 2) 1)) 2)))
Tromp binary: 00000000010111110010111110010111101101011001011110100101111100101111011010110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ q b @ @ p @ @ q a b a
Reverse Polish: p p q a @ b @ @ a @ @ q b @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(q(b)(p(q(a)(b))(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#202XNOR · 10014 cellse.g. q∧¬p(p∧¬q, q→p)

Lambda, short form: λpqab.p (q (p a (q b a)) b) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) b)) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) 1)) ((4 2) ((3 1) 2)))
Tromp binary: 00000000010111110010111100101111101100101111010110100101111101100101111010110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a b @ @ p a @ @ q b a
Reverse Polish: p q p a @ q b @ a @ @ @ b @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(b))(p(a)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#331XNOR · 10014 cellse.g. OR(NOR, AND)

Lambda, short form: λpqab.p (p (q a b) b) (q (p (q a b) b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((q ((p ((q a) b)) b)) a)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((3 ((4 ((3 2) 1)) 1)) 2))
Tromp binary: 0000000001011111001011111001011110110101001011110010111110010111101101010110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ q @ @ p @ @ q a b b a
Reverse Polish: p p q a @ b @ @ b @ @ q p q a @ b @ @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(q(p(q(a)(b))(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#407XNOR · 10014 cellse.g. OR(AND, NOR)

Lambda, short form: λpqab.p (q a (p b (q b a))) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) ((q b) a)))) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) ((3 1) 2)))) ((4 1) ((3 1) 2)))
Tromp binary: 0000000001011111001011110110010111110100101111010110010111110100101111010110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b @ @ q b a @ @ p b @ @ q b a
Reverse Polish: p q a @ p b @ q b @ a @ @ @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(a)(p(b)(q(b)(a))))(p(b)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#160XNOR · 10014 cellse.g. q∧¬p(XOR, p→q)

Lambda, short form: λpqab.p (q (p (q a b) a) b) (q b (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) b)) ((q b) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) 1)) ((3 1) ((4 ((3 2) 1)) 2)))
Tromp binary: 000000000101111100101111001011111001011110110101101001011110100101111100101111011010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a b @ @ q b @ @ p @ @ q a b a
Reverse Polish: p q p q a @ b @ @ a @ @ b @ @ q b @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(b))(q(b)(p(q(a)(b))(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#203XNOR · 10014 cellse.g. q∧¬p(XOR, q→p)

Lambda, short form: λpqab.p (q (p a (q b a)) b) (q b (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) b)) ((q b) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) 1)) ((3 1) ((4 2) ((3 1) 2))))
Tromp binary: 000000000101111100101111001011111011001011110101101001011110100101111101100101111010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a b @ @ q b @ @ p a @ @ q b a
Reverse Polish: p q p a @ q b @ a @ @ @ b @ @ q b @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(b))(q(b)(p(a)(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#333XNOR · 10014 cellse.g. OR(XNOR, AND)

Lambda, short form: λpqab.p (q a (p (q a b) b)) (q (p (q a b) b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) b))) ((q ((p ((q a) b)) b)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) 1))) ((3 ((4 ((3 2) 1)) 1)) 2))
Tromp binary: 000000000101111100101111011001011111001011110110101001011110010111110010111101101010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b b @ @ q @ @ p @ @ q a b b a
Reverse Polish: p q a @ p q a @ b @ @ b @ @ @ q p q a @ b @ @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(b)))(q(p(q(a)(b))(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#415XNOR · 10014 cellse.g. OR(XNOR, NOR)

Lambda, short form: λpqab.p (q a (p b (q b a))) (q (p b (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) ((q b) a)))) ((q ((p b) ((q b) a))) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) ((3 1) 2)))) ((3 ((4 1) ((3 1) 2))) 2))
Tromp binary: 000000000101111100101111011001011111010010111101011001011110010111110100101111010110110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b @ @ q b a @ @ q @ @ p b @ @ q b a a
Reverse Polish: p q a @ p b @ q b @ a @ @ @ @ q p b @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(b)(q(b)(a))))(q(p(b)(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#141XNOR · 10014 cellse.g. q∧¬p(q∧¬p, XNOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (q b (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((q b) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((3 1) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 0000000001011111001011111001011110110100101111010110010111101001011111001011110110100101111010110 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ q b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ q b @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(q(b)(p(q(a)(b))(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#144XNOR · 10014 cellse.g. q∧¬p(p∧¬q, XNOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) b) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) b)) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1)) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110010111110010111101101001011110101101001011111001011110110100101111010110 (97 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ b @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(b))(p(q(a)(b))(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#224XNOR · 10014 cellse.g. XOR(p→q, q∧¬p)

Lambda, short form: λpqab.p (q (p a (q b a)) (p b (q a b))) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) ((p b) ((q a) b)))) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1)))) ((4 2) ((3 1) 2)))
Tromp binary: 000000000101111100101111001011111011001011110101100101111101001011110110100101111101100101111010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b @ @ p a @ @ q b a
Reverse Polish: p q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S)))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(p(b)(q(a)(b))))(p(a)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#235XNOR · 10014 cellse.g. XOR(NOR, AND)

Lambda, short form: λpqab.p (p (q a b) b) (q (p (q a b) b) (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((q ((p ((q a) b)) b)) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2)))
Tromp binary: 00000000010111110010111110010111101101010010111100101111100101111011010100101111100101111010110110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a
Reverse Polish: p p q a @ b @ @ b @ @ q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(q(p(q(a)(b))(b))(p(q(b)(a))(a)))

Where it comes from

XOR ×2 · XNOR ×2

#267XNOR · 10014 cellse.g. XOR(q→p, p∧¬q)

Lambda, short form: λpqab.p (p (q a b) a) (q (p (q b a) b) (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((q ((p ((q b) a)) b)) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2)))
Tromp binary: 000000000101111100101111100101111011010110010111100101111100101111010110100101111100101111011010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a
Reverse Polish: p p q a @ b @ @ a @ @ q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(q(p(q(b)(a))(b))(p(q(a)(b))(a)))

Where it comes from

XOR ×2 · XNOR ×2

#308XNOR · 10014 cellse.g. XOR(NAND, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) (p b (q b a))) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) ((p b) ((q b) a)))) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2)))) ((4 1) ((3 1) 2)))
Tromp binary: 00000000010111110010111100101111101100101111011010010111110100101111010110010111110100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a @ @ p b @ @ q b a
Reverse Polish: p q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(p(b)(q(b)(a))))(p(b)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#435XNOR · 10014 cellse.g. OR(AND, XNOR)

Lambda, short form: λpqab.p (q a (p (q a b) (q b a))) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) ((q b) a)))) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) ((3 1) 2)))) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 00000000010111110010111101100101111100101111011010010111101011001011111001011110110100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b @ @ q b a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q a @ p q a @ b @ @ q b @ a @ @ @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(q(b)(a))))(p(q(a)(b))(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#441XNOR · 10014 cellse.g. OR(NOR, XNOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (q (p (q a b) (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((q ((p ((q a) b)) ((q b) a))) a)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2))
Tromp binary: 00000000010111110010111110010111101101001011110101100101111001011111001011110110100101111010110110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q a b @ @ q b a a
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ q p q a @ b @ @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(q(p(q(a)(b))(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#145XNOR · 10014 cellse.g. q∧¬p(XOR, XNOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) b) (q b (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) b)) ((q b) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) 1)) ((3 1) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 00000000010111110010111100101111100101111011010010111101011010010111101001011111001011110110100101111010110 (107 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a b @ @ q b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ b @ @ q b @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(K(KI))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(b))(q(b)(p(q(a)(b))(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#443XNOR · 10014 cellse.g. OR(XNOR, XNOR)

Lambda, short form: λpqab.p (q a (p (q a b) (q b a))) (q (p (q a b) (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) ((q b) a)))) ((q ((p ((q a) b)) ((q b) a))) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) ((3 1) 2)))) ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2))
Tromp binary: 0000000001011111001011110110010111110010111101101001011110101100101111001011111001011110110100101111010110110 (109 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q a b @ @ q b a a
Reverse Polish: p q a @ p q a @ b @ @ q b @ a @ @ @ @ q p q a @ b @ @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(q(b)(a))))(q(p(q(a)(b))(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

11 IMPLIES (p -> q) 1011 · 32 programs · 216 cells

#155IMPLIES (p -> q) · 101192 cellslambda16.txt

Lambda, short form: λpqab.p (q a b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) a))))
De Bruijn: λλλλ((4 ((3 2) 1)) 2)
Tromp binary: 000000000101111100101111011010110 (33 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b a
Reverse Polish: p q a @ b @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(b))(a)

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×3 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×3 · ¬Q ×16 · NAND ×3 · q→p ×3

#422IMPLIES (p -> q) · 10114 cellse.g. OR(Q, ¬P)

Lambda, short form: λpqab.q a (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p b) a)))))
De Bruijn: λλλλ((3 2) ((4 1) 2))
Tromp binary: 000000000101111011001011111010110 (33 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p b a
Reverse Polish: q a @ p b @ a @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => q(a)(p(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#332IMPLIES (p -> q) · 10114 cellse.g. OR(¬P, AND)

Lambda, short form: λpqab.p (p (q a b) b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) a))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) 2)
Tromp binary: 00000000010111110010111110010111101101010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b a
Reverse Polish: p p q a @ b @ @ b @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#346IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, Q)

Lambda, short form: λpqab.p (q a (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((q a) b))) a))))
De Bruijn: λλλλ((4 ((3 2) ((3 2) 1))) 2)
Tromp binary: 00000000010111110010111101100101111011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ q a b a
Reverse Polish: p q a @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))I))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#408IMPLIES (p -> q) · 10114 cellse.g. OR(Q, NOR)

Lambda, short form: λpqab.q a (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p b) ((q b) a))))))
De Bruijn: λλλλ((3 2) ((4 1) ((3 1) 2)))
Tromp binary: 0000000001011110110010111110100101111010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p b @ @ q b a
Reverse Polish: q a @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(a)(p(b)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#430IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, ¬P)

Lambda, short form: λpqab.p (q a (p b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) a))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) 2))) 2)
Tromp binary: 000000000101111100101111011001011111010110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b a a
Reverse Polish: p q a @ p b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#450IMPLIES (p -> q) · 10114 cellse.g. OR(Q, p→q)

Lambda, short form: λpqab.q a (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((3 2) ((4 ((3 2) 1)) 2))
Tromp binary: 00000000010111101100101111100101111011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p @ @ q a b a
Reverse Polish: q a @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => q(a)(p(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#456IMPLIES (p -> q) · 10114 cellse.g. OR(¬P, p→q)

Lambda, short form: λpqab.p (p (q a b) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) a))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) 2)
Tromp binary: 000000000101111100101111100101111011010110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a a
Reverse Polish: p p q a @ b @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#320IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, q∧¬p)

Lambda, short form: λpqab.p (q a (p b (q a b))) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) ((q a) b)))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) ((3 2) 1)))) 2)
Tromp binary: 0000000001011111001011110110010111110100101111011010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b @ @ q a b a
Reverse Polish: p q a @ p b @ q a @ b @ @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S)))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(b)(q(a)(b))))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#334IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, AND)

Lambda, short form: λpqab.p (q a (p (q a b) b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) b))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) 1))) 2)
Tromp binary: 0000000001011111001011110110010111110010111101101010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b b a
Reverse Polish: p q a @ p q a @ b @ @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI)))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#344IMPLIES (p -> q) · 10114 cellse.g. OR(NOR, Q)

Lambda, short form: λpqab.p (q a b) (q (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 ((3 2) 1)) 2))
Tromp binary: 000000000101111100101111011010010111100101111011010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q @ @ q a b a
Reverse Polish: p q a @ b @ @ q q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK)))
JavaScript: p => q => a => b => p(q(a)(b))(q(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#416IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, NOR)

Lambda, short form: λpqab.p (q a (p b (q b a))) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) ((q b) a)))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) ((3 1) 2)))) 2)
Tromp binary: 0000000001011111001011110110010111110100101111010110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b @ @ q b a a
Reverse Polish: p q a @ p b @ q b @ a @ @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(b)(q(b)(a))))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#421IMPLIES (p -> q) · 10114 cellse.g. OR(AND, ¬P)

Lambda, short form: λpqab.p (q a (p b a)) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) a))) ((p b) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) 2))) ((4 1) 2))
Tromp binary: 00000000010111110010111101100101111101011001011111010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b a @ @ p b a
Reverse Polish: p q a @ p b @ a @ @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(a)(p(b)(a)))(p(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#436IMPLIES (p -> q) · 10114 cellse.g. OR(Q, XNOR)

Lambda, short form: λpqab.q a (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((3 2) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 000000000101111011001011111001011110110100101111010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p @ @ q a b @ @ q b a
Reverse Polish: q a @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(a)(p(q(a)(b))(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#442IMPLIES (p -> q) · 10114 cellse.g. OR(¬P, XNOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) a))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) 2)
Tromp binary: 0000000001011111001011111001011110110100101111010110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a a
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#458IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, p→q)

Lambda, short form: λpqab.p (q a (p (q a b) a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) a))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) 2))) 2)
Tromp binary: 00000000010111110010111101100101111100101111011010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b a a
Reverse Polish: p q a @ p q a @ b @ @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#236IMPLIES (p -> q) · 10114 cellse.g. XOR(¬P, AND)

Lambda, short form: λpqab.p (p (q a b) b) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) b)) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2))
Tromp binary: 000000000101111100101111100101111011010100101111100101111010110110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b b @ @ p @ @ q b a a
Reverse Polish: p p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(a)(b))(b))(p(q(b)(a))(a))

Where it comes from

XOR ×2 · XNOR ×2

#248IMPLIES (p -> q) · 10114 cellse.g. XOR(NOR, Q)

Lambda, short form: λpqab.p (q a b) (q (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) b)) ((q ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 2) 1)) ((3 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110110100101111001011110110100101111010110 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a b @ @ q @ @ q a b @ @ q b a
Reverse Polish: p q a @ b @ @ q q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(a)(b))(q(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#294IMPLIES (p -> q) · 10114 cellse.g. XOR(NAND, P)

Lambda, short form: λpqab.p (q (p a b) (p b a)) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) ((p b) a))) ((p b) a)))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) ((4 1) 2))) ((4 1) 2))
Tromp binary: 0000000001011111001011110010111110110100101111101011001011111010110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b @ @ p b a @ @ p b a
Reverse Polish: p q p a @ b @ @ p b @ a @ @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(p(a)(b))(p(b)(a)))(p(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#307IMPLIES (p -> q) · 10114 cellse.g. XOR(¬Q, OR)

Lambda, short form: λpqab.q (p a (q a b)) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) ((q a) b))) ((p b) ((q b) a))))))
De Bruijn: λλλλ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2)))
Tromp binary: 00000000010111100101111101100101111011010010111110100101111010110 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a
Reverse Polish: q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(p(a)(q(a)(b)))(p(b)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#345IMPLIES (p -> q) · 10114 cellse.g. OR(XNOR, Q)

Lambda, short form: λpqab.p (q a (q a b)) (q (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((q a) b))) ((q ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((3 2) 1))) ((3 ((3 2) 1)) 2))
Tromp binary: 00000000010111110010111101100101111011010010111100101111011010110 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ q a b @ @ q @ @ q a b a
Reverse Polish: p q a @ q a @ b @ @ @ q q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))I))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK)))
JavaScript: p => q => a => b => p(q(a)(q(a)(b)))(q(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#429IMPLIES (p -> q) · 10114 cellse.g. OR(XNOR, ¬P)

Lambda, short form: λpqab.p (q a (p b a)) (q (p b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) a))) ((q ((p b) a)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) 2))) ((3 ((4 1) 2)) 2))
Tromp binary: 0000000001011111001011110110010111110101100101111001011111010110110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b a @ @ q @ @ p b a a
Reverse Polish: p q a @ p b @ a @ @ @ q p b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(b)(a)))(q(p(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#444IMPLIES (p -> q) · 10114 cellse.g. OR(p→q, XNOR)

Lambda, short form: λpqab.p (q a (p (q a b) (q b a))) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) ((q b) a)))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) ((3 1) 2)))) 2)
Tromp binary: 000000000101111100101111011001011111001011110110100101111010110110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b @ @ q b a a
Reverse Polish: p q a @ p q a @ b @ @ q b @ a @ @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(q(b)(a))))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#159IMPLIES (p -> q) · 10114 cellse.g. q∧¬p(p∧¬q, p→q)

Lambda, short form: λpqab.p (q (p (q a b) a) b) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) b)) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) 1)) ((4 ((3 2) 1)) 2))
Tromp binary: 00000000010111110010111100101111100101111011010110100101111100101111011010110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a b @ @ p @ @ q a b a
Reverse Polish: p q p q a @ b @ @ a @ @ b @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(b))(p(q(a)(b))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#448IMPLIES (p -> q) · 10114 cellse.g. OR(q∧¬p, p→q)

Lambda, short form: λpqab.p (p (q a b) a) (q a (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((q a) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((3 2) ((4 ((3 2) 1)) 2)))
Tromp binary: 000000000101111100101111100101111011010110010111101100101111100101111011010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ q a @ @ p @ @ q a b a
Reverse Polish: p p q a @ b @ @ a @ @ q a @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(q(a)(p(q(a)(b))(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#449IMPLIES (p -> q) · 10114 cellse.g. OR(AND, p→q)

Lambda, short form: λpqab.p (q a (p (q a b) a)) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) a))) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) 2))) ((4 ((3 2) 1)) 2))
Tromp binary: 000000000101111100101111011001011111001011110110101100101111100101111011010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b a @ @ p @ @ q a b a
Reverse Polish: p q a @ p q a @ b @ @ a @ @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(a)))(p(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#455IMPLIES (p -> q) · 10114 cellse.g. OR(NOR, p→q)

Lambda, short form: λpqab.p (p (q a b) a) (q (p (q a b) a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) a)) ((q ((p ((q a) b)) a)) a)))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) 2)) ((3 ((4 ((3 2) 1)) 2)) 2))
Tromp binary: 000000000101111100101111100101111011010110010111100101111100101111011010110110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b a @ @ q @ @ p @ @ q a b a a
Reverse Polish: p p q a @ b @ @ a @ @ q p q a @ b @ @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(a)(b))(a))(q(p(q(a)(b))(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#319IMPLIES (p -> q) · 10114 cellse.g. OR(XNOR, q∧¬p)

Lambda, short form: λpqab.p (q a (p b (q a b))) (q (p b (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p b) ((q a) b)))) ((q ((p b) ((q a) b))) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 1) ((3 2) 1)))) ((3 ((4 1) ((3 2) 1))) 2))
Tromp binary: 000000000101111100101111011001011111010010111101101001011110010111110100101111011010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p b @ @ q a b @ @ q @ @ p b @ @ q a b a
Reverse Polish: p q a @ p b @ q a @ b @ @ @ @ q p b @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(KK)S)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(b)(q(a)(b))))(q(p(b)(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#457IMPLIES (p -> q) · 10114 cellse.g. OR(XNOR, p→q)

Lambda, short form: λpqab.p (q a (p (q a b) a)) (q (p (q a b) a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q a) b)) a))) ((q ((p ((q a) b)) a)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 2) 1)) 2))) ((3 ((4 ((3 2) 1)) 2)) 2))
Tromp binary: 00000000010111110010111101100101111100101111011010110010111100101111100101111011010110110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q a b a @ @ q @ @ p @ @ q a b a a
Reverse Polish: p q a @ p q a @ b @ @ a @ @ @ q p q a @ b @ @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(a)(b))(a)))(q(p(q(a)(b))(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#434IMPLIES (p -> q) · 10114 cellse.g. OR(q∧¬p, XNOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (q a (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((q a) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((3 2) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 00000000010111110010111110010111101101001011110101100101111011001011111001011110110100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ q a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ q a @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(q(a)(p(q(a)(b))(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#223IMPLIES (p -> q) · 10114 cellse.g. XOR(XNOR, q∧¬p)

Lambda, short form: λpqab.p (q (p a (q b a)) (p b (q a b))) (q (p b (q a b)) (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) ((p b) ((q a) b)))) ((q ((p b) ((q a) b))) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) ((4 1) ((3 2) 1)))) ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2))))
Tromp binary: 00000000010111110010111100101111101100101111010110010111110100101111011010010111100101111101001011110110100101111101100101111010110 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a @ @ p b @ @ q a b @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a
Reverse Polish: p q p a @ q b @ a @ @ @ p b @ q a @ b @ @ @ @ q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(KK)S)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(p(b)(q(a)(b))))(q(p(b)(q(a)(b)))(p(a)(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

#281IMPLIES (p -> q) · 10114 cellse.g. XOR(q→p, XOR)

Lambda, short form: λpqab.p (p (q a b) (q b a)) (q (p (q b a) (q a b)) (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q a) b)) ((q b) a))) ((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 ((3 2) 1)) ((3 1) 2))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 0000000001011111001011111001011110110100101111010110010111100101111100101111010110010111101101001011111001011110110100101111010110 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q a b @ @ q b a @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p p q a @ b @ @ q b @ a @ @ @ q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(q(a)(b))(q(b)(a)))(q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

12 NOT Q 0101 · 21 programs · 168 cells

#170NOT Q · 010188 cellslambda16.txt

Lambda, short form: λpqab.q b a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) a))))
De Bruijn: λλλλ((3 1) 2)
Tromp binary: 000000000101111010110 (21 bits)
Polish (prefix): λp λq λa λb @ @ q b a
Reverse Polish: q b @ a @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(KK)S))(KK))
JavaScript: p => q => a => b => q(b)(a)

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×2 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×2 · ¬Q ×16 · NAND ×2 · q→p ×2

#173NOT Q · 01014 cellse.g. q∧¬p(Q, ¬Q)

Lambda, short form: λpqab.q b (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((q b) a)))))
De Bruijn: λλλλ((3 1) ((3 1) 2))
Tromp binary: 0000000001011110100101111010110 (31 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ q b a
Reverse Polish: q b @ q b @ a @ @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => q(b)(q(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#471NOT Q · 01014 cellse.g. OR(¬Q, ¬Q)

Lambda, short form: λpqab.q (q b a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((q b) a)) a))))
De Bruijn: λλλλ((3 ((3 1) 2)) 2)
Tromp binary: 00000000010111100101111010110110 (32 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ q b a a
Reverse Polish: q q b @ a @ @ a @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK))
JavaScript: p => q => a => b => q(q(b)(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#186NOT Q · 01014 cellse.g. q∧¬p(Q, NAND)

Lambda, short form: λpqab.q b (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((3 1) ((4 ((3 1) 2)) 2))
Tromp binary: 0000000001011110100101111100101111010110110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p @ @ q b a a
Reverse Polish: q b @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => q(b)(p(q(b)(a))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#201NOT Q · 01014 cellse.g. q∧¬p(Q, q→p)

Lambda, short form: λpqab.q b (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q b) ((p a) ((q b) a))))))
De Bruijn: λλλλ((3 1) ((4 2) ((3 1) 2)))
Tromp binary: 0000000001011110100101111101100101111010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q b @ @ p a @ @ q b a
Reverse Polish: q b @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(b)(p(a)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#361NOT Q · 01014 cellse.g. OR(¬Q, p∧¬q)

Lambda, short form: λpqab.q (p (q b a) b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) b)) a))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) 1)) 2)
Tromp binary: 0000000001011110010111110010111101011010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a b a
Reverse Polish: q p q b @ a @ @ b @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK))
JavaScript: p => q => a => b => q(p(q(b)(a))(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#417NOT Q · 01014 cellse.g. OR(¬Q, NOR)

Lambda, short form: λpqab.q (p b (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) ((q b) a))) a))))
De Bruijn: λλλλ((3 ((4 1) ((3 1) 2))) 2)
Tromp binary: 0000000001011110010111110100101111010110110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b @ @ q b a a
Reverse Polish: q p b @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => q(p(b)(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#171NOT Q · 01014 cellse.g. q∧¬p(q∧¬p, ¬Q)

Lambda, short form: λpqab.p (q b a) (q b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 1) ((3 1) 2)))
Tromp binary: 00000000010111110010111101011001011110100101111010110 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q b @ @ q b a
Reverse Polish: p q b @ a @ @ q b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(b)(a))(q(b)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#172NOT Q · 01014 cellse.g. q∧¬p(AND, ¬Q)

Lambda, short form: λpqab.p (q b (q b a)) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((q b) a))) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 1) ((3 1) 2))) ((3 1) 2))
Tromp binary: 00000000010111110010111101001011110101100101111010110 (53 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ q b a @ @ q b a
Reverse Polish: p q b @ q b @ a @ @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(S(S(KS)(S(KK)S))(KK))))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(b)(q(b)(a)))(q(b)(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#465NOT Q · 01014 cellse.g. OR(p∧¬q, ¬Q)

Lambda, short form: λpqab.p (q (q b a) a) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) a)) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) 2)) ((3 1) 2))
Tromp binary: 000000000101111100101111001011110101101100101111010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a a @ @ q b a
Reverse Polish: p q q b @ a @ @ a @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK)))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(q(b)(a))(a))(q(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#468NOT Q · 01014 cellse.g. OR(NOR, ¬Q)

Lambda, short form: λpqab.p (q b a) (q (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 ((3 1) 2)) 2))
Tromp binary: 000000000101111100101111010110010111100101111010110110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q @ @ q b a a
Reverse Polish: p q b @ a @ @ q q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK)))
JavaScript: p => q => a => b => p(q(b)(a))(q(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#184NOT Q · 01014 cellse.g. q∧¬p(q∧¬p, NAND)

Lambda, short form: λpqab.p (p (q b a) a) (q b (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((q b) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((3 1) ((4 ((3 1) 2)) 2)))
Tromp binary: 00000000010111110010111110010111101011011001011110100101111100101111010110110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ q b @ @ p @ @ q b a a
Reverse Polish: p p q b @ a @ @ a @ @ q b @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(q(b)(p(q(b)(a))(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#200NOT Q · 01014 cellse.g. q∧¬p(AND, q→p)

Lambda, short form: λpqab.p (q b (p a (q b a))) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p a) ((q b) a)))) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 1) ((4 2) ((3 1) 2)))) ((4 2) ((3 1) 2)))
Tromp binary: 00000000010111110010111101001011111011001011110101100101111101100101111010110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p a @ @ q b a @ @ p a @ @ q b a
Reverse Polish: p q b @ p a @ q b @ a @ @ @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(b)(p(a)(q(b)(a))))(p(a)(q(b)(a)))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#357NOT Q · 01014 cellse.g. OR(NOR, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (q (p (q b a) b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((q ((p ((q b) a)) b)) a)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((3 ((4 ((3 1) 2)) 1)) 2))
Tromp binary: 0000000001011111001011111001011110101101001011110010111110010111101011010110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ q @ @ p @ @ q b a b a
Reverse Polish: p p q b @ a @ @ b @ @ q p q b @ a @ @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(q(p(q(b)(a))(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#409NOT Q · 01014 cellse.g. OR(p∧¬q, NOR)

Lambda, short form: λpqab.p (q (p b (q b a)) a) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) a)) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) 2)) ((4 1) ((3 1) 2)))
Tromp binary: 0000000001011111001011110010111110100101111010110110010111110100101111010110 (76 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a a @ @ p b @ @ q b a
Reverse Polish: p q p b @ q b @ a @ @ @ a @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(a))(p(b)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#276NOT Q · 01014 cellse.g. XOR(¬P, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 000000000101111100101111100101111010110010111101101001011111001011110110100101111010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#291NOT Q · 01014 cellse.g. XOR(XNOR, P)

Lambda, short form: λpqab.p (q (p b a) (p a b)) (q (p a b) (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) ((p a) b))) ((q ((p a) b)) ((p b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) ((4 2) 1))) ((3 ((4 2) 1)) ((4 1) 2)))
Tromp binary: 00000000010111110010111100101111101011001011111011010010111100101111101101001011111010110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a @ @ p a b @ @ q @ @ p a b @ @ p b a
Reverse Polish: p q p b @ a @ @ p a @ b @ @ @ q p a @ b @ @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(a))(p(a)(b)))(q(p(a)(b))(p(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#226NOT Q · 01014 cellse.g. XOR(NAND, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) (p a (q b a))) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) ((p a) ((q b) a)))) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2)))) ((4 2) ((3 1) 2)))
Tromp binary: 000000000101111100101111001011111010010111101101001011111011001011110101100101111101100101111010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a @ @ p a @ @ q b a
Reverse Polish: p q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(p(a)(q(b)(a))))(p(a)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#241NOT Q · 01014 cellse.g. XOR(q→p, AND)

Lambda, short form: λpqab.p (p (q b a) a) (q (p (q a b) b) (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((q ((p ((q a) b)) b)) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2)))
Tromp binary: 000000000101111100101111100101111010110110010111100101111100101111011010100101111100101111010110110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a
Reverse Polish: p p q b @ a @ @ a @ @ q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(q(p(q(a)(b))(b))(p(q(b)(a))(a)))

Where it comes from

XOR ×2 · XNOR ×2

#261NOT Q · 01014 cellse.g. XOR(NOR, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (q (p (q b a) b) (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((q ((p ((q b) a)) b)) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2)))
Tromp binary: 00000000010111110010111110010111101011010010111100101111100101111010110100101111100101111011010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a
Reverse Polish: p p q b @ a @ @ b @ @ q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(q(p(q(b)(a))(b))(p(q(a)(b))(a)))

Where it comes from

XOR ×2 · XNOR ×2

#306NOT Q · 01014 cellse.g. XOR(p→q, OR)

Lambda, short form: λpqab.p (q (p b (q b a)) (p a (q a b))) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) ((p a) ((q a) b)))) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1)))) ((4 1) ((3 1) 2)))
Tromp binary: 00000000010111110010111100101111101001011110101100101111101100101111011010010111110100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b @ @ p b @ @ q b a
Reverse Polish: p q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(p(a)(q(a)(b))))(p(b)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

13 NAND 0111 · 32 programs · 216 cells

#183NAND · 011192 cellslambda16.txt

Lambda, short form: λpqab.p (q b a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) a))))
De Bruijn: λλλλ((4 ((3 1) 2)) 2)
Tromp binary: 000000000101111100101111010110110 (33 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a a
Reverse Polish: p q b @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(b)(a))(a)

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×3 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×3 · ¬Q ×16 · NAND ×3 · q→p ×3

#431NAND · 01114 cellse.g. OR(¬Q, ¬P)

Lambda, short form: λpqab.q (p b a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) a)) a))))
De Bruijn: λλλλ((3 ((4 1) 2)) 2)
Tromp binary: 000000000101111001011111010110110 (33 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b a a
Reverse Polish: q p b @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK))
JavaScript: p => q => a => b => q(p(b)(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#321NAND · 01114 cellse.g. OR(¬Q, q∧¬p)

Lambda, short form: λpqab.q (p b (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) ((q a) b))) a))))
De Bruijn: λλλλ((3 ((4 1) ((3 2) 1))) 2)
Tromp binary: 0000000001011110010111110100101111011010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b @ @ q a b a
Reverse Polish: q p b @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK))
JavaScript: p => q => a => b => q(p(b)(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#358NAND · 01114 cellse.g. OR(¬P, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) a))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) 2)
Tromp binary: 00000000010111110010111110010111101011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b a
Reverse Polish: p p q b @ a @ @ b @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#432NAND · 01114 cellse.g. OR(NAND, ¬P)

Lambda, short form: λpqab.p (q (p b a) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) 2)) 2)
Tromp binary: 000000000101111100101111001011111010110110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a a a
Reverse Polish: p q p b @ a @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(b)(a))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#472NAND · 01114 cellse.g. OR(NAND, ¬Q)

Lambda, short form: λpqab.p (q (q b a) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) 2)) 2)
Tromp binary: 00000000010111110010111100101111010110110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a a a
Reverse Polish: p q q b @ a @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(q(b)(a))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#482NAND · 01114 cellse.g. OR(¬P, NAND)

Lambda, short form: λpqab.p (p (q b a) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) a))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) 2)
Tromp binary: 000000000101111100101111100101111010110110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a a
Reverse Polish: p p q b @ a @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#485NAND · 01114 cellse.g. OR(¬Q, NAND)

Lambda, short form: λpqab.q (p (q b a) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) a)) a))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) 2)) 2)
Tromp binary: 00000000010111100101111100101111010110110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a a a
Reverse Polish: q p q b @ a @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => q(p(q(b)(a))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#322NAND · 01114 cellse.g. OR(NAND, q∧¬p)

Lambda, short form: λpqab.p (q (p b (q a b)) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q a) b))) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 2) 1))) 2)) 2)
Tromp binary: 0000000001011111001011110010111110100101111011010110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q a b a a
Reverse Polish: p q p b @ q a @ b @ @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(b)(q(a)(b)))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#362NAND · 01114 cellse.g. OR(NAND, p∧¬q)

Lambda, short form: λpqab.p (q (p (q b a) b) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) b)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 1)) 2)) 2)
Tromp binary: 0000000001011111001011110010111110010111101011010110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a b a a
Reverse Polish: p q p q b @ a @ @ b @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(b))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#372NAND · 01114 cellse.g. OR(¬P, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) a))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) 2)
Tromp binary: 0000000001011111001011111001011110101100101111011010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b a
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#375NAND · 01114 cellse.g. OR(¬Q, XOR)

Lambda, short form: λpqab.q (p (q b a) (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q b) a)) ((q a) b))) a))))
De Bruijn: λλλλ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2)
Tromp binary: 000000000101111001011111001011110101100101111011010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q b a @ @ q a b a
Reverse Polish: q p q b @ a @ @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK))
JavaScript: p => q => a => b => q(p(q(b)(a))(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#418NAND · 01114 cellse.g. OR(NAND, NOR)

Lambda, short form: λpqab.p (q (p b (q b a)) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) 2)) 2)
Tromp binary: 0000000001011111001011110010111110100101111010110110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a a a
Reverse Polish: p q p b @ q b @ a @ @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#423NAND · 01114 cellse.g. OR(p∧¬q, ¬P)

Lambda, short form: λpqab.p (q (p b a) a) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) a)) ((p b) a)))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) 2)) ((4 1) 2))
Tromp binary: 00000000010111110010111100101111101011011001011111010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a a @ @ p b a
Reverse Polish: p q p b @ a @ @ a @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(p(b)(a))(a))(p(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#462NAND · 01114 cellse.g. OR(q∧¬p, ¬Q)

Lambda, short form: λpqab.p (q b a) (q a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 2) ((3 1) 2)))
Tromp binary: 000000000101111100101111010110010111101100101111010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q a @ @ q b a
Reverse Polish: p q b @ a @ @ q a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(b)(a))(q(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#486NAND · 01114 cellse.g. OR(NAND, NAND)

Lambda, short form: λpqab.p (q (p (q b a) a) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) 2)) 2)
Tromp binary: 00000000010111110010111100101111100101111010110110110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a a a
Reverse Polish: p q p q b @ a @ @ a @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#225NAND · 01114 cellse.g. XOR(¬Q, q∧¬p)

Lambda, short form: λpqab.q (p b (q a b)) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p b) ((q a) b))) ((p a) ((q b) a))))))
De Bruijn: λλλλ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2)))
Tromp binary: 00000000010111100101111101001011110110100101111101100101111010110 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a
Reverse Polish: q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(p(b)(q(a)(b)))(p(a)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#253NAND · 01114 cellse.g. XOR(q→p, Q)

Lambda, short form: λpqab.p (q b a) (q (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) a)) ((q ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 1) 2)) ((3 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110101100101111001011110110100101111010110 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b a @ @ q @ @ q a b @ @ q b a
Reverse Polish: p q b @ a @ @ q q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(b)(a))(q(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#262NAND · 01114 cellse.g. XOR(¬P, p∧¬q)

Lambda, short form: λpqab.p (p (q b a) b) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) b)) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2))
Tromp binary: 000000000101111100101111100101111010110100101111100101111011010110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a b @ @ p @ @ q a b a
Reverse Polish: p p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(b)(a))(b))(p(q(a)(b))(a))

Where it comes from

XOR ×2 · XNOR ×2

#292NAND · 01114 cellse.g. XOR(p→q, P)

Lambda, short form: λpqab.p (q (p b a) (p a b)) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) ((p a) b))) ((p b) a)))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) ((4 2) 1))) ((4 1) 2))
Tromp binary: 0000000001011111001011110010111110101100101111101101001011111010110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a @ @ p a b @ @ p b a
Reverse Polish: p q p b @ a @ @ p a @ b @ @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(p(b)(a))(p(a)(b)))(p(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#376NAND · 01114 cellse.g. OR(NAND, XOR)

Lambda, short form: λpqab.p (q (p (q b a) (q a b)) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) ((q a) b))) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2)) 2)
Tromp binary: 000000000101111100101111001011111001011110101100101111011010110110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a @ @ q a b a a
Reverse Polish: p q p q b @ a @ @ q a @ b @ @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(q(a)(b)))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#424NAND · 01114 cellse.g. OR(XOR, ¬P)

Lambda, short form: λpqab.p (q (p b a) a) (q a (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) a)) a)) ((q a) ((p b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 1) 2)) 2)) ((3 2) ((4 1) 2)))
Tromp binary: 0000000001011111001011110010111110101101100101111011001011111010110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b a a @ @ q a @ @ p b a
Reverse Polish: p q p b @ a @ @ a @ @ q a @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(b)(a))(a))(q(a)(p(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#466NAND · 01114 cellse.g. OR(XOR, ¬Q)

Lambda, short form: λpqab.p (q (q b a) a) (q a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q b) a)) a)) ((q a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((3 1) 2)) 2)) ((3 2) ((3 1) 2)))
Tromp binary: 00000000010111110010111100101111010110110010111101100101111010110 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q b a a @ @ q a @ @ q b a
Reverse Polish: p q q b @ a @ @ a @ @ q a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK)))))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(q(b)(a))(a))(q(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#185NAND · 01114 cellse.g. q∧¬p(AND, NAND)

Lambda, short form: λpqab.p (q b (p (q b a) a)) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q b) ((p ((q b) a)) a))) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 1) ((4 ((3 1) 2)) 2))) ((4 ((3 1) 2)) 2))
Tromp binary: 00000000010111110010111101001011111001011110101101100101111100101111010110110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q b @ @ p @ @ q b a a @ @ p @ @ q b a a
Reverse Polish: p q b @ p q b @ a @ @ a @ @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(b)(p(q(b)(a))(a)))(p(q(b)(a))(a))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#474NAND · 01114 cellse.g. OR(q∧¬p, NAND)

Lambda, short form: λpqab.p (p (q b a) a) (q a (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((q a) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((3 2) ((4 ((3 1) 2)) 2)))
Tromp binary: 000000000101111100101111100101111010110110010111101100101111100101111010110110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ q a @ @ p @ @ q b a a
Reverse Polish: p p q b @ a @ @ a @ @ q a @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(q(a)(p(q(b)(a))(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#477NAND · 01114 cellse.g. OR(p∧¬q, NAND)

Lambda, short form: λpqab.p (q (p (q b a) a) a) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) a)) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) 2)) ((4 ((3 1) 2)) 2))
Tromp binary: 000000000101111100101111001011111001011110101101101100101111100101111010110110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a a @ @ p @ @ q b a a
Reverse Polish: p q p q b @ a @ @ a @ @ a @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(a))(p(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#481NAND · 01114 cellse.g. OR(NOR, NAND)

Lambda, short form: λpqab.p (p (q b a) a) (q (p (q b a) a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) a)) ((q ((p ((q b) a)) a)) a)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) 2)) ((3 ((4 ((3 1) 2)) 2)) 2))
Tromp binary: 000000000101111100101111100101111010110110010111100101111100101111010110110110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a a @ @ q @ @ p @ @ q b a a a
Reverse Polish: p p q b @ a @ @ a @ @ q p q b @ a @ @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(b)(a))(a))(q(p(q(b)(a))(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#410NAND · 01114 cellse.g. OR(XOR, NOR)

Lambda, short form: λpqab.p (q (p b (q b a)) a) (q a (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) a)) ((q a) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) 2)) ((3 2) ((4 1) ((3 1) 2))))
Tromp binary: 000000000101111100101111001011111010010111101011011001011110110010111110100101111010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a a @ @ q a @ @ p b @ @ q b a
Reverse Polish: p q p b @ q b @ a @ @ @ a @ @ q a @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(a))(q(a)(p(b)(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#478NAND · 01114 cellse.g. OR(XOR, NAND)

Lambda, short form: λpqab.p (q (p (q b a) a) a) (q a (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q b) a)) a)) a)) ((q a) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 1) 2)) 2)) 2)) ((3 2) ((4 ((3 1) 2)) 2)))
Tromp binary: 00000000010111110010111100101111100101111010110110110010111101100101111100101111010110110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q b a a a @ @ q a @ @ p @ @ q b a a
Reverse Polish: p q p q b @ a @ @ a @ @ a @ @ q a @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(q(p(q(b)(a))(a))(a))(q(a)(p(q(b)(a))(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#371NAND · 01114 cellse.g. OR(NOR, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (q (p (q b a) (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((q ((p ((q b) a)) ((q a) b))) a)))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2))
Tromp binary: 00000000010111110010111110010111101011001011110110100101111001011111001011110101100101111011010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q b a @ @ q a b a
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ q p q b @ a @ @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK)))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(q(p(q(b)(a))(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#275NAND · 01114 cellse.g. XOR(NOR, XOR)

Lambda, short form: λpqab.p (p (q b a) (q a b)) (q (p (q b a) (q a b)) (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p ((q b) a)) ((q a) b))) ((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 ((3 1) 2)) ((3 2) 1))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 0000000001011111001011111001011110101100101111011010010111100101111100101111010110010111101101001011111001011110110100101111010110 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p p q b @ a @ @ q a @ b @ @ @ q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(q(b)(a))(q(a)(b)))(q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

#305NAND · 01114 cellse.g. XOR(XNOR, OR)

Lambda, short form: λpqab.p (q (p b (q b a)) (p a (q a b))) (q (p a (q a b)) (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p b) ((q b) a))) ((p a) ((q a) b)))) ((q ((p a) ((q a) b))) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 1) ((3 1) 2))) ((4 2) ((3 2) 1)))) ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2))))
Tromp binary: 00000000010111110010111100101111101001011110101100101111101100101111011010010111100101111101100101111011010010111110100101111010110 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p b @ @ q b a @ @ p a @ @ q a b @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a
Reverse Polish: p q p b @ q b @ a @ @ @ p a @ q a @ b @ @ @ @ q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(b)(q(b)(a)))(p(a)(q(a)(b))))(q(p(a)(q(a)(b)))(p(b)(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

14 CONVERSE (q -> p) 1101 · 32 programs · 216 cells

#198CONVERSE (q -> p) · 110192 cellslambda16.txt

Lambda, short form: λpqab.p a (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q b) a)))))
De Bruijn: λλλλ((4 2) ((3 1) 2))
Tromp binary: 000000000101111101100101111010110 (33 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q b a
Reverse Polish: p a @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(a)(q(b)(a))

Where it comes from

q∧¬p ×2 · AND ×2 · Q ×16 · p∧¬q ×2 · XOR ×4 · P ×16 · OR ×3 · NOR ×2 · ¬P ×16 · XNOR ×4 · p→q ×3 · ¬Q ×16 · NAND ×3 · q→p ×3

#389CONVERSE (q -> p) · 11014 cellse.g. OR(¬Q, P)

Lambda, short form: λpqab.q (p a b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) b)) a))))
De Bruijn: λλλλ((3 ((4 2) 1)) 2)
Tromp binary: 000000000101111001011111011010110 (33 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a b a
Reverse Polish: q p a @ b @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK))
JavaScript: p => q => a => b => q(p(a)(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#335CONVERSE (q -> p) · 11014 cellse.g. OR(¬Q, AND)

Lambda, short form: λpqab.q (p (q a b) b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) b)) a))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) 1)) 2)
Tromp binary: 0000000001011110010111110010111101101010110 (43 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b b a
Reverse Polish: q p q a @ b @ @ b @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK))
JavaScript: p => q => a => b => q(p(q(a)(b))(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#391CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, P)

Lambda, short form: λpqab.p a (q (p a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p a) b)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 2) 1)) 2))
Tromp binary: 000000000101111101100101111001011111011010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p a b a
Reverse Polish: p a @ q p a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#411CONVERSE (q -> p) · 11014 cellse.g. OR(P, NOR)

Lambda, short form: λpqab.p a (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 2) ((4 1) ((3 1) 2)))
Tromp binary: 00000000010111110110010111110100101111010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p b @ @ q b a
Reverse Polish: p a @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(a)(p(b)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#473CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, ¬Q)

Lambda, short form: λpqab.p a (q (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((q b) a)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((3 1) 2)) 2))
Tromp binary: 00000000010111110110010111100101111010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ q b a a
Reverse Polish: p a @ q q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK)))
JavaScript: p => q => a => b => p(a)(q(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#493CONVERSE (q -> p) · 11014 cellse.g. OR(P, q→p)

Lambda, short form: λpqab.p a (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 2) ((4 2) ((3 1) 2)))
Tromp binary: 000000000101111101100101111101100101111010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p a @ @ q b a
Reverse Polish: p a @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(a)(p(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#499CONVERSE (q -> p) · 11014 cellse.g. OR(¬Q, q→p)

Lambda, short form: λpqab.q (p a (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) ((q b) a))) a))))
De Bruijn: λλλλ((3 ((4 2) ((3 1) 2))) 2)
Tromp binary: 00000000010111100101111101100101111010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a @ @ q b a a
Reverse Polish: q p a @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => q(p(a)(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#337CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, AND)

Lambda, short form: λpqab.p a (q (p (q a b) b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p ((q a) b)) b)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 ((3 2) 1)) 1)) 2))
Tromp binary: 0000000001011111011001011110010111110010111101101010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p @ @ q a b b a
Reverse Polish: p a @ q p q a @ b @ @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(q(a)(b))(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#363CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, p∧¬q)

Lambda, short form: λpqab.p a (q (p (q b a) b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p ((q b) a)) b)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 ((3 1) 2)) 1)) 2))
Tromp binary: 0000000001011111011001011110010111110010111101011010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p @ @ q b a b a
Reverse Polish: p a @ q p q b @ a @ @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(q(b)(a))(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#385CONVERSE (q -> p) · 11014 cellse.g. OR(NOR, P)

Lambda, short form: λpqab.p (p a b) (q (p a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((q ((p a) b)) a)))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((3 ((4 2) 1)) 2))
Tromp binary: 00000000010111110010111110110100101111001011111011010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ q @ @ p a b a
Reverse Polish: p p a @ b @ @ q p a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK)))
JavaScript: p => q => a => b => p(p(a)(b))(q(p(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#419CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, NOR)

Lambda, short form: λpqab.p a (q (p b (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p b) ((q b) a))) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 1) ((3 1) 2))) 2))
Tromp binary: 0000000001011111011001011110010111110100101111010110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p b @ @ q b a a
Reverse Polish: p a @ q p b @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(b)(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#439CONVERSE (q -> p) · 11014 cellse.g. OR(P, XNOR)

Lambda, short form: λpqab.p a (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 2) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111011001011111001011110110100101111010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p a @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(a)(p(q(a)(b))(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#445CONVERSE (q -> p) · 11014 cellse.g. OR(¬Q, XNOR)

Lambda, short form: λpqab.q (p (q a b) (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) ((q b) a))) a))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2)
Tromp binary: 000000000101111001011111001011110110100101111010110110 (54 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b @ @ q b a a
Reverse Polish: q p q a @ b @ @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => q(p(q(a)(b))(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#463CONVERSE (q -> p) · 11014 cellse.g. OR(AND, ¬Q)

Lambda, short form: λpqab.p (q a (q b a)) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((q b) a))) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 2) ((3 1) 2))) ((3 1) 2))
Tromp binary: 000000000101111100101111011001011110101100101111010110 (54 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ q b a @ @ q b a
Reverse Polish: p q a @ q b @ a @ @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK))))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(a)(q(b)(a)))(q(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#501CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, q→p)

Lambda, short form: λpqab.p a (q (p a (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p a) ((q b) a))) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 2) ((3 1) 2))) 2))
Tromp binary: 00000000010111110110010111100101111101100101111010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p a @ @ q b a a
Reverse Polish: p a @ q p a @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(a)(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#239CONVERSE (q -> p) · 11014 cellse.g. XOR(¬Q, AND)

Lambda, short form: λpqab.q (p (q a b) b) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) b)) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2))
Tromp binary: 00000000010111100101111100101111011010100101111100101111010110110 (65 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a
Reverse Polish: q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => q(p(q(a)(b))(b))(p(q(b)(a))(a))

Where it comes from

XOR ×2 · XNOR ×2

#252CONVERSE (q -> p) · 11014 cellse.g. XOR(NAND, Q)

Lambda, short form: λpqab.p (q (q a b) (q b a)) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) ((q b) a))) ((q b) a)))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) ((3 1) 2))) ((3 1) 2))
Tromp binary: 0000000001011111001011110010111101101001011110101100101111010110 (64 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b @ @ q b a @ @ q b a
Reverse Polish: p q q a @ b @ @ q b @ a @ @ @ q b @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK))))))))(K(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(q(q(a)(b))(q(b)(a)))(q(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#289CONVERSE (q -> p) · 11014 cellse.g. XOR(NOR, P)

Lambda, short form: λpqab.p (p a b) (q (p a b) (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((q ((p a) b)) ((p b) a))))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((3 ((4 2) 1)) ((4 1) 2)))
Tromp binary: 0000000001011111001011111011010010111100101111101101001011111010110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ q @ @ p a b @ @ p b a
Reverse Polish: p p a @ b @ @ q p a @ b @ @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(a)(b))(q(p(a)(b))(p(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#304CONVERSE (q -> p) · 11014 cellse.g. XOR(¬P, OR)

Lambda, short form: λpqab.p (p a (q a b)) (p b (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((p b) ((q b) a))))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2)))
Tromp binary: 000000000101111100101111101100101111011010010111110100101111010110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ p b @ @ q b a
Reverse Polish: p p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(p(b)(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

#387CONVERSE (q -> p) · 11014 cellse.g. OR(XNOR, P)

Lambda, short form: λpqab.p (q a (p a b)) (q (p a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) b))) ((q ((p a) b)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) 1))) ((3 ((4 2) 1)) 2))
Tromp binary: 0000000001011111001011110110010111110110100101111001011111011010110 (67 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a b @ @ q @ @ p a b a
Reverse Polish: p q a @ p a @ b @ @ @ q p a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(a)(b)))(q(p(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#447CONVERSE (q -> p) · 11014 cellse.g. OR(q→p, XNOR)

Lambda, short form: λpqab.p a (q (p (q a b) (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p ((q a) b)) ((q b) a))) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2))
Tromp binary: 000000000101111101100101111001011111001011110110100101111010110110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p @ @ q a b @ @ q b a a
Reverse Polish: p a @ q p q a @ b @ @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(q(a)(b))(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#469CONVERSE (q -> p) · 11014 cellse.g. OR(XNOR, ¬Q)

Lambda, short form: λpqab.p (q a (q b a)) (q (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((q b) a))) ((q ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((3 1) 2))) ((3 ((3 1) 2)) 2))
Tromp binary: 00000000010111110010111101100101111010110010111100101111010110110 (65 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ q b a @ @ q @ @ q b a a
Reverse Polish: p q a @ q b @ a @ @ @ q q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK))))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(S(S(KS)(S(KK)S))(KK)))))(KK)))
JavaScript: p => q => a => b => p(q(a)(q(b)(a)))(q(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#199CONVERSE (q -> p) · 11014 cellse.g. q∧¬p(q∧¬p, q→p)

Lambda, short form: λpqab.p (p a (q b a)) (q b (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((q b) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((3 1) ((4 2) ((3 1) 2))))
Tromp binary: 00000000010111110010111110110010111101011001011110100101111101100101111010110 (77 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ q b @ @ p a @ @ q b a
Reverse Polish: p p a @ q b @ a @ @ @ q b @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(K(S(S(KS)(S(KK)S))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(q(b)(p(a)(q(b)(a))))

Where it comes from

q∧¬p ×1 · AND ×1 · p∧¬q ×1 · NOR ×1

#489CONVERSE (q -> p) · 11014 cellse.g. OR(AND, q→p)

Lambda, short form: λpqab.p (q a (p a (q b a))) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) ((q b) a)))) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) ((3 1) 2)))) ((4 2) ((3 1) 2)))
Tromp binary: 000000000101111100101111011001011111011001011110101100101111101100101111010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a @ @ q b a @ @ p a @ @ q b a
Reverse Polish: p q a @ p a @ q b @ a @ @ @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(a)(p(a)(q(b)(a))))(p(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#491CONVERSE (q -> p) · 11014 cellse.g. OR(p∧¬q, q→p)

Lambda, short form: λpqab.p (q (p a (q b a)) a) (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) a)) ((p a) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) 2)) ((4 2) ((3 1) 2)))
Tromp binary: 000000000101111100101111001011111011001011110101101100101111101100101111010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a a @ @ p a @ @ q b a
Reverse Polish: p q p a @ q b @ a @ @ @ a @ @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(a))(p(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#495CONVERSE (q -> p) · 11014 cellse.g. OR(NOR, q→p)

Lambda, short form: λpqab.p (p a (q b a)) (q (p a (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((q ((p a) ((q b) a))) a)))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((3 ((4 2) ((3 1) 2))) 2))
Tromp binary: 000000000101111100101111101100101111010110010111100101111101100101111010110110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ q @ @ p a @ @ q b a a
Reverse Polish: p p a @ q b @ a @ @ @ q p a @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(q(p(a)(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#359CONVERSE (q -> p) · 11014 cellse.g. OR(XNOR, p∧¬q)

Lambda, short form: λpqab.p (q a (p (q b a) b)) (q (p (q b a) b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) b))) ((q ((p ((q b) a)) b)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) 1))) ((3 ((4 ((3 1) 2)) 1)) 2))
Tromp binary: 000000000101111100101111011001011111001011110101101001011110010111110010111101011010110 (87 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a b @ @ q @ @ p @ @ q b a b a
Reverse Polish: p q a @ p q b @ a @ @ b @ @ @ q p q b @ a @ @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(b)))(q(p(q(b)(a))(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#497CONVERSE (q -> p) · 11014 cellse.g. OR(XNOR, q→p)

Lambda, short form: λpqab.p (q a (p a (q b a))) (q (p a (q b a)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) ((q b) a)))) ((q ((p a) ((q b) a))) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) ((3 1) 2)))) ((3 ((4 2) ((3 1) 2))) 2))
Tromp binary: 00000000010111110010111101100101111101100101111010110010111100101111101100101111010110110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a @ @ q b a @ @ q @ @ p a @ @ q b a a
Reverse Polish: p q a @ p a @ q b @ a @ @ @ @ q p a @ q b @ a @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(a)(q(b)(a))))(q(p(a)(q(b)(a)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#437CONVERSE (q -> p) · 11014 cellse.g. OR(p∧¬q, XNOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) a) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) a)) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2)) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 00000000010111110010111100101111100101111011010010111101011011001011111001011110110100101111010110 (98 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ a @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(a))(p(q(a)(b))(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#263CONVERSE (q -> p) · 11014 cellse.g. XOR(XNOR, p∧¬q)

Lambda, short form: λpqab.p (q (p (q a b) a) (p (q b a) b)) (q (p (q b a) b) (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) ((p ((q b) a)) b))) ((q ((p ((q b) a)) b)) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1))) ((3 ((4 ((3 1) 2)) 1)) ((4 ((3 2) 1)) 2)))
Tromp binary: 00000000010111110010111100101111100101111011010110010111110010111101011010010111100101111100101111010110100101111100101111011010110 (131 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b @ @ q @ @ p @ @ q b a b @ @ p @ @ q a b a
Reverse Polish: p q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ @ q p q b @ a @ @ b @ @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(p(q(b)(a))(b)))(q(p(q(b)(a))(b))(p(q(a)(b))(a)))

Where it comes from

XOR ×2 · XNOR ×2

#278CONVERSE (q -> p) · 11014 cellse.g. XOR(p→q, XOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) (p (q b a) (q a b))) (p (q a b) (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b)))) ((p ((q a) b)) ((q b) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1)))) ((4 ((3 2) 1)) ((3 1) 2)))
Tromp binary: 0000000001011111001011110010111110010111101101001011110101100101111100101111010110010111101101001011111001011110110100101111010110 (130 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ @ p q a @ b @ @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b))))(p(q(a)(b))(q(b)(a)))

Where it comes from

XOR ×2 · XNOR ×2

15 TRUE 1111 · 63 programs · 680 cells

#213TRUE · 1111396 cellslambda16.txt

Lambda, short form: λpqab.a
Lambda, fully bracketed: λp.(λq.(λa.(λb.a)))
De Bruijn: λλλλ2
Tromp binary: 00000000110 (11 bits)
Polish (prefix): λp λq λa λb a
Reverse Polish: a λb λa λq λp
SKI combinators: K(KK)
JavaScript: p => q => a => b => a

Where it comes from

q∧¬p ×1 · AND ×1 · Q ×16 · p∧¬q ×1 · XOR ×2 · P ×16 · OR ×17 · NOR ×1 · ¬P ×16 · XNOR ×2 · p→q ×17 · ¬Q ×16 · NAND ×17 · q→p ×17 · TRUE ×256

#502TRUE · 111116 cellse.g. OR(q∧¬p, TRUE)

Lambda, short form: λpqab.p a (q a a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) a)))))
De Bruijn: λλλλ((4 2) ((3 2) 2))
Tromp binary: 0000000001011111011001011110110110 (34 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a a
Reverse Polish: p a @ q a @ a @ @ λb λa λq λp
SKI combinators: S(K(S(K(S(KK)))))(S(S(KS)(S(KK)S))(K(SS(KI))))
JavaScript: p => q => a => b => p(a)(q(a)(a))

Where it comes from

OR ×4 · p→q ×4 · NAND ×4 · q→p ×4

#503TRUE · 111116 cellse.g. OR(AND, TRUE)

Lambda, short form: λpqab.p (q a a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) a)) a))))
De Bruijn: λλλλ((4 ((3 2) 2)) 2)
Tromp binary: 0000000001011111001011110110110110 (34 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a a a
Reverse Polish: p q a @ a @ @ a @ λb λa λq λp
SKI combinators: S(K(S(K(S(KK)))))(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(K(SS(KI))))))(K(KI)))
JavaScript: p => q => a => b => p(q(a)(a))(a)

Where it comes from

OR ×4 · p→q ×4 · NAND ×4 · q→p ×4

#504TRUE · 11118 cellse.g. OR(Q, TRUE)

Lambda, short form: λpqab.q a a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) a))))
De Bruijn: λλλλ((3 2) 2)
Tromp binary: 0000000001011110110110 (22 bits)
Polish (prefix): λp λq λa λb @ @ q a a
Reverse Polish: q a @ a @ λb λa λq λp
SKI combinators: K(S(K(S(KK)))(SS(KI)))
JavaScript: p => q => a => b => q(a)(a)

Where it comes from

OR ×2 · p→q ×2 · NAND ×2 · q→p ×2

#506TRUE · 11118 cellse.g. OR(P, TRUE)

Lambda, short form: λpqab.p a a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) a))))
De Bruijn: λλλλ((4 2) 2)
Tromp binary: 00000000010111110110110 (23 bits)
Polish (prefix): λp λq λa λb @ @ p a a
Reverse Polish: p a @ a @ λb λa λq λp
SKI combinators: S(KK)(S(K(S(KK)))(SS(KI)))
JavaScript: p => q => a => b => p(a)(a)

Where it comes from

OR ×2 · p→q ×2 · NAND ×2 · q→p ×2

#505TRUE · 11118 cellse.g. OR(XOR, TRUE)

Lambda, short form: λpqab.p (q a a) (q a a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) a)) ((q a) a)))))
De Bruijn: λλλλ((4 ((3 2) 2)) ((3 2) 2))
Tromp binary: 000000000101111100101111011011001011110110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a a @ @ q a a
Reverse Polish: p q a @ a @ @ q a @ a @ @ λb λa λq λp
SKI combinators: S(K(S(K(S(KK)))))(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))(K(SS(KI))))))(K(SS(KI))))
JavaScript: p => q => a => b => p(q(a)(a))(q(a)(a))

Where it comes from

OR ×2 · p→q ×2 · NAND ×2 · q→p ×2

#347TRUE · 11114 cellse.g. OR(¬Q, Q)

Lambda, short form: λpqab.q (q a b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((q a) b)) a))))
De Bruijn: λλλλ((3 ((3 2) 1)) 2)
Tromp binary: 00000000010111100101111011010110 (32 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ q a b a
Reverse Polish: q q a @ b @ @ a @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK))
JavaScript: p => q => a => b => q(q(a)(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#386TRUE · 11114 cellse.g. OR(¬P, P)

Lambda, short form: λpqab.p (p a b) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) a))))
De Bruijn: λλλλ((4 ((4 2) 1)) 2)
Tromp binary: 0000000001011111001011111011010110 (34 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b a
Reverse Polish: p p a @ b @ @ a @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK))
JavaScript: p => q => a => b => p(p(a)(b))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#425TRUE · 11114 cellse.g. OR(P, ¬P)

Lambda, short form: λpqab.p a (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p b) a)))))
De Bruijn: λλλλ((4 2) ((4 1) 2))
Tromp binary: 0000000001011111011001011111010110 (34 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p b a
Reverse Polish: p a @ p b @ a @ @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(a)(p(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#464TRUE · 11114 cellse.g. OR(Q, ¬Q)

Lambda, short form: λpqab.q a (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((q b) a)))))
De Bruijn: λλλλ((3 2) ((3 1) 2))
Tromp binary: 00000000010111101100101111010110 (32 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ q b a
Reverse Polish: q a @ q b @ a @ @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => q(a)(q(b)(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#251TRUE · 11114 cellse.g. XOR(¬Q, Q)

Lambda, short form: λpqab.q (q a b) (q b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((q a) b)) ((q b) a)))))
De Bruijn: λλλλ((3 ((3 2) 1)) ((3 1) 2))
Tromp binary: 000000000101111001011110110100101111010110 (42 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ q a b @ @ q b a
Reverse Polish: q q a @ b @ @ q b @ a @ @ λb λa λq λp
SKI combinators: K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => q(q(a)(b))(q(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#290TRUE · 11114 cellse.g. XOR(¬P, P)

Lambda, short form: λpqab.p (p a b) (p b a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) b)) ((p b) a)))))
De Bruijn: λλλλ((4 ((4 2) 1)) ((4 1) 2))
Tromp binary: 000000000101111100101111101101001011111010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a b @ @ p b a
Reverse Polish: p p a @ b @ @ p b @ a @ @ λb λa λq λp
SKI combinators: S(KK)(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(S(S(KS)(S(KK)S))(KK)))
JavaScript: p => q => a => b => p(p(a)(b))(p(b)(a))

Where it comes from

XOR ×2 · XNOR ×2

#348TRUE · 11114 cellse.g. OR(NAND, Q)

Lambda, short form: λpqab.p (q (q a b) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((q a) b)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((3 2) 1)) 2)) 2)
Tromp binary: 00000000010111110010111100101111011010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ q a b a a
Reverse Polish: p q q a @ b @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(q(a)(b))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#349TRUE · 11114 cellse.g. OR(q→p, Q)

Lambda, short form: λpqab.p a (q (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((q a) b)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((3 2) 1)) 2))
Tromp binary: 00000000010111110110010111100101111011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ q a b a
Reverse Polish: p a @ q q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(K(S(KS)))(S(S(KS)(S(KK)(S(KS)K)))I)))(KK)))
JavaScript: p => q => a => b => p(a)(q(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#388TRUE · 11114 cellse.g. OR(p→q, P)

Lambda, short form: λpqab.p (q a (p a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) b))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) 1))) 2)
Tromp binary: 000000000101111100101111011001011111011010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a b a
Reverse Polish: p q a @ p a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))K)))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#390TRUE · 11114 cellse.g. OR(NAND, P)

Lambda, short form: λpqab.p (q (p a b) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) b)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 2) 1)) 2)) 2)
Tromp binary: 000000000101111100101111001011111011010110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a b a a
Reverse Polish: p q p a @ b @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))K))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(a)(b))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#400TRUE · 11114 cellse.g. OR(¬P, OR)

Lambda, short form: λpqab.p (p a (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) a))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) 2)
Tromp binary: 000000000101111100101111101100101111011010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b a
Reverse Polish: p p a @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#403TRUE · 11114 cellse.g. OR(¬Q, OR)

Lambda, short form: λpqab.q (p a (q a b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p a) ((q a) b))) a))))
De Bruijn: λλλλ((3 ((4 2) ((3 2) 1))) 2)
Tromp binary: 00000000010111100101111101100101111011010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p a @ @ q a b a
Reverse Polish: q p a @ q a @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK))
JavaScript: p => q => a => b => q(p(a)(q(a)(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#426TRUE · 11114 cellse.g. OR(OR, ¬P)

Lambda, short form: λpqab.p a (q a (p b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p b) a))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 1) 2)))
Tromp binary: 000000000101111101100101111011001011111010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p b a
Reverse Polish: p a @ q a @ p b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KK)(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(a)(q(a)(p(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#433TRUE · 11114 cellse.g. OR(q→p, ¬P)

Lambda, short form: λpqab.p a (q (p b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p b) a)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 1) 2)) 2))
Tromp binary: 000000000101111101100101111001011111010110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p b a a
Reverse Polish: p a @ q p b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KK)(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#453TRUE · 11114 cellse.g. OR(P, p→q)

Lambda, short form: λpqab.p a (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 2) ((4 ((3 2) 1)) 2))
Tromp binary: 000000000101111101100101111100101111011010110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p @ @ q a b a
Reverse Polish: p a @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(p(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#459TRUE · 11114 cellse.g. OR(¬Q, p→q)

Lambda, short form: λpqab.q (p (q a b) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q ((p ((q a) b)) a)) a))))
De Bruijn: λλλλ((3 ((4 ((3 2) 1)) 2)) 2)
Tromp binary: 00000000010111100101111100101111011010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q @ @ p @ @ q a b a a
Reverse Polish: q p q a @ b @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => q(p(q(a)(b))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#467TRUE · 11114 cellse.g. OR(OR, ¬Q)

Lambda, short form: λpqab.p a (q a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((q b) a))))))
De Bruijn: λλλλ((4 2) ((3 2) ((3 1) 2)))
Tromp binary: 00000000010111110110010111101100101111010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ q b a
Reverse Polish: p a @ q a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => p(a)(q(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#470TRUE · 11114 cellse.g. OR(p→q, ¬Q)

Lambda, short form: λpqab.p (q a (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((q b) a))) a))))
De Bruijn: λλλλ((4 ((3 2) ((3 1) 2))) 2)
Tromp binary: 00000000010111110010111101100101111010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ q b a a
Reverse Polish: p q a @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(K(S(KS)))(S(KK))))(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#476TRUE · 11114 cellse.g. OR(Q, NAND)

Lambda, short form: λpqab.q a (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((3 2) ((4 ((3 1) 2)) 2))
Tromp binary: 00000000010111101100101111100101111010110110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p @ @ q b a a
Reverse Polish: q a @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => q(a)(p(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#479TRUE · 11114 cellse.g. OR(P, NAND)

Lambda, short form: λpqab.p a (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 2) ((4 ((3 1) 2)) 2))
Tromp binary: 000000000101111101100101111100101111010110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ p @ @ q b a a
Reverse Polish: p a @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(p(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#490TRUE · 11114 cellse.g. OR(Q, q→p)

Lambda, short form: λpqab.q a (p a (q b a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((q a) ((p a) ((q b) a))))))
De Bruijn: λλλλ((3 2) ((4 2) ((3 1) 2)))
Tromp binary: 00000000010111101100101111101100101111010110 (44 bits)
Polish (prefix): λp λq λa λb @ @ q a @ @ p a @ @ q b a
Reverse Polish: q a @ p a @ q b @ a @ @ @ λb λa λq λp
SKI combinators: S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))
JavaScript: p => q => a => b => q(a)(p(a)(q(b)(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#496TRUE · 11114 cellse.g. OR(¬P, q→p)

Lambda, short form: λpqab.p (p a (q b a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) a))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) 2)
Tromp binary: 000000000101111100101111101100101111010110110 (45 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a a
Reverse Polish: p p a @ q b @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#323TRUE · 11114 cellse.g. OR(q→p, q∧¬p)

Lambda, short form: λpqab.p a (q (p b (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p b) ((q a) b))) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 1) ((3 2) 1))) 2))
Tromp binary: 0000000001011111011001011110010111110100101111011010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p b @ @ q a b a
Reverse Polish: p a @ q p b @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(b)(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#336TRUE · 11114 cellse.g. OR(NAND, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) 2)) 2)
Tromp binary: 0000000001011111001011110010111110010111101101010110110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b a a
Reverse Polish: p q p q a @ b @ @ b @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#360TRUE · 11114 cellse.g. OR(p→q, p∧¬q)

Lambda, short form: λpqab.p (q a (p (q b a) b)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) b))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) 1))) 2)
Tromp binary: 0000000001011111001011110110010111110010111101011010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a b a
Reverse Polish: p q a @ p q b @ a @ @ b @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(b)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#402TRUE · 11114 cellse.g. OR(p→q, OR)

Lambda, short form: λpqab.p (q a (p a (q a b))) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) ((q a) b)))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) ((3 2) 1)))) 2)
Tromp binary: 00000000010111110010111101100101111101100101111011010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a @ @ q a b a
Reverse Polish: p q a @ p a @ q a @ b @ @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(a)(q(a)(b))))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#404TRUE · 11114 cellse.g. OR(NAND, OR)

Lambda, short form: λpqab.p (q (p a (q a b)) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q a) b))) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 2) 1))) 2)) 2)
Tromp binary: 00000000010111110010111100101111101100101111011010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q a b a a
Reverse Polish: p q p a @ q a @ b @ @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(a)(q(a)(b)))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#405TRUE · 11114 cellse.g. OR(q→p, OR)

Lambda, short form: λpqab.p a (q (p a (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p a) ((q a) b))) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 2) ((3 2) 1))) 2))
Tromp binary: 00000000010111110110010111100101111101100101111011010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p a @ @ q a b a
Reverse Polish: p a @ q p a @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(a)(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#412TRUE · 11114 cellse.g. OR(OR, NOR)

Lambda, short form: λpqab.p a (q a (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 1) ((3 1) 2))))
Tromp binary: 0000000001011111011001011110110010111110100101111010110 (55 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p b @ @ q b a
Reverse Polish: p a @ q a @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(a)(q(a)(p(b)(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#454TRUE · 11114 cellse.g. OR(OR, p→q)

Lambda, short form: λpqab.p a (q a (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 ((3 2) 1)) 2)))
Tromp binary: 00000000010111110110010111101100101111100101111011010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p @ @ q a b a
Reverse Polish: p a @ q a @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(a)(q(a)(p(q(a)(b))(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#460TRUE · 11114 cellse.g. OR(NAND, p→q)

Lambda, short form: λpqab.p (q (p (q a b) a) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) 2)) 2)
Tromp binary: 00000000010111110010111100101111100101111011010110110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a a a
Reverse Polish: p q p q a @ b @ @ a @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#461TRUE · 11114 cellse.g. OR(q→p, p→q)

Lambda, short form: λpqab.p a (q (p (q a b) a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p ((q a) b)) a)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 ((3 2) 1)) 2)) 2))
Tromp binary: 00000000010111110110010111100101111100101111011010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p @ @ q a b a a
Reverse Polish: p a @ q p q a @ b @ @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(q(a)(b))(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#480TRUE · 11114 cellse.g. OR(OR, NAND)

Lambda, short form: λpqab.p a (q a (p (q b a) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p ((q b) a)) a))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 ((3 1) 2)) 2)))
Tromp binary: 00000000010111110110010111101100101111100101111010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p @ @ q b a a
Reverse Polish: p a @ q a @ p q b @ a @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))
JavaScript: p => q => a => b => p(a)(q(a)(p(q(b)(a))(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#484TRUE · 11114 cellse.g. OR(p→q, NAND)

Lambda, short form: λpqab.p (q a (p (q b a) a)) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) a))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) 2))) 2)
Tromp binary: 00000000010111110010111101100101111100101111010110110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a a a
Reverse Polish: p q a @ p q b @ a @ @ a @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(a)))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#487TRUE · 11114 cellse.g. OR(q→p, NAND)

Lambda, short form: λpqab.p a (q (p (q b a) a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p ((q b) a)) a)) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 ((3 1) 2)) 2)) 2))
Tromp binary: 00000000010111110110010111100101111100101111010110110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p @ @ q b a a a
Reverse Polish: p a @ q p q b @ a @ @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(q(b)(a))(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#494TRUE · 11114 cellse.g. OR(OR, q→p)

Lambda, short form: λpqab.p a (q a (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 2) ((3 1) 2))))
Tromp binary: 00000000010111110110010111101100101111101100101111010110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p a @ @ q b a
Reverse Polish: p a @ q a @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(a)(q(a)(p(a)(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#498TRUE · 11114 cellse.g. OR(p→q, q→p)

Lambda, short form: λpqab.p (q a (p a (q b a))) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) ((q b) a)))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) ((3 1) 2)))) 2)
Tromp binary: 00000000010111110010111101100101111101100101111010110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a @ @ q b a a
Reverse Polish: p q a @ p a @ q b @ a @ @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(a)(q(b)(a))))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#500TRUE · 11114 cellse.g. OR(NAND, q→p)

Lambda, short form: λpqab.p (q (p a (q b a)) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) 2)) 2)
Tromp binary: 00000000010111110010111100101111101100101111010110110110 (56 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a a a
Reverse Polish: p q p a @ q b @ a @ @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#374TRUE · 11114 cellse.g. OR(p→q, XOR)

Lambda, short form: λpqab.p (q a (p (q b a) (q a b))) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) ((q a) b)))) a))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) ((3 2) 1)))) 2)
Tromp binary: 000000000101111100101111011001011111001011110101100101111011010110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a @ @ q a b a
Reverse Polish: p q a @ p q b @ a @ @ q a @ b @ @ @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(K(KK))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(q(a)(b))))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#377TRUE · 11114 cellse.g. OR(q→p, XOR)

Lambda, short form: λpqab.p a (q (p (q b a) (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q ((p ((q b) a)) ((q a) b))) a)))))
De Bruijn: λλλλ((4 2) ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2))
Tromp binary: 000000000101111101100101111001011111001011110101100101111011010110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q @ @ p @ @ q b a @ @ q a b a
Reverse Polish: p a @ q p q b @ a @ @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK)))
JavaScript: p => q => a => b => p(a)(q(p(q(b)(a))(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#440TRUE · 11114 cellse.g. OR(OR, XNOR)

Lambda, short form: λpqab.p a (q a (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p a) ((q a) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 2) ((3 2) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 000000000101111101100101111011001011111001011110110100101111010110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p a @ @ q a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p a @ q a @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(a)(q(a)(p(q(a)(b))(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#446TRUE · 11114 cellse.g. OR(NAND, XNOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) a) a
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) a)) a))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2)) 2)
Tromp binary: 000000000101111100101111001011111001011110110100101111010110110110 (66 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a a a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ a @ @ a @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(K(KK))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(a))(a)

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#399TRUE · 11114 cellse.g. OR(NOR, OR)

Lambda, short form: λpqab.p (p a (q a b)) (q (p a (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((q ((p a) ((q a) b))) a)))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((3 ((4 2) ((3 2) 1))) 2))
Tromp binary: 000000000101111100101111101100101111011010010111100101111101100101111011010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ q @ @ p a @ @ q a b a
Reverse Polish: p p a @ q a @ b @ @ @ q p a @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(q(p(a)(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#451TRUE · 11114 cellse.g. OR(p∧¬q, p→q)

Lambda, short form: λpqab.p (q (p (q a b) a) a) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) a)) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) 2)) ((4 ((3 2) 1)) 2))
Tromp binary: 000000000101111100101111001011111001011110110101101100101111100101111011010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a a @ @ p @ @ q a b a
Reverse Polish: p q p q a @ b @ @ a @ @ a @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(a))(p(q(a)(b))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#475TRUE · 11114 cellse.g. OR(AND, NAND)

Lambda, short form: λpqab.p (q a (p (q b a) a)) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) a))) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) 2))) ((4 ((3 1) 2)) 2))
Tromp binary: 000000000101111100101111011001011111001011110101101100101111100101111010110110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a a @ @ p @ @ q b a a
Reverse Polish: p q a @ p q b @ a @ @ a @ @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(a)))(p(q(b)(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#488TRUE · 11114 cellse.g. OR(q∧¬p, q→p)

Lambda, short form: λpqab.p (p a (q b a)) (q a (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((q a) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((3 2) ((4 2) ((3 1) 2))))
Tromp binary: 000000000101111100101111101100101111010110010111101100101111101100101111010110 (78 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ q a @ @ p a @ @ q b a
Reverse Polish: p p a @ q b @ a @ @ @ q a @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(q(a)(p(a)(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#401TRUE · 11114 cellse.g. OR(XNOR, OR)

Lambda, short form: λpqab.p (q a (p a (q a b))) (q (p a (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p a) ((q a) b)))) ((q ((p a) ((q a) b))) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 2) ((3 2) 1)))) ((3 ((4 2) ((3 2) 1))) 2))
Tromp binary: 00000000010111110010111101100101111101100101111011010010111100101111101100101111011010110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p a @ @ q a b @ @ q @ @ p a @ @ q a b a
Reverse Polish: p q a @ p a @ q a @ b @ @ @ @ q p a @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(KS)(S(K(S(KS)))(S(KK)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(a)(q(a)(b))))(q(p(a)(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#452TRUE · 11114 cellse.g. OR(XOR, p→q)

Lambda, short form: λpqab.p (q (p (q a b) a) a) (q a (p (q a b) a))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) a)) ((q a) ((p ((q a) b)) a))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) 2)) ((3 2) ((4 ((3 2) 1)) 2)))
Tromp binary: 00000000010111110010111100101111100101111011010110110010111101100101111100101111011010110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a a @ @ q a @ @ p @ @ q a b a
Reverse Polish: p q p q a @ b @ @ a @ @ a @ @ q a @ p q a @ b @ @ a @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(a))(q(a)(p(q(a)(b))(a)))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#483TRUE · 11114 cellse.g. OR(XNOR, NAND)

Lambda, short form: λpqab.p (q a (p (q b a) a)) (q (p (q b a) a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) a))) ((q ((p ((q b) a)) a)) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) 2))) ((3 ((4 ((3 1) 2)) 2)) 2))
Tromp binary: 00000000010111110010111101100101111100101111010110110010111100101111100101111010110110110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a a @ @ q @ @ p @ @ q b a a a
Reverse Polish: p q a @ p q b @ a @ @ a @ @ @ q p q b @ a @ @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(a)))(q(p(q(b)(a))(a))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#492TRUE · 11114 cellse.g. OR(XOR, q→p)

Lambda, short form: λpqab.p (q (p a (q b a)) a) (q a (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p a) ((q b) a))) a)) ((q a) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 2) ((3 1) 2))) 2)) ((3 2) ((4 2) ((3 1) 2))))
Tromp binary: 00000000010111110010111100101111101100101111010110110010111101100101111101100101111010110 (89 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p a @ @ q b a a @ @ q a @ @ p a @ @ q b a
Reverse Polish: p q p a @ q b @ a @ @ @ a @ @ q a @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(a)(q(b)(a)))(a))(q(a)(p(a)(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#227TRUE · 11114 cellse.g. XOR(q→p, q∧¬p)

Lambda, short form: λpqab.p (p a (q b a)) (q (p b (q a b)) (p a (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q b) a))) ((q ((p b) ((q a) b))) ((p a) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 1) 2))) ((3 ((4 1) ((3 2) 1))) ((4 2) ((3 1) 2))))
Tromp binary: 000000000101111100101111101100101111010110010111100101111101001011110110100101111101100101111010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q b a @ @ q @ @ p b @ @ q a b @ @ p a @ @ q b a
Reverse Polish: p p a @ q b @ a @ @ @ q p b @ q a @ b @ @ @ p a @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(KK)S))))))(S(S(KS)(S(KK)(S(KS)(S(K(S(KS)))(S(KK))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(b)(a)))(q(p(b)(q(a)(b)))(p(a)(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

#240TRUE · 11114 cellse.g. XOR(NAND, AND)

Lambda, short form: λpqab.p (q (p (q a b) b) (p (q b a) a)) (p (q b a) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) b)) ((p ((q b) a)) a))) ((p ((q b) a)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 1)) ((4 ((3 1) 2)) 2))) ((4 ((3 1) 2)) 2))
Tromp binary: 000000000101111100101111001011111001011110110101001011111001011110101101100101111100101111010110110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b b @ @ p @ @ q b a a @ @ p @ @ q b a a
Reverse Polish: p q p q a @ b @ @ b @ @ p q b @ a @ @ a @ @ @ p q b @ a @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(K(KI))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(b))(p(q(b)(a))(a)))(p(q(b)(a))(a))

Where it comes from

XOR ×2 · XNOR ×2

#264TRUE · 11114 cellse.g. XOR(p→q, p∧¬q)

Lambda, short form: λpqab.p (q (p (q a b) a) (p (q b a) b)) (p (q a b) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) a)) ((p ((q b) a)) b))) ((p ((q a) b)) a)))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) 2)) ((4 ((3 1) 2)) 1))) ((4 ((3 2) 1)) 2))
Tromp binary: 000000000101111100101111001011111001011110110101100101111100101111010110100101111100101111011010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b a @ @ p @ @ q b a b @ @ p @ @ q a b a
Reverse Polish: p q p q a @ b @ @ a @ @ p q b @ a @ @ b @ @ @ p q a @ b @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(K(K(KI)))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(KK)))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(a))(p(q(b)(a))(b)))(p(q(a)(b))(a))

Where it comes from

XOR ×2 · XNOR ×2

#303TRUE · 11114 cellse.g. XOR(NOR, OR)

Lambda, short form: λpqab.p (p a (q a b)) (q (p a (q a b)) (p b (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((p a) ((q a) b))) ((q ((p a) ((q a) b))) ((p b) ((q b) a)))))))
De Bruijn: λλλλ((4 ((4 2) ((3 2) 1))) ((3 ((4 2) ((3 2) 1))) ((4 1) ((3 1) 2))))
Tromp binary: 000000000101111100101111101100101111011010010111100101111101100101111011010010111110100101111010110 (99 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ p a @ @ q a b @ @ q @ @ p a @ @ q a b @ @ p b @ @ q b a
Reverse Polish: p p a @ q a @ b @ @ @ q p a @ q a @ b @ @ @ p b @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(KS)(S(K(S(KS)))(S(KK))))))))(S(S(KS)(S(KK)(S(KS)(S(KK)S))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(p(a)(q(a)(b)))(q(p(a)(q(a)(b)))(p(b)(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

#373TRUE · 11114 cellse.g. OR(XNOR, XOR)

Lambda, short form: λpqab.p (q a (p (q b a) (q a b))) (q (p (q b a) (q a b)) a)
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q a) ((p ((q b) a)) ((q a) b)))) ((q ((p ((q b) a)) ((q a) b))) a)))))
De Bruijn: λλλλ((4 ((3 2) ((4 ((3 1) 2)) ((3 2) 1)))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) 2))
Tromp binary: 0000000001011111001011110110010111110010111101011001011110110100101111001011111001011110101100101111011010110 (109 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q a @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q b a @ @ q a b a
Reverse Polish: p q a @ p q b @ a @ @ q a @ b @ @ @ @ q p q b @ a @ @ q a @ b @ @ @ a @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(K(KK)))
JavaScript: p => q => a => b => p(q(a)(p(q(b)(a))(q(a)(b))))(q(p(q(b)(a))(q(a)(b)))(a))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#438TRUE · 11114 cellse.g. OR(XOR, XNOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) a) (q a (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) a)) ((q a) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) 2)) ((3 2) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 0000000001011111001011110010111110010111101101001011110101101100101111011001011111001011110110100101111010110 (109 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a a @ @ q a @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ a @ @ q a @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(K(KK)))))))(S(K(S(S(KS)(S(K(S(KS)))(S(KK))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(a))(q(a)(p(q(a)(b))(q(b)(a))))

Where it comes from

OR ×1 · p→q ×1 · NAND ×1 · q→p ×1

#277TRUE · 11114 cellse.g. XOR(XNOR, XOR)

Lambda, short form: λpqab.p (q (p (q a b) (q b a)) (p (q b a) (q a b))) (q (p (q b a) (q a b)) (p (q a b) (q b a)))
Lambda, fully bracketed: λp.(λq.(λa.(λb.((p ((q ((p ((q a) b)) ((q b) a))) ((p ((q b) a)) ((q a) b)))) ((q ((p ((q b) a)) ((q a) b))) ((p ((q a) b)) ((q b) a)))))))
De Bruijn: λλλλ((4 ((3 ((4 ((3 2) 1)) ((3 1) 2))) ((4 ((3 1) 2)) ((3 2) 1)))) ((3 ((4 ((3 1) 2)) ((3 2) 1))) ((4 ((3 2) 1)) ((3 1) 2))))
Tromp binary: 00000000010111110010111100101111100101111011010010111101011001011111001011110101100101111011010010111100101111100101111010110010111101101001011111001011110110100101111010110 (173 bits)
Polish (prefix): λp λq λa λb @ @ p @ @ q @ @ p @ @ q a b @ @ q b a @ @ p @ @ q b a @ @ q a b @ @ q @ @ p @ @ q b a @ @ q a b @ @ p @ @ q a b @ @ q b a
Reverse Polish: p q p q a @ b @ @ q b @ a @ @ @ p q b @ a @ @ q a @ b @ @ @ @ q p q b @ a @ @ q a @ b @ @ @ p q a @ b @ @ q b @ a @ @ @ @ λb λa λq λp
SKI combinators: S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK))))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI)))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(K(S(S(KS)(S(KK)(S(KS)K)))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(S(KS)(S(KK)(S(KS)(S(KK)(S(KS)K)))))(K(S(S(KS)(S(KK)S))(KK)))))))(KI))))))(S(S(KS)(S(K(S(KS)))(S(K(S(K(S(KS)))))(S(KS)(S(KK)(S(KS)K))))))(K(S(S(KS)(S(KK)S))(KK)))))
JavaScript: p => q => a => b => p(q(p(q(a)(b))(q(b)(a)))(p(q(b)(a))(q(a)(b))))(q(p(q(b)(a))(q(a)(b)))(p(q(a)(b))(q(b)(a))))

Where it comes from

XOR ×2 · XNOR ×2

Built from the verified gates-of-gates data. For every program, the short form, de Bruijn form, binary, Polish and reverse Polish forms were each read back and compared with the original term, and the lambda term, its SKI translation and its JavaScript version were each run on all four inputs and gave the gate's truth table. Tromp diagrams are drawn from the same terms. The maps come from the same verified grid, and every program's marked cells add up to its cell count, all 4,096 in total.