4 ms·
A single point basis (like X = \z. z K S K for which X X = K K, X X X = K, and X (X X) = S) is not in itself a combinator. A combinator is not just a closed la
by tromp 6y ago
A single point basis (like X = \z. z K S K for which
X X = K K, X X X = K, and X (X X) = S) is not in itself a combinator.
A combinator is not just a closed lambda term;
it must have all lambdas in leading position.
Like S = \x \y \z. x z (y z)
- a1369209993 6y ago> A single point basis [...] is not in itself a combinator. > A combinator [...] must have all lambdas in leading position. What's your opinion on: ωabcd = bd(cd) if a has no normal form[0][1] or = c if b has no normal form or = d if c has no normal form or = dd otherwise where SII = ωωωω Ω = SII(SII) = ωωωω(ωωωω) S = ωΩ = ω(ωωωω(ωωωω)) K = ωωΩ = ωω(ωωωω(ωωωω)) I = ωωωΩ = ωωω(ωωωω(ωωωω)) as a single-'combinator' basis? 0: Aka, does not halt. 1: Evaluation diverges if a (or b or c, if queried) is somthing like: SII(C(C(B(ωωx(KI)K)(SII))Ω)I) (from https://en.wikipedia.org/wiki/Combinatory_logic#Undecidability_of_combinatorial_calculus https://en.wikipedia.org/wiki/Combinatory_logic#Undecidabili...) that tries to diagonalize ω.
- tromp 6y agoSuch a combinator ω cannot exist.
- Uzomidy 6y agoDoes this mean that the Y combinator, Y = λf.(λx.f (x x)) (λx.f (x x)), is not a combinator?