User talk:Hakerh400/Question for AI models

My reasoning about how to solve this question: it's obviously possible for X to apply its argument to some fixed sequence of arguments, so we could solve the problem by finding a, b, c, such that Sabc is K and Kabc is S. Kabc is ac, and Sabc is (ac)(bc) – there's no argument we can give to S to make it work like K, so we need four arguments, i.e. Sabcd is K and Kabcd is S. Kabcd is (ac)d and Sabc is (ac)(bc)d; let e = ac, now we need to find e(bc)d = K and ed = S. This is trivially possible with e=I, bc=KK, and d=S; there are plenty of ways to solve for abc, e.g. a = KI, b = K, c = K, d = S. As a check: K(KI)KKS is ((KI)K)S is IS is S, and S(KI)KKS is ((KI)K)(KK)S is I(KK)S is (KK)s is K. Thus, to solve the problem, just translate λx.x(KI)KKS from lambda calculus to SKI calculus and you get a working model of X. (Note that AI models don't use reasoning at all, but rather pattern-matching; as such I wouldn't expect them to be able to produce the appropriate argument unless they had seen something similar in their training data.) --ais523 18:06, 8 February 2025 (UTC)