Prompt

Create a λ-Term fold that, when applied to a Church nat N, a function F, an initial value X, and a Church N-Tuple, performs a right-fold over the N-tuple. In other words, create a generic fold<N,F,X,t> function for N-tuples. Example:

(fold λf.λx.(f x) F X λt(t 1)) == (F 1 X)
(fold λf.λx.(f (f x)) F X λt(t 1 2)) == (F 1 (F 2 X))
(fold λf.λx.(f (f (f x))) F X λt(t 1 2 3)) == (F 1 (F 2 (F 3 X)))

Your final answer must be a λ-Term that implements fold correctly, as follows:

fold = term_here

Answer

Below is a possible solution, in HVM3:

@nat(n) = ~ n {
  0: λf λx x
  n: λf λx !&{f0 f1}=f (@nat(n) f0 (f1 x))
}

@fold = λn λt λF λX
  ! fS = (λA λt λe0 (A t λB λx (e0 λe1 (B λC (F x (e1 C))))))
  ! fZ = (λt λe0 (t (e0 λe1 (e1 X))))
  (n fS fZ t λx(x λx(x)))

@main = (@fold @nat(3) λt(t 1 2 3))

VictorTaelin/agi_moment_prompt.md

Prompt

Answer