iterate

{-
Generate a list of the specified length given a seed value and transition
function

Examples:

```
./iterate +10 Natural (λ(x : Natural) → x * +2) +1
= [ +1, +2, +4, +8, +16, +32, +64, +128, +256, +512 ]

./iterate +0 Natural (λ(x : Natural) → x * +2) +1
= [] : List Natural
```
-}
    let iterate
        : Natural → ∀(a : Type) → (a → a) → a → List a
        =   λ(n : Natural)
          → λ(a : Type)
          → λ(f : a → a)
          → λ(x : a)
          → List/build
            a
            (   λ(list : Type)
              → λ(cons : a → list → list)
              → List/fold
                { index : Natural, value : {} }
                ( List/indexed
                  {}
                  ( List/build
                    {}
                    (   λ(list : Type)
                      → λ(cons : {} → list → list)
                      → Natural/fold n list (cons {=})
                    )
                  )
                )
                list
                (   λ(y : { index : Natural, value : {} })
                  → cons (Natural/fold y.index a f x)
                )
            )

in  iterate