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

let example0 =
        assert
      :   iterate 10 Natural (λ(x : Natural) → x * 2) 1
        ≡ [ 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ]

let example1 =
        assert
      : iterate 0 Natural (λ(x : Natural) → x * 2) 1 ≡ ([] : List Natural)

in  iterate
