{-
Transform a list by applying a function to each element

Examples:

```
./map Natural Bool Natural/even [ +2, +3, +5 ]
= [ True, False, False ]

./map Natural Bool Natural/even ([] : List Natural)
= [] : List Bool
```
-}
    let map
        : ∀(a : Type) → ∀(b : Type) → (a → b) → List a → List b
        =   λ(a : Type)
          → λ(b : Type)
          → λ(f : a → b)
          → λ(xs : List a)
          → List/build
            b
            (   λ(list : Type)
              → λ(cons : b → list → list)
              → List/fold a xs list (λ(x : a) → cons (f x))
            )

in  map