{-
Only keep elements of the list where the supplied function returns `True`

Examples:
-}
let filter
    : ∀(a : Type) → (a → Bool) → List a → List a
    =   λ(a : Type)
      → λ(f : a → Bool)
      → λ(xs : List a)
      → List/build
          a
          (   λ(list : Type)
            → λ(cons : a → list → list)
            → List/fold
                a
                xs
                list
                (λ(x : a) → λ(xs : list) → if f x then cons x xs else xs)
          )

let example0 = assert : filter Natural Natural/even [ 2, 3, 5 ] ≡ [ 2 ]

let example1 = assert : filter Natural Natural/odd [ 2, 3, 5 ] ≡ [ 3, 5 ]

in  filter