{-
Only keep an `Optional` element if the supplied function returns `True`
-}
let filter
    : ∀(a : Type) → (a → Bool) → Optional a → Optional a
    =   λ(a : Type)
      → λ(f : a → Bool)
      → λ(xs : Optional a)
      → (   λ(a : Type)
          → λ ( build
              :   ∀(optional : Type)
                → ∀(some : a → optional)
                → ∀(none : optional)
                → optional
              )
          → build (Optional a) (λ(x : a) → Some x) (None a)
        )
          a
          (   λ(optional : Type)
            → λ(some : a → optional)
            → λ(none : optional)
            → merge
                { Some = λ(x : a) → if f x then some x else none, None = none }
                xs
          )

let example0 = assert : filter Natural Natural/even (Some 2) ≡ Some 2

let example1 = assert : filter Natural Natural/odd (Some 2) ≡ None Natural

in  filter