Functor.fm

T Functor<F: Type -> Type>
| Functor.new(
  map: <A: Type, B: Type> -> (A -> B) -> F(A) -> F(B)
  );

Functor.map<F: Type -> Type>(f: Functor(F)): <A: Type, B: Type> -> (A -> B) -> F(A) -> F(B)
  case f:
  | f.map;

Functor.const<F: Type -> Type>(f: Functor(F)): <A: Type, B: Type> -> A -> F(B) -> F(A)
  <A, B> (a)
  Functor.map<>(f)<,>(Function.const<,>(a))

// VerifiedFunctor is a Functor
// with map satisfying the functor laws
//   map id == id
//   map (f . g) == map f . map g
T VerifiedFunctor<F: Type -> Type, f: Functor(F)>
| VerifiedFunctor.new(
  id: <A: Type> ->
      (fa: F(A)) -> Equal(F(A), Functor.map<F>(f)<A, A>(Function.id<A>, fa), Function.id<F(A)>(fa)),
  comp: <A: Type, B: Type, C: Type> ->
      (fa: F(A)) -> (g: B -> C) -> (h: A -> B) ->
      Equal(F(C),
            Functor.map<F>(f)<A, C>(Function.comp<A, B, C>(g, h), fa),
            Function.comp<F(A), F(B), F(C)>(Functor.map<F>(f)<B, C>(g), Functor.map<F>(f)<A, B>(h))(fa))
  );