record Functor {l : Level} (F : Set l -> Set l) : Set (suc l) where
 field
  fmap : {A B : Set l} -> (A -> B) -> (F A) -> (F B)
 field -- laws
  preserve-id : {A : Set l} (x : F A) → fmap id x ≡ id x
  covariant   : {A B C : Set l} (f : A -> B) -> (g : B -> C) -> (x : F A)
                   -> fmap (g ∙ f) x ≡ ((fmap g) ∙ (fmap f)) x
 field -- proof assistant
  fmap-equiv : {A B : Set l} {f g : A -> B} ->
    ((x : A) -> f x ≡ g x) -> (fx : F A) -> fmap f fx ≡ fmap g fx