module Synonyms;

open import Stdlib.Prelude;

Ty1 : Type;
Ty1 := Bool → Bool;

Ty2 : Type;
Ty2 := Ty1;

k : Ty2;
k x := x;

Num : Type;
Num := {A : Type} → (A → A) → A → A;

-- we need the explicit `{_}` since we do not normalize types in the arity checker
czero : Num;
czero {_} f x := x;

csuc : Num → Num;
csuc n {_} f := f ∘ n {_} f;

end;