module TypeAlias;

type T := t : T;

type T2 := t2 : T2;

alias : Type := T;

x : alias := t;

id : Type → Type
  | x := x;

syntax fixity composition := binary {assoc := right};

syntax operator ⊙ composition;

⊙ : (Type → Type) → (Type → Type) → Type → Type
  | f g x := f (g x);

x2 : (id ⊙ id) alias := t;

flip
  : (Type → Type → Type) → id Type → Type → (id ⊙ id) Type
  | f a b := f b a;

type Pair (A : Type) (B : Type) :=
  mkPair : id T → id (id A) → B → Pair A B;

p : {A : Type} → A → Pair A A
  | a := mkPair t a a;

x' : flip Pair (id _) T2 := mkPair x t2 t;

funAlias : Type -> Type
  | a := a -> a;

f : funAlias T := \ {t := t};

f' : funAlias T
  | t := t;