module TypeAlias;

type T :=
 t : T;

type T2 :=
 t2 : T2;

alias : Type;
alias := T;

x : alias;
x := t;

id : Type → Type;
id x := x;

infixr 9 ⊙;
⊙ : (Type → Type) → (Type → Type) → Type → Type;
⊙ f g x := f (g x);

x2 : (id ⊙ id) alias;
x2 := t;

flip : (Type → Type → Type) → id Type → Type → (id ⊙ id) Type;
flip 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;
p a := mkPair t a a;

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

end;