juvix/tests/Core/positive/test050.jvc

-- Church numerals with pattern matching

def czero : Π A : Type, (A → A) → A → A :=
  λ(A : Type) λ(f : A → A) λ(x : A) x;

def csuc : (Π A : Type, (A → A) → A → A) → Π A : Type, (A → A) → A → A :=
  λ(n : Π A : Type, (A → A) → A → A) λ(A : Type) λ(f : A → A) λ(x : A) f (n A f x);

def num : Nat → Π A : Type, (A → A) → A → A :=
  λ(n : Nat) match n : Nat with : Π A : Type, (A → A) → A → A {
    zero := czero;
    suc (n : Nat) := csuc (num n);
  };

def toNat : (Π A : Type, (A → A) → A → A) → Nat :=
  λ(n : Π A : Type, (A → A) → A → A) n Nat suc zero;

def toInt : Nat → Int :=
  λ(n : Nat) case n of {
    zero := 0;
    suc n := toInt n + 1;
  };

toInt (toNat (num (suc (suc (suc zero)))))