juvix/tests/positive/Termination/Data/Nat.mjuvix

module Data.Nat;
  inductive ℕ  {
    zero : ℕ;
    suc : ℕ → ℕ;
  };

  infixl 6 +;
  + : ℕ → ℕ → ℕ;
  + zero b ≔ b;
  + (suc a) b ≔ suc (a + b);

  infixl 7 *;
  * : ℕ → ℕ → ℕ;
  * zero b ≔ zero;
  * (suc a) b ≔ b + a * b;

  import Data.Bool;
  open Data.Bool;

  even : ℕ → Bool;
  odd : ℕ → Bool;

  even zero ≔ true;
  even (suc n) ≔ odd n;

  odd zero ≔ false;
  odd (suc n) ≔ even n;
end;