module Data.Nat;

open import Data.String;
open import Data.Int;

inductive Nat {
  zero : Nat;
  suc : Nat → Nat;
};

foreign c {
  void* natInd(int n, void* zeroCtor, juvix_function_t* sucCtor) {
    if (n <= 0) return zeroCtor;
    return ((void* (*) (juvix_function_t*, void*))sucCtor->fun)(sucCtor, natInd(n - 1, zeroCtor, sucCtor));
  \}
};

axiom natInd : Int → Nat → (Nat → Nat) → Nat;

compile natInd {
  c ↦ "natInd";
};

natToInt : Nat → Int;
natToInt zero ≔ Int_0;
natToInt (suc n) ≔ Int_1 + (natToInt n);

natToStr : Nat → String;
natToStr n ≔ intToStr (natToInt n);

intToNat : Int → Nat;
intToNat x ≔ natInd x zero suc;

end;