module Stdlib.Data.Nat;

import Stdlib.Data.Nat.Base open hiding {+; *; div; mod} public;
-- should be re-exported qualified
import Stdlib.Data.Nat.Base as Nat;
import Stdlib.Data.String.Base open;

import Stdlib.Trait.Eq open public;
import Stdlib.Trait.Ord open public;
import Stdlib.Trait.Show open public;
import Stdlib.Trait.Natural open public;

-- should be re-exported qualified
import Stdlib.Data.Nat.Ord as Nat;

--- Converts a ;Nat; into a ;String;.
builtin nat-to-string
axiom natToString : Nat -> String;

--- Partial function that converts a ;String; into a ;Nat;.
builtin string-to-nat
axiom stringToNat : String -> Nat;

{-# specialize: true, inline: case #-}
instance
eqNatI : Eq Nat := mkEq (Nat.==);

{-# specialize: true, inline: case #-}
instance
ordNatI : Ord Nat := mkOrd Nat.compare;

instance
showNatI : Show Nat := mkShow natToString;

{-# specialize: true, inline: case #-}
instance
naturalNatI : Natural Nat :=
  mkNatural@{
    + := (Nat.+);
    * := (Nat.*);
    div := Nat.div;
    mod := Nat.mod;
    fromNat (x : Nat) : Nat := x
  };