module Data.Number

import Data.Object

export restrict(Eq a) Num a {
  (+)(x :: a, y :: a) :: a;
  (*)(x :: a, y :: a) :: a;
  (-)(x :: a, y :: a) :: a;
};

export restrict(Num a) Signed a {
  negate(x :: a) :: a;
  abs(x :: a) :: a;
  signum(x :: a) :: a;
};

export restrict(Num a) Unsigned a {
};

export class Bounded a {
  minBound :: a;
  maxBound :: a;
};

export datatype Ordering = Before | Equal | After;

export class restrict(Eq a) Ord a {
  compare(_ :: a, _ :: a) :: Ordering;

  (<)(x :: a, y :: b) :: Bool
  {
    case compare(x,y) {
      Before -> True;
      _      -> False;
    }
  }

  (>)(x :: a, y :: b) :: Bool
  {
    case compare(x,y) {
      After -> True;
      _     -> False;
    }
  }

  (<=)(x :: a, y :: b) :: Bool
  {
    case compare(x,y) {
      After -> False;
      _     -> True;
    }
  }

  (>=)(x :: a, y :: b) :: Bool
  {
    case compare(x,y) {
      Before -> False;
      _      -> True;
    }
  }

  max(x :: a, y :: b)  :: a
  {
    case compare(x,y) {
      Before -> y;
      _      -> x;
    }
  }

  min(x :: a, y :: b)  :: b
  {
    case compare(x,y) {
      After  -> y;
      _      -> x;
  }
}

export class Enum a {
  succ(a) :: a;
  pred(a) :: a;
  toEnum(Integer) :: a;
  fromEnum(a) :: Integer;
  enumFromTo(a, a) :: [a];
  enumFromThenTo(a, a, a) :: [a];
}

export restrict(Ord a, Num a)
createEnum(s :: a, e :: a, m :: a) :: [a] = s : createEnum(s + m, e, m);

export restrict(Ord a, Num a)
diff(x :: a, y :: a) :: a = if x > y then x - y else y - x;