{-# LANGUAGE NoImplicitPrelude #-}
{-# OPTIONS_GHC -fno-warn-tabs #-}

module Hcompta.Expr.Ord where

import Data.Bool
import Data.Ord (Ord(..))

import Hcompta.Expr.Bool
import Hcompta.Expr.Eq
import Hcompta.Expr.Dup

-- * Class 'Expr_Ord'

class
 ( Expr_Bool repr
 , Expr_Eq repr
 ) => Expr_Ord repr where
	lt :: Ord a => repr a -> repr a -> repr Bool
	
	le :: Ord a => repr a -> repr a -> repr Bool
	le x y = (x `lt` y) `or` (x `eq` y)
	
	ge :: Ord a => repr a -> repr a -> repr Bool
	ge x y = neg (x `lt` y)
	
	gt :: Ord a => repr a -> repr a -> repr Bool
	gt x y = neg (x `le` y)

instance -- Expr_Ord Dup
 ( Expr_Ord r1
 , Expr_Ord r2
 ) => Expr_Ord (Dup r1 r2) where
	lt (x1 `Dup` x2) (y1 `Dup` y2) = lt x1 y1 `Dup` lt x2 y2
	le (x1 `Dup` x2) (y1 `Dup` y2) = le x1 y1 `Dup` le x2 y2
	ge (x1 `Dup` x2) (y1 `Dup` y2) = ge x1 y1 `Dup` ge x2 y2
	gt (x1 `Dup` x2) (y1 `Dup` y2) = gt x1 y1 `Dup` gt x2 y2