{-# LANGUAGE ViewPatterns #-}
-- | This module includes several minor combinators and some rewrite rules for their efficient application.
module Data.RangeMin.Internal.Combinators where

import Control.Monad(join, liftM2)

{-# RULES
	"on/id" forall f . f `on` id = f;
	"liftM2/app" forall f g h x . liftM2 f g h x = f (g x) (h x);
	"on/on"	forall f g h . (f `on` g) `on` h = f `on` (g . h);
	"onPair/onPair" forall f g x . onPair f (onPair g x) = onPair (f . g) x;
	".:/on" forall f g h  . (f .: g) `on` h = f .: (g `on` h)
	#-}

infixr 9 .:
infixl 8 `on`

{-# INLINE [1] on #-}
-- | @(f `on` g) x y@ is equivalent to @f (g x) (g y)@.
on :: (a -> a -> b) -> (c -> a) -> c -> c -> b
f `on` g = \ (g -> x) (g -> y) -> f x y

{-# INLINE [1] onPair #-}
-- | @onPair f (x, y)@ is equivalent to @(f x, f y)@.
onPair :: (a -> b) -> (a, a) -> (b, b)
onPair f (f -> x', f -> y') = (x', y')

{-# INLINE (.:) #-}
-- | @(f .: g) x y@ is equivalent to @f (g x y)@.
(.:) :: (a -> b) -> (c -> d -> a) -> c -> d -> b
f .: g = \x y -> f (g x y)

{-# INLINE switch #-}
-- | @switch x y p@ is equivalent to @if p then x else y@.
switch :: a -> a -> Bool -> a
switch x y p = if p then x else y

{-# INLINE both #-}
both :: (a -> b) -> (a -> c) -> a -> (b, c)
both f g = \ x -> (f x, g x)