import Prelude
#endif
+import Control.Compositor
import Control.Arrow
- (Arrow(arr, (>>>), (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
+ (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
import Control.Monad (liftM, ap, MonadPlus(..))
import Control.Monad.Instances ()
import Data.Monoid (Monoid(..))
returnA,
(^>>), (>>^),
-- ** Right-to-left variants
- (<<<), (<<^), (^<<),
+ (<<^), (^<<),
-- * Monoid operations
ArrowZero(..), ArrowPlus(..),
-- * Conditionals
import Control.Monad
import Control.Monad.Fix
+import Control.Compositor
infixr 5 <+>
infixr 3 ***
infixr 3 &&&
infixr 2 +++
infixr 2 |||
-infixr 1 >>>, ^>>, >>^
-infixr 1 <<<, ^<<, <<^
+infixr 1 ^>>, >>^
+infixr 1 ^<<, <<^
-- | The basic arrow class.
-- Any instance must define either 'arr' or 'pure' (which are synonyms),
--- as well as '>>>' and 'first'. The other combinators have sensible
+-- as well as 'first'. The other combinators have sensible
-- default definitions, which may be overridden for efficiency.
-class Arrow a where
+class Compositor a => Arrow a where
-- | Lift a function to an arrow: you must define either this
-- or 'pure'.
pure :: (b -> c) -> a b c
pure = arr
- -- | Left-to-right composition of arrows.
- (>>>) :: a b c -> a c d -> a b d
-
-- | Send the first component of the input through the argument
-- arrow, and copy the rest unchanged to the output.
first :: a b c -> a (b,d) (c,d)
f &&& g = arr (\b -> (b,b)) >>> f *** g
{-# RULES
+"identity"
+ arr id = identity
"compose/arr" forall f g .
arr f >>> arr g = arr (f >>> g)
"first/arr" forall f .
instance Arrow (->) where
arr f = f
- f >>> g = g . f
first f = f *** id
second f = id *** f
-- (f *** g) ~(x,y) = (f x, g y)
newtype Kleisli m a b = Kleisli { runKleisli :: a -> m b }
+instance Monad m => Compositor (Kleisli m) where
+ identity = Kleisli return
+ Kleisli f >>> Kleisli g = Kleisli (\b -> f b >>= g)
+
instance Monad m => Arrow (Kleisli m) where
arr f = Kleisli (return . f)
- Kleisli f >>> Kleisli g = Kleisli (\b -> f b >>= g)
first (Kleisli f) = Kleisli (\ ~(b,d) -> f b >>= \c -> return (c,d))
second (Kleisli f) = Kleisli (\ ~(d,b) -> f b >>= \c -> return (d,c))
(>>^) :: Arrow a => a b c -> (c -> d) -> a b d
a >>^ f = a >>> arr f
--- | Right-to-left composition, for a better fit with arrow notation.
-(<<<) :: Arrow a => a c d -> a b c -> a b d
-f <<< g = g >>> f
-
-- | Precomposition with a pure function (right-to-left variant).
(<<^) :: Arrow a => a c d -> (b -> c) -> a b d
a <<^ f = a <<< arr f
--- /dev/null
+-----------------------------------------------------------------------------
+-- |
+-- Module : Control.Compositor
+-- Copyright : (c) Ashley Yakeley 2007
+-- License : BSD-style (see the LICENSE file in the distribution)
+--
+-- Maintainer : ashley@semantic.org
+-- Stability : experimental
+-- Portability : portable
+
+module Control.Compositor where
+
+infixr 1 >>>, <<<
+
+class Compositor comp where
+ identity :: comp a a
+
+ -- | Left-to-right composition
+ (>>>) :: comp a b -> comp b c -> comp a c
+
+{-# RULES
+"identity/left" forall p .
+ identity >>> p = p
+"identity/right" forall p .
+ p >>> identity = p
+"association" forall p q r .
+ (p >>> q) >>> r = p >>> (q >>> r)
+ #-}
+
+instance Compositor (->) where
+ identity = id
+ p >>> q = q . p
+
+-- | Right-to-left composition
+(<<<) :: Compositor comp => comp b c -> comp a b -> comp a c
+f <<< g = g >>> f
+