From 975e5259824fb2270d8be72765979f773417ff13 Mon Sep 17 00:00:00 2001
From: Ashley Yakeley <ashley@semantic.org>
Date: Sat, 13 Oct 2007 07:48:51 +0000
Subject: [PATCH] new Control.Compositor module

The Compositor class is a superclass of Arrow.
---
 Control/Applicative.hs |    3 ++-
 Control/Arrow.hs       |   26 ++++++++++++--------------
 Control/Compositor.hs  |   37 +++++++++++++++++++++++++++++++++++++
 base.cabal             |    1 +
 4 files changed, 52 insertions(+), 15 deletions(-)
 create mode 100644 Control/Compositor.hs

diff --git a/Control/Applicative.hs b/Control/Applicative.hs
index c22c55d..cb76bcc 100644
--- a/Control/Applicative.hs
+++ b/Control/Applicative.hs
@@ -39,8 +39,9 @@ module Control.Applicative (
 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(..))
diff --git a/Control/Arrow.hs b/Control/Arrow.hs
index 2710be6..a339adf 100644
--- a/Control/Arrow.hs
+++ b/Control/Arrow.hs
@@ -25,7 +25,7 @@ module Control.Arrow (
 		returnA,
 		(^>>), (>>^),
 		-- ** Right-to-left variants
-		(<<<), (<<^), (^<<),
+		(<<^), (^<<),
 		-- * Monoid operations
 		ArrowZero(..), ArrowPlus(..),
 		-- * Conditionals
@@ -40,21 +40,22 @@ import Prelude
 
 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'.
@@ -65,9 +66,6 @@ class Arrow a where
 	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)
@@ -97,6 +95,8 @@ class Arrow a where
 	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 .
@@ -117,7 +117,6 @@ class Arrow a where
 
 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)
@@ -128,9 +127,12 @@ instance Arrow (->) where
 
 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))
 
@@ -147,10 +149,6 @@ f ^>> a = arr f >>> a
 (>>^) :: 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
diff --git a/Control/Compositor.hs b/Control/Compositor.hs
new file mode 100644
index 0000000..7cc6381
--- /dev/null
+++ b/Control/Compositor.hs
@@ -0,0 +1,37 @@
+-----------------------------------------------------------------------------
+-- |
+-- 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
+
diff --git a/base.cabal b/base.cabal
index 687b04b..14bcf08 100644
--- a/base.cabal
+++ b/base.cabal
@@ -69,6 +69,7 @@ Library {
     exposed-modules:
         Control.Applicative,
         Control.Arrow,
+        Control.Compositor,
         Control.Concurrent,
         Control.Concurrent.Chan,
         Control.Concurrent.MVar,
-- 
1.7.10.4