X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=Control%2FArrow.hs;h=2710be6e9c469e3b05da06b1013ad64e4eac610b;hb=567080c906535534628b1ab83a4a4425dcd4bb5e;hp=35cc00de97b22eed44bfbda106ebe27c3eb33cad;hpb=746ef6a7fd71bb1e9ebe3cd107c5f9f79f3b7a68;p=haskell-directory.git

diff --git a/Control/Arrow.hs b/Control/Arrow.hs
index 35cc00d..2710be6 100644
--- a/Control/Arrow.hs
+++ b/Control/Arrow.hs
@@ -16,9 +16,27 @@
 --	Firenze, Italy, pp229-240.
 -- See these papers for the equations these combinators are expected to
 -- satisfy.  These papers and more information on arrows can be found at
--- <http://www.soi.city.ac.uk/~ross/arrows/>.
-
-module Control.Arrow where
+-- <http://www.haskell.org/arrows/>.
+
+module Control.Arrow (
+		-- * Arrows
+		Arrow(..), Kleisli(..),
+		-- ** Derived combinators
+		returnA,
+		(^>>), (>>^),
+		-- ** Right-to-left variants
+		(<<<), (<<^), (^<<),
+		-- * Monoid operations
+		ArrowZero(..), ArrowPlus(..),
+		-- * Conditionals
+		ArrowChoice(..),
+		-- * Arrow application
+		ArrowApply(..), ArrowMonad(..), leftApp,
+		-- * Feedback
+		ArrowLoop(..)
+	) where
+
+import Prelude
 
 import Control.Monad
 import Control.Monad.Fix
@@ -28,11 +46,8 @@ infixr 3 ***
 infixr 3 &&&
 infixr 2 +++
 infixr 2 |||
-infixr 1 >>>
-infixr 1 <<<
-
------------------------------------------------------------------------------
--- * Arrows
+infixr 1 >>>, ^>>, >>^
+infixr 1 <<<, ^<<, <<^
 
 -- | The basic arrow class.
 --   Any instance must define either 'arr' or 'pure' (which are synonyms),
@@ -81,6 +96,23 @@ class Arrow a where
 	(&&&) :: a b c -> a b c' -> a b (c,c')
 	f &&& g = arr (\b -> (b,b)) >>> f *** g
 
+{-# RULES
+"compose/arr"	forall f g .
+		arr f >>> arr g = arr (f >>> g)
+"first/arr"	forall f .
+		first (arr f) = arr (first f)
+"second/arr"	forall f .
+		second (arr f) = arr (second f)
+"product/arr"	forall f g .
+		arr f *** arr g = arr (f *** g)
+"fanout/arr"	forall f g .
+		arr f &&& arr g = arr (f &&& g)
+"compose/first"	forall f g .
+		first f >>> first g = first (f >>> g)
+"compose/second" forall f g .
+		second f >>> second g = second (f >>> g)
+ #-}
+
 -- Ordinary functions are arrows.
 
 instance Arrow (->) where
@@ -88,11 +120,13 @@ instance Arrow (->) where
 	f >>> g = g . f
 	first f = f *** id
 	second f = id *** f
-	(f *** g) ~(x,y) = (f x, g y)
+--	(f *** g) ~(x,y) = (f x, g y)
+--	sorry, although the above defn is fully H'98, nhc98 can't parse it.
+	(***) f g ~(x,y) = (f x, g y)
 
 -- | Kleisli arrows of a monad.
 
-newtype Kleisli m a b = Kleisli (a -> m b)
+newtype Kleisli m a b = Kleisli { runKleisli :: a -> m b }
 
 instance Monad m => Arrow (Kleisli m) where
 	arr f = Kleisli (return . f)
@@ -100,21 +134,30 @@ instance Monad m => Arrow (Kleisli m) where
 	first (Kleisli f) = Kleisli (\ ~(b,d) -> f b >>= \c -> return (c,d))
 	second (Kleisli f) = Kleisli (\ ~(d,b) -> f b >>= \c -> return (d,c))
 
------------------------------------------------------------------------------
--- ** Derived combinators
-
 -- | The identity arrow, which plays the role of 'return' in arrow notation.
 
 returnA :: Arrow a => a b b
 returnA = arr id
 
--- | Right-to-left composition, for a better fit with arrow notation.
+-- | Precomposition with a pure function.
+(^>>) :: Arrow a => (b -> c) -> a c d -> a b d
+f ^>> a = arr f >>> a
 
+-- | Postcomposition with a pure function.
+(>>^) :: 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
 
------------------------------------------------------------------------------
--- * Monoid operations
+-- | Precomposition with a pure function (right-to-left variant).
+(<<^) :: Arrow a => a c d -> (b -> c) -> a b d
+a <<^ f = a <<< arr f
+
+-- | Postcomposition with a pure function (right-to-left variant).
+(^<<) :: Arrow a => (c -> d) -> a b c -> a b d
+f ^<< a = arr f <<< a
 
 class Arrow a => ArrowZero a where
 	zeroArrow :: a b c
@@ -128,11 +171,8 @@ class ArrowZero a => ArrowPlus a where
 instance MonadPlus m => ArrowPlus (Kleisli m) where
 	Kleisli f <+> Kleisli g = Kleisli (\x -> f x `mplus` g x)
 
------------------------------------------------------------------------------
--- * Conditionals
-
 -- | Choice, for arrows that support it.  This class underlies the
---   [if] and [case] constructs in arrow notation.
+--   @if@ and @case@ constructs in arrow notation.
 --   Any instance must define 'left'.  The other combinators have sensible
 --   default definitions, which may be overridden for efficiency.
 
@@ -170,6 +210,21 @@ class Arrow a => ArrowChoice a where
 			where	untag (Left x) = x
 				untag (Right y) = y
 
+{-# RULES
+"left/arr"	forall f .
+		left (arr f) = arr (left f)
+"right/arr"	forall f .
+		right (arr f) = arr (right f)
+"sum/arr"	forall f g .
+		arr f +++ arr g = arr (f +++ g)
+"fanin/arr"	forall f g .
+		arr f ||| arr g = arr (f ||| g)
+"compose/left"	forall f g .
+		left f >>> left g = left (f >>> g)
+"compose/right"	forall f g .
+		right f >>> right g = right (f >>> g)
+ #-}
+
 instance ArrowChoice (->) where
 	left f = f +++ id
 	right f = id +++ f
@@ -182,9 +237,6 @@ instance Monad m => ArrowChoice (Kleisli m) where
 	f +++ g = (f >>> arr Left) ||| (g >>> arr Right)
 	Kleisli f ||| Kleisli g = Kleisli (either f g)
 
------------------------------------------------------------------------------
--- * Arrow application
-
 -- | Some arrows allow application of arrow inputs to other inputs.
 
 class Arrow a => ArrowApply a where
@@ -214,12 +266,9 @@ leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)
 leftApp f = arr ((\b -> (arr (\() -> b) >>> f >>> arr Left, ())) |||
 		 (\d -> (arr (\() -> d) >>> arr Right, ()))) >>> app
 
------------------------------------------------------------------------------
--- * Feedback
-
 -- | The 'loop' operator expresses computations in which an output value is
 --   fed back as input, even though the computation occurs only once.
---   It underlies the [rec] value recursion construct in arrow notation.
+--   It underlies the @rec@ value recursion construct in arrow notation.
 
 class Arrow a => ArrowLoop a where
 	loop :: a (b,d) (c,d) -> a b c