X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=Control%2FArrow.hs;h=2710be6e9c469e3b05da06b1013ad64e4eac610b;hb=5031aad924a8b70b5fc4fe4bb1321c007afcab21;hp=237c37f88cc76b017300a860ba67f61911230bfb;hpb=88fcddd13e62ecf456249b535dd72a290feac0ad;p=ghc-base.git

diff --git a/Control/Arrow.hs b/Control/Arrow.hs
index 237c37f..2710be6 100644
--- a/Control/Arrow.hs
+++ b/Control/Arrow.hs
@@ -1,5 +1,5 @@
 -----------------------------------------------------------------------------
---
+-- |
 -- Module      :  Control.Arrow
 -- Copyright   :  (c) Ross Paterson 2002
 -- License     :  BSD-style (see the LICENSE file in the distribution)
@@ -8,26 +8,33 @@
 -- Stability   :  experimental
 -- Portability :  portable
 --
--- $Id: Arrow.hs,v 1.1 2002/02/26 18:19:17 ross Exp $
---
 -- Basic arrow definitions, based on
---
---	"Generalising Monads to Arrows", by John Hughes, Science of
---	Computer Programming 37, pp67-111, May 2000.
---
--- plus a couple of definitions (returnA and loop) from
---
---	"A New Notation for Arrows", by Ross Paterson, in ICFP 2001,
+--	/Generalising Monads to Arrows/, by John Hughes,
+--	/Science of Computer Programming/ 37, pp67-111, May 2000.
+-- plus a couple of definitions ('returnA' and 'loop') from
+--	/A New Notation for Arrows/, by Ross Paterson, in /ICFP 2001/,
 --	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
 
@@ -39,99 +46,210 @@ infixr 3 ***
 infixr 3 &&&
 infixr 2 +++
 infixr 2 |||
-infixr 1 >>>
-infixr 1 <<<
+infixr 1 >>>, ^>>, >>^
+infixr 1 <<<, ^<<, <<^
 
------------------------------------------------------------------------------
--- Arrow classes
+-- | 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
+--   default definitions, which may be overridden for efficiency.
 
 class Arrow a where
+
+	-- | Lift a function to an arrow: you must define either this
+	--   or 'pure'.
 	arr :: (b -> c) -> a b c
+	arr = pure
+
+	-- | A synonym for 'arr': you must define one or other of them.
+	pure :: (b -> c) -> a b c
+	pure = arr
+
+	-- | Left-to-right composition of arrows.
 	(>>>) :: a b c -> a c d -> a b d
-	first :: a b c -> a (b,d) (c,d)
 
-	-- The following combinators are placed in the class so that they
-	-- can be overridden with more efficient versions if required.
-	-- Any replacements should satisfy these equations.
+	-- | 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)
 
+	-- | A mirror image of 'first'.
+	--
+	--   The default definition may be overridden with a more efficient
+	--   version if desired.
 	second :: a b c -> a (d,b) (d,c)
 	second f = arr swap >>> first f >>> arr swap
 			where	swap ~(x,y) = (y,x)
 
+	-- | Split the input between the two argument arrows and combine
+	--   their output.  Note that this is in general not a functor.
+	--
+	--   The default definition may be overridden with a more efficient
+	--   version if desired.
 	(***) :: a b c -> a b' c' -> a (b,b') (c,c')
 	f *** g = first f >>> second g
 
+	-- | Fanout: send the input to both argument arrows and combine
+	--   their output.
+	--
+	--   The default definition may be overridden with a more efficient
+	--   version if desired.
 	(&&&) :: a b c -> a b c' -> a b (c,c')
 	f &&& g = arr (\b -> (b,b)) >>> f *** g
 
-	-- Some people prefer the name pure to arr, so both are allowed,
-	-- but you must define one of them:
+{-# 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)
+ #-}
 
-	pure :: (b -> c) -> a b c
-	pure = arr
-	arr = pure
+-- Ordinary functions are arrows.
 
------------------------------------------------------------------------------
--- Derived combinators
+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)
+--	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.
 
--- The counterpart of return in arrow notation:
+newtype Kleisli m a b = Kleisli { runKleisli :: a -> m b }
+
+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))
+
+-- | The identity arrow, which plays the role of 'return' in arrow notation.
 
 returnA :: Arrow a => a b b
 returnA = arr id
 
--- Mirror image of >>>, 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
 
+instance MonadPlus m => ArrowZero (Kleisli m) where
+	zeroArrow = Kleisli (\x -> mzero)
+
 class ArrowZero a => ArrowPlus a where
 	(<+>) :: a b c -> a b c -> a b c
 
------------------------------------------------------------------------------
--- Conditionals
+instance MonadPlus m => ArrowPlus (Kleisli m) where
+	Kleisli f <+> Kleisli g = Kleisli (\x -> f x `mplus` g x)
+
+-- | Choice, for arrows that support it.  This class underlies the
+--   @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.
 
 class Arrow a => ArrowChoice a where
-	left :: a b c -> a (Either b d) (Either c d)
 
-	-- The following combinators are placed in the class so that they
-	-- can be overridden with more efficient versions if required.
-	-- Any replacements should satisfy these equations.
+	-- | Feed marked inputs through the argument arrow, passing the
+	--   rest through unchanged to the output.
+	left :: a b c -> a (Either b d) (Either c d)
 
+	-- | A mirror image of 'left'.
+	--
+	--   The default definition may be overridden with a more efficient
+	--   version if desired.
 	right :: a b c -> a (Either d b) (Either d c)
 	right f = arr mirror >>> left f >>> arr mirror
 			where	mirror (Left x) = Right x
 				mirror (Right y) = Left y
 
+	-- | Split the input between the two argument arrows, retagging
+	--   and merging their outputs.
+	--   Note that this is in general not a functor.
+	--
+	--   The default definition may be overridden with a more efficient
+	--   version if desired.
 	(+++) :: a b c -> a b' c' -> a (Either b b') (Either c c')
 	f +++ g = left f >>> right g
 
+	-- | Fanin: Split the input between the two argument arrows and
+	--   merge their outputs.
+	--
+	--   The default definition may be overridden with a more efficient
+	--   version if desired.
 	(|||) :: a b d -> a c d -> a (Either b c) d
 	f ||| g = f +++ g >>> arr untag
 			where	untag (Left x) = x
 				untag (Right y) = y
 
------------------------------------------------------------------------------
--- Arrow application
+{-# 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
+	f +++ g = (Left . f) ||| (Right . g)
+	(|||) = either
+
+instance Monad m => ArrowChoice (Kleisli m) where
+	left f = f +++ arr id
+	right f = arr id +++ f
+	f +++ g = (f >>> arr Left) ||| (g >>> arr Right)
+	Kleisli f ||| Kleisli g = Kleisli (either f g)
+
+-- | Some arrows allow application of arrow inputs to other inputs.
 
 class Arrow a => ArrowApply a where
 	app :: a (a b c, b) c
 
--- Any instance of ArrowApply can be made into an instance if ArrowChoice
--- by defining left = leftApp, where
+instance ArrowApply (->) where
+	app (f,x) = f x
 
-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
+instance Monad m => ArrowApply (Kleisli m) where
+	app = Kleisli (\(Kleisli f, x) -> f x)
 
--- The ArrowApply class is equivalent to Monad: any monad gives rise to
--- a Kliesli arrow (see below), and any instance of ArrowApply defines
--- a monad:
+-- | The 'ArrowApply' class is equivalent to 'Monad': any monad gives rise
+--   to a 'Kleisli' arrow, and any instance of 'ArrowApply' defines a monad.
 
 newtype ArrowApply a => ArrowMonad a b = ArrowMonad (a () b)
 
@@ -141,66 +259,23 @@ instance ArrowApply a => Monad (ArrowMonad a) where
 			arr (\x -> let ArrowMonad h = f x in (h, ())) >>>
 			app)
 
------------------------------------------------------------------------------
--- Feedback
+-- | Any instance of 'ArrowApply' can be made into an instance of
+--   'ArrowChoice' by defining 'left' = 'leftApp'.
+
+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
 
--- The following operator expresses computations in which a value is
--- recursively defined through the computation, even though the computation
--- occurs only once:
+-- | 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.
 
 class Arrow a => ArrowLoop a where
 	loop :: a (b,d) (c,d) -> a b c
 
------------------------------------------------------------------------------
--- Arrow instances
-
--- Ordinary functions are arrows.
-
-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)
-
-instance ArrowChoice (->) where
-	left f = f +++ id
-	right f = id +++ f
-	f +++ g = (Left . f) ||| (Right . g)
-	(|||) = either
-
-instance ArrowApply (->) where
-	app (f,x) = f x
-
 instance ArrowLoop (->) where
 	loop f b = let (c,d) = f (b,d) in c
 
------------------------------------------------------------------------------
--- Kleisli arrows of a monad
-
-newtype Kleisli m a b = Kleisli (a -> m b)
-
-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))
-
-instance MonadPlus m => ArrowZero (Kleisli m) where
-	zeroArrow = Kleisli (\x -> mzero)
-
-instance MonadPlus m => ArrowPlus (Kleisli m) where
-	Kleisli f <+> Kleisli g = Kleisli (\x -> f x `mplus` g x)
-
-instance Monad m => ArrowChoice (Kleisli m) where
-	left f = f +++ arr id
-	right f = arr id +++ f
-	f +++ g = (f >>> arr Left) ||| (g >>> arr Right)
-	Kleisli f ||| Kleisli g = Kleisli (either f g)
-
-instance Monad m => ArrowApply (Kleisli m) where
-	app = Kleisli (\(Kleisli f, x) -> f x)
-
 instance MonadFix m => ArrowLoop (Kleisli m) where
 	loop (Kleisli f) = Kleisli (liftM fst . mfix . f')
 		where	f' x y = f (x, snd y)