fix nhc98 build: need a qualified Prelude import

[ghc-base.git] / Control / Arrow.hs

diff --git a/Control/Arrow.hs b/Control/Arrow.hs
index f6ee713..66c7745 100644 (file)
--- a/Control/Arrow.hs
+++ b/Control/Arrow.hs
@@ -22,7 +22,10 @@ module Control.Arrow (
                -- * Arrows
                Arrow(..), Kleisli(..),
                -- ** Derived combinators
-               returnA, (<<<),
+               returnA,
+               (^>>), (>>^),
+               -- ** Right-to-left variants
+               (<<^), (^<<),
                -- * Monoid operations
                ArrowZero(..), ArrowPlus(..),
                -- * Conditionals
@@ -33,25 +36,27 @@ module Control.Arrow (
                ArrowLoop(..)
        ) where
 
-import Prelude
+import Prelude hiding (id,(.))
+import qualified Prelude
 
 import Control.Monad
 import Control.Monad.Fix
+import Control.Category
 
 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 Category a => Arrow a where
 
        -- | Lift a function to an arrow: you must define either this
        --   or 'pure'.
@@ -62,9 +67,6 @@ 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)
@@ -93,11 +95,29 @@ class Arrow a where
        (&&&) :: a b c -> a b c' -> a b (c,c')
        f &&& g = arr (\b -> (b,b)) >>> f *** g
 
+{-# RULES
+"identity"
+               arr id = id
+"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
        arr f = f
-       f >>> g = g . f
        first f = f *** id
        second f = id *** f
 --     (f *** g) ~(x,y) = (f x, g y)
@@ -106,11 +126,14 @@ instance Arrow (->) where
 
 -- | 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 => Category (Kleisli m) where
+       id = Kleisli return
+       (Kleisli f) . (Kleisli g) = Kleisli (\b -> g b >>= f)
 
 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))
 
@@ -119,10 +142,21 @@ instance Monad m => Arrow (Kleisli m) where
 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
 
-(<<<) :: Arrow a => a c d -> a b c -> a b d
-f <<< g = g >>> f
+-- | Postcomposition with a pure function.
+(>>^) :: Arrow a => a b c -> (c -> d) -> a b d
+a >>^ f = a >>> arr 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
+
+-- | 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
@@ -175,6 +209,21 @@ 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