[project @ 2005-03-14 15:22:51 by simonmar]

[ghc-base.git] / Control / Monad / Fix.hs

diff --git a/Control/Monad/Fix.hs b/Control/Monad/Fix.hs
index f69d790..c2b1669 100644 (file)
--- a/Control/Monad/Fix.hs
+++ b/Control/Monad/Fix.hs
@@ -1,24 +1,17 @@
-{-# OPTIONS -fno-implicit-prelude #-}
 -----------------------------------------------------------------------------
--- 
+-- |
 -- Module      :  Control.Monad.Fix
 -- Copyright   :  (c) Andy Gill 2001,
---               (c) Oregon Graduate Institute of Science and Technology, 2001
--- License     :  BSD-style (see the file libraries/core/LICENSE)
--- 
+--               (c) Oregon Graduate Institute of Science and Technology, 2002
+-- License     :  BSD-style (see the file libraries/base/LICENSE)
 -- Maintainer  :  libraries@haskell.org
 -- Stability   :  experimental
 -- Portability :  portable
 --
--- $Id: Fix.hs,v 1.3 2002/03/14 12:09:49 simonmar Exp $
+-- Monadic fixpoints.
 --
--- The Fix monad.
---
---       Inspired by the paper:
---       \em{Functional Programming with Overloading and
---           Higher-Order Polymorphism},
---         \A[HREF="http://www.cse.ogi.edu/~mpj"]{Mark P Jones},
---               Advanced School of Functional Programming, 1995.}
+-- For a detailed discussion, see Levent Erkok's thesis,
+-- /Value Recursion in Monadic Computations/, Oregon Graduate Institute, 2002.
 --
 -----------------------------------------------------------------------------
 
@@ -29,29 +22,52 @@ module Control.Monad.Fix (
        fix     -- :: (a -> a) -> a
   ) where
 
-#ifdef __GLASGOW_HASKELL__
--- MonadFix is needed by System.IO, so it is below the Prelude.
-import Control.Monad
-import GHC.Base
-import GHC.Err
-import Data.Maybe
-#endif
-
+import Prelude
 import System.IO
 
+-- | @'fix' f@ is the least fixed point of the function @f@,
+-- i.e. the least defined @x@ such that @f x = x@.
 fix :: (a -> a) -> a
 fix f = let x = f x in x
 
+-- | Monads having fixed points with a \'knot-tying\' semantics.
+-- Instances of 'MonadFix' should satisfy the following laws:
+--
+-- [/purity/]
+--     @'mfix' ('return' . h)  =  'return' ('fix' h)@
+--
+-- [/left shrinking/ (or /tightening/)]
+--     @'mfix' (\\x -> a >>= \\y -> f x y)  =  \\y -> 'mfix' (\\x -> f x y)@
+--
+-- [/sliding/]
+--     @'mfix' ('Control.Monad.liftM' h . f)  =  'Control.Monad.liftM' h ('mfix' (f . h))@,
+--     for strict @h@.
+--
+-- [/nesting/]
+--     @'mfix' (\\x -> 'mfix' (\\y -> f x y))  =  'mfix' (\\x -> f x x)@
+--
+-- This class is used in the translation of the recursive @do@ notation
+-- supported by GHC and Hugs.
 class (Monad m) => MonadFix m where
+       -- | The fixed point of a monadic computation.
+       -- @'mfix' f@ executes the action @f@ only once, with the eventual
+       -- output fed back as the input.  Hence @f@ should not be strict,
+       -- for then @'mfix' f@ would diverge.
        mfix :: (a -> m a) -> m a
 
+-- Instances of MonadFix for Prelude monads
+
+-- Maybe:
 instance MonadFix Maybe where
-       mfix f = let
-               a = f $ case a of
-                       Just x -> x
-                       _      -> error "empty mfix argument"
-               in a
+    mfix f = let a = f (unJust a) in a
+             where unJust (Just x) = x
 
-instance MonadFix IO where
-       mfix = fixIO
+-- List:
+instance MonadFix [] where
+    mfix f = case fix (f . head) of
+               []    -> []
+               (x:_) -> x : mfix (tail . f)
 
+-- IO:
+instance MonadFix IO where
+    mfix = fixIO