/usr/lib/hugs/packages/base/Control/Monad/Fix.hs is in libhugs-base-bundled 98.200609.21-5.3ubuntu1.
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-- |
-- Module : Control.Monad.Fix
-- Copyright : (c) Andy Gill 2001,
-- (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
--
-- Monadic fixpoints.
--
-- For a detailed discussion, see Levent Erkok's thesis,
-- /Value Recursion in Monadic Computations/, Oregon Graduate Institute, 2002.
--
-----------------------------------------------------------------------------
module Control.Monad.Fix (
MonadFix(
mfix -- :: (a -> m a) -> m a
),
fix -- :: (a -> a) -> a
) where
import Prelude
import System.IO
import Control.Monad.Instances ()
-- | @'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) = a >>= \\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 (unJust a) in a
where unJust (Just x) = x
-- List:
instance MonadFix [] where
mfix f = case fix (f . head) of
[] -> []
(x:_) -> x : mfix (tail . f)
-- IO:
instance MonadFix IO where
mfix = fixIO
instance MonadFix ((->) r) where
mfix f = \ r -> let a = f a r in a
|