{-# LANGUAGE Trustworthy #-} ----------------------------------------------------------------------------- -- | -- 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), fix ) where import Prelude import System.IO import Data.Function (fix) import GHC.ST -- | 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 instance MonadFix Maybe where mfix f = let a = f (unJust a) in a where unJust (Just x) = x unJust Nothing = error "mfix Maybe: Nothing" instance MonadFix [] where mfix f = case fix (f . head) of [] -> [] (x:_) -> x : mfix (tail . f) instance MonadFix IO where mfix = fixIO instance MonadFix ((->) r) where mfix f = \ r -> let a = f a r in a instance MonadFix (Either e) where mfix f = let a = f (unRight a) in a where unRight (Right x) = x unRight (Left _) = error "mfix Either: Left" instance MonadFix (ST s) where mfix = fixST