1 -----------------------------------------------------------------------------
3 -- Module : Control.Monad.Fix
4 -- Copyright : (c) Andy Gill 2001,
5 -- (c) Oregon Graduate Institute of Science and Technology, 2002
6 -- License : BSD-style (see the file libraries/base/LICENSE)
7 -- Maintainer : libraries@haskell.org
8 -- Stability : experimental
9 -- Portability : portable
13 -- For a detailed discussion, see Levent Erkok's thesis,
14 -- /Value Recursion in Monadic Computations/, Oregon Graduate Institute, 2002.
16 -----------------------------------------------------------------------------
18 module Control.Monad.Fix (
20 mfix -- :: (a -> m a) -> m a
22 fix -- :: (a -> a) -> a
28 -- | @'fix' f@ is the least fixed point of the function @f@,
29 -- i.e. the least defined @x@ such that @f x = x@.
31 fix f = let x = f x in x
33 -- | Monads having fixed points with a \'knot-tying\' semantics.
34 -- Instances of 'MonadFix' should satisfy the following laws:
37 -- @'mfix' ('return' . h) = 'return' ('fix' h)@
39 -- [/left shrinking/ (or /tightening/)]
40 -- @'mfix' (\\x -> a >>= \\y -> f x y) = \\y -> 'mfix' (\\x -> f x y)@
43 -- @'mfix' ('Control.Monad.liftM' h . f) = 'Control.Monad.liftM' h ('mfix' (f . h))@,
47 -- @'mfix' (\\x -> 'mfix' (\\y -> f x y)) = 'mfix' (\\x -> f x x)@
49 -- This class is used in the translation of the recursive @do@ notation
50 -- supported by GHC and Hugs.
51 class (Monad m) => MonadFix m where
52 -- | The fixed point of a monadic computation.
53 -- @'mfix' f@ executes the action @f@ only once, with the eventual
54 -- output fed back as the input. Hence @f@ should not be strict,
55 -- for then @'mfix' f@ would diverge.
56 mfix :: (a -> m a) -> m a
58 -- Instances of MonadFix for Prelude monads
61 instance MonadFix Maybe where
62 mfix f = let a = f (unJust a) in a
63 where unJust (Just x) = x
66 instance MonadFix [] where
67 mfix f = case fix (f . head) of
69 (x:_) -> x : mfix (tail . f)
72 instance MonadFix IO where