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
27 import Control.Monad.Instances ()
28 import Data.Function (fix)
30 import Hugs.Prelude (MonadFix(mfix))
34 -- | Monads having fixed points with a \'knot-tying\' semantics.
35 -- Instances of 'MonadFix' should satisfy the following laws:
38 -- @'mfix' ('return' . h) = 'return' ('fix' h)@
40 -- [/left shrinking/ (or /tightening/)]
41 -- @'mfix' (\\x -> a >>= \\y -> f x y) = a >>= \\y -> 'mfix' (\\x -> f x y)@
44 -- @'mfix' ('Control.Monad.liftM' h . f) = 'Control.Monad.liftM' h ('mfix' (f . h))@,
48 -- @'mfix' (\\x -> 'mfix' (\\y -> f x y)) = 'mfix' (\\x -> f x x)@
50 -- This class is used in the translation of the recursive @do@ notation
51 -- supported by GHC and Hugs.
52 class (Monad m) => MonadFix m where
53 -- | The fixed point of a monadic computation.
54 -- @'mfix' f@ executes the action @f@ only once, with the eventual
55 -- output fed back as the input. Hence @f@ should not be strict,
56 -- for then @'mfix' f@ would diverge.
57 mfix :: (a -> m a) -> m a
58 #endif /* !__HUGS__ */
60 -- Instances of MonadFix for Prelude monads
63 instance MonadFix Maybe where
64 mfix f = let a = f (unJust a) in a
65 where unJust (Just x) = x
66 unJust Nothing = error "mfix Maybe: Nothing"
69 instance MonadFix [] where
70 mfix f = case fix (f . head) of
72 (x:_) -> x : mfix (tail . f)
75 instance MonadFix IO where
78 instance MonadFix ((->) r) where
79 mfix f = \ r -> let a = f a r in a