+++ /dev/null
------------------------------------------------------------------------------
--- |
--- 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 ()
-import Data.Function (fix)
-
--- | 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