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
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Monad.Fix

Description

Monadic fixpoints.

For a detailed discussion, see Levent Erkok's thesis, Value Recursion in Monadic Computations, Oregon Graduate Institute, 2002.

Synopsis

Documentation

class Monad m => MonadFix m where Source

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 (liftM h . f) = 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.

Methods

mfix :: (a -> m a) -> m a Source

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.

Instances

MonadFix []
MonadFix IO
MonadFix Maybe
MonadFix Identity
MonadFix ((->) r)
MonadFix (Either e)
MonadFix (ST s)
MonadFix (ST s)

fix :: (a -> a) -> a Source

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x.