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Control.Monad.Fix

Description

Monadic fixpoints.

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

class Monad m => MonadFix m whereSource

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 aSource

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.

fix :: (a -> a) -> aSource

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

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