base-4.3.1.0: Basic libraries

Portability portable experimental libraries@haskell.org

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 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 (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.

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.

Instances

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

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`.