
Control.Monad.Fix  Portability  portable  Stability  experimental  Maintainer  libraries@haskell.org 





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 
Monads having fixed points with a 'knottying' 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) = \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  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  


fix :: (a > a) > a 
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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