base-4.10.1.0: Basic libraries

Description

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

Synopsis

# Documentation

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.

Minimal complete definition

mfix

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

 MonadFix [] # Since: 2.1 Methodsmfix :: (a -> [a]) -> [a] # # Since: 2.1 Methodsmfix :: (a -> Maybe a) -> Maybe a # # Since: 2.1 Methodsmfix :: (a -> IO a) -> IO a # # Since: 4.9.0.0 Methodsmfix :: (a -> Par1 a) -> Par1 a # # Since: 4.8.0.0 Methodsmfix :: (a -> Last a) -> Last a # # Since: 4.8.0.0 Methodsmfix :: (a -> First a) -> First a # # Since: 4.8.0.0 Methodsmfix :: (a -> Product a) -> Product a # # Since: 4.8.0.0 Methodsmfix :: (a -> Sum a) -> Sum a # # Since: 4.8.0.0 Methodsmfix :: (a -> Dual a) -> Dual a # # Since: 4.8.0.0 Methodsmfix :: (a -> Identity a) -> Identity a # # Since: 4.9.0.0 Methodsmfix :: (a -> NonEmpty a) -> NonEmpty a # # Since: 4.9.0.0 Methodsmfix :: (a -> Option a) -> Option a # # Since: 4.9.0.0 Methodsmfix :: (a -> Last a) -> Last a # # Since: 4.9.0.0 Methodsmfix :: (a -> First a) -> First a # # Since: 4.9.0.0 Methodsmfix :: (a -> Max a) -> Max a # # Since: 4.9.0.0 Methodsmfix :: (a -> Min a) -> Min a # # Since: 4.3.0.0 Methodsmfix :: (a -> Either e a) -> Either e a # MonadFix (ST s) # Since: 2.1 Methodsmfix :: (a -> ST s a) -> ST s a # MonadFix (ST s) # Since: 2.1 Methodsmfix :: (a -> ST s a) -> ST s a # MonadFix f => MonadFix (Rec1 * f) # Since: 4.9.0.0 Methodsmfix :: (a -> Rec1 * f a) -> Rec1 * f a # MonadFix f => MonadFix (Alt * f) # Since: 4.8.0.0 Methodsmfix :: (a -> Alt * f a) -> Alt * f a # MonadFix ((->) LiftedRep LiftedRep r) # Since: 2.1 Methodsmfix :: (a -> (LiftedRep -> LiftedRep) r a) -> (LiftedRep -> LiftedRep) r a # (MonadFix f, MonadFix g) => MonadFix ((:*:) * f g) # Since: 4.9.0.0 Methodsmfix :: (a -> (* :*: f) g a) -> (* :*: f) g a # (MonadFix f, MonadFix g) => MonadFix (Product * f g) # Since: 4.9.0.0 Methodsmfix :: (a -> Product * f g a) -> Product * f g a # MonadFix f => MonadFix (M1 * i c f) # Since: 4.9.0.0 Methodsmfix :: (a -> M1 * i c f a) -> M1 * i c f a #

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.