base-4.11.1.0: Basic libraries

Copyright (c) Andy Gill 2001(c) Oregon Graduate Institute of Science and Technology 2002 BSD-style (see the file libraries/base/LICENSE) [email protected] experimental portable Trustworthy Haskell2010

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 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

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.

For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120


This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120


Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix' argument, hence the recursion is reintroduced.