Copyright (c) Dan Doel BSD3 dan.doel@gmail.com experimental non-portable (multi-parameter type classes) Safe Haskell98

Description

Adapted from the paper /Backtracking, Interleaving, and Terminating Monad Transformers/, by Oleg Kiselyov, Chung-chieh Shan, Daniel P. Friedman, Amr Sabry (http://www.cs.rutgers.edu/~ccshan/logicprog/LogicT-icfp2005.pdf)

Synopsis

# Documentation

Minimal implementation: msplit

Minimal complete definition

msplit

Methods

msplit :: m a -> m (Maybe (a, m a)) #

Attempts to split the computation, giving access to the first result. Satisfies the following laws:

msplit mzero                == return Nothing
msplit (return a mplus m) == return (Just (a, m))

interleave :: m a -> m a -> m a #

Fair disjunction. It is possible for a logical computation to have an infinite number of potential results, for instance:

odds = return 1 mplus liftM (2+) odds

Such computations can cause problems in some circumstances. Consider:

do x <- odds mplus return 2
if even x then return x else mzero

Such a computation may never consider the 'return 2', and will therefore never terminate. By contrast, interleave ensures fair consideration of both branches of a disjunction

(>>-) :: m a -> (a -> m b) -> m b infixl 1 #

Fair conjunction. Similarly to the previous function, consider the distributivity law for MonadPlus:

(mplus a b) >>= k = (a >>= k) mplus (b >>= k)

If 'a >>= k' can backtrack arbitrarily many tmes, (b >>= k) may never be considered. (>>-) takes similar care to consider both branches of a disjunctive computation.

ifte :: m a -> (a -> m b) -> m b -> m b #

Logical conditional. The equivalent of Prolog's soft-cut. If its first argument succeeds at all, then the results will be fed into the success branch. Otherwise, the failure branch is taken. satisfies the following laws:

ifte (return a) th el           == th a
ifte mzero th el                == el
ifte (return a mplus m) th el == th a mplus (m >>= th)

once :: m a -> m a #

Pruning. Selects one result out of many. Useful for when multiple results of a computation will be equivalent, or should be treated as such.

Instances

msplit m >>= reflect == m
Inverts a logic computation. If m succeeds with at least one value, lnot m fails. If m fails, then lnot m succeeds the value ().