|Portability||non-portable (multi-parameter type classes)|
A backtracking, logic programming monad.
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)
Minimal implementation: msplit
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))
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
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.
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)
Pruning. Selects one result out of many. Useful for when multiple results of a computation will be equivalent, or should be treated as such.
The inverse of msplit. Satisfies the following law:
msplit m >>= reflect == m