logict-0.2.1: A backtracking logic-programming monad.ContentsIndex
Portabilitynon-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)

class MonadPlus m => MonadLogic m where
msplit :: m a -> m (Maybe (a, m a))
interleave :: m a -> m a -> m a
(>>-) :: m a -> (a -> m b) -> m b
ifte :: m a -> (a -> m b) -> m b -> m b
once :: m a -> m a
reflect :: MonadLogic m => Maybe (a, m a) -> m a
class MonadPlus m => MonadLogic m where
Minimal implementation: msplit
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

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.
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reflect :: MonadLogic m => Maybe (a, m a) -> m a

The inverse of msplit. Satisfies the following law:

 msplit m >>= reflect == m
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