logict- A backtracking logic-programming monad.

Copyright(c) Dan Doel
Portabilitynon-portable (multi-parameter type classes)
Safe HaskellSafe-Inferred



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 Source

Minimal implementation: msplit

Minimal complete definition



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

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 Source

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 Source

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 Source

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 Source

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

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

The inverse of msplit. Satisfies the following law:

msplit m >>= reflect == m

lnot :: MonadLogic m => m a -> m () Source

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