Copyright | (c) Dan Doel |
---|---|

License | BSD3 |

Maintainer | dan.doel@gmail.com |

Stability | experimental |

Portability | non-portable (multi-parameter type classes) |

Safe Haskell | Safe |

Language | Haskell98 |

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)

## Synopsis

- class MonadPlus m => MonadLogic m where
- reflect :: MonadLogic m => Maybe (a, m a) -> m a
- lnot :: MonadLogic m => m a -> m ()

# Documentation

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 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)

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

MonadLogic [] # | |

Monad m => MonadLogic (LogicT m) # | |

Defined in Control.Monad.Logic | |

MonadLogic m => MonadLogic (ReaderT e m) # | |

Defined in Control.Monad.Logic.Class | |

MonadLogic m => MonadLogic (StateT s m) # | |

Defined in Control.Monad.Logic.Class | |

MonadLogic m => MonadLogic (StateT s m) # | |

Defined in Control.Monad.Logic.Class | |

(MonadLogic m, Monoid w) => MonadLogic (WriterT w m) # | |

Defined in Control.Monad.Logic.Class | |

(MonadLogic m, Monoid w) => MonadLogic (WriterT w m) # | |

Defined in Control.Monad.Logic.Class |

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

The inverse of msplit. Satisfies the following law:

msplit m >>= reflect == m

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

.