Control.Monad.Logic

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://okmij.org/ftp/papers/LogicT.pdf).

Documentation

module Control.Monad.Logic.Class

The Logic monad

type Logic = LogicT Identity

The basic Logic monad, for performing backtracking computations returning values of type a.

logic :: (forall r. (a -> r -> r) -> r -> r) -> Logic a

A smart constructor for Logic computations.

runLogic :: Logic a -> (a -> r -> r) -> r -> r

Runs a Logic computation with the specified initial success and failure continuations.

observe :: Logic a -> a

Extracts the first result from a Logic computation.

observeMany :: Int -> Logic a -> [a]

Extracts up to a given number of results from a Logic computation.

observeAll :: Logic a -> [a]

Extracts all results from a Logic computation.

The LogicT monad transformer

newtype LogicT m a

A monad transformer for performing backtracking computations layered over another monad m.

Constructors

LogicT

Fields

• unLogicT :: forall r. (a -> m r -> m r) -> m r -> m r

Instances

MonadTrans LogicT

Defined in Control.Monad.Logic

Methods

lift :: Monad m => m a -> LogicT m a

MonadState s m => MonadState s (LogicT m)

Defined in Control.Monad.Logic

Methods

get :: LogicT m s

put :: s -> LogicT m ()

state :: (s -> (a, s)) -> LogicT m a

MonadReader r m => MonadReader r (LogicT m)

Defined in Control.Monad.Logic

Methods

ask :: LogicT m r

local :: (r -> r) -> LogicT m a -> LogicT m a

reader :: (r -> a) -> LogicT m a

MonadError e m => MonadError e (LogicT m)

Defined in Control.Monad.Logic

Methods

throwError :: e -> LogicT m a

catchError :: LogicT m a -> (e -> LogicT m a) -> LogicT m a

Monad (LogicT m)

Defined in Control.Monad.Logic

Methods

(>>=) :: LogicT m a -> (a -> LogicT m b) -> LogicT m b

(>>) :: LogicT m a -> LogicT m b -> LogicT m b

return :: a -> LogicT m a

fail :: String -> LogicT m a

Functor (LogicT f)

Defined in Control.Monad.Logic

Methods

fmap :: (a -> b) -> LogicT f a -> LogicT f b

(<$) :: a -> LogicT f b -> LogicT f a

MonadFail (LogicT m)

Defined in Control.Monad.Logic

Methods

fail :: String -> LogicT m a

Applicative (LogicT f)

Defined in Control.Monad.Logic

Methods

pure :: a -> LogicT f a

(<*>) :: LogicT f (a -> b) -> LogicT f a -> LogicT f b

liftA2 :: (a -> b -> c) -> LogicT f a -> LogicT f b -> LogicT f c

(*>) :: LogicT f a -> LogicT f b -> LogicT f b

(<*) :: LogicT f a -> LogicT f b -> LogicT f a

(Monad m, Foldable m) => Foldable (LogicT m)

Defined in Control.Monad.Logic

Methods

fold :: Monoid m0 => LogicT m m0 -> m0

foldMap :: Monoid m0 => (a -> m0) -> LogicT m a -> m0

foldr :: (a -> b -> b) -> b -> LogicT m a -> b

foldr' :: (a -> b -> b) -> b -> LogicT m a -> b

foldl :: (b -> a -> b) -> b -> LogicT m a -> b

foldl' :: (b -> a -> b) -> b -> LogicT m a -> b

foldr1 :: (a -> a -> a) -> LogicT m a -> a

foldl1 :: (a -> a -> a) -> LogicT m a -> a

toList :: LogicT m a -> [a]

null :: LogicT m a -> Bool

length :: LogicT m a -> Int

elem :: Eq a => a -> LogicT m a -> Bool

maximum :: Ord a => LogicT m a -> a

minimum :: Ord a => LogicT m a -> a

sum :: Num a => LogicT m a -> a

product :: Num a => LogicT m a -> a

Foldable (LogicT Identity)

Defined in Control.Monad.Logic

Methods

fold :: Monoid m => LogicT Identity m -> m

foldMap :: Monoid m => (a -> m) -> LogicT Identity a -> m

foldr :: (a -> b -> b) -> b -> LogicT Identity a -> b

foldr' :: (a -> b -> b) -> b -> LogicT Identity a -> b

foldl :: (b -> a -> b) -> b -> LogicT Identity a -> b

foldl' :: (b -> a -> b) -> b -> LogicT Identity a -> b

foldr1 :: (a -> a -> a) -> LogicT Identity a -> a

foldl1 :: (a -> a -> a) -> LogicT Identity a -> a

toList :: LogicT Identity a -> [a]

null :: LogicT Identity a -> Bool

length :: LogicT Identity a -> Int

elem :: Eq a => a -> LogicT Identity a -> Bool

maximum :: Ord a => LogicT Identity a -> a

minimum :: Ord a => LogicT Identity a -> a

sum :: Num a => LogicT Identity a -> a

product :: Num a => LogicT Identity a -> a

Traversable (LogicT Identity)

Defined in Control.Monad.Logic

Methods

traverse :: Applicative f => (a -> f b) -> LogicT Identity a -> f (LogicT Identity b)

sequenceA :: Applicative f => LogicT Identity (f a) -> f (LogicT Identity a)

mapM :: Monad m => (a -> m b) -> LogicT Identity a -> m (LogicT Identity b)

sequence :: Monad m => LogicT Identity (m a) -> m (LogicT Identity a)

MonadIO m => MonadIO (LogicT m)

Defined in Control.Monad.Logic

Methods

liftIO :: IO a -> LogicT m a

Alternative (LogicT f)

Defined in Control.Monad.Logic

Methods

empty :: LogicT f a

(<|>) :: LogicT f a -> LogicT f a -> LogicT f a

some :: LogicT f a -> LogicT f [a]

many :: LogicT f a -> LogicT f [a]

MonadPlus (LogicT m)

Defined in Control.Monad.Logic

Methods

mzero :: LogicT m a

mplus :: LogicT m a -> LogicT m a -> LogicT m a

Monad m => MonadLogic (LogicT m)

Defined in Control.Monad.Logic

Methods

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

interleave :: LogicT m a -> LogicT m a -> LogicT m a

(>>-) :: LogicT m a -> (a -> LogicT m b) -> LogicT m b

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

once :: LogicT m a -> LogicT m a

lnot :: LogicT m a -> LogicT m ()

Semigroup (LogicT m a)

Defined in Control.Monad.Logic

Methods

(<>) :: LogicT m a -> LogicT m a -> LogicT m a

sconcat :: NonEmpty (LogicT m a) -> LogicT m a

stimes :: Integral b => b -> LogicT m a -> LogicT m a

Monoid (LogicT m a)

Defined in Control.Monad.Logic

Methods

mempty :: LogicT m a

mappend :: LogicT m a -> LogicT m a -> LogicT m a

mconcat :: [LogicT m a] -> LogicT m a

runLogicT :: LogicT m a -> (a -> m r -> m r) -> m r -> m r

Runs a LogicT computation with the specified initial success and failure continuations.

observeT :: Monad m => LogicT m a -> m a

Extracts the first result from a LogicT computation, failing otherwise.

observeManyT :: Monad m => Int -> LogicT m a -> m [a]

Extracts up to a given number of results from a LogicT computation.

observeAllT :: Monad m => LogicT m a -> m [a]

Extracts all results from a LogicT computation.

module Control.Monad

module Control.Monad.Trans