Logic

Logic

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.

observeAll :: Logic a -> [a]

Extracts all results from a Logic computation.

LogicT

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

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

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

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

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

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)

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

MonadIO m => MonadIO (LogicT m)

Defined in Control.Monad.Logic

Methods

liftIO :: IO 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

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.

MonadLogic

class MonadPlus m => MonadLogic (m :: * -> *)

Minimal implementation: msplit

Minimal complete definition

msplit

Instances

MonadLogic []

Defined in Control.Monad.Logic.Class

Methods

msplit :: [a] -> [Maybe (a, [a])]

interleave :: [a] -> [a] -> [a]

(>>-) :: [a] -> (a -> [b]) -> [b]

ifte :: [a] -> (a -> [b]) -> [b] -> [b]

once :: [a] -> [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

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

Defined in Control.Monad.Logic.Class

Methods

msplit :: WriterT w m a -> WriterT w m (Maybe (a, WriterT w m a))

interleave :: WriterT w m a -> WriterT w m a -> WriterT w m a

(>>-) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b

ifte :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b -> WriterT w m b

once :: WriterT w m a -> WriterT w m a

MonadLogic m => MonadLogic (StateT s m)

Defined in Control.Monad.Logic.Class

Methods

msplit :: StateT s m a -> StateT s m (Maybe (a, StateT s m a))

interleave :: StateT s m a -> StateT s m a -> StateT s m a

(>>-) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b

ifte :: StateT s m a -> (a -> StateT s m b) -> StateT s m b -> StateT s m b

once :: StateT s m a -> StateT s m a

MonadLogic m => MonadLogic (StateT s m)

Defined in Control.Monad.Logic.Class

Methods

msplit :: StateT s m a -> StateT s m (Maybe (a, StateT s m a))

interleave :: StateT s m a -> StateT s m a -> StateT s m a

(>>-) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b

ifte :: StateT s m a -> (a -> StateT s m b) -> StateT s m b -> StateT s m b

once :: StateT s m a -> StateT s m a

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

Defined in Control.Monad.Logic.Class

Methods

msplit :: WriterT w m a -> WriterT w m (Maybe (a, WriterT w m a))

interleave :: WriterT w m a -> WriterT w m a -> WriterT w m a

(>>-) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b

ifte :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b -> WriterT w m b

once :: WriterT w m a -> WriterT w m a

MonadLogic m => MonadLogic (ReaderT e m)

Defined in Control.Monad.Logic.Class

Methods

msplit :: ReaderT e m a -> ReaderT e m (Maybe (a, ReaderT e m a))

interleave :: ReaderT e m a -> ReaderT e m a -> ReaderT e m a

(>>-) :: ReaderT e m a -> (a -> ReaderT e m b) -> ReaderT e m b

ifte :: ReaderT e m a -> (a -> ReaderT e m b) -> ReaderT e m b -> ReaderT e m b

once :: ReaderT e m a -> ReaderT e m a

msplit :: MonadLogic m => 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 :: MonadLogic m => 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

(>>-) :: MonadLogic m => 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 :: MonadLogic m => 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 :: MonadLogic m => 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.

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 ().