Props.Internal.PropT

Documentation

type Prop a = PropT Identity a

Pure version of PropT

data PropT m a

A monad transformer for setting up constraint problems.

Instances

MonadTrans PropT

Defined in Props.Internal.PropT

Methods

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

Monad m => Monad (PropT m)

Defined in Props.Internal.PropT

Methods

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

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

return :: a -> PropT m a

fail :: String -> PropT m a

Functor m => Functor (PropT m)

Defined in Props.Internal.PropT

Methods

fmap :: (a -> b) -> PropT m a -> PropT m b

(<$) :: a -> PropT m b -> PropT m a

Monad m => Applicative (PropT m)

Defined in Props.Internal.PropT

Methods

pure :: a -> PropT m a

(<*>) :: PropT m (a -> b) -> PropT m a -> PropT m b

liftA2 :: (a -> b -> c) -> PropT m a -> PropT m b -> PropT m c

(*>) :: PropT m a -> PropT m b -> PropT m b

(<*) :: PropT m a -> PropT m b -> PropT m a

MonadIO m => MonadIO (PropT m)

Defined in Props.Internal.PropT

Methods

liftIO :: IO a -> PropT m a

newPVar :: (Monad m, Foldable f, Typeable f, Typeable a) => f a -> PropT m (PVar f a)

Used to create a new propagator variable within the setup for your problem.

f is any Foldable container which contains each of the possible states which the variable could take.

E.g. For a sudoku solver you would use newPVar to create a variable for each cell, passing a Set Int containing the numbers [1..9].

constrain :: Monad m => PVar f a -> PVar g b -> (a -> g b -> g b) -> PropT m ()

constrain the relationship between two PVars. Note that this is a ONE WAY relationship; e.g. constrain a b f will propagate constraints from a to b but not vice versa.

Given PVar f a and PVar g b as arguments, provide a function which will filter/alter the options in g according to the choice.

For a sudoku puzzle you'd have two Pvar Set Int's, each representing a cell on the board. You can constrain b to be a different value than a with the following call:

constrain a b $ \elementA setB -> S.delete elementA setB)

Take a look at some linking functions which are already provided: disjoint, equal, require

solveT :: forall m a r. Monad m => ((forall f x. PVar f x -> x) -> a -> r) -> PropT m a -> m (Maybe r)

Provide an initialization action which constrains the problem, and a finalizer, and solveT will return a result if one exists.

The finalizer is an annoyance caused by the fact that GHC does not yet support Impredicative Types.

For example, if you wrote a solution to the nQueens problem, you might run it like so:

-- Set up the problem for 'n' queens and return their PVar's as a list.
initNQueens :: Int -> Prop [PVar S.Set Coord]
initNQueens = ...

solution :: [Coord]
solution = solve (\readPVar vars -> fmap readPVar vars) (initNQueens 8)
-- or more simply:
solution = solve fmap (initNQueens 8)

which converts PVars into a result.Given an action which initializes and constrains a problem solveT will and returns some container of PVars, solveT will attempt to find a solution which passes all valid constraints.

solveAllT :: forall m a r. Monad m => ((forall f x. PVar f x -> x) -> a -> r) -> PropT m a -> m [r]

Like solveT, but finds ALL possible solutions. There will likely be duplicates.

solve :: forall a r. ((forall f x. PVar f x -> x) -> a -> r) -> Prop a -> Maybe r

Pure version of solveT

solveAll :: forall a r. ((forall f x. PVar f x -> x) -> a -> r) -> Prop a -> [r]

Pure version of solveAllT

readPVar :: Graph -> PVar f a -> a

data PVar (f :: * -> *) a

A propagator variable where the possible values a are contained in the container f.

Instances

Eq (PVar f a)

Nominal equality, Ignores contents

Defined in Props.Internal.PropT

Methods

(==) :: PVar f a -> PVar f a -> Bool

(/=) :: PVar f a -> PVar f a -> Bool

Ord (PVar f a)

Defined in Props.Internal.PropT

Methods

compare :: PVar f a -> PVar f a -> Ordering

(<) :: PVar f a -> PVar f a -> Bool

(<=) :: PVar f a -> PVar f a -> Bool

(>) :: PVar f a -> PVar f a -> Bool

(>=) :: PVar f a -> PVar f a -> Bool

max :: PVar f a -> PVar f a -> PVar f a

min :: PVar f a -> PVar f a -> PVar f a

Show (PVar f a)

Defined in Props.Internal.PropT

Methods

showsPrec :: Int -> PVar f a -> ShowS

show :: PVar f a -> String

showList :: [PVar f a] -> ShowS