Safe Haskell	Safe
Language	Haskell2010

Math.Graph.InGraphMonad

Contents

Orphan instances

Description

This module provides ability to inspect graph data in a specialized monad.

Examples: let example1 = reversibleCompleteG ["a","b","c"] (\a b -> (a ++ b, b ++ a))

show example1 == "([a, b, c] ; [aa = a <-> a, ba / ab = b <-> a, bb = b <-> b, ca / ac = c <-> a, cb / bc = c <-> b, cc = c <-> c])"

example1 `inGraphM` edgesEndingToM "a" == return (fromList ["aa","ba","ca"])

example1 `inGraphM` verticesM == return (fromList ["a","b","c"])

example1 `inGraphM` edgesM == return (fromList ["aa","ab","ac","ba","bb","bc","ca","cb","cc"])

example1 `inGraphM` do { x <- sourceM "ab" ; y <- targetM "ab" ; return (x,y) } == return ("a","b")

Synopsis

newtype InGraphM mon e m a = InGraphM {
- runInGraphM :: ReaderT (Graph mon e) m a
}
inGraphM_bind :: Monad m => InGraphM mon e m a -> (a -> InGraphM mon e m b) -> InGraphM mon e m b
inGraphM_return :: Monad m => a -> InGraphM mon e m a
inGraphM :: Graph mon e -> InGraphM mon e m a -> m a
currentGraphM :: Monad m => InGraphM mon e m (Graph mon e)
actM :: Monad m => e -> mon Bool Bool -> InGraphM mon e m e
actSetM :: (Monad m, Ord e) => Set e -> mon Bool Bool -> InGraphM mon e m (Set e)
elementsM :: (Monad m, Ord e) => InGraphM mon e m (Set e)
borderM :: (GraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m (e, e)
reversibleBorderM :: (ReversibleGraphMonoid mon Bool, Monad m, Ord e) => e -> InGraphM mon e m (e, e)
verticesM :: (Ord e, GraphMonoid mon Bool, Monad m) => InGraphM mon e m (Set e)
edgesM :: (Ord e, GraphMonoid mon Bool, Monad m) => InGraphM mon e m (Set e)
nodesLinkedFromM :: (Monad m, Ord e, GraphMonoid mon Bool) => e -> InGraphM mon e m (Set e)
edgesStartingFromM :: (Monad m, Ord e, GraphMonoid mon Bool) => e -> InGraphM mon e m (Set e)
edgesEndingToM :: (Monad m, Ord e, GraphMonoid mon Bool) => e -> InGraphM mon e m (Set e)
linksM :: (Monad m, Ord e, GraphMonoid mon Bool) => InGraphM mon e m (Set (e, e, e))
reversibleLinksM :: (Monad m, Ord e, ReversibleGraphMonoid mon Bool) => InGraphM mon e m (Set ((e, e), (e, e)))
sourceM :: (GraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m e
targetM :: (GraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m e
inverseM :: (ReversibleGraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m e
isSourceVertexM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool
isTargetVertexM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool
isVertexM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool
isEdgeM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool
hasPathM :: (GraphMonoid mon Bool, Monad m, Eq e) => [e] -> InGraphM mon e m Bool
isEdgeBetweenM :: (Monad m, GraphMonoid mon Bool, Eq e) => e -> e -> e -> InGraphM mon e m Bool
isLoopM :: (Eq e, Monad m, GraphMonoid mon Bool) => e -> InGraphM mon e m Bool
isOneLaneLoopM :: (Eq e, Monad m, ReversibleGraphMonoid mon Bool) => e -> InGraphM mon e m Bool
isBandM :: (Eq e, Monad m, ReversibleGraphMonoid mon Bool) => e -> InGraphM mon e m Bool
liftReaderGraph :: (Monad m, MonadTrans t, MonadReader (Graph mon e) (t m)) => InGraphM mon e m a -> t m a

Documentation

newtype InGraphM mon e m a Source #

Constructors

InGraphM
Fields runInGraphM :: ReaderT (Graph mon e) m a

Instances

Instances details

MonadWriter w m => MonadWriter w (InGraphM mon e m) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods writer :: (a, w) -> InGraphM mon e m a # tell :: w -> InGraphM mon e m () # listen :: InGraphM mon e m a -> InGraphM mon e m (a, w) # pass :: InGraphM mon e m (a, w -> w) -> InGraphM mon e m a #
MonadTrans (InGraphM mon e) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods lift :: Monad m => m a -> InGraphM mon e m a #
Monad m => MonadReader (Graph mon e) (InGraphM mon e m) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods ask :: InGraphM mon e m (Graph mon e) # local :: (Graph mon e -> Graph mon e) -> InGraphM mon e m a -> InGraphM mon e m a # reader :: (Graph mon e -> a) -> InGraphM mon e m a #
MonadIO m => MonadIO (InGraphM mon e m) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods liftIO :: IO a -> InGraphM mon e m a #
Applicative m => Applicative (InGraphM mon e m) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods pure :: a -> InGraphM mon e m a # (<>) :: InGraphM mon e m (a -> b) -> InGraphM mon e m a -> InGraphM mon e m b # liftA2 :: (a -> b -> c) -> InGraphM mon e m a -> InGraphM mon e m b -> InGraphM mon e m c # (>) :: InGraphM mon e m a -> InGraphM mon e m b -> InGraphM mon e m b # (<*) :: InGraphM mon e m a -> InGraphM mon e m b -> InGraphM mon e m a #
Functor m => Functor (InGraphM mon e m) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods fmap :: (a -> b) -> InGraphM mon e m a -> InGraphM mon e m b # (<$) :: a -> InGraphM mon e m b -> InGraphM mon e m a #
Monad m => Monad (InGraphM mon e m) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods (>>=) :: InGraphM mon e m a -> (a -> InGraphM mon e m b) -> InGraphM mon e m b # (>>) :: InGraphM mon e m a -> InGraphM mon e m b -> InGraphM mon e m b # return :: a -> InGraphM mon e m a #
(GraphMonoid mon Bool, Monad m, Ord e) => GraphMonad (InGraphM mon e m) e Source #
Instance details Defined in Math.Graph.InGraphMonad Methods gisVertex :: e -> InGraphM mon e m Bool Source # gsource :: e -> InGraphM mon e m e Source # gtarget :: e -> InGraphM mon e m e Source # gelements :: InGraphM mon e m (Set e) Source # gvertices :: InGraphM mon e m (Set e) Source # gedges :: InGraphM mon e m (Set e) Source # gedgesStartingFrom :: e -> InGraphM mon e m (Set e) Source # gedgesEndingTo :: e -> InGraphM mon e m (Set e) Source # glinks :: InGraphM mon e m (Set (e, e, e)) Source # gloops :: InGraphM mon e m (Set e) Source # gisLoop :: e -> InGraphM mon e m Bool Source # gisEdgeBetween :: e -> e -> e -> InGraphM mon e m Bool Source #
(ReversibleGraphMonoid mon Bool, Monad m, Ord e) => ReversibleGraphMonad (InGraphM mon e m) e Source #
Instance details Defined in Math.Graph.InGraphMonad Methods ginverse :: e -> InGraphM mon e m e Source # greversibleLinks :: InGraphM mon e m (Set ((e, e), (e, e))) Source # goneLaneLoops :: InGraphM mon e m (Set e) Source # gisOneLaneLoop :: e -> InGraphM mon e m Bool Source #
(Monoid a, Applicative m) => Monoid (InGraphM mon e m a) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods mempty :: InGraphM mon e m a # mappend :: InGraphM mon e m a -> InGraphM mon e m a -> InGraphM mon e m a # mconcat :: [InGraphM mon e m a] -> InGraphM mon e m a #
(Applicative m, Semigroup a) => Semigroup (InGraphM mon e m a) Source #
Instance details Defined in Math.Graph.InGraphMonad Methods (<>) :: InGraphM mon e m a -> InGraphM mon e m a -> InGraphM mon e m a # sconcat :: NonEmpty (InGraphM mon e m a) -> InGraphM mon e m a # stimes :: Integral b => b -> InGraphM mon e m a -> InGraphM mon e m a #

inGraphM_bind :: Monad m => InGraphM mon e m a -> (a -> InGraphM mon e m b) -> InGraphM mon e m b Source #

inGraphM_return :: Monad m => a -> InGraphM mon e m a Source #

inGraphM :: Graph mon e -> InGraphM mon e m a -> m a Source #

currentGraphM :: Monad m => InGraphM mon e m (Graph mon e) Source #

actM :: Monad m => e -> mon Bool Bool -> InGraphM mon e m e Source #

actSetM :: (Monad m, Ord e) => Set e -> mon Bool Bool -> InGraphM mon e m (Set e) Source #

elementsM :: (Monad m, Ord e) => InGraphM mon e m (Set e) Source #

borderM :: (GraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m (e, e) Source #

reversibleBorderM :: (ReversibleGraphMonoid mon Bool, Monad m, Ord e) => e -> InGraphM mon e m (e, e) Source #

verticesM :: (Ord e, GraphMonoid mon Bool, Monad m) => InGraphM mon e m (Set e) Source #

edgesM :: (Ord e, GraphMonoid mon Bool, Monad m) => InGraphM mon e m (Set e) Source #

nodesLinkedFromM :: (Monad m, Ord e, GraphMonoid mon Bool) => e -> InGraphM mon e m (Set e) Source #

edgesStartingFromM :: (Monad m, Ord e, GraphMonoid mon Bool) => e -> InGraphM mon e m (Set e) Source #

edgesEndingToM :: (Monad m, Ord e, GraphMonoid mon Bool) => e -> InGraphM mon e m (Set e) Source #

linksM :: (Monad m, Ord e, GraphMonoid mon Bool) => InGraphM mon e m (Set (e, e, e)) Source #

reversibleLinksM :: (Monad m, Ord e, ReversibleGraphMonoid mon Bool) => InGraphM mon e m (Set ((e, e), (e, e))) Source #

sourceM :: (GraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m e Source #

targetM :: (GraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m e Source #

inverseM :: (ReversibleGraphMonoid mon Bool, Monad m) => e -> InGraphM mon e m e Source #

isSourceVertexM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool Source #

isTargetVertexM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool Source #

equally valid implementation. These are equivalent in normal graphs because Bool -> Bool structure has 4 elements, which are related by not operation which switches source and target. From Lawvere,Rosebrugh: Sets for Mathematics, Exercise 10.29. Note however that we are not requiring ReversibleGraphMonoid, which actually contains this not operation. This is a reason to separate these three operations (isSourceVertexM, isTargetVertexM, isVertexM) when digraphs are used.

The left action of the monoid causes the following constraints: In particular, these are valid when the monoid is on the two-element set:

source . target == source

target . source == target

source . source == source

target . target == target

Due to the first two, it's not necessary to distinguish these operations.

isVertexM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool Source #

isEdgeM :: (GraphMonoid mon Bool, Monad m, Eq e) => e -> InGraphM mon e m Bool Source #

hasPathM :: (GraphMonoid mon Bool, Monad m, Eq e) => [e] -> InGraphM mon e m Bool Source #

isEdgeBetweenM :: (Monad m, GraphMonoid mon Bool, Eq e) => e -> e -> e -> InGraphM mon e m Bool Source #

isLoopM :: (Eq e, Monad m, GraphMonoid mon Bool) => e -> InGraphM mon e m Bool Source #

isOneLaneLoopM :: (Eq e, Monad m, ReversibleGraphMonoid mon Bool) => e -> InGraphM mon e m Bool Source #

isBandM :: (Eq e, Monad m, ReversibleGraphMonoid mon Bool) => e -> InGraphM mon e m Bool Source #

liftReaderGraph :: (Monad m, MonadTrans t, MonadReader (Graph mon e) (t m)) => InGraphM mon e m a -> t m a Source #

Orphan instances

(Ord a, GraphMonoid m Bool) => Visitor (Graph m a) Source #
Instance details Associated Types data Fold (Graph m a) :: Type -> Type Source # Methods visit :: Fold (Graph m a) a0 -> Graph m a -> a0 Source #
(Monad m, Ord e, GraphMonoid mon Bool) => GraphMonad (ReaderT (Graph mon e) m) e Source #
Instance details Methods gisVertex :: e -> ReaderT (Graph mon e) m Bool Source # gsource :: e -> ReaderT (Graph mon e) m e Source # gtarget :: e -> ReaderT (Graph mon e) m e Source # gelements :: ReaderT (Graph mon e) m (Set e) Source # gvertices :: ReaderT (Graph mon e) m (Set e) Source # gedges :: ReaderT (Graph mon e) m (Set e) Source # gedgesStartingFrom :: e -> ReaderT (Graph mon e) m (Set e) Source # gedgesEndingTo :: e -> ReaderT (Graph mon e) m (Set e) Source # glinks :: ReaderT (Graph mon e) m (Set (e, e, e)) Source # gloops :: ReaderT (Graph mon e) m (Set e) Source # gisLoop :: e -> ReaderT (Graph mon e) m Bool Source # gisEdgeBetween :: e -> e -> e -> ReaderT (Graph mon e) m Bool Source #
(Monad m, Ord e, ReversibleGraphMonoid mon Bool) => ReversibleGraphMonad (ReaderT (Graph mon e) m) e Source #
Instance details Methods ginverse :: e -> ReaderT (Graph mon e) m e Source # greversibleLinks :: ReaderT (Graph mon e) m (Set ((e, e), (e, e))) Source # goneLaneLoops :: ReaderT (Graph mon e) m (Set e) Source # gisOneLaneLoop :: e -> ReaderT (Graph mon e) m Bool Source #