Contents Additional Graph Utilities Graph Transformer Monad Graph Computations Based on Graph Monads Monadic Graph Accessing Functions Derived Graph Recursion Operators Examples: Graph Algorithms as Instances of Recursion Operators Instances of graphRec Example: Monadic DFS Algorithm(s)
Description
Synopsis
 mapFst :: (a -> b) -> (a, c) -> (b, c) mapSnd :: (a -> b) -> (c, a) -> (c, b) (><) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) orP :: (a -> Bool) -> (b -> Bool) -> (a, b) -> Bool data GT m g a = MGT (m g -> m (a, g)) apply :: GT m g a -> m g -> m (a, g) apply' :: Monad m => GT m g a -> g -> m (a, g) applyWith :: Monad m => (a -> b) -> GT m g a -> m g -> m (b, g) applyWith' :: Monad m => (a -> b) -> GT m g a -> g -> m (b, g) runGT :: Monad m => GT m g a -> m g -> m a condMGT' :: Monad m => (s -> Bool) -> GT m s a -> GT m s a -> GT m s a recMGT' :: Monad m => (s -> Bool) -> GT m s a -> (a -> b -> b) -> b -> GT m s b condMGT :: Monad m => (m s -> m Bool) -> GT m s a -> GT m s a -> GT m s a recMGT :: Monad m => (m s -> m Bool) -> GT m s a -> (a -> b -> b) -> b -> GT m s b getNode :: GraphM m gr => GT m (gr a b) Node getContext :: GraphM m gr => GT m (gr a b) (Context a b) getNodes' :: (Graph gr, GraphM m gr) => GT m (gr a b) [Node] getNodes :: GraphM m gr => GT m (gr a b) [Node] sucGT :: GraphM m gr => Node -> GT m (gr a b) (Maybe [Node]) sucM :: GraphM m gr => Node -> m (gr a b) -> m (Maybe [Node]) graphRec :: GraphM m gr => GT m (gr a b) c -> (c -> d -> d) -> d -> GT m (gr a b) d graphRec' :: (Graph gr, GraphM m gr) => GT m (gr a b) c -> (c -> d -> d) -> d -> GT m (gr a b) d graphUFold :: GraphM m gr => (Context a b -> c -> c) -> c -> GT m (gr a b) c graphNodesM0 :: GraphM m gr => GT m (gr a b) [Node] graphNodesM :: GraphM m gr => GT m (gr a b) [Node] graphNodes :: GraphM m gr => m (gr a b) -> m [Node] graphFilterM :: GraphM m gr => (Context a b -> Bool) -> GT m (gr a b) [Context a b] graphFilter :: GraphM m gr => (Context a b -> Bool) -> m (gr a b) -> m [Context a b] dfsGT :: GraphM m gr => [Node] -> GT m (gr a b) [Node] dfsM :: GraphM m gr => [Node] -> m (gr a b) -> m [Node] dfsM' :: GraphM m gr => m (gr a b) -> m [Node] dffM :: GraphM m gr => [Node] -> GT m (gr a b) [Tree Node] graphDff :: GraphM m gr => [Node] -> m (gr a b) -> m [Tree Node] graphDff' :: GraphM m gr => m (gr a b) -> m [Tree Node]
mapFst :: (a -> b) -> (a, c) -> (b, c)
mapSnd :: (a -> b) -> (c, a) -> (c, b)
(><) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)
orP :: (a -> Bool) -> (b -> Bool) -> (a, b) -> Bool
data GT m g a
Constructors
 MGT (m g -> m (a, g))
Instances
apply :: GT m g a -> m g -> m (a, g)
apply' :: Monad m => GT m g a -> g -> m (a, g)
applyWith :: Monad m => (a -> b) -> GT m g a -> m g -> m (b, g)
applyWith' :: Monad m => (a -> b) -> GT m g a -> g -> m (b, g)
runGT :: Monad m => GT m g a -> m g -> m a
condMGT' :: Monad m => (s -> Bool) -> GT m s a -> GT m s a -> GT m s a
recMGT' :: Monad m => (s -> Bool) -> GT m s a -> (a -> b -> b) -> b -> GT m s b
condMGT :: Monad m => (m s -> m Bool) -> GT m s a -> GT m s a -> GT m s a
recMGT :: Monad m => (m s -> m Bool) -> GT m s a -> (a -> b -> b) -> b -> GT m s b
Graph Computations Based on Graph Monads
getNode :: GraphM m gr => GT m (gr a b) Node
getContext :: GraphM m gr => GT m (gr a b) (Context a b)
getNodes' :: (Graph gr, GraphM m gr) => GT m (gr a b) [Node]
getNodes :: GraphM m gr => GT m (gr a b) [Node]
sucGT :: GraphM m gr => Node -> GT m (gr a b) (Maybe [Node])
sucM :: GraphM m gr => Node -> m (gr a b) -> m (Maybe [Node])
Derived Graph Recursion Operators
graphRec :: GraphM m gr => GT m (gr a b) c -> (c -> d -> d) -> d -> GT m (gr a b) d
encapsulates a simple recursion schema on graphs
graphRec' :: (Graph gr, GraphM m gr) => GT m (gr a b) c -> (c -> d -> d) -> d -> GT m (gr a b) d
graphUFold :: GraphM m gr => (Context a b -> c -> c) -> c -> GT m (gr a b) c
Examples: Graph Algorithms as Instances of Recursion Operators
Instances of graphRec
graphNodesM0 :: GraphM m gr => GT m (gr a b) [Node]
graphNodesM :: GraphM m gr => GT m (gr a b) [Node]
graphNodes :: GraphM m gr => m (gr a b) -> m [Node]
graphFilterM :: GraphM m gr => (Context a b -> Bool) -> GT m (gr a b) [Context a b]
graphFilter :: GraphM m gr => (Context a b -> Bool) -> m (gr a b) -> m [Context a b]