Additional Graph Utilities

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

Graph Transformer Monad

data GT m g a

Constructors

MGT (m g -> m (a, g))

Instances

Monad m => Monad (GT m 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

Graph Computations Based on Graph Monads

Monadic Graph Accessing Functions

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]

Example: Monadic DFS Algorithm(s)

dfsGT :: GraphM m gr => [Node] -> GT m (gr a b) [Node]

Monadic graph algorithms are defined in two steps:

define the (possibly parameterized) graph transformer (e.g., dfsGT) (2) run the graph transformer (applied to arguments) (e.g., dfsM)

dfsM :: GraphM m gr => [Node] -> m (gr a b) -> m [Node]

depth-first search yielding number of nodes

dfsM' :: GraphM m gr => m (gr a b) -> m [Node]

dffM :: GraphM m gr => [Node] -> GT m (gr a b) [Tree Node]

depth-first search yielding dfs forest

graphDff :: GraphM m gr => [Node] -> m (gr a b) -> m [Tree Node]

graphDff' :: GraphM m gr => m (gr a b) -> m [Tree Node]