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Data.Graph.Inductive.Query.Monad
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
Monadic Graph Algorithms
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]
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]
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