fgl-5.5.3.0: Martin Erwig's Functional Graph Library

Description

Synopsis

# Additional Graph Utilities

mapFst :: (a -> b) -> (a, c) -> (b, c) Source #

mapSnd :: (a -> b) -> (c, a) -> (c, b) Source #

(><) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) infixr 8 Source #

orP :: (a -> Bool) -> (b -> Bool) -> (a, b) -> Bool Source #

# Graph Transformer Monad

newtype GT m g a Source #

Constructors

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

Instances

 Monad m => Monad (GT m g) Source # Methods(>>=) :: GT m g a -> (a -> GT m g b) -> GT m g b #(>>) :: GT m g a -> GT m g b -> GT m g b #return :: a -> GT m g a #fail :: String -> GT m g a # Monad m => Functor (GT m g) Source # Methodsfmap :: (a -> b) -> GT m g a -> GT m g b #(<\$) :: a -> GT m g b -> GT m g a # Monad m => Applicative (GT m g) Source # Methodspure :: a -> GT m g a #(<*>) :: GT m g (a -> b) -> GT m g a -> GT m g b #(*>) :: GT m g a -> GT m g b -> GT m g b #(<*) :: GT m g a -> GT m g b -> GT m g a #

apply :: GT m g a -> m g -> m (a, g) Source #

apply' :: Monad m => GT m g a -> g -> m (a, g) Source #

applyWith :: Monad m => (a -> b) -> GT m g a -> m g -> m (b, g) Source #

applyWith' :: Monad m => (a -> b) -> GT m g a -> g -> m (b, g) Source #

runGT :: Monad m => GT m g a -> m g -> m a Source #

condMGT' :: Monad m => (s -> Bool) -> GT m s a -> GT m s a -> GT m s a Source #

recMGT' :: Monad m => (s -> Bool) -> GT m s a -> (a -> b -> b) -> b -> GT m s b Source #

condMGT :: Monad m => (m s -> m Bool) -> GT m s a -> GT m s a -> GT m s a Source #

recMGT :: Monad m => (m s -> m Bool) -> GT m s a -> (a -> b -> b) -> b -> GT m s b Source #

# Graph Computations Based on Graph Monads

## Monadic Graph Accessing Functions

getNode :: GraphM m gr => GT m (gr a b) Node Source #

getContext :: GraphM m gr => GT m (gr a b) (Context a b) Source #

getNodes' :: (Graph gr, GraphM m gr) => GT m (gr a b) [Node] Source #

getNodes :: GraphM m gr => GT m (gr a b) [Node] Source #

sucGT :: GraphM m gr => Node -> GT m (gr a b) (Maybe [Node]) Source #

sucM :: GraphM m gr => Node -> m (gr a b) -> m (Maybe [Node]) Source #

## Derived Graph Recursion Operators

graphRec :: GraphM m gr => GT m (gr a b) c -> (c -> d -> d) -> d -> GT m (gr a b) d Source #

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 Source #

graphUFold :: GraphM m gr => (Context a b -> c -> c) -> c -> GT m (gr a b) c Source #

# Examples: Graph Algorithms as Instances of Recursion Operators

## Instances of graphRec

graphNodesM0 :: GraphM m gr => GT m (gr a b) [Node] Source #

graphNodesM :: GraphM m gr => GT m (gr a b) [Node] Source #

graphNodes :: GraphM m gr => m (gr a b) -> m [Node] Source #

graphFilterM :: GraphM m gr => (Context a b -> Bool) -> GT m (gr a b) [Context a b] Source #

graphFilter :: GraphM m gr => (Context a b -> Bool) -> m (gr a b) -> m [Context a b] Source #

# Example: Monadic DFS Algorithm(s)

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

Monadic graph algorithms are defined in two steps:

1. 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] Source #

depth-first search yielding number of nodes

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

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

depth-first search yielding dfs forest

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

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