fgl-5.4.2.4: Martin Erwig's Functional Graph Library

Safe Haskell | None

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)Source

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

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

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

# Graph Transformer Monad

data GT m g a Source

Constructors

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

Instances

Monad m => Monad (GT m g) |

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 aSource

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

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

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

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

# 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) dSource

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) dSource

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

# 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