Data.Graph.Inductive.Graph

fgl-5.8.3.0: Martin Erwig's Functional Graph Library

Safe Haskell | Safe-Inferred
Language | Haskell98

Data.Graph.Inductive.Graph

Contents

- General Type Defintions
  - Node and Edge Types
  - Types Supporting Inductive Graph View
- Graph Type Classes
- Operations
  - Graph Folds and Maps
  - Graph Projection
  - Graph Construction and Destruction
  - Subgraphs
  - Graph Inspection
  - Context Inspection
- Pretty-printing
- Ordering of Graphs

Description

Static and Dynamic Inductive Graphs

Synopsis

- type Node = Int
- type LNode a = (Node, a)
- type UNode = LNode ()
- type Edge = (Node, Node)
- type LEdge b = (Node, Node, b)
- type UEdge = LEdge ()
- type Adj b = [(b, Node)]
- type Context a b = (Adj b, Node, a, Adj b)
- type MContext a b = Maybe (Context a b)
- type Decomp (g :: Type -> Type -> Type) a b = (MContext a b, g a b)
- type GDecomp (g :: Type -> Type -> Type) a b = (Context a b, g a b)
- type UContext = ([Node], Node, [Node])
- type UDecomp g = (Maybe UContext, g)
- type Path = [Node]
- newtype LPath a = LP {
  - unLPath :: [LNode a]
  }
- type UPath = [UNode]
- class Graph (gr :: Type -> Type -> Type) where
  - empty :: gr a b
  - isEmpty :: gr a b -> Bool
  - match :: Node -> gr a b -> Decomp gr a b
  - mkGraph :: [LNode a] -> [LEdge b] -> gr a b
  - labNodes :: gr a b -> [LNode a]
  - matchAny :: gr a b -> GDecomp gr a b
  - noNodes :: gr a b -> Int
  - nodeRange :: gr a b -> (Node, Node)
  - labEdges :: gr a b -> [LEdge b]
- class Graph gr => DynGraph (gr :: Type -> Type -> Type) where
  - (&) :: Context a b -> gr a b -> gr a b
- insert :: DynGraph gr => Context a b -> gr a b -> gr a b
- order :: Graph gr => gr a b -> Int
- size :: Graph gr => gr a b -> Int
- ufold :: Graph gr => (Context a b -> c -> c) -> c -> gr a b -> c
- gmap :: DynGraph gr => (Context a b -> Context c d) -> gr a b -> gr c d
- nmap :: DynGraph gr => (a -> c) -> gr a b -> gr c b
- emap :: DynGraph gr => (b -> c) -> gr a b -> gr a c
- nemap :: DynGraph gr => (a -> c) -> (b -> d) -> gr a b -> gr c d
- nodes :: Graph gr => gr a b -> [Node]
- edges :: Graph gr => gr a b -> [Edge]
- toEdge :: LEdge b -> Edge
- edgeLabel :: LEdge b -> b
- toLEdge :: Edge -> b -> LEdge b
- newNodes :: Graph gr => Int -> gr a b -> [Node]
- gelem :: Graph gr => Node -> gr a b -> Bool
- insNode :: DynGraph gr => LNode a -> gr a b -> gr a b
- insEdge :: DynGraph gr => LEdge b -> gr a b -> gr a b
- delNode :: Graph gr => Node -> gr a b -> gr a b
- delEdge :: DynGraph gr => Edge -> gr a b -> gr a b
- delLEdge :: (DynGraph gr, Eq b) => LEdge b -> gr a b -> gr a b
- delAllLEdge :: (DynGraph gr, Eq b) => LEdge b -> gr a b -> gr a b
- insNodes :: DynGraph gr => [LNode a] -> gr a b -> gr a b
- insEdges :: DynGraph gr => [LEdge b] -> gr a b -> gr a b
- delNodes :: Graph gr => [Node] -> gr a b -> gr a b
- delEdges :: DynGraph gr => [Edge] -> gr a b -> gr a b
- buildGr :: DynGraph gr => [Context a b] -> gr a b
- mkUGraph :: Graph gr => [Node] -> [Edge] -> gr () ()
- gfiltermap :: DynGraph gr => (Context a b -> MContext c d) -> gr a b -> gr c d
- nfilter :: DynGraph gr => (Node -> Bool) -> gr a b -> gr a b
- labnfilter :: Graph gr => (LNode a -> Bool) -> gr a b -> gr a b
- labfilter :: DynGraph gr => (a -> Bool) -> gr a b -> gr a b
- subgraph :: DynGraph gr => [Node] -> gr a b -> gr a b
- context :: Graph gr => gr a b -> Node -> Context a b
- lab :: Graph gr => gr a b -> Node -> Maybe a
- neighbors :: Graph gr => gr a b -> Node -> [Node]
- lneighbors :: Graph gr => gr a b -> Node -> Adj b
- suc :: Graph gr => gr a b -> Node -> [Node]
- pre :: Graph gr => gr a b -> Node -> [Node]
- lsuc :: Graph gr => gr a b -> Node -> [(Node, b)]
- lpre :: Graph gr => gr a b -> Node -> [(Node, b)]
- out :: Graph gr => gr a b -> Node -> [LEdge b]
- inn :: Graph gr => gr a b -> Node -> [LEdge b]
- outdeg :: Graph gr => gr a b -> Node -> Int
- indeg :: Graph gr => gr a b -> Node -> Int
- deg :: Graph gr => gr a b -> Node -> Int
- hasEdge :: Graph gr => gr a b -> Edge -> Bool
- hasNeighbor :: Graph gr => gr a b -> Node -> Node -> Bool
- hasLEdge :: (Graph gr, Eq b) => gr a b -> LEdge b -> Bool
- hasNeighborAdj :: (Graph gr, Eq b) => gr a b -> Node -> (b, Node) -> Bool
- equal :: (Eq a, Eq b, Graph gr) => gr a b -> gr a b -> Bool
- node' :: Context a b -> Node
- lab' :: Context a b -> a
- labNode' :: Context a b -> LNode a
- neighbors' :: Context a b -> [Node]
- lneighbors' :: Context a b -> Adj b
- suc' :: Context a b -> [Node]
- pre' :: Context a b -> [Node]
- lpre' :: Context a b -> [(Node, b)]
- lsuc' :: Context a b -> [(Node, b)]
- out' :: Context a b -> [LEdge b]
- inn' :: Context a b -> [LEdge b]
- outdeg' :: Context a b -> Int
- indeg' :: Context a b -> Int
- deg' :: Context a b -> Int
- prettify :: (Graph gr, Show a, Show b) => gr a b -> String
- prettyPrint :: (DynGraph gr, Show a, Show b) => gr a b -> IO ()
- newtype OrdGr (gr :: Type -> Type -> Type) a b = OrdGr {
  - unOrdGr :: gr a b
  }

# General Type Defintions

## Node and Edge Types

type Node = Int #

Unlabeled node

type LNode a = (Node, a) #

Labeled node

type UNode = LNode () #

Quasi-unlabeled node

type Edge = (Node, Node) #

Unlabeled edge

type LEdge b = (Node, Node, b) #

Labeled edge

type UEdge = LEdge () #

Quasi-unlabeled edge

## Types Supporting Inductive Graph View

type Adj b = [(b, Node)] #

Labeled links to or from a `Node`.

type Context a b = (Adj b, Node, a, Adj b) #

Links to the `Node`, the `Node` itself, a label, links from the `Node`.

In other words, this captures all information regarding the specified `Node` within a graph.

type MContext a b = Maybe (Context a b) #

type Decomp (g :: Type -> Type -> Type) a b = (MContext a b, g a b) #

`Graph` decomposition - the context removed from a `Graph`, and the rest of the `Graph`.

type GDecomp (g :: Type -> Type -> Type) a b = (Context a b, g a b) #

The same as `Decomp`, only more sure of itself.

type UContext = ([Node], Node, [Node]) #

Unlabeled context.

type UDecomp g = (Maybe UContext, g) #

Unlabeled decomposition.

type Path = [Node] #

Unlabeled path

newtype LPath a #

Labeled path

Constructors

LP |
Fields unLPath :: [LNode a]

#### Instances

Instances details

Show a => Show (LPath a) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods showsPrec :: Int -> LPath a -> ShowS # show :: LPath a -> String # showList :: [LPath a] -> ShowS #
Eq a => Eq (LPath a) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods (==) :: LPath a -> LPath a -> Bool # (/=) :: LPath a -> LPath a -> Bool #
Ord a => Ord (LPath a) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods compare :: LPath a -> LPath a -> Ordering # (<) :: LPath a -> LPath a -> Bool # (<=) :: LPath a -> LPath a -> Bool # (>) :: LPath a -> LPath a -> Bool # (>=) :: LPath a -> LPath a -> Bool # max :: LPath a -> LPath a -> LPath a # min :: LPath a -> LPath a -> LPath a #

type UPath = [UNode] #

Quasi-unlabeled path

# Graph Type Classes

We define two graph classes:

Graph: static, decomposable graphs. Static means that a graph itself cannot be changed

DynGraph: dynamic, extensible graphs. Dynamic graphs inherit all operations from static graphs but also offer operations to extend and change graphs.

Each class contains in addition to its essential operations those derived operations that might be overwritten by a more efficient implementation in an instance definition.

Note that labNodes is essentially needed because the default definition for matchAny is based on it: we need some node from the graph to define matchAny in terms of match. Alternatively, we could have made matchAny essential and have labNodes defined in terms of ufold and matchAny. However, in general, labNodes seems to be (at least) as easy to define as matchAny. We have chosen labNodes instead of the function nodes since nodes can be easily derived from labNodes, but not vice versa.

class Graph (gr :: Type -> Type -> Type) where #

Minimum implementation: `empty`, `isEmpty`, `match`, `mkGraph`, `labNodes`

Minimal complete definition

empty, isEmpty, match, mkGraph, labNodes

Methods

empty :: gr a b #

An empty `Graph`.

isEmpty :: gr a b -> Bool #

True if the given `Graph` is empty.

match :: Node -> gr a b -> Decomp gr a b #

Decompose a `Graph` into the `MContext` found for the given node and the remaining `Graph`.

mkGraph :: [LNode a] -> [LEdge b] -> gr a b #

Create a `Graph` from the list of `LNode`s and `LEdge`s.

For graphs that are also instances of `DynGraph`, `mkGraph ns es` should be equivalent to `(`insEdges` es . `insNodes` ns) `empty``.

labNodes :: gr a b -> [LNode a] #

A list of all `LNode`s in the `Graph`.

matchAny :: gr a b -> GDecomp gr a b #

Decompose a graph into the `Context` for an arbitrarily-chosen `Node` and the remaining `Graph`.

noNodes :: gr a b -> Int #

The number of `Node`s in a `Graph`.

nodeRange :: gr a b -> (Node, Node) #

The minimum and maximum `Node` in a `Graph`.

labEdges :: gr a b -> [LEdge b] #

A list of all `LEdge`s in the `Graph`.

#### Instances

Instances details

Graph Gr # |
Instance details Defined in Data.Graph.Inductive.PatriciaTree Methods empty :: Gr a b # isEmpty :: Gr a b -> Bool # match :: Node -> Gr a b -> Decomp Gr a b # mkGraph :: [LNode a] -> [LEdge b] -> Gr a b # labNodes :: Gr a b -> [LNode a] # matchAny :: Gr a b -> GDecomp Gr a b # noNodes :: Gr a b -> Int # nodeRange :: Gr a b -> (Node, Node) # labEdges :: Gr a b -> [LEdge b] #
Graph Gr # |
Instance details Defined in Data.Graph.Inductive.Tree Methods empty :: Gr a b # isEmpty :: Gr a b -> Bool # match :: Node -> Gr a b -> Decomp Gr a b # mkGraph :: [LNode a] -> [LEdge b] -> Gr a b # labNodes :: Gr a b -> [LNode a] # matchAny :: Gr a b -> GDecomp Gr a b # noNodes :: Gr a b -> Int # nodeRange :: Gr a b -> (Node, Node) # labEdges :: Gr a b -> [LEdge b] #

class Graph gr => DynGraph (gr :: Type -> Type -> Type) where #

Methods

(&) :: Context a b -> gr a b -> gr a b #

Merge the `Context` into the `DynGraph`.

Context adjacencies should only refer to either a Node already in a graph or the node in the Context itself (for loops).

Behaviour is undefined if the specified `Node` already exists in the graph.

#### Instances

Instances details

DynGraph Gr # |
Instance details Defined in Data.Graph.Inductive.PatriciaTree Methods (&) :: Context a b -> Gr a b -> Gr a b #
DynGraph Gr # |
Instance details Defined in Data.Graph.Inductive.Tree Methods (&) :: Context a b -> Gr a b -> Gr a b #

# Operations

insert :: DynGraph gr => Context a b -> gr a b -> gr a b #

A synonym for `&`, to avoid conflicts with the similarly named operator in Data.Function.

order :: Graph gr => gr a b -> Int #

The number of nodes in the graph. An alias for `noNodes`.

size :: Graph gr => gr a b -> Int #

The number of edges in the graph.

Note that this counts every edge found, so if you are representing an unordered graph by having each edge mirrored this will be incorrect.

If you created an unordered graph by either mirroring every edge (including loops!) or using the `undir` function in Data.Graph.Inductive.Basic then you can safely halve the value returned by this.

## Graph Folds and Maps

ufold :: Graph gr => (Context a b -> c -> c) -> c -> gr a b -> c #

Fold a function over the graph by recursively calling `match`.

gmap :: DynGraph gr => (Context a b -> Context c d) -> gr a b -> gr c d #

Map a function over the graph by recursively calling `match`.

nmap :: DynGraph gr => (a -> c) -> gr a b -> gr c b #

Map a function over the `Node` labels in a graph.

emap :: DynGraph gr => (b -> c) -> gr a b -> gr a c #

Map a function over the `Edge` labels in a graph.

nemap :: DynGraph gr => (a -> c) -> (b -> d) -> gr a b -> gr c d #

Map functions over both the `Node` and `Edge` labels in a graph.

## Graph Projection

nodes :: Graph gr => gr a b -> [Node] #

List all `Node`s in the `Graph`.

edges :: Graph gr => gr a b -> [Edge] #

List all `Edge`s in the `Graph`.

toEdge :: LEdge b -> Edge #

Drop the label component of an edge.

edgeLabel :: LEdge b -> b #

The label in an edge.

toLEdge :: Edge -> b -> LEdge b #

Add a label to an edge.

newNodes :: Graph gr => Int -> gr a b -> [Node] #

List N available `Node`s, i.e. `Node`s that are not used in the `Graph`.

gelem :: Graph gr => Node -> gr a b -> Bool #

`True` if the `Node` is present in the `Graph`.

## Graph Construction and Destruction

insNode :: DynGraph gr => LNode a -> gr a b -> gr a b #

Insert a `LNode` into the `Graph`.

insEdge :: DynGraph gr => LEdge b -> gr a b -> gr a b #

Insert a `LEdge` into the `Graph`.

delNode :: Graph gr => Node -> gr a b -> gr a b #

Remove a `Node` from the `Graph`.

delEdge :: DynGraph gr => Edge -> gr a b -> gr a b #

Remove an `Edge` from the `Graph`.

NOTE: in the case of multiple edges, this will delete all such edges from the graph as there is no way to distinguish between them. If you need to delete only a single such edge, please use `delLEdge`.

delLEdge :: (DynGraph gr, Eq b) => LEdge b -> gr a b -> gr a b #

Remove an `LEdge` from the `Graph`.

NOTE: in the case of multiple edges with the same label, this will only delete the first such edge. To delete all such edges, please use `delAllLEdge`.

delAllLEdge :: (DynGraph gr, Eq b) => LEdge b -> gr a b -> gr a b #

Remove all edges equal to the one specified.

insNodes :: DynGraph gr => [LNode a] -> gr a b -> gr a b #

Insert multiple `LNode`s into the `Graph`.

insEdges :: DynGraph gr => [LEdge b] -> gr a b -> gr a b #

Insert multiple `LEdge`s into the `Graph`.

delNodes :: Graph gr => [Node] -> gr a b -> gr a b #

Remove multiple `Node`s from the `Graph`.

delEdges :: DynGraph gr => [Edge] -> gr a b -> gr a b #

Remove multiple `Edge`s from the `Graph`.

buildGr :: DynGraph gr => [Context a b] -> gr a b #

Build a `Graph` from a list of `Context`s.

The list should be in the order such that earlier `Context`s depend upon later ones (i.e. as produced by ``ufold` (:) []`).

mkUGraph :: Graph gr => [Node] -> [Edge] -> gr () () #

Build a quasi-unlabeled `Graph`.

## Subgraphs

gfiltermap :: DynGraph gr => (Context a b -> MContext c d) -> gr a b -> gr c d #

Build a graph out of the contexts for which the predicate is satisfied by recursively calling `match`.

nfilter :: DynGraph gr => (Node -> Bool) -> gr a b -> gr a b #

Returns the subgraph only containing the nodes which satisfy the given predicate.

labnfilter :: Graph gr => (LNode a -> Bool) -> gr a b -> gr a b #

Returns the subgraph only containing the labelled nodes which satisfy the given predicate.

labfilter :: DynGraph gr => (a -> Bool) -> gr a b -> gr a b #

Returns the subgraph only containing the nodes whose labels satisfy the given predicate.

subgraph :: DynGraph gr => [Node] -> gr a b -> gr a b #

Returns the subgraph induced by the supplied nodes.

## Graph Inspection

context :: Graph gr => gr a b -> Node -> Context a b #

Find the context for the given `Node`. Causes an error if the `Node` is not present in the `Graph`.

lab :: Graph gr => gr a b -> Node -> Maybe a #

Find the label for a `Node`.

neighbors :: Graph gr => gr a b -> Node -> [Node] #

Find the neighbors for a `Node`.

lneighbors :: Graph gr => gr a b -> Node -> Adj b #

Find the labelled links coming into or going from a `Context`.

suc :: Graph gr => gr a b -> Node -> [Node] #

Find all `Node`s that have a link from the given `Node`.

pre :: Graph gr => gr a b -> Node -> [Node] #

Find all `Node`s that link to to the given `Node`.

lsuc :: Graph gr => gr a b -> Node -> [(Node, b)] #

Find all `Node`s that are linked from the given `Node` and the label of each link.

lpre :: Graph gr => gr a b -> Node -> [(Node, b)] #

Find all `Node`s that link to the given `Node` and the label of each link.

out :: Graph gr => gr a b -> Node -> [LEdge b] #

Find all outward-bound `LEdge`s for the given `Node`.

inn :: Graph gr => gr a b -> Node -> [LEdge b] #

Find all inward-bound `LEdge`s for the given `Node`.

outdeg :: Graph gr => gr a b -> Node -> Int #

The outward-bound degree of the `Node`.

indeg :: Graph gr => gr a b -> Node -> Int #

The inward-bound degree of the `Node`.

deg :: Graph gr => gr a b -> Node -> Int #

The degree of the `Node`.

hasEdge :: Graph gr => gr a b -> Edge -> Bool #

Checks if there is a directed edge between two nodes.

hasNeighbor :: Graph gr => gr a b -> Node -> Node -> Bool #

Checks if there is an undirected edge between two nodes.

hasLEdge :: (Graph gr, Eq b) => gr a b -> LEdge b -> Bool #

Checks if there is a labelled edge between two nodes.

hasNeighborAdj :: (Graph gr, Eq b) => gr a b -> Node -> (b, Node) -> Bool #

Checks if there is an undirected labelled edge between two nodes.

equal :: (Eq a, Eq b, Graph gr) => gr a b -> gr a b -> Bool #

## Context Inspection

node' :: Context a b -> Node #

The `Node` in a `Context`.

lab' :: Context a b -> a #

The label in a `Context`.

labNode' :: Context a b -> LNode a #

The `LNode` from a `Context`.

neighbors' :: Context a b -> [Node] #

All `Node`s linked to or from in a `Context`.

lneighbors' :: Context a b -> Adj b #

All labelled links coming into or going from a `Context`.

suc' :: Context a b -> [Node] #

All `Node`s linked to in a `Context`.

pre' :: Context a b -> [Node] #

All `Node`s linked from in a `Context`.

lpre' :: Context a b -> [(Node, b)] #

All `Node`s linked from in a `Context`, and the label of the links.

lsuc' :: Context a b -> [(Node, b)] #

All `Node`s linked from in a `Context`, and the label of the links.

out' :: Context a b -> [LEdge b] #

All outward-directed `LEdge`s in a `Context`.

inn' :: Context a b -> [LEdge b] #

All inward-directed `LEdge`s in a `Context`.

outdeg' :: Context a b -> Int #

The outward degree of a `Context`.

indeg' :: Context a b -> Int #

The inward degree of a `Context`.

deg' :: Context a b -> Int #

The degree of a `Context`.

# Pretty-printing

prettify :: (Graph gr, Show a, Show b) => gr a b -> String #

Pretty-print the graph. Note that this loses a lot of information, such as edge inverses, etc.

prettyPrint :: (DynGraph gr, Show a, Show b) => gr a b -> IO () #

Pretty-print the graph to stdout.

# Ordering of Graphs

newtype OrdGr (gr :: Type -> Type -> Type) a b #

OrdGr comes equipped with an Ord instance, so that graphs can be used as e.g. Map keys.

Constructors

OrdGr |
Fields unOrdGr :: gr a b

#### Instances

Instances details

Read (gr a b) => Read (OrdGr gr a b) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods readsPrec :: Int -> ReadS (OrdGr gr a b) # readList :: ReadS [OrdGr gr a b] # readPrec :: ReadPrec (OrdGr gr a b) # readListPrec :: ReadPrec [OrdGr gr a b] #
Show (gr a b) => Show (OrdGr gr a b) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods showsPrec :: Int -> OrdGr gr a b -> ShowS # show :: OrdGr gr a b -> String # showList :: [OrdGr gr a b] -> ShowS #
(Graph gr, Ord a, Ord b) => Eq (OrdGr gr a b) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods (==) :: OrdGr gr a b -> OrdGr gr a b -> Bool # (/=) :: OrdGr gr a b -> OrdGr gr a b -> Bool #
(Graph gr, Ord a, Ord b) => Ord (OrdGr gr a b) # |
Instance details Defined in Data.Graph.Inductive.Graph Methods compare :: OrdGr gr a b -> OrdGr gr a b -> Ordering # (<) :: OrdGr gr a b -> OrdGr gr a b -> Bool # (<=) :: OrdGr gr a b -> OrdGr gr a b -> Bool # (>) :: OrdGr gr a b -> OrdGr gr a b -> Bool # (>=) :: OrdGr gr a b -> OrdGr gr a b -> Bool # max :: OrdGr gr a b -> OrdGr gr a b -> OrdGr gr a b # min :: OrdGr gr a b -> OrdGr gr a b -> OrdGr gr a b #