fgl-5.4.2.4: Martin Erwig's Functional Graph Library

Data.Graph.Inductive.Graph

Description

Static and Dynamic Inductive Graphs

Synopsis

# General Type Defintions

## Node and Edge Types

type Node = IntSource

Unlabeled node

type LNode a = (Node, a)Source

Labeled node

type UNode = LNode ()Source

Quasi-unlabeled node

type Edge = (Node, Node)Source

Unlabeled edge

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

Labeled edge

type UEdge = LEdge ()Source

Quasi-unlabeled edge

## Types Supporting Inductive Graph View

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

Labeled links to or from a `Node`.

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

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

type Decomp g a b = (MContext a b, g a b)Source

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

type GDecomp g a b = (Context a b, g a b)Source

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

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

Unlabeled context.

type UDecomp g = (Maybe UContext, g)Source

Unlabeled decomposition.

type Path = [Node]Source

Unlabeled path

newtype LPath a Source

Labeled path

Constructors

 LP [LNode a]

Instances

 Eq a => Eq (LPath a) Ord a => Ord (LPath a) Show a => Show (LPath a)

type UPath = [UNode]Source

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 whereSource

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

Methods

empty :: gr a bSource

An empty `Graph`.

isEmpty :: gr a b -> BoolSource

True if the given `Graph` is empty.

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

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

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

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

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

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

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

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

noNodes :: gr a b -> IntSource

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

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

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

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

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

Instances

 Graph Gr Graph Gr

class Graph gr => DynGraph gr whereSource

Methods

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

Merge the `Context` into the `DynGraph`.

Instances

 DynGraph Gr DynGraph Gr

# Operations

## Graph Folds and Maps

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

Fold a function over the graph.

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

Map a function over the graph.

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

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

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

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

## Graph Projection

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

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

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

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

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

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

gelem :: Graph gr => Node -> gr a b -> BoolSource

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

## Graph Construction and Destruction

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

Insert a `LNode` into the `Graph`.

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

Insert a `LEdge` into the `Graph`.

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

Remove a `Node` from the `Graph`.

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

Remove an `Edge` from the `Graph`.

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

Remove an `LEdge` from the `Graph`.

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

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

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

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

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

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

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

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

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

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

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

Build a quasi-unlabeled `Graph`.

## Graph Inspection

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

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 aSource

Find the label for a `Node`.

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

Find the neighbors for a `Node`.

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

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

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

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

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

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)]Source

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]Source

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

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

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

outdeg :: Graph gr => gr a b -> Node -> IntSource

The outward-bound degree of the `Node`.

indeg :: Graph gr => gr a b -> Node -> IntSource

The inward-bound degree of the `Node`.

deg :: Graph gr => gr a b -> Node -> IntSource

The degree of the `Node`.

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

## Context Inspection

node' :: Context a b -> NodeSource

The `Node` in a `Context`.

lab' :: Context a b -> aSource

The label in a `Context`.

labNode' :: Context a b -> LNode aSource

The `LNode` from a `Context`.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

outdeg' :: Context a b -> IntSource

The outward degree of a `Context`.

indeg' :: Context a b -> IntSource

The inward degree of a `Context`.

deg' :: Context a b -> IntSource

The degree of a `Context`.