fgl-5.5.2.3: Martin Erwig's Functional Graph Library

Safe Haskell Safe-Inferred Haskell98

Data.Graph.Inductive.Graph

Description

Static and Dynamic Inductive Graphs

Synopsis

# General Type Defintions

## Node and Edge Types

type Node = Int Source

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`.

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

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 FieldsunLPath :: [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 where Source

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

Minimal complete definition

Methods

empty :: gr a b Source

An empty `Graph`.

isEmpty :: gr a b -> Bool Source

True if the given `Graph` is empty.

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

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

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

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] Source

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

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

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

noNodes :: gr a b -> Int Source

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 where Source

Methods

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

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 -> c Source

Fold a function over the graph.

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

Map a function over the graph.

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

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

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

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

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

Map functions over both the `Node` and `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`.

toEdge :: LEdge b -> Edge Source

Drop the label component of an edge.

edgeLabel :: LEdge b -> b Source

The label in an edge.

toLEdge :: Edge -> b -> LEdge b Source

Add a label to an edge.

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 -> Bool Source

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

## Graph Construction and Destruction

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

Insert a `LNode` into the `Graph`.

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

Insert a `LEdge` into the `Graph`.

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

Remove a `Node` from the `Graph`.

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

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 Source

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 `delAllLedges`.

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

Remove all edges equal to the one specified.

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

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

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

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

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

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

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

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

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

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 () () Source

Build a quasi-unlabeled `Graph`.

## Subgraphs

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

Build a graph out of the contexts for which the predicate is true.

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

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

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

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

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

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

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

Returns the subgraph induced by the supplied nodes.

## Graph Inspection

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

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 Source

Find the label for a `Node`.

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

Find the neighbors for a `Node`.

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

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

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 -> Int Source

The outward-bound degree of the `Node`.

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

The inward-bound degree of the `Node`.

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

The degree of the `Node`.

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

Checks if there is a directed edge between two nodes.

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

Checks if there is an undirected edge between two nodes.

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

Checks if there is a labelled edge between two nodes.

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

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 Source

## Context Inspection

node' :: Context a b -> Node Source

The `Node` in a `Context`.

lab' :: Context a b -> a Source

The label in a `Context`.

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

The `LNode` from a `Context`.

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

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

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

All labelled links coming into or going from 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 -> Int Source

The outward degree of a `Context`.

indeg' :: Context a b -> Int Source

The inward degree of a `Context`.

deg' :: Context a b -> Int Source

The degree of a `Context`.

# Pretty-printing

prettify :: (DynGraph gr, Show a, Show b) => gr a b -> String Source

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 () Source

Pretty-print the graph to stdout.

# Ordering of Graphs

newtype OrdGr gr a b Source

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

Constructors

 OrdGr FieldsunOrdGr :: gr a b

Instances

 (Graph gr, Ord a, Ord b) => Eq (OrdGr gr a b) (Graph gr, Ord a, Ord b) => Ord (OrdGr gr a b) Read (gr a b) => Read (OrdGr gr a b) Show (gr a b) => Show (OrdGr gr a b)