fgl-5.5.0.1: 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
  - Graph Inspection
  - Context Inspection
- Pretty-printing

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 a b = (MContext a b, g a b)
- type GDecomp g 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 [LNode a]
- type UPath = [UNode]
- class Graph gr 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 where
  - (&) :: Context a b -> gr a b -> gr a b
- 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
- nodes :: Graph gr => gr a b -> [Node]
- edges :: Graph gr => gr a b -> [Edge]
- 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
- 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 () ()
- 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]
- 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
- 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]
- 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 :: (DynGraph gr, Show a, Show b) => gr a b -> String
- prettyPrint :: (DynGraph gr, Show a, Show b) => gr a b -> IO ()

# 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`.

type MContext a b = Maybe (Context a b)

type Decomp g 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 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 [LNode a] |

Instances

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

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

Graph Gr |
Graph Gr |

class Graph gr => DynGraph gr where

Methods

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

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

Fold a function over the graph.

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

Map a function over the graph.

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.

## 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`.

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`.

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

Remove an `LEdge` from the `Graph`.

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.

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

Build a quasi-unlabeled `Graph`.

## 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`.

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`.

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`.

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 :: (DynGraph 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.