Safe Haskell | None |
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Discrete Bayesian Network Library.

It is a very preliminary version. It has only been tested on very simple examples where it worked. It should be considered as experimental and not used in any production work.

Look at the Bayes.Examples and Bayes.Examples.Tutorial in this package to see how to use the library.

In Bayes.Examples.Influence you'll find additional examples about influence diagrams.

- class Graph g where
- addVertex :: Vertex -> b -> g a b -> g a b
- removeVertex :: Vertex -> g a b -> g a b
- vertexValue :: g a b -> Vertex -> Maybe b
- changeVertexValue :: Vertex -> b -> g a b -> Maybe (g a b)
- someVertex :: g a b -> Maybe Vertex
- hasNoVertices :: g a b -> Bool
- allVertices :: g a b -> [Vertex]
- allVertexValues :: g a b -> [b]
- allNodes :: g a b -> [(Vertex, b)]
- isLinkedWithAnEdge :: g a b -> Vertex -> Vertex -> Bool
- addEdge :: Edge -> a -> g a b -> g a b
- removeEdge :: Edge -> g a b -> g a b
- edgeVertices :: g a b -> Edge -> Maybe (Vertex, Vertex)
- edgeValue :: g a b -> Edge -> Maybe a
- someEdge :: g a b -> Maybe Edge
- hasNoEdges :: g a b -> Bool
- endVertex :: g a b -> Edge -> Maybe Vertex
- startVertex :: g a b -> Edge -> Maybe Vertex
- allEdges :: g a b -> [Edge]
- allEdgeValues :: g a b -> [a]
- emptyGraph :: g a b
- isEmpty :: g a b -> Bool
- oriented :: g a b -> Bool
- neighbors :: g a b -> Vertex -> Maybe [Vertex]

- class Graph g => UndirectedGraph g where
- class Graph g => DirectedGraph g where
- class FoldableWithVertex g where
- foldrWithVertex :: (Vertex -> a -> b -> b) -> b -> g c a -> b
- foldlWithVertex' :: (b -> Vertex -> a -> b) -> b -> g c a -> b

- class Graph g => NamedGraph g where
- addLabeledVertex :: String -> Vertex -> b -> g a b -> g a b
- vertexLabel :: g a b -> Vertex -> Maybe String

- data GraphMonad g e f a
- type GMState g e f = (AuxiliaryState, g e f)
- graphNode :: NamedGraph g => String -> f -> GraphMonad g e f Vertex
- runGraph :: Graph g => GraphMonad g e f a -> (a, g e f)
- execGraph :: Graph g => GraphMonad g e f a -> g e f
- evalGraph :: Graph g => GraphMonad g e f a -> a
- emptyAuxiliaryState :: (Map k a, Int)
- getNewEmptyVariable :: NamedGraph g => Maybe String -> f -> GraphMonad g e f Vertex
- isRoot :: DirectedGraph g => g a b -> Vertex -> Bool
- rootNode :: DirectedGraph g => g a b -> Maybe Vertex
- parentNodes :: DirectedGraph g => g a b -> Vertex -> [Vertex]
- childrenNodes :: DirectedGraph g => g a b -> Vertex -> [Vertex]
- data Vertex
- data Edge
- edge :: Vertex -> Vertex -> Edge
- newEdge :: Graph g => Vertex -> Vertex -> e -> GraphMonad g e f ()
- getVertex :: Graph g => String -> GraphMonad g e f (Maybe Vertex)
- edgeEndPoints :: Edge -> (Vertex, Vertex)
- connectedGraph :: Graph g => g a b -> Bool
- dag :: DirectedGraph g => g a b -> Bool
- printGraphValues :: (Graph (SimpleGraph n), Show b) => SimpleGraph n e b -> IO ()
- type DirectedSG = SimpleGraph DE
- type UndirectedSG = SimpleGraph UE
- type SBN f = DirectedSG () f
- varMap :: SimpleGraph n e v -> Map String Vertex
- displaySimpleGraph :: (Vertex -> n -> Maybe String) -> (Vertex -> n -> Maybe String) -> (Edge -> e -> Maybe String) -> (Edge -> e -> Maybe String) -> SimpleGraph local e n -> String
- type BayesianNetwork g f = g () f
- testEdgeRemoval_prop :: DirectedSG String String -> Property
- testVertexRemoval_prop :: DirectedSG String String -> Property

# Graph

## Graph classes

Graph class used for graph processing algorithms. A graph processing algorithm does not have to know how the graph is implemented nor if it is directed or undirected

addVertex :: Vertex -> b -> g a b -> g a bSource

Add a new vertex

removeVertex :: Vertex -> g a b -> g a bSource

Remove a vertex

vertexValue :: g a b -> Vertex -> Maybe bSource

Get the vertex value if the vertex is found in the graph

changeVertexValue :: Vertex -> b -> g a b -> Maybe (g a b)Source

Change the vertex value if the vertex is found in the graph

someVertex :: g a b -> Maybe VertexSource

Generate a "random" vertex

hasNoVertices :: g a b -> BoolSource

Check is the graph has no vertrex

allVertices :: g a b -> [Vertex]Source

Generate all vertices

allVertexValues :: g a b -> [b]Source

Get all the values

allNodes :: g a b -> [(Vertex, b)]Source

Get all nodes

isLinkedWithAnEdge :: g a b -> Vertex -> Vertex -> BoolSource

Check if two vertices are linked by a vertex

addEdge :: Edge -> a -> g a b -> g a bSource

Add an edge

removeEdge :: Edge -> g a b -> g a bSource

Remove an dedge

edgeVertices :: g a b -> Edge -> Maybe (Vertex, Vertex)Source

Vertices for an edge

edgeValue :: g a b -> Edge -> Maybe aSource

Edge value if the edge is found in the graph

someEdge :: g a b -> Maybe EdgeSource

Return a "random" edge

hasNoEdges :: g a b -> BoolSource

Check if the graph has no edges

endVertex :: g a b -> Edge -> Maybe VertexSource

One extremity of the edge (which is the end only for directed edge)

startVertex :: g a b -> Edge -> Maybe VertexSource

One extremity of the edge (which is the start only for directed edge)

allEdges :: g a b -> [Edge]Source

All edges of the graph

allEdgeValues :: g a b -> [a]Source

All values of the graph

emptyGraph :: g a bSource

Returns an empty graph

isEmpty :: g a b -> BoolSource

Check if the graph is empty

oriented :: g a b -> BoolSource

Check if the graph is oriented

neighbors :: g a b -> Vertex -> Maybe [Vertex]Source

All the neighbors of a vertex

Graph UndirectedSG | SimpleGraph is an instance of Graph. |

Graph DirectedSG | SimpleGraph is an instance of Graph. |

class Graph g => UndirectedGraph g whereSource

Undirected graph

class Graph g => DirectedGraph g whereSource

Directed graph

class FoldableWithVertex g whereSource

The foldable class is limited. For a graph g we may need the vertex in addition to the value

foldrWithVertex :: (Vertex -> a -> b -> b) -> b -> g c a -> bSource

Fold with vertex

foldlWithVertex' :: (b -> Vertex -> a -> b) -> b -> g c a -> bSource

FoldableWithVertex (SimpleGraph local) |

class Graph g => NamedGraph g whereSource

A named graph is a graph where the vertices have a name. This name is not a vertex value. Putting this name in the vertex value would make algorithm less readable. A vertex name is only useful to display the graph. Labeled graph has a different meaning in graph theory.

addLabeledVertex :: String -> Vertex -> b -> g a b -> g a bSource

Add a vertex with a vertex name in addition to the value

vertexLabel :: g a b -> Vertex -> Maybe StringSource

Returns the vertex label

## Graph Monad

data GraphMonad g e f a Source

Graph monad.
The monad used to simplify the description of a new graph
g is the graph type. e the edge type. f the node type (generally a `Factor`

)

Monad (GraphMonad g e f) | |

MonadState (GMState g e f) (GraphMonad g e f) |

type GMState g e f = (AuxiliaryState, g e f)Source

The state of the graph monad : the graph and auxiliary data useful during the construction

graphNode :: NamedGraph g => String -> f -> GraphMonad g e f VertexSource

Add a node in the graph using the graph monad

runGraph :: Graph g => GraphMonad g e f a -> (a, g e f)Source

execGraph :: Graph g => GraphMonad g e f a -> g e fSource

evalGraph :: Graph g => GraphMonad g e f a -> aSource

emptyAuxiliaryState :: (Map k a, Int)Source

getNewEmptyVariable :: NamedGraph g => Maybe String -> f -> GraphMonad g e f VertexSource

Generate a new unique unamed empty variable

isRoot :: DirectedGraph g => g a b -> Vertex -> BoolSource

rootNode :: DirectedGraph g => g a b -> Maybe VertexSource

Get the root node for the graph

parentNodes :: DirectedGraph g => g a b -> Vertex -> [Vertex]Source

Return the parents of a node

childrenNodes :: DirectedGraph g => g a b -> Vertex -> [Vertex]Source

Return the children of a node

## Support functions for Graph constructions

Vertex type used to identify a vertex in a graph

Edge type used to identify and edge in a graph

newEdge :: Graph g => Vertex -> Vertex -> e -> GraphMonad g e f ()Source

Add a new labeled edge to the graph

getVertex :: Graph g => String -> GraphMonad g e f (Maybe Vertex)Source

Get a named vertex from the graph monad

edgeEndPoints :: Edge -> (Vertex, Vertex)Source

Endpoints of an edge

connectedGraph :: Graph g => g a b -> BoolSource

Check if the graph is connected

dag :: DirectedGraph g => g a b -> BoolSource

Check if the graph is a directed Acyclic graph

printGraphValues :: (Graph (SimpleGraph n), Show b) => SimpleGraph n e b -> IO ()Source

Print the values of the graph vertices

# SimpleGraph implementation

## The SimpleGraph type

type DirectedSG = SimpleGraph DESource

Directed simple graph

type UndirectedSG = SimpleGraph UESource

Undirected simple graph

type SBN f = DirectedSG () fSource

An implementation of the BayesianNetwork using the simple graph and no value for the edges

displaySimpleGraph :: (Vertex -> n -> Maybe String) -> (Vertex -> n -> Maybe String) -> (Edge -> e -> Maybe String) -> (Edge -> e -> Maybe String) -> SimpleGraph local e n -> StringSource

## Bayesian network

type BayesianNetwork g f = g () fSource

Bayesian network. g must be a directed graph and f a factor