algebraic-graphs-0.0.5: A library for algebraic graph construction and transformation

Copyright (c) Andrey Mokhov 2016-2017 MIT (see the file LICENSE) andrey.mokhov@gmail.com experimental None Haskell2010

Algebra.Graph.Relation.Transitive

Contents

Description

An abstract implementation of transitive binary relations. Use Algebra.Graph.Class for polymorphic construction and manipulation.

Synopsis

# Data structure

The TransitiveRelation data type represents a transitive binary relation over a set of elements. Transitive relations satisfy all laws of the Transitive type class and, in particular, the closure axiom:

y /= empty ==> x * y + x * z + y * z == x * y + y * z

For example, the following holds:

path xs == (clique xs :: TransitiveRelation Int)

The Show instance produces transitively closed expressions:

show (1 * 2         :: TransitiveRelation Int) == "edge 1 2"
show (1 * 2 + 2 * 3 :: TransitiveRelation Int) == "edges [(1,2),(1,3),(2,3)]"

Instances

 Ord a => Eq (TransitiveRelation a) Source # Methods (Num a, Ord a) => Num (TransitiveRelation a) Source # Methods (Ord a, Show a) => Show (TransitiveRelation a) Source # MethodsshowList :: [TransitiveRelation a] -> ShowS # Source # Ord a => Graph (TransitiveRelation a) Source # Associated Typestype Vertex (TransitiveRelation a) :: * Source # Methods type Vertex (TransitiveRelation a) Source # type Vertex (TransitiveRelation a) = a

Construct a transitive relation from a Relation. Complexity: O(1) time.

Extract the underlying relation. Complexity: O(n * m * log(m)) time.