Algebra.Graph.Relation.Reflexive

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

Data structure

data ReflexiveRelation a

The ReflexiveRelation data type represents a reflexive binary relation over a set of elements. Reflexive relations satisfy all laws of the Reflexive type class and, in particular, the self-loop axiom:

vertex x == vertex x * vertex x

The Show instance produces reflexively closed expressions:

show (1     :: ReflexiveRelation Int) == "edge 1 1"
show (1 * 2 :: ReflexiveRelation Int) == "edges [(1,1),(1,2),(2,2)]"

Instances

Ord a => Eq (ReflexiveRelation a)

Methods

(==) :: ReflexiveRelation a -> ReflexiveRelation a -> Bool

(/=) :: ReflexiveRelation a -> ReflexiveRelation a -> Bool

(Num a, Ord a) => Num (ReflexiveRelation a)

Methods

(+) :: ReflexiveRelation a -> ReflexiveRelation a -> ReflexiveRelation a

(-) :: ReflexiveRelation a -> ReflexiveRelation a -> ReflexiveRelation a

(*) :: ReflexiveRelation a -> ReflexiveRelation a -> ReflexiveRelation a

negate :: ReflexiveRelation a -> ReflexiveRelation a

abs :: ReflexiveRelation a -> ReflexiveRelation a

signum :: ReflexiveRelation a -> ReflexiveRelation a

fromInteger :: Integer -> ReflexiveRelation a

(Ord a, Show a) => Show (ReflexiveRelation a)

Methods

showsPrec :: Int -> ReflexiveRelation a -> ShowS

show :: ReflexiveRelation a -> String

showList :: [ReflexiveRelation a] -> ShowS

Ord a => Reflexive (ReflexiveRelation a)

Ord a => Graph (ReflexiveRelation a)

Associated Types

type Vertex (ReflexiveRelation a) :: *

Methods

empty :: ReflexiveRelation a

vertex :: Vertex (ReflexiveRelation a) -> ReflexiveRelation a

overlay :: ReflexiveRelation a -> ReflexiveRelation a -> ReflexiveRelation a

connect :: ReflexiveRelation a -> ReflexiveRelation a -> ReflexiveRelation a

type Vertex (ReflexiveRelation a)

type Vertex (ReflexiveRelation a) = a

fromRelation :: Relation a -> ReflexiveRelation a

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

toRelation :: Ord a => ReflexiveRelation a -> Relation a

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