Copyright	Guillaume Sabbagh 2022
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.Categories.FinGrph

Contents

Graph
- Getters
- Smart constructors
Graph homomorphism
- Getters
- Smart constructor
FinGrph

Description

The FinGrph category has finite multidigraphs as objects and multidigraph homomorphisms as morphisms.

Synopsis

data Arrow n e = Arrow {
- sourceArrow :: n
- targetArrow :: n
- labelArrow :: e
}
data Graph n e
nodes :: Graph n e -> Set n
edges :: Graph n e -> Set (Arrow n e)
graph :: Eq n => Set n -> Set (Arrow n e) -> Maybe (Graph n e)
unsafeGraph :: Set n -> Set (Arrow n e) -> Graph n e
data GraphHomomorphism n e
nodeMap :: GraphHomomorphism n e -> Map n n
edgeMap :: GraphHomomorphism n e -> Map (Arrow n e) (Arrow n e)
checkGraphHomomorphism :: (Eq n, Eq e) => GraphHomomorphism n e -> Bool
graphHomomorphism :: (Eq n, Eq e) => Map n n -> Map (Arrow n e) (Arrow n e) -> Graph n e -> Maybe (GraphHomomorphism n e)
unsafeGraphHomomorphism :: Map n n -> Map (Arrow n e) (Arrow n e) -> Graph n e -> GraphHomomorphism n e
data FinGrph n e = FinGrph
underlyingGraph :: (FiniteCategory c m o, Morphism m o) => c -> Graph o m
underlyingGraphFormat :: (FiniteCategory c m o, Morphism m o) => (o -> a) -> (m -> b) -> c -> Graph a b

Graph

data Arrow n e Source #

An Arrow is composed of a source node, a target node and a label.

Constructors

Arrow
Fields sourceArrow :: n targetArrow :: n labelArrow :: e

Instances

Instances details

(Eq n, Eq e) => Eq (Arrow n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods (==) :: Arrow n e -> Arrow n e -> Bool (/=) :: Arrow n e -> Arrow n e -> Bool
(Show n, Show e) => Show (Arrow n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods showsPrec :: Int -> Arrow n e -> ShowS show :: Arrow n e -> String showList :: [Arrow n e] -> ShowS
(PrettyPrint n, PrettyPrint e) => PrettyPrint (Arrow n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods pprint :: Arrow n e -> String Source #

data Graph n e Source #

A Graph is a set of nodes and a set of Arrows.

Graph is private, use smart constructor graph.

Instances

Instances details

(Eq n, Eq e) => Eq (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods (==) :: Graph n e -> Graph n e -> Bool (/=) :: Graph n e -> Graph n e -> Bool
(Show n, Show e) => Show (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods showsPrec :: Int -> Graph n e -> ShowS show :: Graph n e -> String showList :: [Graph n e] -> ShowS
(PrettyPrint n, PrettyPrint e, Eq n, Eq e) => PrettyPrint (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods pprint :: Graph n e -> String Source #
(Eq n, Eq e) => Morphism (GraphHomomorphism n e) (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods (@?) :: GraphHomomorphism n e -> GraphHomomorphism n e -> Maybe (GraphHomomorphism n e) Source # source :: GraphHomomorphism n e -> Graph n e Source # target :: GraphHomomorphism n e -> Graph n e Source #
(Eq n, Eq e, Show n, Show e) => Category (FinGrph n e) (GraphHomomorphism n e) (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods identity :: FinGrph n e -> Graph n e -> GraphHomomorphism n e Source # ar :: FinGrph n e -> Graph n e -> Graph n e -> Set (GraphHomomorphism n e) Source # genAr :: FinGrph n e -> Graph n e -> Graph n e -> Set (GraphHomomorphism n e) Source # decompose :: FinGrph n e -> GraphHomomorphism n e -> [GraphHomomorphism n e] Source #

Getters

nodes :: Graph n e -> Set n Source #

The set of nodes of the graph.

edges :: Graph n e -> Set (Arrow n e) Source #

The set of arrows of the graph.

Smart constructors

graph :: Eq n => Set n -> Set (Arrow n e) -> Maybe (Graph n e) Source #

Smart constructor of Graph.

unsafeGraph :: Set n -> Set (Arrow n e) -> Graph n e Source #

Unsafe constructor of Graph, does not check the Graph structure.

Graph homomorphism

data GraphHomomorphism n e Source #

A GraphHomomorphism is composed of a map between the nodes of the graphs, a map between the edges of the graphs, and the target Graph so that we can recover it from the morphism.

It must follow axioms such that the image of an arrow is not torn appart, that is why the constructor is private. Use the smart constructor graphHomomorphism instead.

Instances

Instances details

(Eq n, Eq e) => Eq (GraphHomomorphism n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods (==) :: GraphHomomorphism n e -> GraphHomomorphism n e -> Bool (/=) :: GraphHomomorphism n e -> GraphHomomorphism n e -> Bool
(Show n, Show e) => Show (GraphHomomorphism n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods showsPrec :: Int -> GraphHomomorphism n e -> ShowS show :: GraphHomomorphism n e -> String showList :: [GraphHomomorphism n e] -> ShowS
(PrettyPrint n, PrettyPrint e, Eq n, Eq e) => PrettyPrint (GraphHomomorphism n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods pprint :: GraphHomomorphism n e -> String Source #
(Eq n, Eq e) => Morphism (GraphHomomorphism n e) (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods (@?) :: GraphHomomorphism n e -> GraphHomomorphism n e -> Maybe (GraphHomomorphism n e) Source # source :: GraphHomomorphism n e -> Graph n e Source # target :: GraphHomomorphism n e -> Graph n e Source #
(Eq n, Eq e, Show n, Show e) => Category (FinGrph n e) (GraphHomomorphism n e) (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods identity :: FinGrph n e -> Graph n e -> GraphHomomorphism n e Source # ar :: FinGrph n e -> Graph n e -> Graph n e -> Set (GraphHomomorphism n e) Source # genAr :: FinGrph n e -> Graph n e -> Graph n e -> Set (GraphHomomorphism n e) Source # decompose :: FinGrph n e -> GraphHomomorphism n e -> [GraphHomomorphism n e] Source #

Getters

nodeMap :: GraphHomomorphism n e -> Map n n Source #

The mapping of nodes.

edgeMap :: GraphHomomorphism n e -> Map (Arrow n e) (Arrow n e) Source #

The mapping of edges.

Smart constructor

checkGraphHomomorphism :: (Eq n, Eq e) => GraphHomomorphism n e -> Bool Source #

Check wether the structure of GraphHomomorphism is respected or not.

graphHomomorphism :: (Eq n, Eq e) => Map n n -> Map (Arrow n e) (Arrow n e) -> Graph n e -> Maybe (GraphHomomorphism n e) Source #

The smart constructor of GraphHomomorphism.

unsafeGraphHomomorphism :: Map n n -> Map (Arrow n e) (Arrow n e) -> Graph n e -> GraphHomomorphism n e Source #

Unsafe constructor of GraphHomomorphism which does not check the structure of the GraphHomomorphism.

FinGrph

data FinGrph n e Source #

The category of finite graphs.

Constructors

FinGrph

Instances

Instances details

Eq (FinGrph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods (==) :: FinGrph n e -> FinGrph n e -> Bool (/=) :: FinGrph n e -> FinGrph n e -> Bool
Show (FinGrph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods showsPrec :: Int -> FinGrph n e -> ShowS show :: FinGrph n e -> String showList :: [FinGrph n e] -> ShowS
(PrettyPrint n, PrettyPrint e, Eq n, Eq e) => PrettyPrint (FinGrph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods pprint :: FinGrph n e -> String Source #
(Eq n, Eq e, Show n, Show e) => Category (FinGrph n e) (GraphHomomorphism n e) (Graph n e) Source #
Instance details Defined in Math.Categories.FinGrph Methods identity :: FinGrph n e -> Graph n e -> GraphHomomorphism n e Source # ar :: FinGrph n e -> Graph n e -> Graph n e -> Set (GraphHomomorphism n e) Source # genAr :: FinGrph n e -> Graph n e -> Graph n e -> Set (GraphHomomorphism n e) Source # decompose :: FinGrph n e -> GraphHomomorphism n e -> [GraphHomomorphism n e] Source #

underlyingGraph :: (FiniteCategory c m o, Morphism m o) => c -> Graph o m Source #

Return the underlying graph of a FiniteCategory.

underlyingGraphFormat :: (FiniteCategory c m o, Morphism m o) => (o -> a) -> (m -> b) -> c -> Graph a b Source #

Return the underlying graph of a FiniteCategory and apply formatting functions on objects and arrows.