Safe Haskell	Safe
Language	Haskell2010

Abstract.Morphism

Synopsis

Documentation

class Eq m => Morphism m where Source #

Minimal complete definition

compose, domain, codomain, id, isMonomorphism, isEpimorphism, isIsomorphism

Associated Types

type Obj m :: * Source #

Methods

compose :: m -> m -> m Source #

Apply the first argument first (compose f g = g . f)

domain :: m -> Obj m Source #

codomain :: m -> Obj m Source #

id :: Obj m -> m Source #

isMonomorphism :: m -> Bool Source #

isEpimorphism :: m -> Bool Source #

isIsomorphism :: m -> Bool Source #

Instances

Morphism (GraphMorphism a b) Source #
Associated Types type Obj (GraphMorphism a b) :: * Source # Methods compose :: GraphMorphism a b -> GraphMorphism a b -> GraphMorphism a b Source # domain :: GraphMorphism a b -> Obj (GraphMorphism a b) Source # codomain :: GraphMorphism a b -> Obj (GraphMorphism a b) Source # id :: Obj (GraphMorphism a b) -> GraphMorphism a b Source # isMonomorphism :: GraphMorphism a b -> Bool Source # isEpimorphism :: GraphMorphism a b -> Bool Source # isIsomorphism :: GraphMorphism a b -> Bool Source #
Morphism (TypedGraphMorphism a b) Source #
Associated Types type Obj (TypedGraphMorphism a b) :: * Source # Methods compose :: TypedGraphMorphism a b -> TypedGraphMorphism a b -> TypedGraphMorphism a b Source # domain :: TypedGraphMorphism a b -> Obj (TypedGraphMorphism a b) Source # codomain :: TypedGraphMorphism a b -> Obj (TypedGraphMorphism a b) Source # id :: Obj (TypedGraphMorphism a b) -> TypedGraphMorphism a b Source # isMonomorphism :: TypedGraphMorphism a b -> Bool Source # isEpimorphism :: TypedGraphMorphism a b -> Bool Source # isIsomorphism :: TypedGraphMorphism a b -> Bool Source #
Morphism (RuleMorphism a b) Source #
Associated Types type Obj (RuleMorphism a b) :: * Source # Methods compose :: RuleMorphism a b -> RuleMorphism a b -> RuleMorphism a b Source # domain :: RuleMorphism a b -> Obj (RuleMorphism a b) Source # codomain :: RuleMorphism a b -> Obj (RuleMorphism a b) Source # id :: Obj (RuleMorphism a b) -> RuleMorphism a b Source # isMonomorphism :: RuleMorphism a b -> Bool Source # isEpimorphism :: RuleMorphism a b -> Bool Source # isIsomorphism :: RuleMorphism a b -> Bool Source #

data MorphismType Source #

Enum for the types of morphisms that can be used / found

Constructors

GenericMorphism
Monomorphism
Epimorphism
Isomorphism

Instances

Enum MorphismType Source #
Methods succ :: MorphismType -> MorphismType # pred :: MorphismType -> MorphismType # toEnum :: Int -> MorphismType # fromEnum :: MorphismType -> Int # enumFrom :: MorphismType -> [MorphismType] # enumFromThen :: MorphismType -> MorphismType -> [MorphismType] # enumFromTo :: MorphismType -> MorphismType -> [MorphismType] # enumFromThenTo :: MorphismType -> MorphismType -> MorphismType -> [MorphismType] #
Show MorphismType Source #
Methods showsPrec :: Int -> MorphismType -> ShowS # show :: MorphismType -> String # showList :: [MorphismType] -> ShowS #

type Span m = (m, m) Source #

class Morphism m => FindMorphism m where Source #

Minimal complete definition

findMorphisms, induceSpanMorphism, partialInjectiveMatches, findCospanCommuter

Methods

findMorphisms :: MorphismType -> Obj m -> Obj m -> [m] Source #

Given a type t of MorphismType and two objects A and B, it finds all the matches m : A -> B in which m is of the type t

findMonomorphisms :: Obj m -> Obj m -> [m] Source #

Given two objects A and B, finds all monomorphisms from A to B

findEpimorphisms :: Obj m -> Obj m -> [m] Source #

Given two objects A and B, finds all epimorphisms from A to B

findIsomorphisms :: Obj m -> Obj m -> [m] Source #

Given two objects A and B, finds all isomorphisms from A to B

findAllMorphisms :: Obj m -> Obj m -> [m] Source #

Given two objects A and B, finds all morphisms from A to B

induceSpanMorphism :: [m] -> [m] -> m Source #

Given two lists of TypedGraphMorphism fi : Ai -> B and gi : Ai -> C it induces a Morphism h : B -> C shuch that h . fi = gi for all i. The lists must have the same length and must not be empty.

partialInjectiveMatches :: m -> m -> [m] Source #

Given a NAC n : L -> N and a match m : L -> G, finds the morphisms from N to G that are injective out of the image of n

findCospanCommuter :: MorphismType -> m -> m -> [m] Source #

Given two TypedGraphMorphism f : B -> A and g : C -> A it finds a list of Morphisms hi : B -> C shuch that f . ¬g = hi for all i.