Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Category.Unify

Contents

Morphism
Path
Entity
Application

Description

unification of categories, i.e. projecting morphisms by dropping the parameterization by there domain and range.

Synopsis

data SomeMorphism m where
- SomeMorphism :: m x y -> SomeMorphism m
data SomeObjectClass m where
- SomeObjectClass :: Transformable (ObjectClass m) Typ => Struct (ObjectClass m) x -> SomeObjectClass m
data SomeMorphismSite s m x where
- SomeMorphismDomain :: m x y -> SomeMorphismSite From m x
- SomeMorphismRange :: m x y -> SomeMorphismSite To m y
data SomePath m where
- SomePath :: Path m x y -> SomePath m
somePath :: SomePathSite s m x -> SomePath m
data SomePathSite s m x where
- SomePathDomain :: Path m x y -> SomePathSite From m x
- SomePathRange :: Path m x y -> SomePathSite To m y
data SomeEntity m where
- SomeEntity :: Entity x => Struct (ObjectClass m) x -> x -> SomeEntity m
data SomeApplication h where
- SomeApplication :: h x y -> x -> SomeApplication h

Morphism

data SomeMorphism m where Source #

some morphism.

Constructors

SomeMorphism :: m x y -> SomeMorphism m

Instances

Instances details

Show2 m => Show (SomeMorphism m) Source #
Instance details Defined in OAlg.Category.Unify Methods showsPrec :: Int -> SomeMorphism m -> ShowS # show :: SomeMorphism m -> String # showList :: [SomeMorphism m] -> ShowS #
(EmbeddableMorphismTyp m, Typeable m, Eq2 m) => Eq (SomeMorphism m) Source #
Instance details Defined in OAlg.Category.Unify Methods (==) :: SomeMorphism m -> SomeMorphism m -> Bool # (/=) :: SomeMorphism m -> SomeMorphism m -> Bool #
Validable2 m => Validable (SomeMorphism m) Source #
Instance details Defined in OAlg.Category.Unify Methods valid :: SomeMorphism m -> Statement Source #
(EmbeddableMorphismTyp m, Entity2 m) => Entity (SomeMorphism m) Source #
Instance details Defined in OAlg.Category.Unify
(EmbeddableMorphismTyp m, Entity2 m) => Oriented (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Associated Types type Point (SomeMorphism m) Source # Methods orientation :: SomeMorphism m -> Orientation (Point (SomeMorphism m)) Source # start :: SomeMorphism m -> Point (SomeMorphism m) Source # end :: SomeMorphism m -> Point (SomeMorphism m) Source #
type Point (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition type Point (SomeMorphism m) = SomeObjectClass m

data SomeObjectClass m where Source #

some object class.

Constructors

SomeObjectClass :: Transformable (ObjectClass m) Typ => Struct (ObjectClass m) x -> SomeObjectClass m

Instances

Instances details

Show (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify Methods showsPrec :: Int -> SomeObjectClass m -> ShowS # show :: SomeObjectClass m -> String # showList :: [SomeObjectClass m] -> ShowS #
Eq (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify Methods (==) :: SomeObjectClass m -> SomeObjectClass m -> Bool # (/=) :: SomeObjectClass m -> SomeObjectClass m -> Bool #
Dualisable (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify Methods toDual :: SomeObjectClass m -> Dual (SomeObjectClass m) Source # fromDual :: Dual (SomeObjectClass m) -> SomeObjectClass m Source #
Validable (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify Methods valid :: SomeObjectClass m -> Statement Source #
Typeable m => Entity (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify
type Dual (SomeObjectClass m :: Type) Source #
Instance details Defined in OAlg.Category.Unify type Dual (SomeObjectClass m :: Type) = SomeObjectClass (Op2 m)

data SomeMorphismSite s m x where Source #

some morphism given by a Site.

Constructors

SomeMorphismDomain :: m x y -> SomeMorphismSite From m x
SomeMorphismRange :: m x y -> SomeMorphismSite To m y

Instances

Instances details

Dualisable (SomeMorphismSite 'To m y) Source #
Instance details Defined in OAlg.Category.Unify Methods toDual :: SomeMorphismSite 'To m y -> Dual (SomeMorphismSite 'To m y) Source # fromDual :: Dual (SomeMorphismSite 'To m y) -> SomeMorphismSite 'To m y Source #
type Dual (SomeMorphismSite s m y :: Type) Source #
Instance details Defined in OAlg.Category.Unify type Dual (SomeMorphismSite s m y :: Type) = SomeMorphismSite (Dual s) (Op2 m) y

Path

data SomePath m where Source #

some path

Constructors

SomePath :: Path m x y -> SomePath m

Instances

Instances details

Show2 m => Show (SomePath m) Source #
Instance details Defined in OAlg.Category.Unify Methods showsPrec :: Int -> SomePath m -> ShowS # show :: SomePath m -> String # showList :: [SomePath m] -> ShowS #
Morphism m => Dualisable (SomePath m) Source #
Instance details Defined in OAlg.Category.Unify Methods toDual :: SomePath m -> Dual (SomePath m) Source # fromDual :: Dual (SomePath m) -> SomePath m Source #
type Dual (SomePath m :: Type) Source #
Instance details Defined in OAlg.Category.Unify type Dual (SomePath m :: Type) = SomePath (Op2 m)

somePath :: SomePathSite s m x -> SomePath m Source #

embedding.

data SomePathSite s m x where Source #

some path parameterized either by its domain or range.

Constructors

SomePathDomain :: Path m x y -> SomePathSite From m x
SomePathRange :: Path m x y -> SomePathSite To m y

Instances

Instances details

Morphism m => Dualisable (SomePathSite 'To m y) Source #
Instance details Defined in OAlg.Category.Unify Methods toDual :: SomePathSite 'To m y -> Dual (SomePathSite 'To m y) Source # fromDual :: Dual (SomePathSite 'To m y) -> SomePathSite 'To m y Source #
type Dual (SomePathSite s m y :: Type) Source #
Instance details Defined in OAlg.Category.Unify type Dual (SomePathSite s m y :: Type) = SomePathSite (Dual s) (Op2 m) y

Entity

data SomeEntity m where Source #

some entity x in x having the given ObjectClass m as structure.

Constructors

SomeEntity :: Entity x => Struct (ObjectClass m) x -> x -> SomeEntity m

Application

data SomeApplication h where Source #

some application.

Constructors

SomeApplication :: h x y -> x -> SomeApplication h