Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
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 :: Type -> Type -> Type) where
- SomeMorphism :: forall (m :: Type -> Type -> Type) x y. m x y -> SomeMorphism m
data SomeObjectClass (m :: Type -> Type -> Type) where
- SomeObjectClass :: forall (m :: Type -> Type -> Type) x. Transformable (ObjectClass m) Typ => Struct (ObjectClass m) x -> SomeObjectClass m
data SomeMorphismSite (s :: Site) (m :: Type -> Type -> Type) x where
- SomeMorphismDomain :: forall (m :: Type -> Type -> Type) x y. m x y -> SomeMorphismSite 'From m x
- SomeMorphismRange :: forall (m :: Type -> Type -> Type) x1 x. m x1 x -> SomeMorphismSite 'To m x
someOne :: forall (c :: Type -> Type -> Type). Category c => SomeObjectClass c -> SomeMorphism c
data SomeCmpb3 (c :: Type -> Type -> Type) where
- SomeCmpb3 :: forall (c :: Type -> Type -> Type) x w y z. c x w -> c y x -> c z y -> SomeCmpb3 c
data SomeCmpb2 (c :: Type -> Type -> Type) where
- SomeCmpb2 :: forall (c :: Type -> Type -> Type) y z x. c y z -> c x y -> SomeCmpb2 c
smCmpb2 :: forall (h :: Type -> Type -> Type). Category h => SomeCmpb2 h -> SomeMorphism h
data SomePath (m :: Type -> Type -> Type) where
- SomePath :: forall (m :: Type -> Type -> Type) x y. Path m x y -> SomePath m
somePath :: forall (s :: Site) (m :: Type -> Type -> Type) x. SomePathSite s m x -> SomePath m
data SomePathSite (s :: Site) (m :: Type -> Type -> Type) x where
- SomePathDomain :: forall (m :: Type -> Type -> Type) x y. Path m x y -> SomePathSite 'From m x
- SomePathRange :: forall (m :: Type -> Type -> Type) x1 x. Path m x1 x -> SomePathSite 'To m x
data SomeEntity (m :: Type -> Type -> Type) where
- SomeEntity :: forall x (m :: Type -> Type -> Type). Entity x => Struct (ObjectClass m) x -> x -> SomeEntity m
data SomeApplication (h :: Type -> Type -> Type) where
- SomeApplication :: forall (h :: Type -> Type -> Type) x y. h x y -> x -> SomeApplication h
xSomeAppl :: (Morphism m, Transformable (ObjectClass m) XStd) => m x y -> X (SomeApplication m)

Morphism

data SomeMorphism (m :: Type -> Type -> Type) where Source #

some morphism.

Constructors

SomeMorphism :: forall (m :: Type -> Type -> Type) x y. 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 #
(Morphism m, TransformableObjectClassTyp 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 #
(Morphism m, TransformableObjectClassTyp m, Entity2 m) => Oriented (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods orientation :: SomeMorphism m -> Orientation (Point (SomeMorphism m)) Source # start :: SomeMorphism m -> Point (SomeMorphism m) Source # end :: SomeMorphism m -> Point (SomeMorphism m) Source #
EqPoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
Typeable m => TypeablePoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
type Point (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (SomeMorphism m) = SomeObjectClass m

data SomeObjectClass (m :: Type -> Type -> Type) where Source #

some object class.

Constructors

SomeObjectClass :: forall (m :: Type -> Type -> Type) x. 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 #
type Dual (SomeObjectClass m :: Type) Source #
Instance details Defined in OAlg.Category.Unify type Dual (SomeObjectClass m :: Type) = SomeObjectClass (Op2 m)

data SomeMorphismSite (s :: Site) (m :: Type -> Type -> Type) x where Source #

some morphism given by a Site.

Constructors

SomeMorphismDomain :: forall (m :: Type -> Type -> Type) x y. m x y -> SomeMorphismSite 'From m x
SomeMorphismRange :: forall (m :: Type -> Type -> Type) x1 x. m x1 x -> SomeMorphismSite 'To m x

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

someOne :: forall (c :: Type -> Type -> Type). Category c => SomeObjectClass c -> SomeMorphism c Source #

some cOne for some object class.

data SomeCmpb3 (c :: Type -> Type -> Type) where Source #

some composable morphisms.

Constructors

SomeCmpb3 :: forall (c :: Type -> Type -> Type) x w y z. c x w -> c y x -> c z y -> SomeCmpb3 c

data SomeCmpb2 (c :: Type -> Type -> Type) where Source #

some composable morphisms.

Constructors

SomeCmpb2 :: forall (c :: Type -> Type -> Type) y z x. c y z -> c x y -> SomeCmpb2 c

smCmpb2 :: forall (h :: Type -> Type -> Type). Category h => SomeCmpb2 h -> SomeMorphism h Source #

composing the two composables.

Path

data SomePath (m :: Type -> Type -> Type) where Source #

some path

Constructors

SomePath :: forall (m :: Type -> Type -> Type) x y. 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 :: forall (s :: Site) (m :: Type -> Type -> Type) x. SomePathSite s m x -> SomePath m Source #

embedding.

data SomePathSite (s :: Site) (m :: Type -> Type -> Type) x where Source #

some path parameterized either by its domain or range.

Constructors

SomePathDomain :: forall (m :: Type -> Type -> Type) x y. Path m x y -> SomePathSite 'From m x
SomePathRange :: forall (m :: Type -> Type -> Type) x1 x. Path m x1 x -> SomePathSite 'To m x

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 :: Type -> Type -> Type) where Source #

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

Constructors

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

Application

data SomeApplication (h :: Type -> Type -> Type) where Source #

some application.

Constructors

SomeApplication :: forall (h :: Type -> Type -> Type) x y. h x y -> x -> SomeApplication h

xSomeAppl :: (Morphism m, Transformable (ObjectClass m) XStd) => m x y -> X (SomeApplication m) Source #

random variable for some application.