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

OAlg.Entity.Definition

Contents

Entity
Entity1
Entity2
Basic Entities
- Empty

Description

definition of entities. All algebraic structures defined here are based on them. They are showable, distinguishable, validable and typeable.

Synopsis

class (Show a, Eq a, Validable a, Typeable a) => Entity a
data Ent
class (Show1 a, Eq1 a, Validable1 a, Typeable a) => Entity1 a
class (Show2 h, Eq2 h, Validable2 h, Typeable h) => Entity2 h
data Empty
empty :: Empty -> x
data Empty2 a b
empty2 :: Empty2 a b -> x

Entity

class (Show a, Eq a, Validable a, Typeable a) => Entity a Source #

entity.

Instances

Instances details

Entity N Source #
Instance details Defined in OAlg.Entity.Definition
Entity Q Source #
Instance details Defined in OAlg.Entity.Definition
Entity Z Source #
Instance details Defined in OAlg.Entity.Definition
Entity Symbol Source #
Instance details Defined in OAlg.Entity.Definition
Entity Empty Source #
Instance details Defined in OAlg.Entity.Definition
Entity N' Source #
Instance details Defined in OAlg.Entity.Natural
Entity W' Source #
Instance details Defined in OAlg.Entity.Natural
Entity Integer Source #
Instance details Defined in OAlg.Entity.Definition
Entity () Source #
Instance details Defined in OAlg.Entity.Definition
Entity Char Source #
Instance details Defined in OAlg.Entity.Definition
Entity Int Source #
Instance details Defined in OAlg.Entity.Definition
(EmbeddableMorphismTyp m, Entity2 m) => Entity (SomeMorphism m) Source #
Instance details Defined in OAlg.Category.Unify
Typeable m => Entity (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify
Entity x => Entity (Op x) Source #
Instance details Defined in OAlg.Entity.Definition
(Additive x, FibredOriented x) => Entity (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
Galoisian x => Entity (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => Entity (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Typeable x => Entity (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => Entity (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Distributive k => Entity (DiagonalForm k) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Number k => Entity (DiagonalFormStrictPositive k) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Oriented a => Entity (RowTrafo a) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Semiring r => Entity (Vector r) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector
Entity x => Entity (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol
Entity x => Entity (U x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol
(Entity i, Ord i) => Entity (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
(Entity i, Ord i) => Entity (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
(Entity x, Ord x) => Entity (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set
Entity a => Entity (R a) Source #
Instance details Defined in OAlg.Entity.Sum.SumSymbol
Fibred f => Entity (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
Multiplicative c => Entity (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
Entity p => Entity (Orientation p) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
Oriented q => Entity (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
Entity a => Entity [a] Source #
Instance details Defined in OAlg.Entity.Definition
(Typeable n, Typeable m) => Entity (Quiver n m) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver
(Typeable n, Entity a) => Entity (FinList n a) Source #
Instance details Defined in OAlg.Entity.FinList
(Oriented x, Typeable p) => Entity (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
(Entity x, Entity i, Ord i) => Entity (Col i x) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries
(Entity x, Entity j, Ord j) => Entity (Row j x) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries
(Typeable x, Typeable y) => Entity (GLApp x y) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
(Typeable x, Typeable y) => Entity (TrApp x y) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
(Oriented a, Integral r) => Entity (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
(Oriented a, Number r) => Entity (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
(Entity x, Entity i, Ord i) => Entity (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph
(Entity x, Entity i, Ord i) => Entity (PSequence i x) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence
(Typeable c, Typeable k) => Entity (Free k c) Source #
Instance details Defined in OAlg.Entity.Slice.Free
(Entity a, Entity r) => Entity (LinearCombination r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
(Fibred a, Semiring r, Commutative r) => Entity (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
(Fibred a, Semiring r, Commutative r) => Entity (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
(Semiring r, Commutative r, Entity a) => Entity (SumSymbol r a) Source #
Instance details Defined in OAlg.Entity.Sum.SumSymbol
(KnownNat b, Entity r) => Entity (Digits b r) Source #
Instance details Defined in OAlg.Structure.Number.Definition
(Entity a, Entity b) => Entity (a, b) Source #
Instance details Defined in OAlg.Entity.Definition
(Entity x, Entity i, Entity j, Ord i, Ord j) => Entity (Entries i j x) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries
(Semiring r, Typeable x, Typeable y) => Entity (HomSymbol r x y) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector
(Oriented c, Sliced i c, Typeable s) => Entity (Slice s i c) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Multiplicative c, Sliced i c, Typeable s) => Entity (SliceFactor s i c) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Typeable s, Typeable x, Typeable y) => Entity (SliceFactorDrop s x y) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Typeable s, Typeable a, Typeable b) => Entity (HomOp s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(Typeable s, Typeable a, Typeable b) => Entity (IdHom s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(ForgetfulTyp s, Typeable s, Typeable a, Typeable b) => Entity (IsoOp s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(Multiplicative a, Typeable n) => Entity (FactorChain 'From n a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition
(Multiplicative a, Typeable n) => Entity (FactorChain 'To n a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition
(Oriented a, Typeable t, Typeable n, Typeable m) => Entity (Diagram t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Multiplicative a, Typeable t, Typeable n, Typeable m) => Entity (Transformation t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation
(Typeable i, Typeable c, Typeable x, Typeable y) => Entity (SliceCokernelKernel i c x y) Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction
(ForgetfulTyp s, Typeable f, Typeable s, Typeable a, Typeable b) => Entity (IsoOpMap f s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(Typeable f, Typeable s, Typeable a, Typeable b) => Entity (OpMap f s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(Typeable s, Typeable p, Typeable t, Typeable n, Typeable m, Typeable a) => Entity (Cone s p t n m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition
(Distributive a, Typeable s, Typeable p, Typeable t, Typeable n, Typeable m) => Entity (ConeZeroHead s p t n ('S m) a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition
(Distributive a, XStandardOrtPerspective p a, Typeable p, Typeable t, Typeable n, Typeable m) => Entity (Limes Dst p t n m a) Source #
Instance details Defined in OAlg.Limes.Definition
(Multiplicative a, XStandardOrtPerspective p a, Typeable p, Typeable t, Typeable n, Typeable m) => Entity (Limes Mlt p t n m a) Source #
Instance details Defined in OAlg.Limes.Definition

data Ent Source #

indexing Entitys.

Instances

Instances details

Transformable Abl Ent Source #
Instance details Defined in OAlg.Structure.Additive.Definition Methods tau :: Struct Abl x -> Struct Ent x Source #
Transformable Add Ent Source #
Instance details Defined in OAlg.Structure.Additive.Definition Methods tau :: Struct Add x -> Struct Ent x Source #
Transformable Dst Ent Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tau :: Struct Dst x -> Struct Ent x Source #
Transformable Fbr Ent Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Methods tau :: Struct Fbr x -> Struct Ent x Source #
Transformable FbrOrt Ent Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Methods tau :: Struct FbrOrt x -> Struct Ent x Source #
Transformable Mlt Ent Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tau :: Struct Mlt x -> Struct Ent x Source #
Transformable Ort Ent Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct Ort x -> Struct Ent x Source #
Transformable (Alg k) Ent Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Ent x Source #
Transformable (Vec k) Ent Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition Methods tau :: Struct (Vec k) x -> Struct Ent x Source #
type Structure Ent x Source #
Instance details Defined in OAlg.Entity.Definition type Structure Ent x = Entity x

Entity1

class (Show1 a, Eq1 a, Validable1 a, Typeable a) => Entity1 a Source #

entity for parameterized types.

Instances

Instances details

Entity1 (Proxy :: Type -> Type) Source #
Instance details Defined in OAlg.Entity.Definition
Typeable k => Entity1 (Free k) Source #
Instance details Defined in OAlg.Entity.Slice.Free

Entity2

class (Show2 h, Eq2 h, Validable2 h, Typeable h) => Entity2 h Source #

entity for two parameterized types.

Instances

Instances details

Entity2 Empty2 Source #
Instance details Defined in OAlg.Entity.Definition
Entity2 GLApp Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Entity2 TrApp Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
(Entity2 h, EmbeddableMorphismTyp h) => Entity2 (Path h) Source #
Instance details Defined in OAlg.Category.Path
Semiring r => Entity2 (HomSymbol r) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector
Typeable s => Entity2 (SliceFactorDrop s) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
Typeable s => Entity2 (HomOp s) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
Typeable s => Entity2 (IdHom s) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(ForgetfulTyp s, Typeable s) => Entity2 (IsoOp s) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
Entity2 h => Entity2 (OpHom h) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(Entity2 h, Typeable t) => Entity2 (Forget t h) Source #
Instance details Defined in OAlg.Entity.Definition
(Entity2 f, Entity2 g) => Entity2 (Either2 f g) Source #
Instance details Defined in OAlg.Entity.Definition
(Typeable i, Typeable c) => Entity2 (SliceCokernelKernel i c) Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction
(ForgetfulTyp s, Typeable f, Typeable s) => Entity2 (IsoOpMap f s) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
(Typeable f, Typeable s) => Entity2 (OpMap f s) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition

Basic Entities

Empty

data Empty Source #

the empty entity.

Instances

Instances details

Show Empty Source #
Instance details Defined in OAlg.Entity.Definition Methods showsPrec :: Int -> Empty -> ShowS # show :: Empty -> String # showList :: [Empty] -> ShowS #
Eq Empty Source #
Instance details Defined in OAlg.Entity.Definition Methods (==) :: Empty -> Empty -> Bool # (/=) :: Empty -> Empty -> Bool #
Ord Empty Source #
Instance details Defined in OAlg.Entity.Definition Methods compare :: Empty -> Empty -> Ordering # (<) :: Empty -> Empty -> Bool # (<=) :: Empty -> Empty -> Bool # (>) :: Empty -> Empty -> Bool # (>=) :: Empty -> Empty -> Bool # max :: Empty -> Empty -> Empty # min :: Empty -> Empty -> Empty #
Validable Empty Source #
Instance details Defined in OAlg.Entity.Definition Methods valid :: Empty -> Statement Source #
Entity Empty Source #
Instance details Defined in OAlg.Entity.Definition

empty :: Empty -> x Source #

the empty function.

data Empty2 a b Source #

the empty entity2.

Instances

Instances details

Eq2 Empty2 Source #
Instance details Defined in OAlg.Entity.Definition Methods eq2 :: Empty2 x y -> Empty2 x y -> Bool Source #
Show2 Empty2 Source #
Instance details Defined in OAlg.Entity.Definition Methods show2 :: Empty2 a b -> String Source #
Validable2 Empty2 Source #
Instance details Defined in OAlg.Entity.Definition Methods valid2 :: Empty2 x y -> Statement Source #
Entity2 Empty2 Source #
Instance details Defined in OAlg.Entity.Definition
Show (Empty2 a b) Source #
Instance details Defined in OAlg.Entity.Definition Methods showsPrec :: Int -> Empty2 a b -> ShowS # show :: Empty2 a b -> String # showList :: [Empty2 a b] -> ShowS #
Eq (Empty2 a b) Source #
Instance details Defined in OAlg.Entity.Definition Methods (==) :: Empty2 a b -> Empty2 a b -> Bool # (/=) :: Empty2 a b -> Empty2 a b -> Bool #
Validable (Empty2 x y) Source #
Instance details Defined in OAlg.Entity.Definition Methods valid :: Empty2 x y -> Statement Source #

empty2 :: Empty2 a b -> x Source #

the empty function.