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

OAlg.Structure.Definition

Contents

Structure
Transformable
Some Structure Types

Description

introducing the idiom of Structures as parameterized constraints.

Synopsis

type family Structure s x :: Constraint
data Struct s x where
- Struct :: Structure s x => Struct s x
class Transformable s t where
- tau :: Struct s x -> Struct t x
class Transformable1 f s where
- tau1 :: Struct s x -> Struct s (f x)
class Transformable1 Op s => TransformableOp s
class Transformable s Typ => ForgetfulTyp s
data Typ
data Ord'

Structure

type family Structure s x :: Constraint Source #

parameterized constraint for a type x.

Instances

Instances details

type Structure Bol x Source #
Instance details Defined in OAlg.Data.Boolean.Definition type Structure Bol x = Boolean x
type Structure Ent x Source #
Instance details Defined in OAlg.Entity.Definition type Structure Ent x = Entity x
type Structure Abl x Source #
Instance details Defined in OAlg.Structure.Additive.Definition type Structure Abl x = Abelian x
type Structure Add x Source #
Instance details Defined in OAlg.Structure.Additive.Definition type Structure Add x = Additive x
type Structure Ord' x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Ord' x = Ord x
type Structure Typ x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Typ x = Typeable x
type Structure Dst x Source #
Instance details Defined in OAlg.Structure.Distributive.Definition type Structure Dst x = Distributive x
type Structure Fbr x Source #
Instance details Defined in OAlg.Structure.Fibred.Definition type Structure Fbr x = Fibred x
type Structure FbrOrt x Source #
Instance details Defined in OAlg.Structure.Fibred.Definition type Structure FbrOrt x = FibredOriented x
type Structure Mlt x Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition type Structure Mlt x = Multiplicative x
type Structure Ort x Source #
Instance details Defined in OAlg.Structure.Oriented.Definition type Structure Ort x = Oriented x
type Structure Type x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Type x = ()
type Structure (Alg k) x Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition type Structure (Alg k) x = (Algebraic x, k ~ Scalar x)
type Structure (Vec k) x Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition type Structure (Vec k) x = (Vectorial x, k ~ Scalar x)

data Struct s x where Source #

attest that the type x admits the constrains given by the parameter s.

Constructors

Struct :: Structure s x => Struct s x

Instances

Instances details

Transformable s Typ => TestEquality (Struct s :: Type -> Type) Source #
Instance details Defined in OAlg.Structure.Definition Methods testEquality :: forall (a :: k) (b :: k). Struct s a -> Struct s b -> Maybe (a :~: b) #
Eq1 (Struct s) Source #
Instance details Defined in OAlg.Structure.Definition Methods eq1 :: Struct s x -> Struct s x -> Bool Source #
Show1 (Struct s) Source #
Instance details Defined in OAlg.Structure.Definition Methods show1 :: Struct s x -> String Source #
Singular (Struct s) Source #
Instance details Defined in OAlg.Structure.Definition
Validable1 (Struct s) Source #
Instance details Defined in OAlg.Data.Validable Methods valid1 :: Struct s x -> Statement Source #
Show (Struct s x) Source #
Instance details Defined in OAlg.Structure.Definition Methods showsPrec :: Int -> Struct s x -> ShowS # show :: Struct s x -> String # showList :: [Struct s x] -> ShowS #
Eq (Struct s x) Source #
Instance details Defined in OAlg.Structure.Definition Methods (==) :: Struct s x -> Struct s x -> Bool # (/=) :: Struct s x -> Struct s x -> Bool #
Validable (Struct s x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Struct s x -> Statement Source #

Transformable

class Transformable s t where Source #

transforming structural attests.

Methods

tau :: Struct s x -> Struct t x Source #

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

class Transformable1 f s where Source #

transforming structural attests.

Methods

tau1 :: Struct s x -> Struct s (f x) Source #

Instances

Instances details

Transformable1 Op Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tau1 :: Struct Dst x -> Struct Dst (Op x) Source #
Transformable1 Op Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tau1 :: Struct Mlt x -> Struct Mlt (Op x) Source #
Transformable1 Op Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau1 :: Struct Ort x -> Struct Ort (Op x) Source #
Transformable1 Op (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau1 :: Struct (Alg k) x -> Struct (Alg k) (Op x) Source #

class Transformable1 Op s => TransformableOp s Source #

helper class to avoid undecidable instances.

Instances

Instances details

TransformableOp Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition
TransformableOp Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
TransformableOp Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Definition

class Transformable s Typ => ForgetfulTyp s Source #

helper class to avoid undecidable instances.

Instances

Instances details

ForgetfulTyp Abl Source #
Instance details Defined in OAlg.Structure.Additive.Definition
ForgetfulTyp Add Source #
Instance details Defined in OAlg.Structure.Additive.Definition
ForgetfulTyp Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition
ForgetfulTyp Fbr Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
ForgetfulTyp FbrOrt Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
ForgetfulTyp Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
ForgetfulTyp Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
ForgetfulTyp (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulTyp (Vec k) Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition

Some Structure Types

data Typ Source #

Typeable structures.

Instances

Instances details

EmbeddableMorphism GLApp Typ Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
EmbeddableMorphism TrApp Typ Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Transformable Abl Typ Source #
Instance details Defined in OAlg.Structure.Additive.Definition Methods tau :: Struct Abl x -> Struct Typ x Source #
Transformable Add Typ Source #
Instance details Defined in OAlg.Structure.Additive.Definition Methods tau :: Struct Add x -> Struct Typ x Source #
Transformable Dst Typ Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tau :: Struct Dst x -> Struct Typ x Source #
Transformable Fbr Typ Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Methods tau :: Struct Fbr x -> Struct Typ x Source #
Transformable FbrOrt Typ Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Methods tau :: Struct FbrOrt x -> Struct Typ x Source #
Transformable Mlt Typ Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tau :: Struct Mlt x -> Struct Typ x Source #
Transformable Ort Typ Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct Ort x -> Struct Typ x Source #
(Semiring r, Commutative r) => EmbeddableMorphism (HomSymbol r) Typ Source #
Instance details Defined in OAlg.Entity.Matrix.Vector
EmbeddableMorphism (SliceFactorDrop s) Typ Source #
Instance details Defined in OAlg.Entity.Slice.Definition
EmbeddableMorphism h Typ => EmbeddableMorphism (OpHom h) Typ Source #
Instance details Defined in OAlg.Hom.Oriented.Definition
Transformable (Alg k) Typ Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Typ x Source #
Transformable (Vec k) Typ Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition Methods tau :: Struct (Vec k) x -> Struct Typ x Source #
(Multiplicative c, Sliced i c) => EmbeddableMorphism (SliceCokernelKernel i c) Typ Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction
type Structure Typ x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Typ x = Typeable x

data Ord' Source #

type for ordered structures.

Instances

Instances details

type Structure Ord' x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Ord' x = Ord x