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
data Struct s x where
- Struct :: forall s x. Structure s x => Struct s x
tauTuple :: Struct s x -> Struct t x -> Struct (s, t) x
tauFst :: Struct (s, t) x -> Struct s x
tauSnd :: Struct (s, t) x -> Struct t x
type family Structure2 m x y
data Struct2 m x y where
- Struct2 :: forall m x y. Structure2 m x y => Struct2 m x y
class Transformable s t where
- tau :: Struct s x -> Struct t x
tauType :: Struct s x -> Struct Type x
type Transformable1 (f :: Type -> Type) s = TransformableG f s s
tau1 :: Transformable1 f s => Struct s x -> Struct s (f x)
class Transformable s Typ => TransformableTyp s
class Transformable s Type => TransformableType s
class TransformableG (t :: Type -> Type) u v where
- tauG :: Struct u x -> Struct v (t x)
tauG' :: TransformableG t u v => q t -> Struct u x -> Struct v (t x)
class TransformableG o s s => TransformableGRefl (o :: Type -> Type) s
data Typ
tauTyp :: Transformable s Typ => Struct s x -> Struct Typ x
data Ord'
data Bol
data SubStruct t s
tauGSubStruct :: TransformableG t u v => Struct (SubStruct u s) x -> Struct v (t x)
tauSubStruct :: Struct (SubStruct t s) x -> Struct t x

Structure

type family Structure s x Source #

parameterized constraint for a type x.

Instances

Instances details

type Structure EqE x Source #
Instance details Defined in OAlg.Data.Validable type Structure EqE x = (Show x, Eq x, XStandard x)
type Structure XStd x Source #
Instance details Defined in OAlg.Data.Validable type Structure XStd x = XStandard x
type Structure Ent x Source #
Instance details Defined in OAlg.Entity.Definition type Structure Ent x = Entity x
type Structure EntOrd x Source #
Instance details Defined in OAlg.Entity.Definition type Structure EntOrd x = (Entity x, Ord x)
type Structure SldFr x Source #
Instance details Defined in OAlg.Entity.Slice.Free type Structure SldFr x = SlicedFree 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 Bol x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Bol x = Boolean 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 DstX x Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition type Structure DstX x = (Distributive x, XStandardOrtOrientation 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.FibredOriented type Structure FbrOrt x = FibredOriented x
type Structure FbrOrtX x Source #
Instance details Defined in OAlg.Structure.FibredOriented type Structure FbrOrtX x = (FibredOriented x, XStandard x, XStandardPoint x)
type Structure Mlt x Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition type Structure Mlt x = Multiplicative x
type Structure MltX x Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition type Structure MltX x = (Multiplicative x, XStandardMlt x)
type Structure EqEOrt x Source #
Instance details Defined in OAlg.Structure.Oriented.Definition type Structure EqEOrt x = (Show x, ShowPoint x, Eq x, EqPoint x, XStandard x, XStandardPoint x)
type Structure Ort x Source #
Instance details Defined in OAlg.Structure.Oriented.Definition type Structure Ort x = Oriented x
type Structure OrtX x Source #
Instance details Defined in OAlg.Structure.Oriented.Definition type Structure OrtX x = (Oriented x, XStandard x, XStandardPoint x)
type Structure OrtSiteX x Source #
Instance details Defined in OAlg.Structure.Oriented.X type Structure OrtSiteX x = (Oriented x, XStandardOrtSiteTo x, XStandardOrtSiteFrom x)
type Structure Type x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Type x = ()
type Structure (Sld i) x Source #
Instance details Defined in OAlg.Entity.Slice.Sliced type Structure (Sld i) x = Sliced i 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)
type Structure (SubStruct t s) x Source #
Instance details Defined in OAlg.Structure.Definition type Structure (SubStruct t s) x = Structure t x
type Structure (s, t) x Source #
Instance details Defined in OAlg.Structure.Definition type Structure (s, t) x = (Structure s x, Structure t x)

data Struct s x where Source #

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

Constructors

Struct :: forall s x. 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 :: 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 #

tauTuple :: Struct s x -> Struct t x -> Struct (s, t) x Source #

the product structure.

tauFst :: Struct (s, t) x -> Struct s x Source #

the first struct according to (s,t).

tauSnd :: Struct (s, t) x -> Struct t x Source #

the second struct according to (s,t).

type family Structure2 m x y Source #

parameterized constraint for a two types x and y.

data Struct2 m x y where Source #

attest that the two types x and y admit the constraint given by the parameter s.

Constructors

Struct2 :: forall m x y. Structure2 m x y => Struct2 m x y

Instances

Instances details

Eq2 (Struct2 m) Source #
Instance details Defined in OAlg.Structure.Definition Methods eq2 :: Struct2 m x y -> Struct2 m x y -> Bool Source #
Show2 (Struct2 m) Source #
Instance details Defined in OAlg.Structure.Definition Methods show2 :: Struct2 m a b -> String Source #
Validable2 (Struct2 m) Source #
Instance details Defined in OAlg.Data.Validable Methods valid2 :: Struct2 m x y -> Statement Source #
Show (Struct2 m x y) Source #
Instance details Defined in OAlg.Structure.Definition Methods showsPrec :: Int -> Struct2 m x y -> ShowS # show :: Struct2 m x y -> String # showList :: [Struct2 m x y] -> ShowS #
Eq (Struct2 m x y) Source #
Instance details Defined in OAlg.Structure.Definition Methods (==) :: Struct2 m x y -> Struct2 m x y -> Bool # (/=) :: Struct2 m x y -> Struct2 m x y -> Bool #
Validable (Struct2 m x y) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Struct2 m x y -> 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 EqE Type Source #
Instance details Defined in OAlg.Data.Validable Methods tau :: Struct EqE x -> Struct Type x Source #
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 Dst Type Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tau :: Struct Dst x -> Struct Type x Source #
Transformable DstX Add Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Add x Source #
Transformable DstX Typ Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Typ x Source #
Transformable DstX Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Dst x Source #
Transformable DstX Fbr Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Fbr x Source #
Transformable DstX FbrOrt Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct FbrOrt x Source #
Transformable DstX Mlt Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Mlt x Source #
Transformable DstX Ort Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Ort x Source #
Transformable DstX Type Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct Type 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.FibredOriented Methods tau :: Struct FbrOrt x -> Struct Ent x Source #
Transformable FbrOrt Typ Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrt x -> Struct Typ x Source #
Transformable FbrOrt Fbr Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrt x -> Struct Fbr x Source #
Transformable FbrOrt Ort Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrt x -> Struct Ort x Source #
Transformable FbrOrt Type Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrt x -> Struct Type x Source #
Transformable FbrOrtX Typ Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX x -> Struct Typ x Source #
Transformable FbrOrtX Fbr Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX x -> Struct Fbr x Source #
Transformable FbrOrtX FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX x -> Struct FbrOrt x Source #
Transformable FbrOrtX Ort Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX x -> Struct Ort x Source #
Transformable FbrOrtX Type Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX x -> Struct Type 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 Mlt Type Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tau :: Struct Mlt x -> Struct Type x Source #
Transformable MltX Typ Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods tau :: Struct MltX x -> Struct Typ x Source #
Transformable MltX Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods tau :: Struct MltX x -> Struct Mlt x Source #
Transformable MltX Ort Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods tau :: Struct MltX x -> Struct Ort x Source #
Transformable MltX Type Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods tau :: Struct MltX x -> Struct Type x Source #
Transformable EqEOrt Type Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct EqEOrt x -> Struct Type 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 Ort Type Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct Ort x -> Struct Type x Source #
Transformable OrtX XStd Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct XStd x Source #
Transformable OrtX Typ Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct Typ x Source #
Transformable OrtX EqEOrt Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct EqEOrt x Source #
Transformable OrtX Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct Ort x Source #
Transformable OrtX Type Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct Type x Source #
Transformable OrtSiteX Typ Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods tau :: Struct OrtSiteX x -> Struct Typ x Source #
Transformable OrtSiteX Ort Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods tau :: Struct OrtSiteX x -> Struct Ort x Source #
Transformable OrtSiteX Type Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods tau :: Struct OrtSiteX 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 t (SubStruct t s) Source #
Instance details Defined in OAlg.Structure.Definition Methods tau :: Struct t x -> Struct (SubStruct t 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 #
Transformable (s, SldFr) SldFr Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct SldFr x Source #
Transformable s Add => Transformable (s, SldFr) Add Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct Add x Source #
Transformable s Dst => Transformable (s, SldFr) Dst Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct Dst x Source #
Transformable s Fbr => Transformable (s, SldFr) Fbr Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct Fbr x Source #
Transformable s FbrOrt => Transformable (s, SldFr) FbrOrt Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct FbrOrt x Source #
Transformable s Mlt => Transformable (s, SldFr) Mlt Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct Mlt x Source #
Transformable s Ort => Transformable (s, SldFr) Ort Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct Ort x Source #
Transformable s Add => Transformable (s, Sld i) Add Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct Add x Source #
Transformable s Dst => Transformable (s, Sld i) Dst Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct Dst x Source #
Transformable s Fbr => Transformable (s, Sld i) Fbr Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct Fbr x Source #
Transformable s FbrOrt => Transformable (s, Sld i) FbrOrt Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct FbrOrt x Source #
Transformable s Mlt => Transformable (s, Sld i) Mlt Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct Mlt x Source #
Transformable s Ort => Transformable (s, Sld i) Ort Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct Ort x Source #
Transformable (s, Sld i) Type Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct Type x Source #
Attestable k => Transformable (s, SldFr) (Sld (Free k)) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods tau :: Struct (s, SldFr) x -> Struct (Sld (Free k)) x Source #
Transformable (s, Sld i) (Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tau :: Struct (s, Sld i) x -> Struct (Sld i) x Source #

tauType :: Struct s x -> Struct Type x Source #

transformbing to Type-structure.

type Transformable1 (f :: Type -> Type) s = TransformableG f s s Source #

transforming structural attests.

tau1 :: Transformable1 f s => Struct s x -> Struct s (f x) Source #

transformation1. (needed for backward compatibility!).

class Transformable s Typ => TransformableTyp s Source #

helper class to avoid undecidable instances.

Instances

Instances details

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

class Transformable s Type => TransformableType s Source #

helper class to avoid undecidable instances.

Instances

Instances details

TransformableType EqE Source #
Instance details Defined in OAlg.Data.Validable
TransformableType Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition
TransformableType DstX Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition
TransformableType FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableType Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
TransformableType MltX Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition
TransformableType Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
TransformableType OrtX Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
TransformableType OrtSiteX Source #
Instance details Defined in OAlg.Structure.Oriented.X
TransformableType (s, Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced

class TransformableG (t :: Type -> Type) u v where Source #

transforming structural attests.

Methods

tauG :: Struct u x -> Struct v (t x) Source #

Instances

Instances details

TransformableG Id OrtX EqE Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tauG :: Struct OrtX x -> Struct EqE (Id x) Source #
TransformableG Id OrtX EqEOrt Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tauG :: Struct OrtX x -> Struct EqEOrt (Id x) Source #
TransformableG Matrix Dst Dst Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods tauG :: Struct Dst x -> Struct Dst (Matrix x) Source #
TransformableG Matrix DstX DstX Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods tauG :: Struct DstX x -> Struct DstX (Matrix x) Source #
TransformableG Op Dst Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tauG :: Struct Dst x -> Struct Dst (Op x) Source #
TransformableG Op DstX DstX Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tauG :: Struct DstX x -> Struct DstX (Op x) Source #
TransformableG Op FbrOrt FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tauG :: Struct FbrOrt x -> Struct FbrOrt (Op x) Source #
TransformableG Op FbrOrtX FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tauG :: Struct FbrOrtX x -> Struct FbrOrtX (Op x) Source #
TransformableG Op Mlt Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tauG :: Struct Mlt x -> Struct Mlt (Op x) Source #
TransformableG Op MltX MltX Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods tauG :: Struct MltX x -> Struct MltX (Op x) Source #
TransformableG Op EqEOrt EqEOrt Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite Methods tauG :: Struct EqEOrt x -> Struct EqEOrt (Op x) Source #
TransformableG Op Ort Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite Methods tauG :: Struct Ort x -> Struct Ort (Op x) Source #
TransformableG Op OrtX OrtX Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite Methods tauG :: Struct OrtX x -> Struct OrtX (Op x) Source #
TransformableG Op OrtSiteX OrtSiteX Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods tauG :: Struct OrtSiteX x -> Struct OrtSiteX (Op x) Source #
TransformableG Pnt OrtX EqE Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tauG :: Struct OrtX x -> Struct EqE (Pnt x) Source #
TransformableG Pnt OrtX EqEOrt Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tauG :: Struct OrtX x -> Struct EqEOrt (Pnt x) Source #
TransformableG [] EntOrd EntOrd Source #
Instance details Defined in OAlg.Entity.Definition Methods tauG :: Struct EntOrd x -> Struct EntOrd [x] Source #
TransformableG d s Type Source #
Instance details Defined in OAlg.Structure.Definition Methods tauG :: Struct s x -> Struct Type (d x) Source #
(TransformableG d s u, TransformableG d s v) => TransformableG d s (u, v) Source #
Instance details Defined in OAlg.Structure.Definition Methods tauG :: Struct s x -> Struct (u, v) (d x) Source #
TransformableG Op (Sld i) (Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tauG :: Struct (Sld i) x -> Struct (Sld i) (Op x) Source #
TransformableG Op (Alg k) (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tauG :: Struct (Alg k) x -> Struct (Alg k) (Op x) Source #
TransformableG Op (Dst, t) Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tauG :: Struct (Dst, t) x -> Struct Dst (Op x) Source #
TransformableG Op (Mlt, t) Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tauG :: Struct (Mlt, t) x -> Struct Mlt (Op x) Source #
TransformableG Op (Ort, t) Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite Methods tauG :: Struct (Ort, t) x -> Struct Ort (Op x) Source #
TransformableG Op (s, Sld i) (Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced Methods tauG :: Struct (s, Sld i) x -> Struct (Sld i) (Op x) Source #
(Attestable m, n ~ (m + 1)) => TransformableG (SDualBi (Diagram ('Chain 'From) n m)) OrtSiteX EqE Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods tauG :: Struct OrtSiteX x -> Struct EqE (SDualBi (Diagram ('Chain 'From) n m) x) Source #
(Attestable m, n ~ (m + 1)) => TransformableG (SDualBi (Diagram ('Chain 'To) n m)) OrtSiteX EqE Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods tauG :: Struct OrtSiteX x -> Struct EqE (SDualBi (Diagram ('Chain 'To) n m) x) Source #

tauG' :: TransformableG t u v => q t -> Struct u x -> Struct v (t x) Source #

prefixing a proxy.

class TransformableG o s s => TransformableGRefl (o :: Type -> Type) s Source #

helper class to avoid undecidable instances.

Instances

Instances details

TransformableGRefl Matrix Dst Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
TransformableGRefl Matrix DstX Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
TransformableGRefl Op Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition
TransformableGRefl Op DstX Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition
TransformableGRefl Op FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableGRefl Op Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
TransformableGRefl Op Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
TransformableGRefl Op OrtX Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
TransformableGRefl Op OrtSiteX Source #
Instance details Defined in OAlg.Structure.Oriented.X
TransformableGRefl Op (Dst, Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced
TransformableGRefl Op (Mlt, Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced
TransformableGRefl Op (Ort, Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced

Some Structure Types

data Typ Source #

type index for Typeable structures.

Instances

Instances details

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 DstX Typ Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX 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.FibredOriented Methods tau :: Struct FbrOrt x -> Struct Typ x Source #
Transformable FbrOrtX Typ Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX 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 MltX Typ Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods tau :: Struct MltX 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 #
Transformable OrtX Typ Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct Typ x Source #
Transformable OrtSiteX Typ Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods tau :: Struct OrtSiteX x -> Struct Typ 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 (Vec k) Typ Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition Methods tau :: Struct (Vec k) x -> Struct Typ x Source #
type Structure Typ x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Typ x = Typeable x

tauTyp :: Transformable s Typ => Struct s x -> Struct Typ x Source #

tau to Typ

data Ord' Source #

type index for ordered structures.

Instances

Instances details

ApplicativeG Set (Map Ord') (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods amapG :: Map Ord' x y -> Set x -> Set y Source #
FunctorialG Set (Map Ord') (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set
type Structure Ord' x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Ord' x = Ord x

data Bol Source #

type index for Boolean structures.

Instances

Instances details

type Structure Bol x Source #
Instance details Defined in OAlg.Structure.Definition type Structure Bol x = Boolean x

data SubStruct t s Source #

type index for parameterized sub structures.

Instances

Instances details

Transformable t (SubStruct t s) Source #
Instance details Defined in OAlg.Structure.Definition Methods tau :: Struct t x -> Struct (SubStruct t s) x Source #
type Structure (SubStruct t s) x Source #
Instance details Defined in OAlg.Structure.Definition type Structure (SubStruct t s) x = Structure t x

tauGSubStruct :: TransformableG t u v => Struct (SubStruct u s) x -> Struct v (t x) Source #

generalized transformation of a sub structure.

tauSubStruct :: Struct (SubStruct t s) x -> Struct t x Source #

transforming a sub structure to its base.