Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
Language	Haskell2010

OAlg.Structure.FibredOriented

Contents

Fibred Oriented
X
Proposition
Orphan instances

Description

definition of FibredOriented structures.

Synopsis

class (Fibred d, Oriented d, Root d ~ Orientation (Point d)) => FibredOriented d
data FbrOrt
class (TransformableFbr s, TransformableOrt s, Transformable s FbrOrt) => TransformableFbrOrt s
tauFbrOrt :: Transformable s FbrOrt => Struct s x -> Struct FbrOrt x
xoFbrOrt :: XOrtOrientation f -> XFbrOrt f
xFbrOrtOrnt :: X p -> XFbrOrt (Orientation p)
type XFbrOrt = X
data FbrOrtX
prpFbrOrt :: FibredOriented f => XFbrOrt f -> Statement

Fibred Oriented

class (Fibred d, Oriented d, Root d ~ Orientation (Point d)) => FibredOriented d Source #

Fibred and Oriented structure with matching root and orientation.

Property Let d be a FibredOriented structure, then holds:

root .=. orientation.

Note FibredOriented structures are required for Distributive structures.

Instances

Instances details

FibredOriented N Source #
Instance details Defined in OAlg.Structure.FibredOriented
FibredOriented Q Source #
Instance details Defined in OAlg.Structure.FibredOriented
FibredOriented Z Source #
Instance details Defined in OAlg.Structure.FibredOriented
FibredOriented N' Source #
Instance details Defined in OAlg.Entity.Natural
FibredOriented W' Source #
Instance details Defined in OAlg.Entity.Natural
FibredOriented Integer Source #
Instance details Defined in OAlg.Structure.FibredOriented
FibredOriented () Source #
Instance details Defined in OAlg.Structure.FibredOriented
FibredOriented Int Source #
Instance details Defined in OAlg.Structure.FibredOriented
FibredOriented x => FibredOriented (Id x) Source #
Instance details Defined in OAlg.Structure.FibredOriented
(Additive x, FibredOriented x) => FibredOriented (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
FibredOriented x => FibredOriented (Op x) Source #
Instance details Defined in OAlg.Structure.FibredOriented
Entity p => FibredOriented (Orientation p) Source #
Instance details Defined in OAlg.Structure.FibredOriented
(Semiring r, Commutative r, FibredOriented m) => FibredOriented (Sum r m) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
(Semiring r, Commutative r, FibredOriented m) => FibredOriented (SumForm r m) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
(Distributive x, Typeable t, Typeable n) => FibredOriented (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero
(Distributive a, Typeable t, Typeable n, Typeable m) => FibredOriented (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation

data FbrOrt Source #

type representing the class of FibredOriented structures.

Instances

Instances details

TransformableTyp FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableFbr FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableFbrOrt FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableOrt FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableOp FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
Transformable Dst FbrOrt Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tau :: Struct Dst x -> Struct FbrOrt x Source #
Transformable DstX FbrOrt Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods tau :: Struct DstX x -> Struct FbrOrt 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 FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tau :: Struct FbrOrtX x -> Struct FbrOrt x Source #
TransformableGRefl Op FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableG Op FbrOrt FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tauG :: Struct FbrOrt x -> Struct FbrOrt (Op 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 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 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 #
type Structure FbrOrt x Source #
Instance details Defined in OAlg.Structure.FibredOriented type Structure FbrOrt x = FibredOriented x

class (TransformableFbr s, TransformableOrt s, Transformable s FbrOrt) => TransformableFbrOrt s Source #

helper class to avoid undecidable instances.

Instances

Instances details

TransformableFbrOrt Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition
TransformableFbrOrt DstX Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition
TransformableFbrOrt FbrOrt Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableFbrOrt FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableFbrOrt (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
TransformableFbrOrt s => TransformableFbrOrt (s, SldFr) Source #
Instance details Defined in OAlg.Entity.Slice.Free
TransformableFbrOrt s => TransformableFbrOrt (s, Sld i) Source #
Instance details Defined in OAlg.Entity.Slice.Sliced

tauFbrOrt :: Transformable s FbrOrt => Struct s x -> Struct FbrOrt x Source #

tau for FbrOrt.

X

xoFbrOrt :: XOrtOrientation f -> XFbrOrt f Source #

the associated random variable for validation FibredOriented structures.

xFbrOrtOrnt :: X p -> XFbrOrt (Orientation p) Source #

random variable for the FibredOriented structure of Orientation p.

type XFbrOrt = X Source #

random variable type for validating FibredOriented structures.

data FbrOrtX Source #

type representing the class FibredOriented equipped with standard random variables.

Instances

Instances details

TransformableType FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableFbr FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableFbrOrt FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableOrt FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
TransformableOp FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented
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 #
TransformableG Op FbrOrtX FbrOrtX Source #
Instance details Defined in OAlg.Structure.FibredOriented Methods tauG :: Struct FbrOrtX x -> Struct FbrOrtX (Op x) Source #
type Structure FbrOrtX x Source #
Instance details Defined in OAlg.Structure.FibredOriented type Structure FbrOrtX x = (FibredOriented x, XStandard x, XStandardPoint x)

Proposition

prpFbrOrt :: FibredOriented f => XFbrOrt f -> Statement Source #

validity for FibredOriented structures.

Orphan instances

FibredOriented f => Dualisable (Sheaf f) Source #
Instance details Methods toDual :: Sheaf f -> Dual (Sheaf f) Source # fromDual :: Dual (Sheaf f) -> Sheaf f Source #
FibredOriented x => Fibred (Op x) Source #
Instance details Methods root :: Op x -> Root (Op x) Source #