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

OAlg.Structure.Oriented.Point

Contents

Point
Applicative
Point Wrapper
Total
Helper Classes

Description

Associating a point type for structured algebraic types.

Synopsis

type family Point x
type EntityPoint x = (ShowPoint x, EqPoint x, ValidablePoint x, TypeablePoint x)
newtype U x = U x
fromU :: U x -> x
type ApplicativePoint (h :: Type -> Type -> Type) = ApplicativeG Pnt h (->)
pmap :: ApplicativePoint h => h x y -> Point x -> Point y
type FunctorialPoint (h :: Type -> Type -> Type) = FunctorialG Pnt h (->)
pmapf :: FunctorialPoint h => h x y -> Point x -> Point y
newtype Pnt x = Pnt (Point x)
idPnt :: Point x ~ Point y => Pnt x -> Pnt y
toPntG :: (Point x -> Point y) -> Pnt x -> Pnt y
fromPntG :: (Pnt x -> Pnt y) -> Point x -> Point y
type Total = SingletonPoint
class Show (Point x) => ShowPoint x
class Eq (Point x) => EqPoint x
class Ord (Point x) => OrdPoint x
class Validable (Point x) => ValidablePoint x
class Typeable (Point x) => TypeablePoint x
class Singleton (Point x) => SingletonPoint x
class XStandard (Point a) => XStandardPoint a

Point

type family Point x Source #

the associated type of points.

Instances

Instances details

type Point N Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point N = ()
type Point Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point Q = ()
type Point Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point Z = ()
type Point Variant Source #
Instance details Defined in OAlg.Data.Variant type Point Variant = ()
type Point N' Source #
Instance details Defined in OAlg.Entity.Natural type Point N' = ()
type Point W' Source #
Instance details Defined in OAlg.Entity.Natural type Point W' = ()
type Point Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point Integer = ()
type Point () Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point () = ()
type Point Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point Int = ()
type Point (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (SomeMorphism m) = SomeObjectClass m
type Point (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (Id x) = Point x
type Point (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition type Point (Matrix x) = Dim' x
type Point (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup type Point (GL2 x) = Point x
type Point (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup type Point (GLT x) = Dim x (Point x)
type Point (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup type Point (Transformation x) = Dim x (Point x)
type Point (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation type Point (ColTrafo x) = Dim x (Point x)
type Point (RowTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation type Point (RowTrafo x) = Dim x (Point x)
type Point (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol type Point (ProductSymbol x) = ()
type Point (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation type Point (Permutation i) = ()
type Point (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation type Point (PermutationForm i) = ()
type Point (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition type Point (Sheaf f) = Root f
type Point (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition type Point (Inv c) = Point c
type Point (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite type Point (Op x) = Point x
type Point (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation type Point (Orientation x) = x
type Point (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path type Point (Path q) = Point q
type Point (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (Pnt x) = Point x
type Point (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (U x) = ()
type Point (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim type Point (Dim x p) = ()
type Point (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition type Point (Product r a) = Point a
type Point (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition type Point (ProductForm r a) = Point a
type Point (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition type Point (Sum r a) = Point a
type Point (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition type Point (SumForm r a) = Point a
type Point (Slice s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition type Point (Slice s i x) = Point x
type Point (SliceFactor s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition type Point (SliceFactor s i x) = Slice s i x
type Point (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero type Point (ConsecutiveZeroHom t n x) = ConsecutiveZero t n x
type Point (Diagram ('Chain t) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition type Point (Diagram ('Chain t) n m a) = Point a
type Point (Diagram ('Parallel d) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition type Point (Diagram ('Parallel d) n m a) = Point a
type Point (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation type Point (DiagramTrafo t n m a) = Diagram t n m a
type Point (Cone s p d ('Parallel t) N2 m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition type Point (Cone s p d ('Parallel t) N2 m a) = Point a

type EntityPoint x = (ShowPoint x, EqPoint x, ValidablePoint x, TypeablePoint x) Source #

Point as Entity.

newtype U x Source #

accosiating () as Point

Constructors

U x

Instances

Instances details

Foldable U Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods fold :: Monoid m => U m -> m # foldMap :: Monoid m => (a -> m) -> U a -> m # foldMap' :: Monoid m => (a -> m) -> U a -> m # foldr :: (a -> b -> b) -> b -> U a -> b # foldr' :: (a -> b -> b) -> b -> U a -> b # foldl :: (b -> a -> b) -> b -> U a -> b # foldl' :: (b -> a -> b) -> b -> U a -> b # foldr1 :: (a -> a -> a) -> U a -> a # foldl1 :: (a -> a -> a) -> U a -> a # toList :: U a -> [a] # null :: U a -> Bool # length :: U a -> Int # elem :: Eq a => a -> U a -> Bool # maximum :: Ord a => U a -> a # minimum :: Ord a => U a -> a # sum :: Num a => U a -> a # product :: Num a => U a -> a #
Functor U Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods fmap :: (a -> b) -> U a -> U b # (<$) :: a -> U b -> U a #
XStandard x => XStandardOrtSite 'From (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods xStandardOrtSite :: XOrtSite 'From (U x) Source #
XStandard x => XStandardOrtSite 'To (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods xStandardOrtSite :: XOrtSite 'To (U x) Source #
Show x => Show (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods showsPrec :: Int -> U x -> ShowS # show :: U x -> String # showList :: [U x] -> ShowS #
Eq x => Eq (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods (==) :: U x -> U x -> Bool # (/=) :: U x -> U x -> Bool #
Ord x => Ord (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods compare :: U x -> U x -> Ordering # (<) :: U x -> U x -> Bool # (<=) :: U x -> U x -> Bool # (>) :: U x -> U x -> Bool # (>=) :: U x -> U x -> Bool # max :: U x -> U x -> U x # min :: U x -> U x -> U x #
Validable x => Validable (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods valid :: U x -> Statement Source #
Entity x => Oriented (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods orientation :: U x -> Orientation (Point (U x)) Source # start :: U x -> Point (U x) Source # end :: U x -> Point (U x) Source #
EqPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandard x => XStandardOrtOrientation (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods xStandardOrtOrientation :: XOrtOrientation (U x) Source #
XStandard x => XStandardOrtSiteFrom (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.X
XStandard x => XStandardOrtSiteTo (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.X
type Point (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (U x) = ()

fromU :: U x -> x Source #

deconstructor.

Applicative

type ApplicativePoint (h :: Type -> Type -> Type) = ApplicativeG Pnt h (->) Source #

applications on Points.

pmap :: ApplicativePoint h => h x y -> Point x -> Point y Source #

the induced mapping of Points given by amapG.

type FunctorialPoint (h :: Type -> Type -> Type) = FunctorialG Pnt h (->) Source #

functorial application for Pnt.

pmapf :: FunctorialPoint h => h x y -> Point x -> Point y Source #

the induced functoiral mapping of Points given by pmap.

Point Wrapper

newtype Pnt x Source #

wrapper for Points.

Constructors

Pnt (Point x)

Instances

Instances details

TransformableGObjectClassRange Pnt OrtX EqualExtOrt Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
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 #
DualisableG OrtX EqualExtOrt Op Pnt Source #
Instance details Defined in OAlg.Category.Dualisable Methods toDualG :: Struct OrtX x -> EqualExtOrt (Pnt x) (Pnt (Op x)) Source # fromDualG :: Struct OrtX x -> EqualExtOrt (Pnt (Op x)) (Pnt x) Source #
ReflexiveG OrtX EqualExtOrt Op Pnt Source #
Instance details Defined in OAlg.Category.Dualisable Methods reflG :: Struct OrtX x -> Inv2 EqualExtOrt (Pnt x) (Pnt (Op (Op x))) Source #
(TransformableGRefl o s, DualisableDistributive s o, TransformableGRefl Matrix s) => ApplicativeMorCo Pnt Matrix s o (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
(TransformableGRefl o s, DualisableDistributive s o, TransformableGRefl Matrix s) => FunctorialHomCo Pnt Matrix s o (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
ApplicativeG Pnt GLApp (->) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods amapG :: GLApp x y -> Pnt x -> Pnt y Source #
ApplicativeG Pnt TrApp (->) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods amapG :: TrApp x y -> Pnt x -> Pnt y Source #
ApplicativeG Pnt h c => ApplicativeG Pnt (Inv2 h) c Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods amapG :: Inv2 h x y -> c (Pnt x) (Pnt y) Source #
ApplicativeG Pnt h c => ApplicativeG Pnt (Id2 h) c Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods amapG :: Id2 h x y -> c (Pnt x) (Pnt y) Source #
ApplicativeG Pnt (HomEmpty s) c Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomEmpty s x y -> c (Pnt x) (Pnt y) Source #
FunctorialG Pnt h c => FunctorialG Pnt (Inv2 h) c Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ApplicativeG Pnt (Ornt s) (->) Source #
Instance details Defined in OAlg.Data.Ornt Methods amapG :: Ornt s x y -> Pnt x -> Pnt y Source #
ApplicativeG Pnt (SliceFactorDrop s) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods amapG :: SliceFactorDrop s x y -> Pnt x -> Pnt y Source #
ApplicativeG Pnt (HomId s) (->) Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomId s x y -> Pnt x -> Pnt y Source #
(Transformable r Type, TransformableOp r) => DualisableG r (->) Op Pnt Source #
Instance details Defined in OAlg.Category.Dualisable Methods toDualG :: Struct r x -> Pnt x -> Pnt (Op x) Source # fromDualG :: Struct r x -> Pnt (Op x) -> Pnt x Source #
Transformable r Type => ReflexiveG r (->) Op Pnt Source #
Instance details Defined in OAlg.Category.Dualisable Methods reflG :: Struct r x -> Inv2 (->) (Pnt x) (Pnt (Op (Op x))) Source #
TransformableGObjectClassDomain Pnt (HomDisj OrtX Op (HomEmpty OrtX)) EqEOrt Source #
Instance details Defined in OAlg.Hom.Definition
(TransformableGRefl o s, DualisableDistributive s o, TransformableGRefl Matrix s) => ApplicativeG Pnt (MorCo Matrix s o) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods amapG :: MorCo Matrix s o x y -> Pnt x -> Pnt y Source #
(Distributive d, Sliced i d, Conic c) => ApplicativeG Pnt (SliceAdjunction i c d) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction Methods amapG :: SliceAdjunction i c d x y -> Pnt x -> Pnt y Source #
(Morphism h, ApplicativePoint h, DualisableG s (->) o Pnt) => ApplicativeG Pnt (HomDisj s o h) (->) Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomDisj s o h x y -> Pnt x -> Pnt y Source #
(Morphism h, ApplicativePoint h, DualisableG s (->) o Pnt) => FunctorialG Pnt (HomDisj s o h) (->) Source #
Instance details Defined in OAlg.Hom.Definition
ApplicativeG Pnt h c => ApplicativeG Pnt (Variant2 v h) c Source #
Instance details Defined in OAlg.Data.Variant Methods amapG :: Variant2 v h x y -> c (Pnt x) (Pnt y) Source #
ShowPoint x => Show (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods showsPrec :: Int -> Pnt x -> ShowS # show :: Pnt x -> String # showList :: [Pnt x] -> ShowS #
EqPoint x => Eq (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods (==) :: Pnt x -> Pnt x -> Bool # (/=) :: Pnt x -> Pnt x -> Bool #
ValidablePoint x => Validable (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods valid :: Pnt x -> Statement Source #
XStandardPoint x => XStandard (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods xStandard :: X (Pnt x) Source #
EqPoint x => EqPoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint x => ShowPoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint x => ValidablePoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint x => XStandardPoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
type Point (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point type Point (Pnt x) = Point x

idPnt :: Point x ~ Point y => Pnt x -> Pnt y Source #

casting a Point.

toPntG :: (Point x -> Point y) -> Pnt x -> Pnt y Source #

to Pnt,

fromPntG :: (Pnt x -> Pnt y) -> Point x -> Point y Source #

from Pnt.

Total

type Total = SingletonPoint Source #

total orientations.

Helper Classes

class Show (Point x) => ShowPoint x Source #

helper class to avoid undecidable instances.

Instances

Instances details

ShowPoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint Variant Source #
Instance details Defined in OAlg.Data.Variant
ShowPoint N' Source #
Instance details Defined in OAlg.Entity.Natural
ShowPoint W' Source #
Instance details Defined in OAlg.Entity.Natural
ShowPoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint x => ShowPoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
Oriented x => ShowPoint (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
ShowPoint x => ShowPoint (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => ShowPoint (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => ShowPoint (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => ShowPoint (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Oriented x => ShowPoint (RowTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
ShowPoint (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol
ShowPoint (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
ShowPoint (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
ShowRoot f => ShowPoint (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
ShowPoint c => ShowPoint (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
ShowPoint x => ShowPoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
Show x => ShowPoint (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
ShowPoint q => ShowPoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
ShowPoint x => ShowPoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ShowPoint (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
ShowPoint a => ShowPoint (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
ShowPoint a => ShowPoint (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
ShowPoint a => ShowPoint (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
ShowPoint a => ShowPoint (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
ShowPoint x => ShowPoint (Slice s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Show1 i, Show x) => ShowPoint (SliceFactor s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Show x, ShowPoint x) => ShowPoint (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero
ShowPoint a => ShowPoint (Diagram ('Chain t) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
ShowPoint a => ShowPoint (Diagram ('Parallel d) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Show a, ShowPoint a) => ShowPoint (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation
ShowPoint a => ShowPoint (Cone s p d ('Parallel t) N2 m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition

class Eq (Point x) => EqPoint x Source #

helper class to avoid undecidable instances.

Instances

Instances details

EqPoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint Variant Source #
Instance details Defined in OAlg.Data.Variant
EqPoint N' Source #
Instance details Defined in OAlg.Entity.Natural
EqPoint W' Source #
Instance details Defined in OAlg.Entity.Natural
EqPoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint x => EqPoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
Oriented x => EqPoint (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
EqPoint x => EqPoint (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => EqPoint (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => EqPoint (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => EqPoint (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Oriented x => EqPoint (RowTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
EqPoint (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol
EqPoint (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
EqPoint (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
EqRoot f => EqPoint (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
EqPoint c => EqPoint (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
EqPoint x => EqPoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
Eq x => EqPoint (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
EqPoint q => EqPoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
EqPoint x => EqPoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
EqPoint (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
EqPoint a => EqPoint (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
EqPoint a => EqPoint (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
EqPoint a => EqPoint (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
EqPoint a => EqPoint (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
EqPoint x => EqPoint (Slice s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Eq1 i, Eq x) => EqPoint (SliceFactor s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Eq x, EqPoint x) => EqPoint (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero
EqPoint a => EqPoint (Diagram ('Chain t) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
EqPoint a => EqPoint (Diagram ('Parallel d) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Eq a, EqPoint a) => EqPoint (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation
EqPoint a => EqPoint (Cone s p d ('Parallel t) N2 m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition

class Ord (Point x) => OrdPoint x Source #

helper class to avoid undecidable instances.

Instances

Instances details

OrdPoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint N' Source #
Instance details Defined in OAlg.Entity.Natural
OrdPoint W' Source #
Instance details Defined in OAlg.Entity.Natural
OrdPoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint x => OrdPoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
OrdPoint x => OrdPoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
Ord x => OrdPoint (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
OrdPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point

class Validable (Point x) => ValidablePoint x Source #

helper class to avoid undecidable instances.

Instances

Instances details

ValidablePoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint Variant Source #
Instance details Defined in OAlg.Data.Variant
ValidablePoint N' Source #
Instance details Defined in OAlg.Entity.Natural
ValidablePoint W' Source #
Instance details Defined in OAlg.Entity.Natural
ValidablePoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint x => ValidablePoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
Oriented x => ValidablePoint (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
ValidablePoint x => ValidablePoint (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => ValidablePoint (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => ValidablePoint (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => ValidablePoint (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Oriented x => ValidablePoint (RowTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
ValidablePoint (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol
ValidablePoint (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
ValidablePoint (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
ValidableRoot f => ValidablePoint (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
ValidablePoint c => ValidablePoint (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
ValidablePoint x => ValidablePoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
Validable x => ValidablePoint (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
ValidablePoint q => ValidablePoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
ValidablePoint x => ValidablePoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
ValidablePoint (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
ValidablePoint a => ValidablePoint (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
ValidablePoint a => ValidablePoint (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
ValidablePoint a => ValidablePoint (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
ValidablePoint a => ValidablePoint (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
ValidablePoint x => ValidablePoint (Slice s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
Sliced i x => ValidablePoint (SliceFactor s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
Distributive x => ValidablePoint (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero
Oriented a => ValidablePoint (Diagram ('Chain t) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
Oriented a => ValidablePoint (Diagram ('Parallel d) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
Oriented a => ValidablePoint (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation
ValidablePoint a => ValidablePoint (Cone s p d ('Parallel t) N2 m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition

class Typeable (Point x) => TypeablePoint x Source #

helper class to avoid undecidable instances.

Instances

Instances details

TypeablePoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint Variant Source #
Instance details Defined in OAlg.Data.Variant
TypeablePoint N' Source #
Instance details Defined in OAlg.Entity.Natural
TypeablePoint W' Source #
Instance details Defined in OAlg.Entity.Natural
TypeablePoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
Typeable m => TypeablePoint (SomeMorphism m) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint x => TypeablePoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
(Typeable x, TypeablePoint x) => TypeablePoint (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
TypeablePoint x => TypeablePoint (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => TypeablePoint (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => TypeablePoint (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
Oriented x => TypeablePoint (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
Oriented x => TypeablePoint (RowTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation
TypeablePoint (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol
TypeablePoint (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
TypeablePoint (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
TypeableRoot f => TypeablePoint (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
TypeablePoint c => TypeablePoint (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
TypeablePoint x => TypeablePoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
Typeable x => TypeablePoint (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
TypeablePoint q => TypeablePoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
TypeablePoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
TypeablePoint (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
TypeablePoint a => TypeablePoint (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
TypeablePoint a => TypeablePoint (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition
TypeablePoint a => TypeablePoint (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
TypeablePoint a => TypeablePoint (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition
TypeablePoint x => TypeablePoint (Slice s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Typeable i, Typeable x, Typeable s) => TypeablePoint (SliceFactor s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Typeable x, Typeable t, Typeable n) => TypeablePoint (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero
TypeablePoint a => TypeablePoint (Diagram ('Chain t) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
TypeablePoint a => TypeablePoint (Diagram ('Parallel d) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Typeable a, Typeable t, Typeable n, Typeable m) => TypeablePoint (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation
TypeablePoint a => TypeablePoint (Cone s p d ('Parallel t) N2 m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition

class Singleton (Point x) => SingletonPoint x Source #

helper class to avoid undecidable instances.

Instances

Instances details

SingletonPoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint N' Source #
Instance details Defined in OAlg.Entity.Natural
SingletonPoint W' Source #
Instance details Defined in OAlg.Entity.Natural
SingletonPoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint x => SingletonPoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint x => SingletonPoint (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup
SingletonPoint (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation
SingletonPoint x => SingletonPoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
Singleton x => SingletonPoint (Orientation x) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
SingletonPoint q => SingletonPoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
SingletonPoint (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
SingletonPoint (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim

class XStandard (Point a) => XStandardPoint a Source #

helper class to avoid undecidable instances.

Instances

Instances details

XStandardPoint N Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint Q Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint Z Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint N' Source #
Instance details Defined in OAlg.Entity.Natural
XStandardPoint Integer Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint () Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint Int Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint x => XStandardPoint (Id x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
XStandardPoint (Matrix Z) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
XStandardPoint x => XStandardPoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite
XStandard p => XStandardPoint (Orientation p) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation
XStandardPoint x => XStandardPoint (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point
(Multiplicative x, Sliced i x, XStandardOrtSite 'From x) => XStandardPoint (SliceFactor 'From i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition
(Multiplicative x, Sliced i x, XStandardOrtSite 'To x) => XStandardPoint (SliceFactor 'To i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition