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

OAlg.Category.Applicative

Contents

Applicative
Generalized

Description

application on values.

Synopsis

type Applicative1 (h :: Type -> Type -> Type) (f :: Type -> Type) = ApplicativeG f h (->)
amap1 :: Applicative1 h f => h x y -> f x -> f y
class ApplicativeG (t :: Type -> Type) (a :: Type -> Type -> Type) (b :: Type -> Type -> Type) where
- amapG :: a x y -> b (t x) (t y)
amapG' :: ApplicativeG t a b => q t a b -> a x y -> b (t x) (t y)
data ApplicationG (t :: Type -> Type) (a :: Type -> Type -> Type) (b :: Type -> Type -> Type) where
- ApplicationG :: forall (t :: Type -> Type) (a :: Type -> Type -> Type) (b :: Type -> Type -> Type). ApplicativeG t a b => ApplicationG t a b
apType :: forall (t :: Type -> Type) (h :: Type -> Type -> Type). ApplicativeG t h (->) => ApplicationG t h (->)
class ApplicativeG (Dual1 d) h c => ApplicativeGDual1 (d :: Type -> Type) (h :: Type -> Type -> Type) (c :: Type -> Type -> Type)
type ApplicativeGBi (d :: Type -> Type) (h :: Type -> Type -> Type) (c :: Type -> Type -> Type) = (ApplicativeG d h c, ApplicativeGDual1 d h c)

Applicative

type Applicative1 (h :: Type -> Type -> Type) (f :: Type -> Type) = ApplicativeG f h (->) Source #

representable hs according to f.

amap1 :: Applicative1 h f => h x y -> f x -> f y Source #

representation of h in (->) according to f.

Generalized

class ApplicativeG (t :: Type -> Type) (a :: Type -> Type -> Type) (b :: Type -> Type -> Type) where Source #

generalized application.

Methods

amapG :: a x y -> b (t x) (t y) Source #

application.

Instances

Instances details

ApplicativeG t EntEmpty2 b Source #
Instance details Defined in OAlg.Entity.Definition Methods amapG :: EntEmpty2 x y -> b (t x) (t y) Source #
ApplicativeG Id GLApp (->) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods amapG :: GLApp x y -> Id x -> Id y Source #
ApplicativeG Id TrApp (->) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods amapG :: TrApp x y -> Id x -> Id y Source #
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 Id h c => ApplicativeG Id (Inv2 h) c Source #
Instance details Defined in OAlg.Data.Identity Methods amapG :: Inv2 h x y -> c (Id x) (Id y) Source #
ApplicativeG Id h c => ApplicativeG Id (Id2 h) c Source #
Instance details Defined in OAlg.Data.Identity Methods amapG :: Id2 h x y -> c (Id x) (Id y) Source #
ApplicativeG Id (HomEmpty s) c Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomEmpty s x y -> c (Id x) (Id y) Source #
ApplicativeG Rt h c => ApplicativeG Rt (Inv2 h) c Source #
Instance details Defined in OAlg.Structure.Fibred.Root Methods amapG :: Inv2 h x y -> c (Rt x) (Rt y) Source #
ApplicativeG Rt (HomEmpty s) c Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomEmpty s x y -> c (Rt x) (Rt 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 #
(Category c, ApplicativeG t m c, TransformableGObjectClass t m c) => ApplicativeG t (Path m) c Source #
Instance details Defined in OAlg.Category.Path Methods amapG :: Path m x y -> c (t x) (t y) Source #
TransformableOrt s => ApplicativeG Id (Ornt s) (->) Source #
Instance details Defined in OAlg.Data.Ornt Methods amapG :: Ornt s x y -> Id x -> Id y Source #
(Semiring r, Commutative r) => ApplicativeG Id (HomSymbol r) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods amapG :: HomSymbol r x y -> Id x -> Id y Source #
ApplicativeG Id (SliceFactorDrop s) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods amapG :: SliceFactorDrop s x y -> Id x -> Id y Source #
ApplicativeG Id (HomId s) (->) Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomId s x y -> Id x -> Id y Source #
ApplicativeG Set (Map EntOrd) (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods amapG :: Map EntOrd x y -> Set x -> Set y Source #
ApplicativeG Set (Map Ord') (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods amapG :: Map Ord' x y -> Set x -> Set y Source #
Transformable s FbrOrt => ApplicativeG Rt (Ornt s) (->) Source #
Instance details Defined in OAlg.Data.Ornt Methods amapG :: Ornt s x y -> Rt x -> Rt y Source #
ApplicativeG Rt (HomSymbol r) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods amapG :: HomSymbol r x y -> Rt x -> Rt y Source #
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 #
ApplicativeG [] (Map s) (->) Source #
Instance details Defined in OAlg.Category.Map Methods amapG :: Map s x y -> [x] -> [y] Source #
(ApplicativeG t f c, ApplicativeG t g c) => ApplicativeG t (Either2 f g) c Source #
Instance details Defined in OAlg.Category.Applicative Methods amapG :: Either2 f g x y -> c (t x) (t y) Source #
ApplicativeG Id (->) (->) Source #
Instance details Defined in OAlg.Data.Identity Methods amapG :: (x -> y) -> Id x -> Id y Source #
ApplicativeG X (->) (->) Source #
Instance details Defined in OAlg.Category.Applicative Methods amapG :: (x -> y) -> X x -> X y Source #
ApplicativeG SomeFinList (->) (->) Source #
Instance details Defined in OAlg.Entity.FinList Methods amapG :: (x -> y) -> SomeFinList x -> SomeFinList y Source #
ApplicativeG Orientation (->) (->) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation Methods amapG :: (x -> y) -> Orientation x -> Orientation y Source #
ApplicativeG Maybe (->) (->) Source #
Instance details Defined in OAlg.Category.Applicative Methods amapG :: (x -> y) -> Maybe x -> Maybe y Source #
ApplicativeG [] (->) (->) Source #
Instance details Defined in OAlg.Category.Applicative Methods amapG :: (x -> y) -> [x] -> [y] Source #
(ApplicativeG d a b, TransformableG d s t) => ApplicativeG d (Sub s a) (Sub t b) Source #
Instance details Defined in OAlg.Category.Definition Methods amapG :: Sub s a x y -> Sub t b (d x) (d y) Source #
ApplicativeG f h (->) => ApplicativeG f (Sub t h) (->) Source #
Instance details Defined in OAlg.Category.Definition Methods amapG :: Sub t h x y -> f x -> f y Source #
(Morphism h, ApplicativeG Id h c, DualisableG s c o Id, c ~ (->)) => ApplicativeG Id (HomDisj s o h) c Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomDisj s o h x y -> c (Id x) (Id y) Source #
(TransformableDst s, TransformableGRefl o s, DualisableDistributive s o, TransformableGRefl Matrix s) => ApplicativeG Id (MorCo Matrix s o) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods amapG :: MorCo Matrix s o x y -> Id x -> Id y Source #
(Distributive d, Sliced i d, Conic c) => ApplicativeG Id (SliceAdjunction i c d) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction Methods amapG :: SliceAdjunction i c d x y -> Id x -> Id y Source #
(HomOriented h, DualisableOriented s o) => ApplicativeG SomeDiagram (HomDisj s o h) (->) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods amapG :: HomDisj s o h x y -> SomeDiagram x -> SomeDiagram y Source #
(TransformableGRefl o s, DualisableDistributive s o, TransformableGRefl Matrix s) => ApplicativeG Rt (MorCo Matrix s o) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods amapG :: MorCo Matrix s o x y -> Rt x -> Rt y Source #
(Morphism h, ApplicativeRoot h, DualisableG s (->) o Rt) => ApplicativeG Rt (HomDisj s o h) (->) Source #
Instance details Defined in OAlg.Hom.Definition Methods amapG :: HomDisj s o h x y -> Rt x -> Rt y Source #
(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 #
(ApplicativeMorCo d m s o (->), DualisableG s (->) o d) => ApplicativeG d (HomCo m s o) (->) Source #
Instance details Defined in OAlg.Data.HomCo Methods amapG :: HomCo m s o x y -> d x -> d y Source #
ApplicativeG Id h c => ApplicativeG Id (Variant2 v h) c Source #
Instance details Defined in OAlg.Data.Variant Methods amapG :: Variant2 v h x y -> c (Id x) (Id y) Source #
ApplicativeG Rt h c => ApplicativeG Rt (Variant2 v h) c Source #
Instance details Defined in OAlg.Data.Variant Methods amapG :: Variant2 v h x y -> c (Rt x) (Rt y) Source #
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 #
(HomOrientedDisjunctive h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (Diagram t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods amapG :: h x y -> SDualBi (Diagram t n m) x -> SDualBi (Diagram t n m) y Source #
(HomOrientedDisjunctive h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (DiagramG Diagram t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Diagram.Diagrammatic Methods amapG :: h x y -> SDualBi (DiagramG Diagram t n m) x -> SDualBi (DiagramG Diagram t n m) y Source #
(HomSlicedOriented i h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (DiagramG (SliceDiagram i) t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction Methods amapG :: h x y -> SDualBi (DiagramG (SliceDiagram i) t n m) x -> SDualBi (DiagramG (SliceDiagram i) t n m) y Source #
(HomOrientedSlicedFree h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (DiagramG DiagramFree t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods amapG :: h x y -> SDualBi (DiagramG DiagramFree t n m) x -> SDualBi (DiagramG DiagramFree t n m) y Source #
(HomMultiplicativeDisjunctive h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (DiagramTrafo t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation Methods amapG :: h x y -> SDualBi (DiagramTrafo t n m) x -> SDualBi (DiagramTrafo t n m) y Source #
HomDistributiveDisjunctive h => ApplicativeG (SDualBi Matrix) h (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods amapG :: h x y -> SDualBi Matrix x -> SDualBi Matrix y Source #
(HomSlicedOriented i h, s ~ Dual (Dual s)) => ApplicativeG (SDualBi (Slice s i)) h (->) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods amapG :: h x y -> SDualBi (Slice s i) x -> SDualBi (Slice s i) y Source #
(HomSlicedMultiplicative i h, s ~ Dual (Dual s)) => ApplicativeG (SDualBi (SliceFactor s i)) h (->) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods amapG :: h x y -> SDualBi (SliceFactor s i) x -> SDualBi (SliceFactor s i) y Source #
(HomOrientedSlicedFree h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (DiagramFree t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods amapG :: h x y -> SDualBi (DiagramFree t n m) x -> SDualBi (DiagramFree t n m) y Source #
(HomOrientedSlicedFree h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (SomeFreeSliceDiagram t n m)) h (->) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods amapG :: h x y -> SDualBi (SomeFreeSliceDiagram t n m) x -> SDualBi (SomeFreeSliceDiagram t n m) y Source #
(HomDistributiveDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeG Cone Dst p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Duality Methods amapG :: h x y -> SDualBi (ConeG Cone Dst p d t n m) x -> SDualBi (ConeG Cone Dst p d t n m) y Source #
(HomMultiplicativeDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeG Cone Mlt p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Duality Methods amapG :: h x y -> SDualBi (ConeG Cone Mlt p d t n m) x -> SDualBi (ConeG Cone Mlt p d t n m) y Source #
(HomDistributiveDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (ConeG ConeZeroHead s p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Duality Methods amapG :: h x y -> SDualBi (ConeG ConeZeroHead s p d t n m) x -> SDualBi (ConeG ConeZeroHead s p d t n m) y Source #
(HomDistributiveDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (Cone Dst p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.Duality Methods amapG :: h x y -> SDualBi (Cone Dst p d t n m) x -> SDualBi (Cone Dst p d t n m) y Source #
(HomMultiplicativeDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (Cone Mlt p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.Duality Methods amapG :: h x y -> SDualBi (Cone Mlt p d t n m) x -> SDualBi (Cone Mlt p d t n m) y Source #
(HomDistributiveDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (ConeZeroHead s p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Duality Methods amapG :: h x y -> SDualBi (ConeZeroHead s p d t n m) x -> SDualBi (ConeZeroHead s p d t n m) y Source #
(HomDistributiveDisjunctive h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConsecutiveZero t n)) h (->) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero Methods amapG :: h x y -> SDualBi (ConsecutiveZero t n) x -> SDualBi (ConsecutiveZero t n) y Source #
(HomDistributiveDisjunctive h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConsecutiveZeroHom t n)) h (->) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero Methods amapG :: h x y -> SDualBi (ConsecutiveZeroHom t n) x -> SDualBi (ConsecutiveZeroHom t n) y Source #
(HomDistributiveDisjunctive h, HomOrientedSlicedFree h, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConsecutiveZeroFree t n)) h (->) Source #
Instance details Defined in OAlg.Limes.Exact.Free Methods amapG :: h x y -> SDualBi (ConsecutiveZeroFree t n) x -> SDualBi (ConsecutiveZeroFree t n) y Source #
(NaturalDiagrammatic (Inv2 (HomFree s)) d ('Parallel 'LeftToRight) N2 N1, NaturalDiagrammatic (Inv2 (HomFree s)) d ('Parallel 'RightToLeft) N2 N1, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeLiftable s p d t n m)) (Inv2 (HomFree s)) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods amapG :: Inv2 (HomFree s) x y -> SDualBi (ConeLiftable s p d t n m) x -> SDualBi (ConeLiftable s p d t n m) y Source #
p ~ Dual (Dual p) => ApplicativeG (SDualBi (LiftableFree p)) (Inv2 (HomFree Dst)) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods amapG :: Inv2 (HomFree Dst) x y -> SDualBi (LiftableFree p) x -> SDualBi (LiftableFree p) y Source #
p ~ Dual (Dual p) => ApplicativeG (SDualBi (LiftableFree p)) (Inv2 (HomFree Mlt)) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods amapG :: Inv2 (HomFree Mlt) x y -> SDualBi (LiftableFree p) x -> SDualBi (LiftableFree p) y Source #
(CategoryDisjunctive h, HomSlicedMultiplicative i h, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (Liftable p i)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods amapG :: Inv2 h x y -> SDualBi (Liftable p i) x -> SDualBi (Liftable p i) y Source #
(CategoryDisjunctive h, HomSlicedDistributive i h, FunctorialOriented h, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (LiftableCone i s p d t n m)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods amapG :: Inv2 h x y -> SDualBi (LiftableCone i s p d t n m) x -> SDualBi (LiftableCone i s p d t n m) y Source #
(CategoryDisjunctive h, HomSlicedDistributive i h, FunctorialOriented h, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeG (LiftableCone i) s p d t n m)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods amapG :: Inv2 h x y -> SDualBi (ConeG (LiftableCone i) s p d t n m) x -> SDualBi (ConeG (LiftableCone i) s p d t n m) y Source #
NaturalConicBi (Inv2 h) c s p d t n m => ApplicativeG (SDualBi (LimesG c s p d t n m)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Limes.Definition.Duality Methods amapG :: Inv2 h x y -> SDualBi (LimesG c s p d t n m) x -> SDualBi (LimesG c s p d t n m) y Source #
(HomDistributiveDisjunctive h, CategoryDisjunctive h, NaturalKernelCokernel (Inv2 h) k c d, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (VarianceG t k c d n)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Limes.Exact.Deviation Methods amapG :: Inv2 h x y -> SDualBi (VarianceG t k c d n) x -> SDualBi (VarianceG t k c d n) y Source #
(HomDistributiveDisjunctive h, CategoryDisjunctive h, NaturalKernelCokernel (Inv2 h) k c d, t ~ Dual (Dual t)) => ApplicativeG (SDualBi (VarianceGHom t k c d n)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Limes.Exact.Deviation Methods amapG :: Inv2 h x y -> SDualBi (VarianceGHom t k c d n) x -> SDualBi (VarianceGHom t k c d n) y Source #
NaturalConicBi (Inv2 h) c s p d t n m => ApplicativeG (SDualBi (LimitsG c s p d t n m)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Limes.Limits.Duality Methods amapG :: Inv2 h x y -> SDualBi (LimitsG c s p d t n m) x -> SDualBi (LimitsG c s p d t n m) y Source #
ApplicativeG (FinList n) (->) (->) Source #
Instance details Defined in OAlg.Entity.FinList Methods amapG :: (x -> y) -> FinList n x -> FinList n y Source #
ApplicativeG (Col i) (->) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries Methods amapG :: (x -> y) -> Col i x -> Col i y Source #
ApplicativeG (Row i) (->) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries Methods amapG :: (x -> y) -> Row i x -> Row i y Source #
ApplicativeG (Word r) (->) (->) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods amapG :: (x -> y) -> Word r x -> Word r y Source #
ApplicativeG (PSequence i) (->) (->) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence Methods amapG :: (x -> y) -> PSequence i x -> PSequence i y Source #
ApplicativeG (LinearCombination r) (->) (->) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods amapG :: (x -> y) -> LinearCombination r x -> LinearCombination r y Source #
(Morphism h, ApplicativeG d h c, DualisableG r c o d, Transformable s r, c ~ (->)) => ApplicativeG (SVal d) (SHom r s o h) c Source #
Instance details Defined in OAlg.Category.SDuality Methods amapG :: SHom r s o h x y -> c (SVal d x) (SVal d y) Source #
(Morphism h, ApplicativeG d h c, DualisableG r c o d, Transformable s r, c ~ (->)) => ApplicativeG (SVal d) (SMorphism r s o h) c Source #
Instance details Defined in OAlg.Category.SDuality Methods amapG :: SMorphism r s o h x y -> c (SVal d x) (SVal d y) Source #
(Morphism h, ApplicativeGBi d h (->), DualisableGBi r (->) o d, Transformable s r) => ApplicativeG (SDualBi d) (SHom r s o h) (->) Source #
Instance details Defined in OAlg.Category.SDuality Methods amapG :: SHom r s o h x y -> SDualBi d x -> SDualBi d y Source #
ApplicativeG (Entries i j) (->) (->) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries Methods amapG :: (x -> y) -> Entries i j x -> Entries i j y Source #
HomOriented h => ApplicativeG (Diagram t n m) h (->) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods amapG :: h x y -> Diagram t n m x -> Diagram t n m y Source #

amapG' :: ApplicativeG t a b => q t a b -> a x y -> b (t x) (t y) Source #

prefixing a proxy.

data ApplicationG (t :: Type -> Type) (a :: Type -> Type -> Type) (b :: Type -> Type -> Type) where Source #

attest of being ApplicativeG.

Constructors

ApplicationG :: forall (t :: Type -> Type) (a :: Type -> Type -> Type) (b :: Type -> Type -> Type). ApplicativeG t a b => ApplicationG t a b

apType :: forall (t :: Type -> Type) (h :: Type -> Type -> Type). ApplicativeG t h (->) => ApplicationG t h (->) Source #

application to (->) based on t,

class ApplicativeG (Dual1 d) h c => ApplicativeGDual1 (d :: Type -> Type) (h :: Type -> Type -> Type) (c :: Type -> Type -> Type) Source #

helper class to avoid undecidable instances.

type ApplicativeGBi (d :: Type -> Type) (h :: Type -> Type -> Type) (c :: Type -> Type -> Type) = (ApplicativeG d h c, ApplicativeGDual1 d h c) Source #

constraint for bi-applicative.