Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.Dual

Description

Dual category for additive types. Use with GAD for efficient reverse mode AD.

Documentation

newtype Dual k a b Source #

Constructors

Dual (b `k` a)

Instances

Instances details

CoerceCat k b a => CoerceCat (Dual k :: Type -> Type -> Type) (a :: Type) (b :: Type) Source #
Instance details Defined in ConCat.Dual Methods coerceC :: Dual k a b Source #
RepCat k a r => RepCat (Dual k :: Type -> Type -> Type) (a :: Type) (r :: Type) Source #
Instance details Defined in ConCat.Dual Methods reprC :: Dual k a r Source # abstC :: Dual k r a Source #
(OkCAR (Dual k a b), IfCat (:>) (Rep (Dual k a b))) => IfCat (:>) (Dual k a b) Source #
Instance details Defined in ConCat.Dual Methods ifC :: IfT (:>) (Dual k a b) Source #
AssociativePCat k => AssociativePCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods lassocP :: Ok3 (Dual k) a b c => Dual k (Prod (Dual k) a (Prod (Dual k) b c)) (Prod (Dual k) (Prod (Dual k) a b) c) Source # rassocP :: Ok3 (Dual k) a b c => Dual k (Prod (Dual k) (Prod (Dual k) a b) c) (Prod (Dual k) a (Prod (Dual k) b c)) Source #
BraidedPCat k => BraidedPCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods swapP :: Ok2 (Dual k) a b => Dual k (Prod (Dual k) a b) (Prod (Dual k) b a) Source #
Category k => Category (Dual k) Source #
Instance details Defined in ConCat.Dual Associated Types type Ok (Dual k) :: Type -> Constraint Source # Methods id :: Ok (Dual k) a => Dual k a a Source # (.) :: forall b c a. Ok3 (Dual k) a b c => Dual k b c -> Dual k a b -> Dual k a c Source #
(BraidedPCat k, ProductCat k) => CoproductPCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods inlP :: Ok2 (Dual k) a b => Dual k a (CoprodP (Dual k) a b) Source # inrP :: Ok2 (Dual k) a b => Dual k b (CoprodP (Dual k) a b) Source # jamP :: Ok (Dual k) a => Dual k (CoprodP (Dual k) a a) a Source #
TerminalCat k => CoterminalCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods ti :: Ok (Dual k) a => Dual k (Counit (Dual k)) a Source #
MonoidalPCat k => MonoidalPCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods (***) :: Ok4 (Dual k) a b c d => Dual k a c -> Dual k b d -> Dual k (Prod (Dual k) a b) (Prod (Dual k) c d) Source # first :: forall a a' b. Ok3 (Dual k) a b a' => Dual k a a' -> Dual k (Prod (Dual k) a b) (Prod (Dual k) a' b) Source # second :: Ok3 (Dual k) a b b' => Dual k b b' -> Dual k (Prod (Dual k) a b) (Prod (Dual k) a b') Source #
CoproductPCat k => ProductCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods exl :: Ok2 (Dual k) a b => Dual k (Prod (Dual k) a b) a Source # exr :: Ok2 (Dual k) a b => Dual k (Prod (Dual k) a b) b Source # dup :: Ok (Dual k) a => Dual k a (Prod (Dual k) a a) Source #
CoterminalCat k => TerminalCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods it :: Ok (Dual k) a => Dual k a (Unit (Dual k)) Source #
UnitCat k => UnitCat (Dual k) Source #
Instance details Defined in ConCat.Dual Methods lunit :: Ok (Dual k) a => Dual k a (Prod (Dual k) (Unit (Dual k)) a) Source # lcounit :: Ok (Dual k) a => Dual k (Prod (Dual k) (Unit (Dual k)) a) a Source # runit :: Ok (Dual k) a => Dual k a (Prod (Dual k) a (Unit (Dual k))) Source # rcounit :: Ok (Dual k) a => Dual k (Prod (Dual k) a (Unit (Dual k))) a Source #
(Category k, TerminalCat k, CoterminalCat k, Ok (Dual k) b) => ConstCat (Dual k) b Source #
Instance details Defined in ConCat.Dual Methods const :: Ok (Dual k) a => b -> Dual k a (ConstObj (Dual k) b) Source # unitArrow :: b -> Dual k (Unit (Dual k)) (ConstObj (Dual k) b) Source #
(Functor h, ZipCat k h, Additive1 h, FunctorCat k h) => FunctorCat (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods fmapC :: Ok2 (Dual k) a b => Dual k a b -> Dual k (h a) (h b) Source # unzipC :: Ok2 (Dual k) a b => Dual k (h (a :* b)) (h a :* h b) Source #
(IxProductCat k h, Functor h, Additive1 h) => IxCoproductPCat (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods inPF :: Ok (Dual k) a => h (Dual k a (h a)) Source # joinPF :: Ok2 (Dual k) a b => h (Dual k b a) -> Dual k (h b) a Source # jamPF :: Ok (Dual k) a => Dual k (h a) a Source #
(IxMonoidalPCat k h, Functor h, Additive1 h) => IxMonoidalPCat (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods crossF :: Ok2 (Dual k) a b => h (Dual k a b) -> Dual k (h a) (h b) Source #
(IxCoproductPCat k h, Functor h, Additive1 h) => IxProductCat (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods exF :: Ok (Dual k) a => h (Dual k (h a) a) Source # forkF :: Ok2 (Dual k) a b => h (Dual k a b) -> Dual k a (h b) Source # replF :: Ok (Dual k) a => Dual k a (h a) Source #
(OkFunctor k h, Additive1 h) => OkFunctor (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods okFunctor :: Ok' (Dual k) a \|- Ok' (Dual k) (h a) Source #
(OkIxProd k h, Additive1 h) => OkIxProd (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods okIxProd :: Ok' (Dual k) a \|- Ok' (Dual k) (h a) Source #
RepresentableCat k g => RepresentableCat (Dual k) g Source #
Instance details Defined in ConCat.Dual Methods tabulateC :: Ok (Dual k) a => Dual k (Rep g -> a) (g a) Source # indexC :: Ok (Dual k) a => Dual k (g a) (Rep g -> a) Source #
ScalarCat k s => ScalarCat (Dual k) s Source #
Instance details Defined in ConCat.Dual Methods scale :: s -> Dual k s s Source #
(Zip h, ZapCat k h, OkF k h) => ZapCat (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods zapC :: Ok2 (Dual k) a b => h (Dual k a b) -> Dual k (h a) (h b) Source #
(Zip h, Additive1 h, FunctorCat k h) => ZipCat (Dual k) h Source #
Instance details Defined in ConCat.Dual Methods zipC :: Ok2 (Dual k) a b => Dual k (h a :* h b) (h (a :* b)) Source #
(PointedCat k h a, Additive a) => AddCat (Dual k) h a Source #
Instance details Defined in ConCat.Dual Methods sumAC :: Dual k (h a) a Source #
DistributiveCat k f g => DistributiveCat (Dual k) g f Source #
Instance details Defined in ConCat.Dual Methods distributeC :: Ok (Dual k) a => Dual k (f (g a)) (g (f a)) Source #
(Additive a, Additive1 h, MinMaxFunctorCat (->) h a, PointedCat k h a) => MinMaxFFunctorCat (Dual k) h a Source #
Instance details Defined in ConCat.Dual Methods minimumCF :: h a -> a :* Dual k (h a) a Source # maximumCF :: h a -> a :* Dual k (h a) a Source #
(AddCat k h a, Additive a, OkF k h) => PointedCat (Dual k) h a Source #
Instance details Defined in ConCat.Dual Methods pointC :: Dual k a (h a) Source #
TraversableCat k f t => TraversableCat (Dual k) t f Source #
Instance details Defined in ConCat.Dual Methods sequenceAC :: Ok (Dual k) a => Dual k (t (f a)) (f (t a)) Source #
HasRep (Dual k a b) Source #
Instance details Defined in ConCat.Dual Associated Types type Rep (Dual k a b) Source # Methods repr :: Dual k a b -> Rep (Dual k a b) Source # abst :: Rep (Dual k a b) -> Dual k a b Source #
OkCAR (Dual k a b) => GenBuses (Dual k a b) Source #
Instance details Defined in ConCat.Dual Methods genBuses' :: Template u v -> [Source] -> BusesM (Buses (Dual k a b)) Source # ty :: Ty Source # unflattenB' :: State [Source] (Buses (Dual k a b)) Source #
type Ok (Dual k) Source #
Instance details Defined in ConCat.Dual type Ok (Dual k) = Ok k &+& Additive
type Rep (Dual k a b) Source #
Instance details Defined in ConCat.Dual type Rep (Dual k a b) = k b a

unDual :: Dual k a b -> b `k` a Source #

type OkF k h = (Additive1 h, OkFunctor k h) Source #

toDual :: forall k a b. (a -> b) -> b `k` a Source #