Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.AdditiveFun

Description

Additive maps

Synopsis

class Additive1 (h :: Type -> Type) where
- additive1 :: Sat Additive a |- Sat Additive (h a)
newtype a -+> b = AddFun (a -> b)
addFun :: (a -> b) -> a -> b
addFun' :: (a -> b) -> a -> b
unAddFun :: (a -+> b) -> a -> b
module ConCat.Additive

Documentation

class Additive1 (h :: Type -> Type) where Source #

Methods

additive1 :: Sat Additive a |- Sat Additive (h a) Source #

Instances

Instances details

Additive1 Product
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive (Product a) Source #
Additive1 Sum
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive (Sum a) Source #
Additive1 Par1
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive (Par1 a) Source #
Additive1 Pair Source #
Instance details Defined in ConCat.Pair Methods additive1 :: Sat Additive a \|- Sat Additive (Pair a) Source #
Additive1 (U1 :: Type -> Type)
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive (U1 a) Source #
KnownNat n => Additive1 (Vector n)
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive (Vector n a) Source #
(AddF f, AddF g) => Additive1 (f :*: g)
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive ((f :*: g) a) Source #
Additive1 ((->) a)
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a0 \|- Sat Additive (a -> a0) Source #
(AddF f, AddF g) => Additive1 (g :.: f)
Instance details Defined in ConCat.Category Methods additive1 :: Sat Additive a \|- Sat Additive ((g :.: f) a) Source #

newtype a -+> b infixr 1 Source #

Additive homomorphisms

Constructors

AddFun (a -> b)

Instances

Instances details

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

addFun :: (a -> b) -> a -> b Source #

addFun' :: (a -> b) -> a -> b Source #

unAddFun :: (a -+> b) -> a -> b Source #

module ConCat.Additive