Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.Additive

Description

Commutative monoid intended to be used with a multiplicative monoid

Synopsis

class Additive a where
- zero :: a
- (^+^) :: a -> a -> a
pointNI :: Pointed h => a -> h a
zipWithNI :: Zip h => (a -> b -> c) -> h a -> h b -> h c
type AddF f = (Pointed f, Zip f)
newtype Add a = Add {
- getAdd :: a
}
type SummableF h = (Representable h, Eq (Rep h), Zip h, Pointed h, Foldable h)
class SummableF h => Summable h
sumA :: (Foldable h, Additive a) => h a -> a

Documentation

class Additive a where Source #

Commutative monoid intended to be used with a multiplicative monoid

Minimal complete definition

Nothing

Methods

zero :: a Source #

default zero :: (Pointed h, Additive b, a ~ h b) => a Source #

(^+^) :: a -> a -> a infixl 6 Source #

default (^+^) :: (Zip h, Additive b, a ~ h b) => Binop a Source #

Instances

Instances details

Additive CDouble Source #
Instance details Defined in ConCat.Additive Methods zero :: CDouble Source # (^+^) :: CDouble -> CDouble -> CDouble Source #
Additive CFloat Source #
Instance details Defined in ConCat.Additive Methods zero :: CFloat Source # (^+^) :: CFloat -> CFloat -> CFloat Source #
Additive CInt Source #
Instance details Defined in ConCat.Additive Methods zero :: CInt Source # (^+^) :: CInt -> CInt -> CInt Source #
Additive CIntMax Source #
Instance details Defined in ConCat.Additive Methods zero :: CIntMax Source # (^+^) :: CIntMax -> CIntMax -> CIntMax Source #
Additive CLLong Source #
Instance details Defined in ConCat.Additive Methods zero :: CLLong Source # (^+^) :: CLLong -> CLLong -> CLLong Source #
Additive CLong Source #
Instance details Defined in ConCat.Additive Methods zero :: CLong Source # (^+^) :: CLong -> CLong -> CLong Source #
Additive CSChar Source #
Instance details Defined in ConCat.Additive Methods zero :: CSChar Source # (^+^) :: CSChar -> CSChar -> CSChar Source #
Additive CShort Source #
Instance details Defined in ConCat.Additive Methods zero :: CShort Source # (^+^) :: CShort -> CShort -> CShort Source #
Additive Int16 Source #
Instance details Defined in ConCat.Additive Methods zero :: Int16 Source # (^+^) :: Int16 -> Int16 -> Int16 Source #
Additive Int32 Source #
Instance details Defined in ConCat.Additive Methods zero :: Int32 Source # (^+^) :: Int32 -> Int32 -> Int32 Source #
Additive Int64 Source #
Instance details Defined in ConCat.Additive Methods zero :: Int64 Source # (^+^) :: Int64 -> Int64 -> Int64 Source #
Additive Int8 Source #
Instance details Defined in ConCat.Additive Methods zero :: Int8 Source # (^+^) :: Int8 -> Int8 -> Int8 Source #
Additive Word16 Source #
Instance details Defined in ConCat.Additive Methods zero :: Word16 Source # (^+^) :: Word16 -> Word16 -> Word16 Source #
Additive Word32 Source #
Instance details Defined in ConCat.Additive Methods zero :: Word32 Source # (^+^) :: Word32 -> Word32 -> Word32 Source #
Additive Word64 Source #
Instance details Defined in ConCat.Additive Methods zero :: Word64 Source # (^+^) :: Word64 -> Word64 -> Word64 Source #
Additive Word8 Source #
Instance details Defined in ConCat.Additive Methods zero :: Word8 Source # (^+^) :: Word8 -> Word8 -> Word8 Source #
Additive Integer Source #
Instance details Defined in ConCat.Additive Methods zero :: Integer Source # (^+^) :: Integer -> Integer -> Integer Source #
Additive () Source #
Instance details Defined in ConCat.Additive Methods zero :: () Source # (^+^) :: () -> () -> () Source #
Additive Bool Source #
Instance details Defined in ConCat.Additive Methods zero :: Bool Source # (^+^) :: Bool -> Bool -> Bool Source #
Additive Double Source #
Instance details Defined in ConCat.Additive Methods zero :: Double Source # (^+^) :: Double -> Double -> Double Source #
Additive Float Source #
Instance details Defined in ConCat.Additive Methods zero :: Float Source # (^+^) :: Float -> Float -> Float Source #
Additive Int Source #
Instance details Defined in ConCat.Additive Methods zero :: Int Source # (^+^) :: Int -> Int -> Int Source #
Additive Word Source #
Instance details Defined in ConCat.Additive Methods zero :: Word Source # (^+^) :: Word -> Word -> Word Source #
OpCon (:*) (Sat Additive) Source #
Instance details Defined in ConCat.Category Methods inOp :: forall (a :: k) (b :: k). (Sat Additive a && Sat Additive b) \|- Sat Additive (a :* b) Source #
OpCon (->) (Sat Additive) Source #
Instance details Defined in ConCat.Category Methods inOp :: forall (a :: k) (b :: k). (Sat Additive a && Sat Additive b) \|- Sat Additive (a -> b) Source #
(RealFloat v, Additive v) => Additive (Complex v) Source #
Instance details Defined in ConCat.Additive Methods zero :: Complex v Source # (^+^) :: Complex v -> Complex v -> Complex v Source #
(AddF Product, Additive v) => Additive (Product v) Source #
Instance details Defined in ConCat.Additive Methods zero :: Product v Source # (^+^) :: Product v -> Product v -> Product v Source #
(AddF Sum, Additive v) => Additive (Sum v) Source #
Instance details Defined in ConCat.Additive Methods zero :: Sum v Source # (^+^) :: Sum v -> Sum v -> Sum v Source #
(AddF Par1, Additive v) => Additive (Par1 v) Source #
Instance details Defined in ConCat.Additive Methods zero :: Par1 v Source # (^+^) :: Par1 v -> Par1 v -> Par1 v Source #
Integral a => Additive (Ratio a) Source #
Instance details Defined in ConCat.Additive Methods zero :: Ratio a Source # (^+^) :: Ratio a -> Ratio a -> Ratio a Source #
Additive a => Additive (Add a) Source #
Instance details Defined in ConCat.Additive Methods zero :: Add a Source # (^+^) :: Add a -> Add a -> Add a Source #
KnownNat n => Additive (Finite n) Source #
Instance details Defined in ConCat.Additive Methods zero :: Finite n Source # (^+^) :: Finite n -> Finite n -> Finite n Source #
Additive a => Additive (Maybe a) Source #
Instance details Defined in ConCat.Additive Methods zero :: Maybe a Source # (^+^) :: Maybe a -> Maybe a -> Maybe a Source #
(AddF (U1 :: Type -> Type), Additive v) => Additive (U1 v) Source #
Instance details Defined in ConCat.Additive Methods zero :: U1 v Source # (^+^) :: U1 v -> U1 v -> U1 v Source #
(Additive v, KnownNat n) => Additive (Vector n v) Source #
Instance details Defined in ConCat.Additive Methods zero :: Vector n v Source # (^+^) :: Vector n v -> Vector n v -> Vector n v Source #
(Additive u, Additive v) => Additive (u, v) Source #
Instance details Defined in ConCat.Additive Methods zero :: (u, v) Source # (^+^) :: (u, v) -> (u, v) -> (u, v) Source #
(Additive u, Additive v, Additive w) => Additive (u, v, w) Source #
Instance details Defined in ConCat.Additive Methods zero :: (u, v, w) Source # (^+^) :: (u, v, w) -> (u, v, w) -> (u, v, w) Source #
(AddF (f :: g), Additive v) => Additive ((f :: g) v) Source #
Instance details Defined in ConCat.Additive Methods zero :: (f :: g) v Source # (^+^) :: (f :: g) v -> (f :: g) v -> (f :: g) v Source #
(Additive u, Additive v, Additive w, Additive x) => Additive (u, v, w, x) Source #
Instance details Defined in ConCat.Additive Methods zero :: (u, v, w, x) Source # (^+^) :: (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) Source #
(AddF ((->) a), Additive v) => Additive (a -> v) Source #
Instance details Defined in ConCat.Additive Methods zero :: a -> v Source # (^+^) :: (a -> v) -> (a -> v) -> a -> v Source #
(AddF (g :.: f), Additive v) => Additive ((g :.: f) v) Source #
Instance details Defined in ConCat.Additive Methods zero :: (g :.: f) v Source # (^+^) :: (g :.: f) v -> (g :.: f) v -> (g :.: f) v Source #

pointNI :: Pointed h => a -> h a Source #

zipWithNI :: Zip h => (a -> b -> c) -> h a -> h b -> h c Source #

type AddF f = (Pointed f, Zip f) Source #

newtype Add a Source #

Monoid under group addition. Alternative to the Sum in Data.Monoid, which uses Num instead of Additive.

Constructors

Add
Fields getAdd :: a

Instances

Instances details

Applicative Add Source #
Instance details Defined in ConCat.Additive Methods pure :: a -> Add a Source # (<>) :: Add (a -> b) -> Add a -> Add b Source # liftA2 :: (a -> b -> c) -> Add a -> Add b -> Add c Source # (>) :: Add a -> Add b -> Add b Source # (<*) :: Add a -> Add b -> Add a Source #
Functor Add Source #
Instance details Defined in ConCat.Additive Methods fmap :: (a -> b) -> Add a -> Add b Source # (<$) :: a -> Add b -> Add a Source #
Additive a => Monoid (Add a) Source #
Instance details Defined in ConCat.Additive Methods mempty :: Add a Source # mappend :: Add a -> Add a -> Add a Source # mconcat :: [Add a] -> Add a Source #
Additive a => Semigroup (Add a) Source #
Instance details Defined in ConCat.Additive Methods (<>) :: Add a -> Add a -> Add a Source # sconcat :: NonEmpty (Add a) -> Add a Source # stimes :: Integral b => b -> Add a -> Add a Source #
Bounded a => Bounded (Add a) Source #
Instance details Defined in ConCat.Additive Methods minBound :: Add a Source # maxBound :: Add a Source #
Read a => Read (Add a) Source #
Instance details Defined in ConCat.Additive Methods readsPrec :: Int -> ReadS (Add a) Source # readList :: ReadS [Add a] Source # readPrec :: ReadPrec (Add a) Source # readListPrec :: ReadPrec [Add a] Source #
Show a => Show (Add a) Source #
Instance details Defined in ConCat.Additive Methods showsPrec :: Int -> Add a -> ShowS Source # show :: Add a -> String Source # showList :: [Add a] -> ShowS Source #
Additive a => Additive (Add a) Source #
Instance details Defined in ConCat.Additive Methods zero :: Add a Source # (^+^) :: Add a -> Add a -> Add a Source #
HasRep (Add a) Source #
Instance details Defined in ConCat.Additive Associated Types type Rep (Add a) Source # Methods repr :: Add a -> Rep (Add a) Source # abst :: Rep (Add a) -> Add a Source #
Eq a => Eq (Add a) Source #
Instance details Defined in ConCat.Additive Methods (==) :: Add a -> Add a -> Bool Source # (/=) :: Add a -> Add a -> Bool Source #
Ord a => Ord (Add a) Source #
Instance details Defined in ConCat.Additive Methods compare :: Add a -> Add a -> Ordering Source # (<) :: Add a -> Add a -> Bool Source # (<=) :: Add a -> Add a -> Bool Source # (>) :: Add a -> Add a -> Bool Source # (>=) :: Add a -> Add a -> Bool Source # max :: Add a -> Add a -> Add a Source # min :: Add a -> Add a -> Add a Source #
type Rep (Add a) Source #
Instance details Defined in ConCat.Additive type Rep (Add a) = a

type SummableF h = (Representable h, Eq (Rep h), Zip h, Pointed h, Foldable h) Source #

class SummableF h => Summable h Source #

Instances

Instances details

SummableF h => Summable h Source #
Instance details Defined in ConCat.Additive

sumA :: (Foldable h, Additive a) => h a -> a Source #