{-# LANGUAGE CPP #-}
{-# LANGUAGE Safe #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE TypeFamilies #-}
{-# OPTIONS_GHC -fno-warn-type-defaults #-}
module Data.Semigroup.Additive where
import safe Control.Applicative
import safe Data.Bool
import safe Data.Complex
import safe Data.Maybe
import safe Data.Either
import safe Data.Distributive
import safe Data.Functor.Rep
import safe Data.Fixed
import safe Data.Group
import safe Data.Int
import safe Data.List.NonEmpty
import safe Data.Ord
import safe Data.Semigroup
import safe Data.Word
import safe Foreign.C.Types (CFloat(..),CDouble(..))
import safe GHC.Generics (Generic)
import safe GHC.Real hiding (Fractional(..), div, (^^), (^), (%))
import safe Numeric.Natural
import safe Prelude
( Eq(..), Ord(..), Show, Applicative(..), Functor(..), Monoid(..), Semigroup(..)
, (.), ($), (<$>), flip, Integer, Float, Double)
import safe qualified Prelude as P
import safe qualified Data.Map as Map
import safe qualified Data.Set as Set
import safe qualified Data.IntMap as IntMap
import safe qualified Data.IntSet as IntSet
infixr 1 -
type (g - f) a = f (g a)
newtype Additive a = Additive { unAdditive :: a } deriving (Eq, Generic, Ord, Show, Functor)
zero :: (Additive-Monoid) a => a
zero = unAdditive mempty
{-# INLINE zero #-}
infixl 6 +
(+) :: (Additive-Semigroup) a => a -> a -> a
a + b = unAdditive (Additive a <> Additive b)
{-# INLINE (+) #-}
subtract :: (Additive-Group) a => a -> a -> a
subtract a b = unAdditive (Additive b << Additive a)
{-# INLINE subtract #-}
instance Applicative Additive where
pure = Additive
Additive f <*> Additive a = Additive (f a)
instance Distributive Additive where
distribute = distributeRep
{-# INLINE distribute #-}
instance Representable Additive where
type Rep Additive = ()
tabulate f = Additive (f ())
{-# INLINE tabulate #-}
index (Additive x) () = x
{-# INLINE index #-}
newtype Multiplicative a = Multiplicative { unMultiplicative :: a } deriving (Eq, Generic, Ord, Show, Functor)
one :: (Multiplicative-Monoid) a => a
one = unMultiplicative mempty
{-# INLINE one #-}
infixl 7 *, \\, /
(*) :: (Multiplicative-Semigroup) a => a -> a -> a
a * b = unMultiplicative (Multiplicative a <> Multiplicative b)
{-# INLINE (*) #-}
(/) :: (Multiplicative-Group) a => a -> a -> a
a / b = unMultiplicative (Multiplicative a << Multiplicative b)
{-# INLINE (/) #-}
(\\) :: (Multiplicative-Group) a => a -> a -> a
(\\) x y = recip x * y
infixr 8 ^^
(^^) :: (Multiplicative-Group) a => a -> Integer -> a
a ^^ n = unMultiplicative $ greplicate n (Multiplicative a)
recip :: (Multiplicative-Group) a => a -> a
recip a = one / a
{-# INLINE recip #-}
instance Applicative Multiplicative where
pure = Multiplicative
Multiplicative f <*> Multiplicative a = Multiplicative (f a)
instance Distributive Multiplicative where
distribute = distributeRep
{-# INLINE distribute #-}
instance Representable Multiplicative where
type Rep Multiplicative = ()
tabulate f = Multiplicative (f ())
{-# INLINE tabulate #-}
index (Multiplicative x) () = x
{-# INLINE index #-}
#define deriveAdditiveSemigroup(ty) \
instance Semigroup (Additive ty) where { \
a <> b = (P.+) <$> a <*> b \
; {-# INLINE (<>) #-} \
}
deriveAdditiveSemigroup(Int)
deriveAdditiveSemigroup(Int8)
deriveAdditiveSemigroup(Int16)
deriveAdditiveSemigroup(Int32)
deriveAdditiveSemigroup(Int64)
deriveAdditiveSemigroup(Integer)
deriveAdditiveSemigroup(Word)
deriveAdditiveSemigroup(Word8)
deriveAdditiveSemigroup(Word16)
deriveAdditiveSemigroup(Word32)
deriveAdditiveSemigroup(Word64)
deriveAdditiveSemigroup(Natural)
deriveAdditiveSemigroup(Uni)
deriveAdditiveSemigroup(Deci)
deriveAdditiveSemigroup(Centi)
deriveAdditiveSemigroup(Milli)
deriveAdditiveSemigroup(Micro)
deriveAdditiveSemigroup(Nano)
deriveAdditiveSemigroup(Pico)
deriveAdditiveSemigroup(Float)
deriveAdditiveSemigroup(CFloat)
deriveAdditiveSemigroup(Double)
deriveAdditiveSemigroup(CDouble)
#define deriveAdditiveMonoid(ty) \
instance Monoid (Additive ty) where { \
mempty = pure 0 \
; {-# INLINE mempty #-} \
}
deriveAdditiveMonoid(Int)
deriveAdditiveMonoid(Int8)
deriveAdditiveMonoid(Int16)
deriveAdditiveMonoid(Int32)
deriveAdditiveMonoid(Int64)
deriveAdditiveMonoid(Integer)
deriveAdditiveMonoid(Word)
deriveAdditiveMonoid(Word8)
deriveAdditiveMonoid(Word16)
deriveAdditiveMonoid(Word32)
deriveAdditiveMonoid(Word64)
deriveAdditiveMonoid(Natural)
deriveAdditiveMonoid(Uni)
deriveAdditiveMonoid(Deci)
deriveAdditiveMonoid(Centi)
deriveAdditiveMonoid(Milli)
deriveAdditiveMonoid(Micro)
deriveAdditiveMonoid(Nano)
deriveAdditiveMonoid(Pico)
deriveAdditiveMonoid(Float)
deriveAdditiveMonoid(CFloat)
deriveAdditiveMonoid(Double)
deriveAdditiveMonoid(CDouble)
#define deriveAdditiveMagma(ty) \
instance Magma (Additive ty) where { \
a << b = (P.-) <$> a <*> b \
; {-# INLINE (<<) #-} \
}
deriveAdditiveMagma(Int)
deriveAdditiveMagma(Int8)
deriveAdditiveMagma(Int16)
deriveAdditiveMagma(Int32)
deriveAdditiveMagma(Int64)
deriveAdditiveMagma(Integer)
deriveAdditiveMagma(Uni)
deriveAdditiveMagma(Deci)
deriveAdditiveMagma(Centi)
deriveAdditiveMagma(Milli)
deriveAdditiveMagma(Micro)
deriveAdditiveMagma(Nano)
deriveAdditiveMagma(Pico)
deriveAdditiveMagma(Float)
deriveAdditiveMagma(CFloat)
deriveAdditiveMagma(Double)
deriveAdditiveMagma(CDouble)
#define deriveAdditiveQuasigroup(ty) \
instance Quasigroup (Additive ty) where { \
}
deriveAdditiveQuasigroup(Int)
deriveAdditiveQuasigroup(Int8)
deriveAdditiveQuasigroup(Int16)
deriveAdditiveQuasigroup(Int32)
deriveAdditiveQuasigroup(Int64)
deriveAdditiveQuasigroup(Integer)
deriveAdditiveQuasigroup(Uni)
deriveAdditiveQuasigroup(Deci)
deriveAdditiveQuasigroup(Centi)
deriveAdditiveQuasigroup(Milli)
deriveAdditiveQuasigroup(Micro)
deriveAdditiveQuasigroup(Nano)
deriveAdditiveQuasigroup(Pico)
deriveAdditiveQuasigroup(Float)
deriveAdditiveQuasigroup(CFloat)
deriveAdditiveQuasigroup(Double)
deriveAdditiveQuasigroup(CDouble)
#define deriveAdditiveLoop(ty) \
instance Loop (Additive ty) where { \
lreplicate n (Additive a) = Additive $ P.fromIntegral n * (-a) \
; {-# INLINE lreplicate #-} \
}
deriveAdditiveLoop(Int)
deriveAdditiveLoop(Int8)
deriveAdditiveLoop(Int16)
deriveAdditiveLoop(Int32)
deriveAdditiveLoop(Int64)
deriveAdditiveLoop(Integer)
deriveAdditiveLoop(Uni)
deriveAdditiveLoop(Deci)
deriveAdditiveLoop(Centi)
deriveAdditiveLoop(Milli)
deriveAdditiveLoop(Micro)
deriveAdditiveLoop(Nano)
deriveAdditiveLoop(Pico)
deriveAdditiveLoop(Float)
deriveAdditiveLoop(CFloat)
deriveAdditiveLoop(Double)
deriveAdditiveLoop(CDouble)
#define deriveAdditiveGroup(ty) \
instance Group (Additive ty) where { \
greplicate n (Additive a) = Additive $ P.fromInteger n * a \
; {-# INLINE greplicate #-} \
}
deriveAdditiveGroup(Int)
deriveAdditiveGroup(Int8)
deriveAdditiveGroup(Int16)
deriveAdditiveGroup(Int32)
deriveAdditiveGroup(Int64)
deriveAdditiveGroup(Integer)
deriveAdditiveGroup(Uni)
deriveAdditiveGroup(Deci)
deriveAdditiveGroup(Centi)
deriveAdditiveGroup(Milli)
deriveAdditiveGroup(Micro)
deriveAdditiveGroup(Nano)
deriveAdditiveGroup(Pico)
deriveAdditiveGroup(Float)
deriveAdditiveGroup(CFloat)
deriveAdditiveGroup(Double)
deriveAdditiveGroup(CDouble)
instance (Additive-Semigroup) a => Semigroup (Additive (Complex a)) where
Additive (a :+ b) <> Additive (c :+ d) = Additive $ (a + b) :+ (c + d)
{-# INLINE (<>) #-}
instance (Additive-Monoid) a => Monoid (Additive (Complex a)) where
mempty = Additive $ zero :+ zero
instance (Additive-Group) a => Magma (Additive (Complex a)) where
Additive (a :+ b) << Additive (c :+ d) = Additive $ (subtract c a) :+ (subtract d b)
{-# INLINE (<<) #-}
instance (Additive-Group) a => Quasigroup (Additive (Complex a))
instance (Additive-Group) a => Loop (Additive (Complex a)) where
lreplicate n = mreplicate n . inv
instance (Additive-Group) a => Group (Additive (Complex a))
instance ((Additive-Group) a, (Multiplicative-Semigroup) a) => Semigroup (Multiplicative (Complex a)) where
Multiplicative (a :+ b) <> Multiplicative (c :+ d) = Multiplicative $ (subtract (b * d) (a * c)) :+ (a * d + b * c)
{-# INLINE (<>) #-}
instance ((Additive-Group) a, (Multiplicative-Monoid) a) => Monoid (Multiplicative (Complex a)) where
mempty = Multiplicative $ one :+ zero
instance ((Additive-Group) a, (Multiplicative-Group) a) => Magma (Multiplicative (Complex a)) where
Multiplicative (a :+ b) << Multiplicative (c :+ d) = Multiplicative $ ((a * c + b * d) / (c * c + d * d)) :+ ((subtract (a * d) (b * c)) / (c * c + d * d))
{-# INLINE (<<) #-}
instance ((Additive-Group) a, (Multiplicative-Group) a) => Quasigroup (Multiplicative (Complex a))
instance ((Additive-Group) a, (Multiplicative-Group) a) => Loop (Multiplicative (Complex a)) where
lreplicate n = mreplicate n . inv
instance ((Additive-Group) a, (Multiplicative-Group) a) => Group (Multiplicative (Complex a))
instance ((Additive-Semigroup) a, (Multiplicative-Semigroup) a) => Semigroup (Additive (Ratio a)) where
Additive (a :% b) <> Additive (c :% d) = Additive $ (a * d + c * b) :% (b * d)
{-# INLINE (<>) #-}
instance ((Additive-Monoid) a, (Multiplicative-Monoid) a) => Monoid (Additive (Ratio a)) where
mempty = Additive $ zero :% one
instance ((Additive-Group) a, (Multiplicative-Monoid) a) => Magma (Additive (Ratio a)) where
Additive (a :% b) << Additive (c :% d) = Additive $ (subtract (c * b) (a * d)) :% (b * d)
{-# INLINE (<<) #-}
instance ((Additive-Group) a, (Multiplicative-Monoid) a) => Quasigroup (Additive (Ratio a))
instance ((Additive-Group) a, (Multiplicative-Monoid) a) => Loop (Additive (Ratio a)) where
lreplicate n = mreplicate n . inv
instance ((Additive-Group) a, (Multiplicative-Monoid) a) => Group (Additive (Ratio a))
instance (Additive-Semigroup) b => Semigroup (Additive (a -> b)) where
(<>) = liftA2 . liftA2 $ (+)
{-# INLINE (<>) #-}
instance (Additive-Monoid) b => Monoid (Additive (a -> b)) where
mempty = pure . pure $ zero
instance Semigroup (Additive [a]) where
(<>) = liftA2 (<>)
instance Monoid (Additive [a]) where
mempty = pure mempty
instance (Additive-Semigroup) a => Semigroup (Multiplicative [a]) where
(<>) = liftA2 . liftA2 $ (+)
{-# INLINE (<>) #-}
instance (Additive-Monoid) a => Monoid (Multiplicative [a]) where
mempty = pure [zero]
instance Semigroup (Additive (NonEmpty a)) where
(<>) = liftA2 (<>)
instance (Additive-Semigroup) a => Semigroup (Multiplicative (NonEmpty a)) where
(<>) = liftA2 (+)
{-# INLINE (<>) #-}
instance (Additive-Semigroup) a => Semigroup (Multiplicative (Min a)) where
Multiplicative a <> Multiplicative b = Multiplicative $ liftA2 (+) a b
instance (Additive-Monoid) a => Monoid (Multiplicative (Min a)) where
mempty = Multiplicative $ pure zero
instance (Additive-Semigroup) a => Semigroup (Additive (Down a)) where
(<>) = liftA2 . liftA2 $ (+)
instance (Additive-Monoid) a => Monoid (Additive (Down a)) where
mempty = pure . pure $ zero
instance Semigroup (Additive ()) where
_ <> _ = pure ()
{-# INLINE (<>) #-}
instance Monoid (Additive ()) where
mempty = pure ()
{-# INLINE mempty #-}
instance Magma (Additive ()) where
_ << _ = pure ()
instance Quasigroup (Additive ())
instance Loop (Additive ())
instance Group (Additive ())
instance Semigroup (Additive Bool) where
a <> b = (P.||) <$> a <*> b
{-# INLINE (<>) #-}
instance Monoid (Additive Bool) where
mempty = pure False
{-# INLINE mempty #-}
instance ((Additive-Semigroup) a, (Additive-Semigroup) b) => Semigroup (Additive (a, b)) where
(<>) = liftA2 $ \(x1,y1) (x2,y2) -> (x1+x2, y1+y2)
instance ((Additive-Monoid) a, (Additive-Monoid) b) => Monoid (Additive (a, b)) where
mempty = pure (zero, zero)
instance ((Additive-Semigroup) a, (Additive-Semigroup) b, (Additive-Semigroup) c) => Semigroup (Additive (a, b, c)) where
(<>) = liftA2 $ \(x1,y1,z1) (x2,y2,z2) -> (x1+x2, y1+y2, z1+z2)
instance ((Additive-Monoid) a, (Additive-Monoid) b, (Additive-Monoid) c) => Monoid (Additive (a, b, c)) where
mempty = pure (zero, zero, zero)
instance (Additive-Semigroup) a => Semigroup (Additive (Maybe a)) where
Additive (Just x) <> Additive (Just y) = Additive . Just $ x + y
Additive (x@Just{}) <> _ = Additive x
Additive Nothing <> y = y
instance (Additive-Semigroup) a => Monoid (Additive (Maybe a)) where
mempty = Additive Nothing
instance ((Additive-Semigroup) a, (Additive-Semigroup) b) => Semigroup (Additive (Either a b)) where
Additive (Right x) <> Additive (Right y) = Additive . Right $ x + y
Additive(x@Right{}) <> _ = Additive x
Additive (Left x) <> Additive (Left y) = Additive . Left $ x + y
Additive (Left _) <> y = y
instance Ord a => Semigroup (Additive (Set.Set a)) where
(<>) = liftA2 Set.union
instance (Ord k, (Additive-Semigroup) a) => Semigroup (Additive (Map.Map k a)) where
(<>) = liftA2 (Map.unionWith (+))
instance (Additive-Semigroup) a => Semigroup (Additive (IntMap.IntMap a)) where
(<>) = liftA2 (IntMap.unionWith (+))
instance Semigroup (Additive IntSet.IntSet) where
(<>) = liftA2 IntSet.union
instance Monoid (Additive IntSet.IntSet) where
mempty = Additive IntSet.empty
instance (Additive-Semigroup) a => Monoid (Additive (IntMap.IntMap a)) where
mempty = Additive IntMap.empty
instance Ord a => Monoid (Additive (Set.Set a)) where
mempty = Additive Set.empty
instance (Ord k, (Additive-Semigroup) a) => Monoid (Additive (Map.Map k a)) where
mempty = Additive Map.empty
#define deriveMultiplicativeSemigroup(ty) \
instance Semigroup (Multiplicative ty) where { \
a <> b = (P.*) <$> a <*> b \
; {-# INLINE (<>) #-} \
}
deriveMultiplicativeSemigroup(Int)
deriveMultiplicativeSemigroup(Int8)
deriveMultiplicativeSemigroup(Int16)
deriveMultiplicativeSemigroup(Int32)
deriveMultiplicativeSemigroup(Int64)
deriveMultiplicativeSemigroup(Integer)
deriveMultiplicativeSemigroup(Word)
deriveMultiplicativeSemigroup(Word8)
deriveMultiplicativeSemigroup(Word16)
deriveMultiplicativeSemigroup(Word32)
deriveMultiplicativeSemigroup(Word64)
deriveMultiplicativeSemigroup(Natural)
deriveMultiplicativeSemigroup(Uni)
deriveMultiplicativeSemigroup(Deci)
deriveMultiplicativeSemigroup(Centi)
deriveMultiplicativeSemigroup(Milli)
deriveMultiplicativeSemigroup(Micro)
deriveMultiplicativeSemigroup(Nano)
deriveMultiplicativeSemigroup(Pico)
deriveMultiplicativeSemigroup(Float)
deriveMultiplicativeSemigroup(CFloat)
deriveMultiplicativeSemigroup(Double)
deriveMultiplicativeSemigroup(CDouble)
#define deriveMultiplicativeMonoid(ty) \
instance Monoid (Multiplicative ty) where { \
mempty = pure 1 \
; {-# INLINE mempty #-} \
}
deriveMultiplicativeMonoid(Int)
deriveMultiplicativeMonoid(Int8)
deriveMultiplicativeMonoid(Int16)
deriveMultiplicativeMonoid(Int32)
deriveMultiplicativeMonoid(Int64)
deriveMultiplicativeMonoid(Integer)
deriveMultiplicativeMonoid(Word)
deriveMultiplicativeMonoid(Word8)
deriveMultiplicativeMonoid(Word16)
deriveMultiplicativeMonoid(Word32)
deriveMultiplicativeMonoid(Word64)
deriveMultiplicativeMonoid(Natural)
deriveMultiplicativeMonoid(Uni)
deriveMultiplicativeMonoid(Deci)
deriveMultiplicativeMonoid(Centi)
deriveMultiplicativeMonoid(Milli)
deriveMultiplicativeMonoid(Micro)
deriveMultiplicativeMonoid(Nano)
deriveMultiplicativeMonoid(Pico)
deriveMultiplicativeMonoid(Float)
deriveMultiplicativeMonoid(CFloat)
deriveMultiplicativeMonoid(Double)
deriveMultiplicativeMonoid(CDouble)
#define deriveMultiplicativeMagma(ty) \
instance Magma (Multiplicative ty) where { \
a << b = (P./) <$> a <*> b \
; {-# INLINE (<<) #-} \
}
deriveMultiplicativeMagma(Uni)
deriveMultiplicativeMagma(Deci)
deriveMultiplicativeMagma(Centi)
deriveMultiplicativeMagma(Milli)
deriveMultiplicativeMagma(Micro)
deriveMultiplicativeMagma(Nano)
deriveMultiplicativeMagma(Pico)
deriveMultiplicativeMagma(Float)
deriveMultiplicativeMagma(CFloat)
deriveMultiplicativeMagma(Double)
deriveMultiplicativeMagma(CDouble)
#define deriveMultiplicativeQuasigroup(ty) \
instance Quasigroup (Multiplicative ty) where { \
}
deriveMultiplicativeQuasigroup(Uni)
deriveMultiplicativeQuasigroup(Deci)
deriveMultiplicativeQuasigroup(Centi)
deriveMultiplicativeQuasigroup(Milli)
deriveMultiplicativeQuasigroup(Micro)
deriveMultiplicativeQuasigroup(Nano)
deriveMultiplicativeQuasigroup(Pico)
deriveMultiplicativeQuasigroup(Float)
deriveMultiplicativeQuasigroup(CFloat)
deriveMultiplicativeQuasigroup(Double)
deriveMultiplicativeQuasigroup(CDouble)
#define deriveMultiplicativeLoop(ty) \
instance Loop (Multiplicative ty) where { \
lreplicate n = mreplicate n . inv \
}
deriveMultiplicativeLoop(Uni)
deriveMultiplicativeLoop(Deci)
deriveMultiplicativeLoop(Centi)
deriveMultiplicativeLoop(Milli)
deriveMultiplicativeLoop(Micro)
deriveMultiplicativeLoop(Nano)
deriveMultiplicativeLoop(Pico)
deriveMultiplicativeLoop(Float)
deriveMultiplicativeLoop(CFloat)
deriveMultiplicativeLoop(Double)
deriveMultiplicativeLoop(CDouble)
#define deriveMultiplicativeGroup(ty) \
instance Group (Multiplicative ty) where { \
greplicate n (Multiplicative a) = Multiplicative $ a P.^^ P.fromInteger n \
; {-# INLINE greplicate #-} \
}
deriveMultiplicativeGroup(Uni)
deriveMultiplicativeGroup(Deci)
deriveMultiplicativeGroup(Centi)
deriveMultiplicativeGroup(Milli)
deriveMultiplicativeGroup(Micro)
deriveMultiplicativeGroup(Nano)
deriveMultiplicativeGroup(Pico)
deriveMultiplicativeGroup(Float)
deriveMultiplicativeGroup(CFloat)
deriveMultiplicativeGroup(Double)
deriveMultiplicativeGroup(CDouble)
instance (Multiplicative-Semigroup) a => Semigroup (Multiplicative (Ratio a)) where
Multiplicative (a :% b) <> Multiplicative (c :% d) = Multiplicative $ (a * c) :% (b * d)
{-# INLINE (<>) #-}
instance (Multiplicative-Monoid) a => Monoid (Multiplicative (Ratio a)) where
mempty = Multiplicative $ unMultiplicative mempty :% unMultiplicative mempty
instance (Multiplicative-Monoid) a => Magma (Multiplicative (Ratio a)) where
Multiplicative (a :% b) << Multiplicative (c :% d) = Multiplicative $ (a * d) :% (b * c)
{-# INLINE (<<) #-}
instance (Multiplicative-Monoid) a => Quasigroup (Multiplicative (Ratio a))
instance (Multiplicative-Monoid) a => Loop (Multiplicative (Ratio a)) where
lreplicate n = mreplicate n . inv
instance (Multiplicative-Monoid) a => Group (Multiplicative (Ratio a))
instance Semigroup (Multiplicative ()) where
_ <> _ = pure ()
{-# INLINE (<>) #-}
instance Monoid (Multiplicative ()) where
mempty = pure ()
{-# INLINE mempty #-}
instance Magma (Multiplicative ()) where
_ << _ = pure ()
{-# INLINE (<<) #-}
instance Quasigroup (Multiplicative ())
instance Loop (Multiplicative ())
instance Group (Multiplicative ())
instance Semigroup (Multiplicative Bool) where
a <> b = (P.&&) <$> a <*> b
{-# INLINE (<>) #-}
instance Monoid (Multiplicative Bool) where
mempty = pure True
{-# INLINE mempty #-}
instance (Multiplicative-Semigroup) a => Semigroup (Multiplicative (Dual a)) where
(<>) = liftA2 . liftA2 $ flip (*)
instance (Multiplicative-Monoid) a => Monoid (Multiplicative (Dual a)) where
mempty = pure . pure $ one
instance (Multiplicative-Semigroup) a => Semigroup (Multiplicative (Down a)) where
(<>) = liftA2 . liftA2 $ (*)
instance (Multiplicative-Monoid) a => Monoid (Multiplicative (Down a)) where
mempty = pure . pure $ one
instance (Multiplicative-Semigroup) a => Semigroup (Multiplicative (Max a)) where
Multiplicative a <> Multiplicative b = Multiplicative $ liftA2 (*) a b
instance (Multiplicative-Monoid) a => Monoid (Multiplicative (Max a)) where
mempty = Multiplicative $ pure one
instance ((Multiplicative-Semigroup) a, (Multiplicative-Semigroup) b) => Semigroup (Multiplicative (a, b)) where
Multiplicative (x1, y1) <> Multiplicative (x2, y2) = Multiplicative (x1 * x2, y1 * y2)
instance (Multiplicative-Semigroup) b => Semigroup (Multiplicative (a -> b)) where
(<>) = liftA2 . liftA2 $ (*)
{-# INLINE (<>) #-}
instance (Multiplicative-Monoid) b => Monoid (Multiplicative (a -> b)) where
mempty = pure . pure $ one
instance (Multiplicative-Semigroup) a => Semigroup (Multiplicative (Maybe a)) where
Multiplicative Nothing <> _ = Multiplicative Nothing
Multiplicative (Just{}) <> Multiplicative Nothing = Multiplicative Nothing
Multiplicative (Just x) <> Multiplicative (Just y) = Multiplicative . Just $ x * y
instance (Multiplicative-Monoid) a => Monoid (Multiplicative (Maybe a)) where
mempty = Multiplicative $ pure one
instance ((Multiplicative-Semigroup) a, (Multiplicative-Semigroup) b) => Semigroup (Multiplicative (Either a b)) where
Multiplicative (Right x) <> Multiplicative (Right y) = Multiplicative . Right $ x * y
Multiplicative (Right{}) <> y = y
Multiplicative (Left x) <> Multiplicative (Left y) = Multiplicative . Left $ x * y
Multiplicative (x@Left{}) <> _ = Multiplicative x
instance Ord a => Semigroup (Multiplicative (Set.Set a)) where
(<>) = liftA2 Set.intersection
instance (Ord k, (Multiplicative-Semigroup) a) => Semigroup (Multiplicative (Map.Map k a)) where
(<>) = liftA2 (Map.intersectionWith (*))
instance (Multiplicative-Semigroup) a => Semigroup (Multiplicative (IntMap.IntMap a)) where
(<>) = liftA2 (IntMap.intersectionWith (*))
instance Semigroup (Multiplicative IntSet.IntSet) where
(<>) = liftA2 IntSet.intersection
instance (Ord k, (Multiplicative-Monoid) k, (Multiplicative-Monoid) a) => Monoid (Multiplicative (Map.Map k a)) where
mempty = Multiplicative $ Map.singleton one one
instance (Multiplicative-Monoid) a => Monoid (Multiplicative (IntMap.IntMap a)) where
mempty = Multiplicative $ IntMap.singleton 0 one