Safe Haskell	Safe
Language	Haskell98

Numeric.Ring.Opposite

Synopsis

newtype Opposite r = Opposite {
- runOpposite :: r
}

Documentation

newtype Opposite r #

http://en.wikipedia.org/wiki/Opposite_ring

Constructors

Opposite
Fields runOpposite :: r

Instances

Functor Opposite #
Instance details Defined in Numeric.Ring.Opposite Methods fmap :: (a -> b) -> Opposite a -> Opposite b # (<$) :: a -> Opposite b -> Opposite a #
Foldable Opposite #
Instance details Defined in Numeric.Ring.Opposite Methods fold :: Monoid m => Opposite m -> m # foldMap :: Monoid m => (a -> m) -> Opposite a -> m # foldr :: (a -> b -> b) -> b -> Opposite a -> b # foldr' :: (a -> b -> b) -> b -> Opposite a -> b # foldl :: (b -> a -> b) -> b -> Opposite a -> b # foldl' :: (b -> a -> b) -> b -> Opposite a -> b # foldr1 :: (a -> a -> a) -> Opposite a -> a # foldl1 :: (a -> a -> a) -> Opposite a -> a # toList :: Opposite a -> [a] # null :: Opposite a -> Bool # length :: Opposite a -> Int # elem :: Eq a => a -> Opposite a -> Bool # maximum :: Ord a => Opposite a -> a # minimum :: Ord a => Opposite a -> a # sum :: Num a => Opposite a -> a # product :: Num a => Opposite a -> a #
Traversable Opposite #
Instance details Defined in Numeric.Ring.Opposite Methods traverse :: Applicative f => (a -> f b) -> Opposite a -> f (Opposite b) # sequenceA :: Applicative f => Opposite (f a) -> f (Opposite a) # mapM :: Monad m => (a -> m b) -> Opposite a -> m (Opposite b) # sequence :: Monad m => Opposite (m a) -> m (Opposite a) #
Traversable1 Opposite #
Instance details Defined in Numeric.Ring.Opposite Methods traverse1 :: Apply f => (a -> f b) -> Opposite a -> f (Opposite b) # sequence1 :: Apply f => Opposite (f b) -> f (Opposite b) #
Foldable1 Opposite #
Instance details Defined in Numeric.Ring.Opposite Methods fold1 :: Semigroup m => Opposite m -> m # foldMap1 :: Semigroup m => (a -> m) -> Opposite a -> m # toNonEmpty :: Opposite a -> NonEmpty a #
LeftModule r s => RightModule r (Opposite s) #
Instance details Defined in Numeric.Ring.Opposite Methods (*.) :: Opposite s -> r -> Opposite s #
RightModule r s => LeftModule r (Opposite s) #
Instance details Defined in Numeric.Ring.Opposite Methods (.*) :: r -> Opposite s -> Opposite s #
Eq r => Eq (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (==) :: Opposite r -> Opposite r -> Bool # (/=) :: Opposite r -> Opposite r -> Bool #
Ord r => Ord (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods compare :: Opposite r -> Opposite r -> Ordering # (<) :: Opposite r -> Opposite r -> Bool # (<=) :: Opposite r -> Opposite r -> Bool # (>) :: Opposite r -> Opposite r -> Bool # (>=) :: Opposite r -> Opposite r -> Bool # max :: Opposite r -> Opposite r -> Opposite r # min :: Opposite r -> Opposite r -> Opposite r #
Read r => Read (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods readsPrec :: Int -> ReadS (Opposite r) # readList :: ReadS [Opposite r] # readPrec :: ReadPrec (Opposite r) # readListPrec :: ReadPrec [Opposite r] #
Show r => Show (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods showsPrec :: Int -> Opposite r -> ShowS # show :: Opposite r -> String # showList :: [Opposite r] -> ShowS #
Idempotent r => Idempotent (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite
Abelian r => Abelian (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite
Additive r => Additive (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (+) :: Opposite r -> Opposite r -> Opposite r # sinnum1p :: Natural -> Opposite r -> Opposite r # sumWith1 :: Foldable1 f => (a -> Opposite r) -> f a -> Opposite r #
Monoidal r => Monoidal (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods zero :: Opposite r # sinnum :: Natural -> Opposite r -> Opposite r # sumWith :: Foldable f => (a -> Opposite r) -> f a -> Opposite r #
Semiring r => Semiring (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite
Multiplicative r => Multiplicative (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (*) :: Opposite r -> Opposite r -> Opposite r # pow1p :: Opposite r -> Natural -> Opposite r # productWith1 :: Foldable1 f => (a -> Opposite r) -> f a -> Opposite r #
Group r => Group (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (-) :: Opposite r -> Opposite r -> Opposite r # negate :: Opposite r -> Opposite r # subtract :: Opposite r -> Opposite r -> Opposite r # times :: Integral n => n -> Opposite r -> Opposite r #
Unital r => Unital (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods one :: Opposite r # pow :: Opposite r -> Natural -> Opposite r # productWith :: Foldable f => (a -> Opposite r) -> f a -> Opposite r #
Band r => Band (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite
Division r => Division (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods recip :: Opposite r -> Opposite r # (/) :: Opposite r -> Opposite r -> Opposite r # (\\) :: Opposite r -> Opposite r -> Opposite r # (^) :: Integral n => Opposite r -> n -> Opposite r #
Commutative r => Commutative (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite
DecidableAssociates r => DecidableAssociates (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods isAssociate :: Opposite r -> Opposite r -> Bool #
DecidableUnits r => DecidableUnits (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods recipUnit :: Opposite r -> Maybe (Opposite r) # isUnit :: Opposite r -> Bool # (^?) :: Integral n => Opposite r -> n -> Maybe (Opposite r) #
DecidableZero r => DecidableZero (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods isZero :: Opposite r -> Bool #
Rig r => Rig (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods fromNatural :: Natural -> Opposite r #
Ring r => Ring (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods fromInteger :: Integer -> Opposite r #
Semiring r => RightModule (Opposite r) (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (*.) :: Opposite r -> Opposite r -> Opposite r #
Semiring r => LeftModule (Opposite r) (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (.*) :: Opposite r -> Opposite r -> Opposite r #