GHC.Num (original) (raw)

Note that [Natural](Numeric-Natural.html#t:Natural "Numeric.Natural")'s [Num](GHC-Num.html#t:Num "GHC.Num") instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Instance details

Defined in GHC.Num

Num Double Source #

Note that due to the presence of NaN, not all elements of [Double](Prelude.html#t:Double "Prelude") have an additive inverse.

>>> **0/0 + (negate 0/0 :: Double)** ****NaN

Also note that due to the presence of -0, [Double](Prelude.html#t:Double "Prelude")'s [Num](GHC-Num.html#t:Num "GHC.Num") instance doesn't have an additive identity

>>> **0 + (-0 :: Double)** ****0.0

Since: base-2.1

Instance details

Defined in GHC.Float

Num Float Source #

Note that due to the presence of NaN, not all elements of [Float](Prelude.html#t:Float "Prelude") have an additive inverse.

>>> **0/0 + (negate 0/0 :: Float)** ****NaN

Also note that due to the presence of -0, [Float](Prelude.html#t:Float "Prelude")'s [Num](GHC-Num.html#t:Num "GHC.Num") instance doesn't have an additive identity

>>> **0 + (-0 :: Float)** ****0.0

Since: base-2.1

Instance details

Defined in GHC.Float

Num Int Source #

Since: base-2.1

Instance details

Defined in GHC.Num

Num Word Source #

Since: base-2.1

Instance details

Defined in GHC.Num

RealFloat a => Num (Complex a) Source #

Since: base-2.1

Instance details

Defined in Data.Complex

Num a => Num (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Num a => Num (Down a) Source #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Num a => Num (Max a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Num a => Num (Min a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Num a => Num (Product a) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Num a => Num (Sum a) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Integral a => Num (Ratio a) Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

HasResolution a => Num (Fixed a) Source #

Since: base-2.1

Instance details

Defined in Data.Fixed

Num a => Num (Op a b) Source #

Instance details

Defined in Data.Functor.Contravariant

Num a => Num (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

(Applicative f, Num a) => Num (Ap f a) Source #

Note that even if the underlying [Num](GHC-Num.html#t:Num "GHC.Num") and [Applicative](Control-Applicative.html#t:Applicative "Control.Applicative") instances are lawful, for most [Applicative](Control-Applicative.html#t:Applicative "Control.Applicative")s, this instance will not be lawful. If you use this instance with the list [Applicative](Control-Applicative.html#t:Applicative "Control.Applicative"), the following customary laws will not hold:

Commutativity:

>>> **Ap [10,20] + Ap [1,2]** ****Ap {getAp = [11,12,21,22]} >>> **Ap [1,2] + Ap [10,20]** ****Ap {getAp = [11,21,12,22]}

Additive inverse:

>>> **Ap [] + negate (Ap [])** ****Ap {getAp = []} >>> **fromInteger 0 :: Ap [] Int** ****Ap {getAp = [0]}

Distributivity:

>>> **Ap [1,2] * (3 + 4)** ****Ap {getAp = [7,14]} >>> **(Ap [1,2] * 3) + (Ap [1,2] * 4)** ****Ap {getAp = [7,11,10,14]}

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Num (f a) => Num (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal