NumHask.Algebra.Additive

Additive classes

Documentation

class Additive a where

or Addition

For practical reasons, we begin the class tree with Additive. Starting with Associative and Unital, or using Semigroup and Monoid from base tends to confuse the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.

\a -> zero + a == a

\a -> a + zero == a

\a b c -> (a + b) + c == a + (b + c)

\a b -> a + b == b + a

By convention, (+) is regarded as commutative, but this is not universal, and the introduction of another symbol which means non-commutative addition seems a bit dogmatic.

>>> zero + 1
1

>>> 1 + 1
2

Methods

(+) :: a -> a -> a infixl 6

zero :: a

Instances

Additive Int16

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int16 -> Int16 -> Int16

zero :: Int16

Additive Int32

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int32 -> Int32 -> Int32

zero :: Int32

Additive Int64

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int64 -> Int64 -> Int64

zero :: Int64

Additive Int8

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int8 -> Int8 -> Int8

zero :: Int8

Additive Word16

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word16 -> Word16 -> Word16

zero :: Word16

Additive Word32

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word32 -> Word32 -> Word32

zero :: Word32

Additive Word64

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word64 -> Word64 -> Word64

zero :: Word64

Additive Word8

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word8 -> Word8 -> Word8

zero :: Word8

Additive Integer

Defined in NumHask.Algebra.Additive

Methods

(+) :: Integer -> Integer -> Integer

zero :: Integer

Additive Natural

Defined in NumHask.Algebra.Additive

Methods

(+) :: Natural -> Natural -> Natural

zero :: Natural

Additive Bool

Defined in NumHask.Algebra.Additive

Methods

(+) :: Bool -> Bool -> Bool

zero :: Bool

Additive Double

Defined in NumHask.Algebra.Additive

Methods

(+) :: Double -> Double -> Double

zero :: Double

Additive Float

Defined in NumHask.Algebra.Additive

Methods

(+) :: Float -> Float -> Float

zero :: Float

Additive Int

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int -> Int -> Int

zero :: Int

Additive Word

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word -> Word -> Word

zero :: Word

Additive a => Additive (Sum a)

Defined in NumHask.Algebra.Additive

Methods

(+) :: Sum a -> Sum a -> Sum a

zero :: Sum a

Additive a => Additive (EuclideanPair a)

Defined in NumHask.Algebra.Metric

Methods

(+) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a

zero :: EuclideanPair a

Additive a => Additive (Complex a)

Defined in NumHask.Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a

zero :: Complex a

Additive a => Additive (Positive a)

Defined in NumHask.Data.Positive

Methods

(+) :: Positive a -> Positive a -> Positive a

zero :: Positive a

(Ord a, EndoBased a, Integral a, Ring a) => Additive (Ratio a)

Defined in NumHask.Data.Rational

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

zero :: Ratio a

Additive a => Additive (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

(+) :: Wrapped a -> Wrapped a -> Wrapped a

zero :: Wrapped a

Additive b => Additive (a -> b)

Defined in NumHask.Algebra.Additive

Methods

(+) :: (a -> b) -> (a -> b) -> a -> b

zero :: a -> b

newtype Sum a

A wrapper for an Additive which distinguishes the additive structure

Since: 0.11.1

Constructors

Sum

Fields

• getSum :: a

Instances

Additive a => Monoid (Sum a)

Defined in NumHask.Algebra.Additive

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Additive a => Semigroup (Sum a)

Defined in NumHask.Algebra.Additive

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Show a => Show (Sum a)

Defined in NumHask.Algebra.Additive

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Eq a => Eq (Sum a)

Defined in NumHask.Algebra.Additive

Methods

(==) :: Sum a -> Sum a -> Bool

(/=) :: Sum a -> Sum a -> Bool

Ord a => Ord (Sum a)

Defined in NumHask.Algebra.Additive

Methods

compare :: Sum a -> Sum a -> Ordering

(<) :: Sum a -> Sum a -> Bool

(<=) :: Sum a -> Sum a -> Bool

(>) :: Sum a -> Sum a -> Bool

(>=) :: Sum a -> Sum a -> Bool

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

Additive a => Additive (Sum a)

Defined in NumHask.Algebra.Additive

Methods

(+) :: Sum a -> Sum a -> Sum a

zero :: Sum a

sum :: (Additive a, Foldable f) => f a -> a

Compute the sum of a Foldable.

>>> sum [0..10]
55

accsum :: (Additive a, Traversable f) => f a -> f a

Compute the accumulating sum of a Traversable.

>>> accsum [0..10]
[0,1,3,6,10,15,21,28,36,45,55]

class Additive a => Subtractive a where

or Subtraction

\a -> a - a == zero

\a -> negate a == zero - a

\a -> negate a + a == zero

\a -> a + negate a == zero

>>> negate 1
-1

>>> 1 - 2
-1

Minimal complete definition

(-) | negate

Methods

negate :: a -> a

(-) :: a -> a -> a infixl 6

Instances

Subtractive Int16

Defined in NumHask.Algebra.Additive

Methods

negate :: Int16 -> Int16

(-) :: Int16 -> Int16 -> Int16

Subtractive Int32

Defined in NumHask.Algebra.Additive

Methods

negate :: Int32 -> Int32

(-) :: Int32 -> Int32 -> Int32

Subtractive Int64

Defined in NumHask.Algebra.Additive

Methods

negate :: Int64 -> Int64

(-) :: Int64 -> Int64 -> Int64

Subtractive Int8

Defined in NumHask.Algebra.Additive

Methods

negate :: Int8 -> Int8

(-) :: Int8 -> Int8 -> Int8

Subtractive Word16

Defined in NumHask.Algebra.Additive

Methods

negate :: Word16 -> Word16

(-) :: Word16 -> Word16 -> Word16

Subtractive Word32

Defined in NumHask.Algebra.Additive

Methods

negate :: Word32 -> Word32

(-) :: Word32 -> Word32 -> Word32

Subtractive Word64

Defined in NumHask.Algebra.Additive

Methods

negate :: Word64 -> Word64

(-) :: Word64 -> Word64 -> Word64

Subtractive Word8

Defined in NumHask.Algebra.Additive

Methods

negate :: Word8 -> Word8

(-) :: Word8 -> Word8 -> Word8

Subtractive Integer

Defined in NumHask.Algebra.Additive

Methods

negate :: Integer -> Integer

(-) :: Integer -> Integer -> Integer

Subtractive Natural

Defined in NumHask.Algebra.Additive

Methods

negate :: Natural -> Natural

(-) :: Natural -> Natural -> Natural

Subtractive Double

Defined in NumHask.Algebra.Additive

Methods

negate :: Double -> Double

(-) :: Double -> Double -> Double

Subtractive Float

Defined in NumHask.Algebra.Additive

Methods

negate :: Float -> Float

(-) :: Float -> Float -> Float

Subtractive Int

Defined in NumHask.Algebra.Additive

Methods

negate :: Int -> Int

(-) :: Int -> Int -> Int

Subtractive Word

Defined in NumHask.Algebra.Additive

Methods

negate :: Word -> Word

(-) :: Word -> Word -> Word

Subtractive a => Subtractive (EuclideanPair a)

Defined in NumHask.Algebra.Metric

Methods

negate :: EuclideanPair a -> EuclideanPair a

(-) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a

Subtractive a => Subtractive (Complex a)

Defined in NumHask.Data.Complex

Methods

negate :: Complex a -> Complex a

(-) :: Complex a -> Complex a -> Complex a

(Ord a, EndoBased a, Integral a, Ring a) => Subtractive (Ratio a)

Defined in NumHask.Data.Rational

Methods

negate :: Ratio a -> Ratio a

(-) :: Ratio a -> Ratio a -> Ratio a

Subtractive a => Subtractive (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

negate :: Wrapped a -> Wrapped a

(-) :: Wrapped a -> Wrapped a -> Wrapped a

Subtractive b => Subtractive (a -> b)

Defined in NumHask.Algebra.Additive

Methods

negate :: (a -> b) -> a -> b

(-) :: (a -> b) -> (a -> b) -> a -> b