Safe Haskell	Safe-Inferred
Language	GHC2021

NumHask.Algebra.Additive

Description

Additive classes

Synopsis

class Additive a where
- (+) :: a -> a -> a
- zero :: a
newtype Sum a = Sum {
- getSum :: a
}
sum :: (Additive a, Foldable f) => f a -> a
accsum :: (Additive a, Traversable f) => f a -> f a
class Additive a => Subtractive a where
- negate :: a -> a
- (-) :: a -> a -> a

Documentation

class Additive a where Source #

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 Source #

zero :: a Source #

Instances

Instances details

Additive Int16 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int16 -> Int16 -> Int16 Source # zero :: Int16 Source #
Additive Int32 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int32 -> Int32 -> Int32 Source # zero :: Int32 Source #
Additive Int64 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int64 -> Int64 -> Int64 Source # zero :: Int64 Source #
Additive Int8 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int8 -> Int8 -> Int8 Source # zero :: Int8 Source #
Additive Word16 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word16 -> Word16 -> Word16 Source # zero :: Word16 Source #
Additive Word32 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word32 -> Word32 -> Word32 Source # zero :: Word32 Source #
Additive Word64 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word64 -> Word64 -> Word64 Source # zero :: Word64 Source #
Additive Word8 Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word8 -> Word8 -> Word8 Source # zero :: Word8 Source #
Additive Integer Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Integer -> Integer -> Integer Source # zero :: Integer Source #
Additive Natural Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Natural -> Natural -> Natural Source # zero :: Natural Source #
Additive Bool Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Bool -> Bool -> Bool Source # zero :: Bool Source #
Additive Double Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Double -> Double -> Double Source # zero :: Double Source #
Additive Float Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Float -> Float -> Float Source # zero :: Float Source #
Additive Int Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int -> Int -> Int Source # zero :: Int Source #
Additive Word Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word -> Word -> Word Source # zero :: Word Source #
Additive a => Additive (Sum a) Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Sum a -> Sum a -> Sum a Source # zero :: Sum a Source #
Additive a => Additive (EuclideanPair a) Source #
Instance details Defined in NumHask.Algebra.Metric Methods (+) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source # zero :: EuclideanPair a Source #
Additive a => Additive (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # zero :: Complex a Source #
(Ord a, EndoBased a, Integral a, Ring a) => Additive (Ratio a) Source #
Instance details Defined in NumHask.Data.Rational Methods (+) :: Ratio a -> Ratio a -> Ratio a Source # zero :: Ratio a Source #
Additive b => Additive (a -> b) Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: (a -> b) -> (a -> b) -> a -> b Source # zero :: a -> b Source #

newtype Sum a Source #

A wrapper for an Additive which distinguishes the additive structure

Constructors

Sum
Fields getSum :: a

Instances

Instances details

Additive a => Monoid (Sum a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in NumHask.Algebra.Additive Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Eq a => Eq (Sum a) Source #
Instance details Defined in NumHask.Algebra.Additive Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Ord a => Ord (Sum a) Source #
Instance details 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) Source #
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Sum a -> Sum a -> Sum a Source # zero :: Sum a Source #

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

Compute the sum of a Foldable.

>>> sum [0..10]
55

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

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 Source #

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 Source #

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

Instances

Instances details

Subtractive Int16 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Int16 -> Int16 Source # (-) :: Int16 -> Int16 -> Int16 Source #
Subtractive Int32 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Int32 -> Int32 Source # (-) :: Int32 -> Int32 -> Int32 Source #
Subtractive Int64 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Int64 -> Int64 Source # (-) :: Int64 -> Int64 -> Int64 Source #
Subtractive Int8 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Int8 -> Int8 Source # (-) :: Int8 -> Int8 -> Int8 Source #
Subtractive Word16 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Word16 -> Word16 Source # (-) :: Word16 -> Word16 -> Word16 Source #
Subtractive Word32 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Word32 -> Word32 Source # (-) :: Word32 -> Word32 -> Word32 Source #
Subtractive Word64 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Word64 -> Word64 Source # (-) :: Word64 -> Word64 -> Word64 Source #
Subtractive Word8 Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Word8 -> Word8 Source # (-) :: Word8 -> Word8 -> Word8 Source #
Subtractive Integer Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source #
Subtractive Natural Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source #
Subtractive Double Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Double -> Double Source # (-) :: Double -> Double -> Double Source #
Subtractive Float Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Float -> Float Source # (-) :: Float -> Float -> Float Source #
Subtractive Int Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Int -> Int Source # (-) :: Int -> Int -> Int Source #
Subtractive Word Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: Word -> Word Source # (-) :: Word -> Word -> Word Source #
Subtractive a => Subtractive (EuclideanPair a) Source #
Instance details Defined in NumHask.Algebra.Metric Methods negate :: EuclideanPair a -> EuclideanPair a Source # (-) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #
Subtractive a => Subtractive (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods negate :: Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source #
(Ord a, EndoBased a, Integral a, Ring a) => Subtractive (Ratio a) Source #
Instance details Defined in NumHask.Data.Rational Methods negate :: Ratio a -> Ratio a Source # (-) :: Ratio a -> Ratio a -> Ratio a Source #
Subtractive b => Subtractive (a -> b) Source #
Instance details Defined in NumHask.Algebra.Additive Methods negate :: (a -> b) -> a -> b Source # (-) :: (a -> b) -> (a -> b) -> a -> b Source #