NumHask.Data

Documentation

newtype Sum a

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum

Fields

• getSum :: a

Instances

Monad Sum

Since: 4.8.0.0

Methods

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

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

return :: a -> Sum a

fail :: String -> Sum a

Functor Sum

Methods

fmap :: (a -> b) -> Sum a -> Sum b

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

Applicative Sum

Since: 4.8.0.0

Methods

pure :: a -> Sum a

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

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

(*>) :: Sum a -> Sum b -> Sum b

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

Bounded a => Bounded (Sum a)

Methods

minBound :: Sum a

maxBound :: Sum a

Eq a => Eq (Sum a)

Methods

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

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

Ord a => Ord (Sum a)

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

Read a => Read (Sum a)

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Associated Types

type Rep (Sum a) :: * -> *

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

AdditiveMagma a => Semigroup (Sum a)

Methods

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

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

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

AdditiveUnital a => Monoid (Sum a)

Methods

mempty :: Sum a

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

mconcat :: [Sum a] -> Sum a

(AdditiveInvertible a, AdditiveUnital a) => AdditiveGroup (Sum a)

Methods

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

(AdditiveUnital a, AdditiveMagma a) => Additive (Sum a)

Methods

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

AdditiveInvertible a => AdditiveInvertible (Sum a)

Methods

negate :: Sum a -> Sum a

AdditiveMagma a => AdditiveCommutative (Sum a)

AdditiveMagma a => AdditiveAssociative (Sum a)

AdditiveUnital a => AdditiveUnital (Sum a)

Methods

zero :: Sum a

AdditiveMagma a => AdditiveMagma (Sum a)

Methods

plus :: Sum a -> Sum a -> Sum a

Generic1 * Sum

Associated Types

type Rep1 Sum (f :: Sum -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Sum f a

to1 :: Rep1 Sum f a -> f a

type Rep (Sum a)

type Rep (Sum a) = D1 * (MetaData "Sum" "NumHask.Data" "numhask-0.2.3.1-5X1V1rZSUVsE9M1b0C2H1i" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))

type Rep1 * Sum

type Rep1 * Sum = D1 * (MetaData "Sum" "NumHask.Data" "numhask-0.2.3.1-5X1V1rZSUVsE9M1b0C2H1i" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product

Fields

• getProduct :: a

Instances

Monad Product

Since: 4.8.0.0

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

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

return :: a -> Product a

fail :: String -> Product a

Functor Product

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Applicative Product

Since: 4.8.0.0

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

(*>) :: Product a -> Product b -> Product b

(<*) :: Product a -> Product b -> Product a

Bounded a => Bounded (Product a)

Methods

minBound :: Product a

maxBound :: Product a

Eq a => Eq (Product a)

Methods

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

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

Ord a => Ord (Product a)

Methods

compare :: Product a -> Product a -> Ordering

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

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

(>) :: Product a -> Product a -> Bool

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

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

Read a => Read (Product a)

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Associated Types

type Rep (Product a) :: * -> *

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

MultiplicativeMagma a => Semigroup (Product a)

Methods

(<>) :: Product a -> Product a -> Product a

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

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

MultiplicativeUnital a => Monoid (Product a)

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

(MultiplicativeUnital a, MultiplicativeInvertible a) => MultiplicativeGroup (Product a)

Methods

(/) :: Product a -> Product a -> Product a

MultiplicativeUnital a => Multiplicative (Product a)

Methods

(*) :: Product a -> Product a -> Product a

MultiplicativeInvertible a => MultiplicativeInvertible (Product a)

Methods

recip :: Product a -> Product a

MultiplicativeMagma a => MultiplicativeCommutative (Product a)

MultiplicativeMagma a => MultiplicativeAssociative (Product a)

MultiplicativeUnital a => MultiplicativeUnital (Product a)

Methods

one :: Product a

MultiplicativeMagma a => MultiplicativeMagma (Product a)

Methods

times :: Product a -> Product a -> Product a

Generic1 * Product

Associated Types

type Rep1 Product (f :: Product -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Product f a

to1 :: Rep1 Product f a -> f a

type Rep (Product a)

type Rep (Product a) = D1 * (MetaData "Product" "NumHask.Data" "numhask-0.2.3.1-5X1V1rZSUVsE9M1b0C2H1i" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))

type Rep1 * Product

type Rep1 * Product = D1 * (MetaData "Product" "NumHask.Data" "numhask-0.2.3.1-5X1V1rZSUVsE9M1b0C2H1i" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))