NumHask.Data.Pair

A Pair is *the* classical higher-kinded number but there is no canon.

Documentation

newtype Pair a

A pair of a's, implemented as a tuple, but api represented as a Pair of a's.

>>> fmap (+1) (Pair 1 2)
Pair 2 3
>>> pure one :: Pair Int
Pair 1 1
>>> (*) <$> Pair 1 2 <*> pure 2
Pair 2 4
>>> foldr (++) [] (Pair [1,2] [3])
[1,2,3]
>>> Pair "a" "pair" `mappend` pure " " `mappend` Pair "string" "mappended"
Pair "a string" "pair mappended"

As a Ring and Field class

>>> Pair 0 1 + zero
Pair 0 1
>>> Pair 0 1 + Pair 2 3
Pair 2 4
>>> Pair 1 1 - one
Pair 0 0
>>> Pair 0 1 * one
Pair 0 1
>>> Pair 0.0 1.0 / one
Pair 0.0 1.0
>>> Pair 11 12 `mod` (pure 6)
Pair 5 0

As an action

>>> Pair 1 2 .+ 3
Pair 4 5

Constructors

Pair' (a, a)

Instances

Monad Pair

Defined in NumHask.Data.Pair

Methods

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

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

return :: a -> Pair a

fail :: String -> Pair a

Functor Pair

Defined in NumHask.Data.Pair

Methods

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

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

Applicative Pair

Defined in NumHask.Data.Pair

Methods

pure :: a -> Pair a

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

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

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

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

Foldable Pair

Defined in NumHask.Data.Pair

Methods

fold :: Monoid m => Pair m -> m

foldMap :: Monoid m => (a -> m) -> Pair a -> m

foldr :: (a -> b -> b) -> b -> Pair a -> b

foldr' :: (a -> b -> b) -> b -> Pair a -> b

foldl :: (b -> a -> b) -> b -> Pair a -> b

foldl' :: (b -> a -> b) -> b -> Pair a -> b

foldr1 :: (a -> a -> a) -> Pair a -> a

foldl1 :: (a -> a -> a) -> Pair a -> a

toList :: Pair a -> [a]

null :: Pair a -> Bool

length :: Pair a -> Int

elem :: Eq a => a -> Pair a -> Bool

maximum :: Ord a => Pair a -> a

minimum :: Ord a => Pair a -> a

sum :: Num a => Pair a -> a

product :: Num a => Pair a -> a

Traversable Pair

Defined in NumHask.Data.Pair

Methods

traverse :: Applicative f => (a -> f b) -> Pair a -> f (Pair b)

sequenceA :: Applicative f => Pair (f a) -> f (Pair a)

mapM :: Monad m => (a -> m b) -> Pair a -> m (Pair b)

sequence :: Monad m => Pair (m a) -> m (Pair a)

Eq1 Pair

Defined in NumHask.Data.Pair

Methods

liftEq :: (a -> b -> Bool) -> Pair a -> Pair b -> Bool

Show1 Pair

Defined in NumHask.Data.Pair

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Pair a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Pair a] -> ShowS

Bounded a => Bounded (Pair a)

Defined in NumHask.Data.Pair

Methods

minBound :: Pair a

maxBound :: Pair a

Eq a => Eq (Pair a)

Defined in NumHask.Data.Pair

Methods

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

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

Show a => Show (Pair a)

Defined in NumHask.Data.Pair

Methods

showsPrec :: Int -> Pair a -> ShowS

show :: Pair a -> String

showList :: [Pair a] -> ShowS

Generic (Pair a)

Defined in NumHask.Data.Pair

Associated Types

type Rep (Pair a) :: Type -> Type

Methods

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

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

Semigroup a => Semigroup (Pair a)

Defined in NumHask.Data.Pair

Methods

(<>) :: Pair a -> Pair a -> Pair a

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

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

(Semigroup a, Monoid a) => Monoid (Pair a)

Defined in NumHask.Data.Pair

Methods

mempty :: Pair a

mappend :: Pair a -> Pair a -> Pair a

mconcat :: [Pair a] -> Pair a

Subtractive a => Subtractive (Pair a)

Defined in NumHask.Data.Pair

Methods

negate :: Pair a -> Pair a

(-) :: Pair a -> Pair a -> Pair a

Additive a => Additive (Pair a)

Defined in NumHask.Data.Pair

Methods

(+) :: Pair a -> Pair a -> Pair a

zero :: Pair a

Divisive a => Divisive (Pair a)

Defined in NumHask.Data.Pair

Methods

recip :: Pair a -> Pair a

(/) :: Pair a -> Pair a -> Pair a

Multiplicative a => Multiplicative (Pair a)

Defined in NumHask.Data.Pair

Methods

(*) :: Pair a -> Pair a -> Pair a

one :: Pair a

Divisive a => DivisiveAction (Pair a)

Defined in NumHask.Data.Pair

Methods

(./) :: Pair a -> Actor (Pair a) -> Pair a

(/.) :: Actor (Pair a) -> Pair a -> Pair a

Multiplicative a => MultiplicativeAction (Pair a)

Defined in NumHask.Data.Pair

Methods

(.*) :: Pair a -> Actor (Pair a) -> Pair a

(*.) :: Actor (Pair a) -> Pair a -> Pair a

Subtractive a => SubtractiveAction (Pair a)

Defined in NumHask.Data.Pair

Methods

(.-) :: Pair a -> Actor (Pair a) -> Pair a

(-.) :: Actor (Pair a) -> Pair a -> Pair a

Additive a => AdditiveAction (Pair a)

Defined in NumHask.Data.Pair

Methods

(.+) :: Pair a -> Actor (Pair a) -> Pair a

(+.) :: Actor (Pair a) -> Pair a -> Pair a

IntegralDomain a => IntegralDomain (Pair a)

Defined in NumHask.Data.Pair

Distributive a => Distributive (Pair a)

Defined in NumHask.Data.Pair

Integral a => Integral (Pair a)

Defined in NumHask.Data.Pair

Methods

div :: Pair a -> Pair a -> Pair a

mod :: Pair a -> Pair a -> Pair a

divMod :: Pair a -> Pair a -> (Pair a, Pair a)

quot :: Pair a -> Pair a -> Pair a

rem :: Pair a -> Pair a -> Pair a

quotRem :: Pair a -> Pair a -> (Pair a, Pair a)

LowerBoundedField a => LowerBoundedField (Pair a)

Defined in NumHask.Data.Pair

Methods

negInfinity :: Pair a

UpperBoundedField a => UpperBoundedField (Pair a)

Defined in NumHask.Data.Pair

Methods

infinity :: Pair a

nan :: Pair a

ExpField a => ExpField (Pair a)

Defined in NumHask.Data.Pair

Methods

exp :: Pair a -> Pair a

log :: Pair a -> Pair a

logBase :: Pair a -> Pair a -> Pair a

(**) :: Pair a -> Pair a -> Pair a

sqrt :: Pair a -> Pair a

Field a => Field (Pair a)

Defined in NumHask.Data.Pair

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Pair a)

Defined in NumHask.Data.Pair

Methods

top :: Pair a

BoundedJoinSemiLattice a => BoundedJoinSemiLattice (Pair a)

Defined in NumHask.Data.Pair

Methods

bottom :: Pair a

MeetSemiLattice a => MeetSemiLattice (Pair a)

Defined in NumHask.Data.Pair

Methods

(/\) :: Pair a -> Pair a -> Pair a

JoinSemiLattice a => JoinSemiLattice (Pair a)

Defined in NumHask.Data.Pair

Methods

(\/) :: Pair a -> Pair a -> Pair a

(Subtractive a, Epsilon a) => Epsilon (Pair a)

Defined in NumHask.Data.Pair

Methods

epsilon :: Pair a

nearZero :: Pair a -> Bool

aboutEqual :: Pair a -> Pair a -> Bool

Signed a => Signed (Pair a)

Defined in NumHask.Data.Pair

Methods

sign :: Pair a -> Pair a

abs :: Pair a -> Pair a

FromIntegral a b => FromIntegral (Pair a) b

Defined in NumHask.Data.Pair

Methods

fromIntegral_ :: b -> Pair a

(ExpField a, Subtractive a, Normed a a) => Metric (Pair a) a

Defined in NumHask.Data.Pair

Methods

distance :: Pair a -> Pair a -> a

(ExpField a, Normed a a) => Normed (Pair a) a

Defined in NumHask.Data.Pair

Methods

norm :: Pair a -> a

FromRatio a b => FromRatio (Pair a) b

Defined in NumHask.Data.Pair

Methods

fromRatio :: Ratio b -> Pair a

(Subtractive a, Normed a a) => Metric (Pair a) (Pair a)

Defined in NumHask.Data.Pair

Methods

distance :: Pair a -> Pair a -> Pair a

Normed a a => Normed (Pair a) (Pair a)

Defined in NumHask.Data.Pair

Methods

norm :: Pair a -> Pair a

type Rep (Pair a)

Defined in NumHask.Data.Pair

type Rep (Pair a) = D1 (MetaData "Pair" "NumHask.Data.Pair" "numhask-0.6.0.2-2vU6ERlgtSAHonXWkOkfPO" True) (C1 (MetaCons "Pair'" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a, a))))

type Actor (Pair a)

Defined in NumHask.Data.Pair

type Actor (Pair a) = a

pattern Pair :: a -> a -> Pair a

the preferred pattern