Safe Haskell	None
Language	Haskell2010

NumHask.Pair

Description

I would have used V2 from the linear package, but wanted to avoid the lens dependency. And there's no canonical treatment out there.

Synopsis

newtype Pair a = Pair' (a, a)
pattern Pair :: a -> a -> Pair a

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 1 / one
Pair 0.0 1.0
>>> Pair 11 12 `mod` (pure 6)
Pair 5 0

As a numhask module

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

representables

>>> distribute [Pair 1 2, Pair 3 4]
Pair [1,3] [2,4]
>>> index (Pair 'l' 'r') False
'l'

Constructors

Pair' (a, a)

Instances

Monad Pair #
Instance details Defined in NumHask.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 #
Instance details Defined in NumHask.Pair Methods fmap :: (a -> b) -> Pair a -> Pair b # (<$) :: a -> Pair b -> Pair a #
Applicative Pair #
Instance details Defined in NumHask.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 #
Instance details Defined in NumHask.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 #
Instance details Defined in NumHask.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) #
Distributive Pair #
Instance details Defined in NumHask.Pair Methods distribute :: Functor f => f (Pair a) -> Pair (f a) # collect :: Functor f => (a -> Pair b) -> f a -> Pair (f b) # distributeM :: Monad m => m (Pair a) -> Pair (m a) # collectM :: Monad m => (a -> Pair b) -> m a -> Pair (m b) #
Representable Pair #
Instance details Defined in NumHask.Pair Associated Types type Rep Pair :: * # Methods tabulate :: (Rep Pair -> a) -> Pair a # index :: Pair a -> Rep Pair -> a #
Eq1 Pair #
Instance details Defined in NumHask.Pair Methods liftEq :: (a -> b -> Bool) -> Pair a -> Pair b -> Bool #
Show1 Pair #
Instance details Defined in NumHask.Pair Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Pair a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Pair a] -> ShowS #
Singleton Pair #
Instance details Defined in NumHask.Pair Methods singleton :: a -> Pair a #
Traversable1 Pair #
Instance details Defined in NumHask.Pair Methods traverse1 :: Apply f => (a -> f b) -> Pair a -> f (Pair b) # sequence1 :: Apply f => Pair (f b) -> f (Pair b) #
Foldable1 Pair #
Instance details Defined in NumHask.Pair Methods fold1 :: Semigroup m => Pair m -> m # foldMap1 :: Semigroup m => (a -> m) -> Pair a -> m # toNonEmpty :: Pair a -> NonEmpty a #
Apply Pair #
Instance details Defined in NumHask.Pair Methods (<.>) :: Pair (a -> b) -> Pair a -> Pair b # (.>) :: Pair a -> Pair b -> Pair b # (<.) :: Pair a -> Pair b -> Pair a # liftF2 :: (a -> b -> c) -> Pair a -> Pair b -> Pair c #
Additive a => AdditiveModule Pair a #
Instance details Defined in NumHask.Pair Methods (.+) :: Pair a -> a -> Pair a # (+.) :: a -> Pair a -> Pair a #
AdditiveGroup a => AdditiveGroupModule Pair a #
Instance details Defined in NumHask.Pair Methods (.-) :: Pair a -> a -> Pair a # (-.) :: a -> Pair a -> Pair a #
Multiplicative a => MultiplicativeModule Pair a #
Instance details Defined in NumHask.Pair Methods (.) :: Pair a -> a -> Pair a # (.) :: a -> Pair a -> Pair a #
MultiplicativeGroup a => MultiplicativeGroupModule Pair a #
Instance details Defined in NumHask.Pair Methods (./) :: Pair a -> a -> Pair a # (/.) :: a -> Pair a -> Pair a #
Additive a => AdditiveBasis Pair a #
Instance details Defined in NumHask.Pair Methods (.+.) :: Pair a -> Pair a -> Pair a #
AdditiveGroup a => AdditiveGroupBasis Pair a #
Instance details Defined in NumHask.Pair Methods (.-.) :: Pair a -> Pair a -> Pair a #
Multiplicative a => MultiplicativeBasis Pair a #
Instance details Defined in NumHask.Pair Methods (.*.) :: Pair a -> Pair a -> Pair a #
MultiplicativeGroup a => MultiplicativeGroupBasis Pair a #
Instance details Defined in NumHask.Pair Methods (./.) :: Pair a -> Pair a -> Pair a #
Eq a => Eq (Pair a) #
Instance details Defined in NumHask.Pair Methods (==) :: Pair a -> Pair a -> Bool # (/=) :: Pair a -> Pair a -> Bool #
(Eq a, Ord a, Signed a, Additive a) => Ord (Pair a) #	L1-based Ord instance
Instance details Defined in NumHask.Pair Methods compare :: Pair a -> Pair a -> Ordering # (<) :: Pair a -> Pair a -> Bool # (<=) :: Pair a -> Pair a -> Bool # (>) :: Pair a -> Pair a -> Bool # (>=) :: Pair a -> Pair a -> Bool # max :: Pair a -> Pair a -> Pair a # min :: Pair a -> Pair a -> Pair a #
Show a => Show (Pair a) #
Instance details Defined in NumHask.Pair Methods showsPrec :: Int -> Pair a -> ShowS # show :: Pair a -> String # showList :: [Pair a] -> ShowS #
Generic (Pair a) #
Instance details Defined in NumHask.Pair Associated Types type Rep (Pair a) :: * -> * # Methods from :: Pair a -> Rep (Pair a) x # to :: Rep (Pair a) x -> Pair a #
Semigroup a => Semigroup (Pair a) #
Instance details Defined in NumHask.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) #
Instance details Defined in NumHask.Pair Methods mempty :: Pair a # mappend :: Pair a -> Pair a -> Pair a # mconcat :: [Pair a] -> Pair a #
Arbitrary a => Arbitrary (Pair a) #
Instance details Defined in NumHask.Pair Methods arbitrary :: Gen (Pair a) # shrink :: Pair a -> [Pair a] #
NFData a => NFData (Pair a) #
Instance details Defined in NumHask.Pair Methods rnf :: Pair a -> () #
Signed a => Signed (Pair a) #
Instance details Defined in NumHask.Pair Methods sign :: Pair a -> Pair a # abs :: Pair a -> Pair a #
(AdditiveInvertible a, Epsilon a) => Epsilon (Pair a) #
Instance details Defined in NumHask.Pair Methods nearZero :: Pair a -> Bool # aboutEqual :: Pair a -> Pair a -> Bool # positive :: Pair a -> Bool # veryPositive :: Pair a -> Bool # veryNegative :: Pair a -> Bool #
Semifield a => Semifield (Pair a) #
Instance details Defined in NumHask.Pair
Field a => Field (Pair a) #
Instance details Defined in NumHask.Pair
ExpField a => ExpField (Pair a) #
Instance details Defined in NumHask.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 #
UpperBoundedField a => UpperBoundedField (Pair a) #
Instance details Defined in NumHask.Pair Methods infinity :: Pair a # nan :: Pair a #
LowerBoundedField a => LowerBoundedField (Pair a) #
Instance details Defined in NumHask.Pair Methods negInfinity :: Pair a #
Integral a => Integral (Pair a) #
Instance details Defined in NumHask.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) #
Semiring a => Semiring (Pair a) #
Instance details Defined in NumHask.Pair
Ring a => Ring (Pair a) #
Instance details Defined in NumHask.Pair
CRing a => CRing (Pair a) #
Instance details Defined in NumHask.Pair
Distribution a => Distribution (Pair a) #
Instance details Defined in NumHask.Pair
MultiplicativeMagma a => MultiplicativeMagma (Pair a) #
Instance details Defined in NumHask.Pair Methods times :: Pair a -> Pair a -> Pair a #
MultiplicativeUnital a => MultiplicativeUnital (Pair a) #
Instance details Defined in NumHask.Pair Methods one :: Pair a #
MultiplicativeMagma a => MultiplicativeAssociative (Pair a) #
Instance details Defined in NumHask.Pair
MultiplicativeMagma a => MultiplicativeCommutative (Pair a) #
Instance details Defined in NumHask.Pair
MultiplicativeInvertible a => MultiplicativeInvertible (Pair a) #
Instance details Defined in NumHask.Pair Methods recip :: Pair a -> Pair a #
MultiplicativeUnital a => Multiplicative (Pair a) #
Instance details Defined in NumHask.Pair Methods (*) :: Pair a -> Pair a -> Pair a #
(MultiplicativeUnital a, MultiplicativeInvertible a) => MultiplicativeGroup (Pair a) #
Instance details Defined in NumHask.Pair Methods (/) :: Pair a -> Pair a -> Pair a #
AdditiveMagma a => AdditiveMagma (Pair a) #
Instance details Defined in NumHask.Pair Methods plus :: Pair a -> Pair a -> Pair a #
AdditiveUnital a => AdditiveUnital (Pair a) #
Instance details Defined in NumHask.Pair Methods zero :: Pair a #
AdditiveMagma a => AdditiveAssociative (Pair a) #
Instance details Defined in NumHask.Pair
AdditiveMagma a => AdditiveCommutative (Pair a) #
Instance details Defined in NumHask.Pair
AdditiveInvertible a => AdditiveInvertible (Pair a) #
Instance details Defined in NumHask.Pair Methods negate :: Pair a -> Pair a #
AdditiveUnital a => Additive (Pair a) #
Instance details Defined in NumHask.Pair Methods (+) :: Pair a -> Pair a -> Pair a #
(AdditiveUnital a, AdditiveInvertible a) => AdditiveGroup (Pair a) #
Instance details Defined in NumHask.Pair Methods (-) :: Pair a -> Pair a -> Pair a #
(ExpField a, Normed a a, MultiplicativeUnital a) => Normed (Pair a) a #
Instance details Defined in NumHask.Pair Methods normL1 :: Pair a -> a # normL2 :: Pair a -> a # normLp :: a -> Pair a -> a #
(ExpField a, Normed a a) => Metric (Pair a) a #
Instance details Defined in NumHask.Pair Methods distanceL1 :: Pair a -> Pair a -> a # distanceL2 :: Pair a -> Pair a -> a # distanceLp :: a -> Pair a -> Pair a -> a #
AdditiveGroup a => Normed (Rect a) (Pair a) #
Instance details Defined in NumHask.Rect Methods normL1 :: Rect a -> Pair a # normL2 :: Rect a -> Pair a # normLp :: Pair a -> Rect a -> Pair a #
type Rep Pair #
Instance details Defined in NumHask.Pair type Rep Pair = Bool
type Rep (Pair a) #
Instance details Defined in NumHask.Pair type Rep (Pair a) = D1 (MetaData "Pair" "NumHask.Pair" "numhask-range-0.2.3.1-J89sQYUYBLeKCiE9B8m0BR" True) (C1 (MetaCons "Pair'" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a, a))))

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

the preferred pattern