Data.Pair

Pair-related type constructor classes. See Data.Fun for similar classes.

Pairings

type PairTy f = forall a b. f a -> f b -> f (a, b)

Type of pair method

class Pair f where

Type constructor class for pair-like things. Generalizes zip. Here are some standard instance templates you can fill in. They're not defined in the general forms below, because they would lead to a lot of overlap.

   instance Applicative f => Pair f where
       pair = liftA2 (,)
   instance (Applicative h, Pair f) => Pair (h :. f) where
       pair = apPair
   instance (Functor g, Pair g, Pair f) => Pair (g :. f)
       where pair = ppPair
   instance (Arrow (~>), Unpair f, Pair g) => Pair (Arrw (~>) f g) where
       pair = arPair
   instance (Monoid_f h, Copair h) => Pair h where
       pair = copair

Also, if you have a type constructor that's a Functor and a Pair, here is a way to define '(*)' for Applicative:

   rf * rx = uncurry ($) $ (rf pair rx)

Methods

pair

Arguments

:: PairTy f

Form a pair-like value (generalizes zip)

Instances

Pair IO

Pair Endo

Pair Id

Pair ((->) u)

Monoid u => Pair ((,) u)

Monoid o => Pair (Const o)

(Pair f, Pair g) => Pair (:*: f g)

(Arrow ~>, Monoid_f (Flip ~> o)) => Pair (Flip ~> o)

(Arrow ~>, Unpair f, Pair g) => Pair (Arrw ~> f g)

apPair :: (Applicative h, Pair f) => PairTy (h :. f)

Handy for Pair instances

ppPair :: (Functor g, Pair g, Pair f) => PairTy (g :. f)

Handy for Pair instances

arPair :: (Arrow ~>, Unpair f, Pair g) => PairTy (Arrw ~> f g)

Pairing of Arrw values. Warning: definition uses arr, so only use if your arrow has a working arr.

Unpairings

type UnpairTy f = forall a b. f (a, b) -> (f a, f b)

Type of unpair method. Generalizes unzip.

class Unpair f where

Dissectable as pairs. Minimal instance definition: either (a) unpair or (b) both of pfst and psnd. A standard template to substitute any Functor f. But watch out for effects!

   instance Functor f => Unpair f where {pfst = fmap fst; psnd = fmap snd}

Methods

unpair

Arguments

:: UnpairTy f

Deconstruct pair-like value

pfst

Arguments

:: f (a, b)

-> f a

First part of pair-like value

psnd

Arguments

:: f (a, b)

-> f b

Second part of pair-like value

Instances

Unpair []

Unpair Endo

Unpair Id

Unpair (Const a)

Dual unpairings

class Copair f where

Dual to Unpair. Especially handy for contravariant functors (Cofunctor) . Use this template (filling in f) :

   instance Cofunctor f => Copair f where
     { cofst = cofmap fst ; cosnd = cofmap snd }

Methods

cofst

Arguments

:: f a

-> f (a, b)

Pair-like value from first part

cosnd

Arguments

:: f b

-> f (a, b)

Pair-like value from second part

Instances

Copair Endo

Copair (Const e)

(Copair f, Copair g) => Copair (:*: f g)

Arrow ~> => Copair (Flip ~> o)

(Functor h, Copair f) => Copair (:. h f)

copair :: (Copair f, Monoid_f f) => PairTy f

Pairing of Copair values. Combines contribution of each.

Misc

pairEdit :: (Functor m, Monoid (m ((c, d) -> (c, d)))) => (m c, m d) -> m ((c, d) -> (c, d))

Turn a pair of sources into a source of pair-editors. See http://conal.net/blog/posts/pairs-sums-and-reactivity/. 'Functor'\/'Monoid' version. See also pairEditM.

pairEditM :: MonadPlus m => (m c, m d) -> m ((c, d) -> (c, d))

Turn a pair of sources into a source of pair-editors. See http://conal.net/blog/posts/pairs-sums-and-reactivity/. Monad version. See also pairEdit.