Data.Pair

Pair-related type constructor classes.

This module is similar to Control.Functor.Pair in the category-extras package, but it does not require a Functor superclass.

Temporarily, there is also Data.Zip, which contains the same functionality with different naming. I'm unsure which I prefer.

Pairpings

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. 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:

    (<*>) = pairWith ($)

Minimum definitions for instances.

Methods

pair

Arguments

:: PairTy f

Generalized pair

Instances

Pair []

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 unpair.

class Unpair f where

Unpairpable. Minimal instance definition: either (a) unpair or (b) both of fsts and snds. A standard template to substitute any Functor f. But watch out for effects!

     instance Functor f => Unpair f where {fsts = fmap fst; snds = fmap snd}

Methods

unpair

Arguments

:: UnpairTy f

generalized unpair

fsts

Arguments

:: f (a, b)

-> f a

First part of pair-like value

snds

Arguments

:: f (a, b)

-> f b

Second part of pair-like value

Instances

Unpair []

Unpair Endo

Unpair Id

Unpair ((->) a)

Unpair ((,) a)

Unpair (Const a)

Dual unpairings

class Copair f where

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

    instance ContraFunctor f => Copair f where
      { cofsts = cofmap fst ; cosnds = cofmap snd }

Methods

cofsts

Arguments

:: f a

-> f (a, b)

Pair-like value from first part

cosnds

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.