Data.Zip

Zip-related type constructor classes.

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

This module defines generalized zip and unzip, so if you use it, you'll have to

   import Prelude hiding (zip,zipWith,zipWith3,unzip)

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

Zippings

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

Type of zip method

class Zip f where

Type constructor class for zip-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 => Zip f where
       zip = liftA2 (,)
   instance (Applicative h, Zip f) => Zip (h :. f) where
       zip = apZip
   instance (Functor g, Zip g, Zip f) => Zip (g :. f)
       where zip = ppZip
   instance (Arrow (~>), Unzip f, Zip g) => Zip (Arrw (~>) f g) where
       zip = arZip
   instance (Monoid_f h, Cozip h) => Zip h where
       zip = cozip

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

   (<*>) = zipWith ($)

Minimum definitions for instances.

Methods

zip

Arguments

:: ZipTy f

Generalized zip

Instances

Zip []

Zip IO

Zip Endo

Zip Id

Zip ((->) u)

Monoid u => Zip ((,) u)

Monoid o => Zip (Const o)

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

(Arrow j, Monoid_f (Flip j o)) => Zip (Flip j o)

(Arrow j, Unzip f, Zip g) => Zip (Arrw j f g)

zipWith :: (Functor f, Zip f) => (a -> b -> c) -> f a -> f b -> f c

Generalized zipWith

zipWith3 :: (Functor f, Zip f) => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Generalized zipWith

apZip :: (Applicative h, Zip f) => ZipTy (h :. f)

Handy for Zip instances

ppZip :: (Functor g, Zip g, Zip f) => ZipTy (g :. f)

Handy for Zip instances

arZip :: (Arrow j, Unzip f, Zip g) => ZipTy (Arrw j f g)

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

Unzipings

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

Type of unzip method. Generalizes unzip.

class Unzip f where

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

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

Minimal complete definition

Nothing

Methods

unzip

Arguments

:: UnzipTy f

generalized unzip

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

Unzip []

Unzip Endo

Unzip Id

Unzip ((->) a)

Unzip ((,) a)

Unzip (Const a)

Dual unzipings

class Cozip f where

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

   instance Cofunctor f => Cozip f where
     { cofsts = cofmap fst ; cosnds = cofmap snd }

Methods

cofsts

Arguments

:: f a

-> f (a, b)

Zip-like value from first part

cosnds

Arguments

:: f b

-> f (a, b)

Zip-like value from second part

Instances

Cozip Endo

Cozip (Const e)

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

Arrow j => Cozip (Flip j o)

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

cozip :: (Cozip f, Monoid_f f) => ZipTy f

Ziping of Cozip 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.