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)

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 ~>, Monoid_f (Flip ~> o)) => Zip (Flip ~> o)

(Arrow ~>, Unzip f, Zip g) => Zip (Arrw ~> 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 ~>, Unzip f, Zip g) => ZipTy (Arrw ~> 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}

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 ~> => Cozip (Flip ~> 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.