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.

Minimal complete definition

zip

Methods

zip :: ZipTy f

Instances

Zip []

Methods

zip :: ZipTy []

Zip IO

Methods

zip :: ZipTy IO

Zip Endo

Methods

zip :: ZipTy Endo

Zip Id

Methods

zip :: ZipTy Id

Zip ((->) u)

Methods

zip :: ZipTy ((->) u)

Monoid u => Zip ((,) u)

Methods

zip :: ZipTy ((,) u)

Monoid o => Zip (Const * o)

Methods

zip :: ZipTy (Const * o)

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

Methods

zip :: ZipTy (f :*: g)

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

Methods

zip :: ZipTy (Flip j o)

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

Methods

zip :: ZipTy (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}

Methods

unzip :: UnzipTy f

fsts :: f (a, b) -> f a

snds :: f (a, b) -> f b

Instances

Unzip []

Methods

unzip :: UnzipTy []

fsts :: [(a, b)] -> [a]

snds :: [(a, b)] -> [b]

Unzip Endo

Methods

unzip :: UnzipTy Endo

fsts :: Endo (a, b) -> Endo a

snds :: Endo (a, b) -> Endo b

Unzip Id

Methods

unzip :: UnzipTy Id

fsts :: Id (a, b) -> Id a

snds :: Id (a, b) -> Id b

Unzip ((->) a)

Methods

unzip :: UnzipTy ((->) a)

fsts :: (a -> (a, b)) -> a -> a

snds :: (a -> (a, b)) -> a -> b

Unzip ((,) a)

Methods

unzip :: UnzipTy ((,) a)

fsts :: (a, (a, b)) -> (a, a)

snds :: (a, (a, b)) -> (a, b)

Unzip (Const * a)

Methods

unzip :: UnzipTy (Const * a)

fsts :: Const * a (a, b) -> Const * a a

snds :: Const * a (a, b) -> Const * a b

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 }

Minimal complete definition

cofsts, cosnds

Methods

cofsts :: f a -> f (a, b)

cosnds :: f b -> f (a, b)

Instances

Cozip Endo

Methods

cofsts :: Endo a -> Endo (a, b)

cosnds :: Endo b -> Endo (a, b)

Cozip (Const * e)

Methods

cofsts :: Const * e a -> Const * e (a, b)

cosnds :: Const * e b -> Const * e (a, b)

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

Methods

cofsts :: (f :*: g) a -> (f :*: g) (a, b)

cosnds :: (f :*: g) b -> (f :*: g) (a, b)

Arrow j => Cozip (Flip j o)

Methods

cofsts :: Flip j o a -> Flip j o (a, b)

cosnds :: Flip j o b -> Flip j o (a, b)

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

Methods

cofsts :: (h :. f) a -> (h :. f) (a, b)

cosnds :: (h :. f) b -> (h :. f) (a, b)

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.