Zipping (computer science) explained

In computer science, zipping is a function which maps a tuple of sequences into a sequence of tuples. This name zip derives from the action of a zipper in that it interleaves two formerly disjoint sequences. The inverse function is unzip.

Example

Given the three words cat, fish and be where |cat| is 3, |fish| is 4 and |be| is 2. Let

\ell denote the length of the longest word which is fish; \ell = 4 . The zip of cat, fish, be is then 4 tuples of elements:(c,f,b)(a,i,e)(t,s,\#)(\#,h,\#)

where # is a symbol not in the original alphabet. In Haskell this truncates to the shortest sequence

\underline{\ell} , where \underline{\ell} = 2 :

zip3 "cat" "fish" "be"-- [('c','f','b'),('a','i','e')]

Definition

Let Σ be an alphabet, # a symbol not in Σ.

Let x₁x₂... x_|x|, y₁y₂... y_|y|, z₁z₂... z_|z|, ... be n words (i.e. finite sequences) of elements of Σ. Let

\ell denote the length of the longest word, i.e. the maximum of |x|, |y|, |z|, ... .

The zip of these words is a finite sequence of n-tuples of elements of, i.e. an element of

((\Sigma\cup\{\# \}) ^{n)} ^{*} :(x _{1,y} _{1,\ldots)(x} _{2,y} _{2,\ldots)\ldots(x} _{\ell,y} _{\ell,\ldots)} ,

where for any index, the w_i is #.

The zip of x, y, z, ... is denoted zip(x, y, z, ...) or x ⋆ y ⋆ z ⋆ ...

The inverse to zip is sometimes denoted unzip.

A variation of the zip operation is defined by:

(x _{1,y} _{1,\ldots)(x} _{2,y} _{2,\ldots)\ldots(x} _{\underline{\ell} },y_,\ldots) where \underline{\ell} is the minimum length of the input words. It avoids the use of an adjoined element \# , but destroys information about elements of the input sequences beyond \underline{\ell} .

In programming languages

Zip functions are often available in programming languages, often referred to as . In Lisp-dialects one can simply the desired function over the desired lists, is variadic in Lisp so it can take an arbitrary number of lists as argument. An example from Clojure:^[1]

`nums' contains an infinite list of numbers (0 1 2 3 ...)(def nums (range))(def tens [10 20 30])(def firstname "Alice")

To zip (0 1 2 3 ...) and [10 20 30] into a vector, invoke `map vector' on them; same with list(map vector nums tens) ; ⇒ ([0 10] [1 20] [2 30])(map list nums tens) ; ⇒ ((0 10) (1 20) (2 30))(map str nums tens) ; ⇒ ("010" "120" "230")

`map' truncates to the shortest sequence; note missing \c and \e from "Alice"(map vector nums tens firstname) ; ⇒ ([0 10 \A] [1 20 \l] [2 30 \i])(map str nums tens firstname) ; ⇒ ("010A" "120l" "230i")

To unzip, apply `map vector' or `map list'(apply map list (map vector nums tens firstname))

⇒ ((0 1 2) (10 20 30) (\A \l \i))

In Common Lisp:(defparameter nums '(1 2 3))(defparameter tens '(10 20 30))(defparameter firstname "Alice")

(mapcar #'list nums tens)

⇒ ((1 10) (2 20) (3 30))

(mapcar #'list nums tens (coerce firstname 'list))

⇒ ((1 10 #\A) (2 20 #\l) (3 30 #\i)) — truncates on shortest list

Unzips(apply #'mapcar #'list (mapcar #'list nums tens (coerce firstname 'list)))

⇒ ((1 2 3) (10 20 30) (#\A #\l #\i))

Languages such as Python provide a function.^[2] in conjunction with the operator unzips a list:^[2] >>> nums = [1, 2, 3]>>> tens = [10, 20, 30]>>> firstname = 'Alice'

>>> zipped = list(zip(nums, tens))>>> zipped[(1, 10), (2, 20), (3, 30)]

>>> list(zip(*zipped)) # unzip[(1, 2, 3), (10, 20, 30)]

>>> zipped2 = list(zip(nums, tens, list(firstname)))>>> zipped2 # zip, truncates on shortest[(1, 10, 'A'), (2, 20, 'l'), (3, 30, 'i')] >>> list(zip(*zipped2)) # unzip[(1, 2, 3), (10, 20, 30), ('A', 'l', 'i')]

Haskell has a method of zipping sequences but requires a specific function for each arity (for two sequences, for three etc.),^[3]

Notes and References

1. http://clojuredocs.org/clojure_core/1.2.0/clojure.core/map map
2. https://docs.python.org/library/functions.html#map map(function, iterable, ...)
3. Web site: Statements — Chapel Documentation 1.25.
4. Web site: std.range - D Programming Language.
5. Web site: Class: Array (Ruby 2.0.0).
6. Web site: https://www.scala-lang.org/api/current/scala/collection/IterableOps.html#zip[B(that:scala.collection.IterableOnce[B]):CC[([e-mail],B) |title=IterableOps |date= |website=scala-lang.org].
7. http://hackage.haskell.org/packages/archive/base/latest/doc/html/Prelude.html#v:zip zip :: [a] -> [b] -> [(a, b)]] from Prelude, Basic libraries similarly the functions and are available for unzipping:-- nums contains an infinite list of numbers [1, 2, 3, ...] nums = [1..]tens = [10, 20, 30]firstname = "Alice"

   zip nums tens-- ⇒ [(1,10), (2,20), (3,30)] — zip, truncates infinite listunzip $ zip nums tens-- ⇒ ([1,2,3], [10,20,30]) — unzip

   zip3 nums tens firstname-- ⇒ [(1,10,'A'), (2,20,'l'), (3,30,'i')] — zip, truncatesunzip3 $ zip3 nums tens firstname-- ⇒ ([1,2,3], [10,20,30], "Ali") — unzip

   Language comparison

   List of languages by support of zip:

   Zip in various languages

   Language	Zip	Zip 3 lists	Zip n lists	Notes
   Chapel				The shape of each iterator, the rank and the extents in each dimension, must be identical.^[3]
   Clojure				Stops after the length of the shortest list.
   Common Lisp				Stops after the length of the shortest list.
   D				The stopping policy defaults to shortest and can be optionally provided as shortest, longest, or requiring the same length.^[4] The second form is an example of UFCS.
   F#
   Haskell				for n > 3 is available in the module Data.List. Stops after the shortest list ends.
   Python				and (3.x) stops after the shortest list ends, whereas (2.x) and (3.x) extends the shorter lists with items
   Ruby				When the list being executed upon (list1) is shorter than the lists being zipped the resulting list is the length of list1. If list1 is longer nil values are used to fill the missing values^[5]
   Scala				If one of the two collections is longer than the other, its remaining elements are ignored.^[6]

   Unzip in various languages

   Language	Unzip	Unzip 3 tuples	Unzip n tuples	Notes
   Clojure
   Common Lisp
   F#
   Haskell				for n > 3 is available in the module
   Python

   See also

   • Map (higher-order function)

   References