{{Short description|Function which maps a tuple of sequences into a sequence of tuples}} {{about|the data mapping function|zipping in software user programs|file compression}} 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 <math>\ell</math> denote the length of the longest word which is ''fish''; <math>\ell = 4</math>. The zip of ''cat'', ''fish'', ''be'' is then 4 tuples of elements:
: <math> (c,f,b)(a,i,e)(t,s,\#)(\#,h,\#)</math>
where ''#'' is a symbol not in the original alphabet. In Haskell this truncates to the shortest sequence <math>\underline{\ell}</math>, where <math>\underline{\ell} = 2</math>:
<syntaxhighlight lang="haskell"> zip3 "cat" "fish" "be" -- [('c','f','b'),('a','i','e')] </syntaxhighlight>
== Definition == Let Σ be an alphabet, # a symbol not in Σ.
Let ''x''<sub>1</sub>''x''<sub>2</sub>... ''x''<sub>|''x''|</sub>, ''y''<sub>1</sub>''y''<sub>2</sub>... ''y''<sub>|''y''|</sub>, ''z''<sub>1</sub>''z''<sub>2</sub>... ''z''<sub>|''z''|</sub>, ... be ''n'' words (i.e. finite sequences) of elements of Σ. Let <math>\ell</math> 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 {{math|(Σ ∪ {#})}}, i.e. an element of <math>((\Sigma\cup\{\# \})^n)^*</math>:
:<math> (x_1,y_1,\ldots)(x_2,y_2,\ldots)\ldots(x_\ell,y_\ell,\ldots)</math>,
where for any index {{math|''i'' > {{abs|''w''}}}}, the ''w<sub>i</sub>'' 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:
:<math> (x_1,y_1,\ldots)(x_2,y_2,\ldots)\ldots(x_{\underline{\ell}},y_{\underline{\ell}},\ldots)</math> where <math>\underline{\ell}</math> is the ''minimum'' length of the input words. It avoids the use of an adjoined element <math>\#</math>, but destroys information about elements of the input sequences beyond <math>\underline{\ell}</math>.
== In programming languages == Zip functions are often available in programming languages, often referred to as {{mono|zip}}. In Lisp-dialects one can simply {{mono|map}} the desired function over the desired lists, {{mono|map}} is variadic in Lisp so it can take an arbitrary number of lists as argument. An example from Clojure:<ref>[http://clojuredocs.org/clojure_core/1.2.0/clojure.core/map map] from ClojureDocs</ref>
<syntaxhighlight lang="clojure"> ;; `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)) </syntaxhighlight>
In Common Lisp: <syntaxhighlight lang="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)) </syntaxhighlight>
Languages such as Python provide a {{mono|zip()}} function.<ref name="pydocs">[https://docs.python.org/library/functions.html#map map(function, iterable, ...)] from section Built-in Functions from Python v2.7.2 documentation</ref> {{mono|zip()}} in conjunction with the {{mono|*}} operator unzips a list:<ref name="pydocs"/> <syntaxhighlight lang="pycon"> >>> 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')] </syntaxhighlight>
Haskell has a method of zipping sequences but requires a specific function for each arity ({{mono|zip}} for two sequences, {{mono|zip3}} for three etc.),<ref>[http://hackage.haskell.org/packages/archive/base/latest/doc/html/Prelude.html#v:zip zip :: <nowiki>[a] -> [b] -> [(a, b)]</nowiki>] from Prelude, Basic libraries</ref> similarly the functions {{mono|unzip}} and {{mono|unzip3}} are available for unzipping: <syntaxhighlight lang="haskell"> -- 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 list unzip $ zip nums tens -- ⇒ ([1,2,3], [10,20,30]) — unzip
zip3 nums tens firstname -- ⇒ [(1,10,'A'), (2,20,'l'), (3,30,'i')] — zip, truncates unzip3 $ zip3 nums tens firstname -- ⇒ ([1,2,3], [10,20,30], "Ali") — unzip </syntaxhighlight>
==Language comparison== List of languages by support of zip:
{| class="wikitable" |+ Zip in various languages |- ! scope="col" | Language ! scope="col" | Zip ! scope="col" | Zip 3 lists ! scope="col" | Zip ''n'' lists ! scope="col" | Notes |- ! scope="row" | Chapel | {{mono|zip (''iter1'' ''iter2'')}} | {{mono|zip (''iter1'' ''iter2'' ''iter3'')}} | {{mono|zip (''iter1'' ... ''itern'')}} | The shape of each iterator, the rank and the extents in each dimension, must be identical.<ref>{{cite web |url=https://chapel-lang.org/docs/language/spec/statements.html#zipper-iteration |title = Statements — Chapel Documentation 1.25}}</ref> |- ! scope="row" | Clojure | {{mono|{{codett|2=clojure|(map list}} ''list1'' ''list2'')}}<br/>{{mono|{{codett|2=clojure|(map vector}} ''list1'' ''list2'')}} | {{mono|{{codett|2=clojure|(map list}} ''list1'' ''list2'' ''list3'')}}<br/>{{mono|{{codett|2=clojure|(map vector}} ''list1'' ''list2'' ''list3'')}} | {{mono|{{codett|2=clojure|(map list}} ''list1'' … ''listn'')}}<br/>{{mono|{{codett|2=clojure|(map vector}} ''list1'' … ''listn'')}} | Stops after the length of the shortest list. |- ! scope="row" | Common Lisp | {{codett|2=lisp|(mapcar #'list list1 list2)}} | {{codett|2=lisp|(mapcar #'list list1 list2 list3)}} | {{codett|2=lisp|(mapcar #'list list1 ... listn)}} | Stops after the length of the shortest list. |- ! scope="row" | D | {{mono|zip(''range1'', ''range2'')}}<br/>{{mono|''range1''.zip(''range2'')}} | {{mono|zip(''range1'', ''range2'',''range3'')}}<br/>{{mono|''range1''.zip(range2, range3)}} | {{mono|zip(''range1'', …, ''rangeN'')}}<br/>{{mono|''range1''.zip(…, rangeN)}} | The stopping policy defaults to shortest and can be optionally provided as shortest, longest, or requiring the same length.<ref>{{cite web |url=http://dlang.org/phobos/std_range.html#zip |title = std.range - D Programming Language}}</ref> The second form is an example of UFCS. |- ! scope="row" | F# | {{mono|List.zip ''list1'' ''list2''}}<br/>{{mono|Seq.zip ''source1'' ''source2''}}<br/>{{mono|Array.zip ''array1'' ''array2''}} | {{mono|List.zip3 ''list1'' ''list2'' ''list3''}}<br/>{{mono|Seq.zip3 ''source1'' ''source2'' ''source3''}}<br/>{{mono|Array.zip3 ''array1'' ''array2'' ''array3''}} | | |- ! scope="row" | Haskell | {{mono|zip ''list1'' ''list2''}} | {{mono|zip3 ''list1'' ''list2'' ''list3''}} | {{mono|zip''n'' ''list1'' … ''listn''}} | {{mono|zipn}} for ''n'' > 3 is available in the module ''Data.List''. Stops after the shortest list ends. |- ! scope="row" | Python | {{mono|zip(''list1'', ''list2'')}} | {{mono|zip(''list1'', ''list2'', ''list3'')}} | {{mono|zip(''list1'', …, ''listn'')}} | {{mono|''zip()''}} and {{mono|''map()''}} (3.x) stops after the shortest list ends, whereas {{mono|''map()''}} (2.x) and {{mono|''itertools.zip_longest()''}} (3.x) extends the shorter lists with {{mono|''None''}} items |- ! scope="row" | Ruby | {{mono|''list1''.zip(''list2'')}} | {{mono|''list1''.zip(''list2'', ''list3'')}} | {{mono|''list1''.zip(''list1'', .., ''listn'')}} | 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<ref>{{Cite web|url=https://docs.ruby-lang.org/en/master/Array.html#method-i-zip|title = Class: Array}}</ref> |- ! scope="row" | Scala | {{mono|''list1''.zip(''list2'')}} | | | If one of the two collections is longer than the other, its remaining elements are ignored.<ref>{{cite web |url=https://www.scala-lang.org/api/current/scala/collection/IterableOps.html#zip[B](that:scala.collection.IterableOnce[B]):CC[(A@scala.annotation.unchecked.uncheckedVariance,B) |title=IterableOps |date= |website=scala-lang.org}}</ref> |}
{| class="wikitable" |+ Unzip in various languages |- ! scope="col" | Language ! scope="col" | Unzip ! scope="col" | Unzip 3 tuples ! scope="col" | Unzip ''n'' tuples ! scope="col" | Notes |- ! scope="row" | Clojure | {{mono|{{codett|2=clojure|(apply map vector}} ''ziplist'')}} | {{mono|{{codett|2=clojure|(apply map vector}} ''ziplist'')}} | {{mono|{{codett|2=clojure|(apply map vector}} ''ziplist'')}} | |- ! scope="row" | Common Lisp | {{codett|2=lisp|(apply #'mapcar #'list ziplist)}} | {{codett|2=lisp|(apply #'mapcar #'list ziplist)}} | {{codett|2=lisp|(apply #'mapcar #'list ziplist)}} | |- ! scope="row" | F# | {{mono|List.unzip ''list1'' ''list2''}}<br/>{{mono|Seq.unzip ''source1'' ''source2''}}<br/>{{mono|Array.unzip ''array1'' ''array2''}} | {{mono|List.unzip3 ''list1'' ''list2'' ''list3''}}<br/>{{mono|Seq.unzip3 ''source1'' ''source2'' ''source3''}}<br/>{{mono|Array.unzip3 ''array1'' ''array2'' ''array3''}} | | |- ! scope="row" | Haskell | {{mono|unzip ''ziplist''}} | {{mono|unzip3 ''ziplist''}} | {{mono|unzip''n'' ''ziplist''}} | {{mono|unzipn}} for ''n'' > 3 is available in the module {{mono|''Data.List''.}} |- ! scope="row" | Python | {{mono|zip(*''zipvlist'')}} | {{mono|zip(*''zipvlist'')}} | {{mono|zip(*''zipvlist'')}} | |}
== See also == {{Portal|Computer programming}} * Map (higher-order function)
==References== <references/>
Category:Articles with example Haskell code Category:Articles with example Lisp (programming language) code Category:Articles with example Clojure code Category:Articles with example Python (programming language) code Category:Data mapping