List comprehension

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A list comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.

Contents

[edit] Overview

Consider the following example in set builder notation.

S=\{\,2\cdot x\mid x \in \mathbb{N},\ x^2>3\,\}

This can be read, "S is the set of all 2 times x where x is an item in the set of natural numbers, for which x squared is greater than 3."

In this annotated version of the example:

S=\{\,\underbrace{2\cdot x}_{\color{Violet}\text{output function}}\mid \underbrace{x}_{\color{Violet}\text{variable}} \in \underbrace{\mathbb{N}}_{\color{Violet}\text{input set}},\ \underbrace{x^2>3}_{\color{Violet}\text{predicate}}\,\}
  • x is the variable representing members of an input set.
  • \mathbb{N} represents the input set, which in this example is the set of natural numbers
  • x2 > 3 is a predicate function acting as a filter on members of the input set.
  • 2\cdot x is an output function producing members of the new set from members of the input set that satisfy the predicate function.
  • {} brackets contain the expression
  • \mid , the vertical bar and the comma are separators.

A list comprehension has the same syntactic components to represent generation of a list in order from an input list or iterator:

  • A variable representing members of an input list.
  • An input list (or iterator).
  • An optional predicate expression.
  • And an output expression producing members of the output list from members of the input iterable that satisfy the predicate.

The order of generation of members of the output list is based on the order of items in the input.

In Haskell's list comprehension syntax, this set-builder construct would be written similarly, as:

s = [ 2*x | x <- [0..], x^2 > 3 ]

Here, the list [0..] represents \mathbb{N}, x^2>3 represents the predicate, and 2*x represents the output expression.

List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.

[edit] History

The SETL programming language (later 1960s) had a set formation construct, and the computer algebra system AXIOM (1973) has a similar construct that processes streams, but the first use of the term "comprehension" for such constructs was in Rod Burstall and John Darlington's description of their functional programming language NPL from 1977.

Burstall and Darlington's work with NPL influenced many functional programming languages during the 1980s but not all included list comprehensions. An exception was the influential pure lazy functional programming language Miranda which was released in 1985. The subsequently developed standard pure lazy functional language, Haskell, includes many of Miranda's features including list comprehensions. The scripting language Python was heavily influenced by the pure lazy school of functional programming and adopted list comprehensions. Pure functional programming remains a niche while Python achieved wider adoption which introduced list comprehensions to a wider audience.

Comprehensions were proposed as a query notation for databases[1] and were implemented in the Kleisli database query language.[2]

[edit] Examples in different programming languages

Main article: Comparison of programming languages (list comprehension)

The following provides a few examples of specific syntax used in programming languages.

Although the original example denotes an infinite list, few languages can express that, so in some of those cases we show how to take a subset of {0,1,...,100} rather than a subset of \mathbb{N}.

[edit] B-Prolog

Further information: BProlog
(L @= [Y : X in 1..100, [Y], (X*X>3, Y is 2*X)]

A list of the form [T : E1 in D1, ..., En in Dn, LocalVars, Goal] is interpreted as a list comprehension in calls to @=/2 and constraints. A list comprehension is translated into a foreach construct with an accumulator.

[edit] Clojure

Further information: Clojure

Clojure generates infinite lazy sequences (similar to Haskell's lazy lists or Python's generators):

(for [x (iterate inc 0) :when (> (* x x) 3)] (* 2 x))

[edit] Common Lisp

Further information: Common Lisp

Although there is no standard list comprehension syntax in the language, a syntax can be created.

Using the loop macro:

(loop for x from 1 to 20 when (> (* x x) 3) collect (* 2 x))

A list comprehension macro can be defined.

(defmacro comprehend (variable input predicate output)
  ;apply output function
  `(mapcar (lambda (,variable) ,output)
    ;to each input that passes the predicate
    (remove-if-not (lambda (,variable) ,predicate) ,input)))
 
(setq 1-20 (loop for x from 1 to 20 collect x))
 
;It can be used like any other construct
(comprehend x 1-20 (> (* x x) 3) (* 2 x))

Additional parameters can be added to this macro but ignored, if the programmer would rather type

(comprehend x from 1-20 where (> (* x x) 3) select (* 2 x))

or something similar.

An infinite lazy sequence can be created in a variety of ways, such as the CLOS object system or a yield macro.

[edit] Erlang

Further information: Erlang

The same example in Erlang:

S = [2*X || X <- lists:seq(0,100), X*X > 3].

[edit] F#

Further information: F#

The F# generator comprehension has the list comprehension syntax elements. Generator comprehensions can be used to generate Lists, Sequences (like lists but evaluated on-demand) and Arrays (not discussed here).

Generators are of the form [for x in collection do ... yield expr] for lists and seq {for x in collection do ... yield expr} for sequences. For example:

> seq { for x in 0..100 do
          if x*x > 3 then yield 2*x } ;;
val it : seq<int> = seq [4; 6; 8; 10; ...]

[edit] Falcon

Further information: Falcon

The "comp" generic method family provides wide support for comprehension. For example, the "mfcomp" method can be applied to an array:

 s = [].mfcomp( { i => if i*i > 3: return 2*i; return oob(1)}, [1:101] )

Falcon can also use functional generators to provide input lists. For example, the following code uses a continuation to create a set of pairs.

 gen = Continuation( function( max, c )
        i = 0
        while i < max: c(++i)
        return oob(0)
     end )
 data = [10,11,12]
 s = Set().mfcomp( {x, y => x+y}, .[gen 3], data )

Method "comp" was introduced in version 0.9.6, and methods "mcomp" and "mfcomp" in version 0.9.6.2.

[edit] Haskell

Further information: Haskell

Please refer to the main example in the overview.

[edit] JavaFX

Further information: JavaFX

Using the for statement and a boolean expression:

  var s = for (i in [1..100][n | n*n > 3]) { 2*i }

[edit] Javascript 1.8

Further information: Javascript
Number.prototype.__iterator__=function(){for (let i=0; i<this; i++) yield i}
 
var s = [2*i for (i in 100) if (i*i>3)]

[edit] Mythryl

Further information: Mythryl
 s = [ 2*i for i in 1..100 where i*i > 3 ];

[edit] OCaml

Further information: OCaml

OCaml Batteries Included has uniform comprehension syntax for lists, arrays, enumerations (like streams), lazy lists (like lists but evaluated on-demand), sets, hashtables, etc.

Comprehension are of the form [? expression | x <- enumeration ; condition; condition ; ... ?].

For instance,

#   [? 2 * x | x <- 0 -- max_int ; x * x > 3 ?];;
- : int Enum.t = <abstr>

or, to compute a list,

#   [? List: 2 * x | x <- 0 -- 5 ; x * x > 3 ?];;
- : int list = [4; 6; 8; 10]

or, to compute a set,

#   [? PSet: 2 * x | x <- 0 -- 5 ; x * x > 3 ?];;
- : int PSet.t = <abstr>

etc.

[edit] Python

Further information: Python syntax and semantics: Generators

The Python programming language has a corresponding syntax for expressing list comprehensions. The near-equivalent in Python to the example above is as follows:

S = [2*x for x in range(101) if x**2 > 3]

List comprehensions were introduced in Python version 2.0.[3]

A generator expression may be used in Python versions 2.4 and above to achieve functional equivalence with S using a generator to iterate an infinite list:

from itertools import count
S = (2*x for x in count() if x**2 > 3)

[edit] Scala

Further information: Scala

Using the for-comprehension:

val s = for (x <- Stream.from(0); if x*x > 3) yield 2*x

[edit] Visual Prolog

Further information: Visual Prolog
S = [ 2*X || X = std::fromTo(1, 100), X^2 > 3 ]

[edit] Similar constructs

[edit] Monad comprehension

In Haskell, a monad comprehension is a generalization of the list comprehension to other monads in functional programming.

[edit] Set comprehension

Version 3 of the Python language introduces syntax for set comprehensions. Similar in form to list comprehensions, set comprehensions generate Python sets instead of lists.

>>> s = {v for v in 'ABCDABCD' if v not in 'CB'}
>>> print(s)
{'A', 'D'}
>>> type(s)
<class 'set'>
>>>

[edit] Dict comprehension

Version 3 of the Python language introduces separate syntax for dictionary comprehensions, similar in form to list comprehensions.

>>> d = {k:v for k,v in enumerate('ABCD') if v not in 'CB'}
>>> print(d)
{0: 'A', 3: 'D'}
>>> type(d)
<class 'dict'>
>>>

[edit] Parallel list comprehension

The Glasgow Haskell Compiler has an extension called parallel list comprehension (also known as zip-comprehension) that permits multiple independent branches of qualifiers within the list comprehension syntax. Whereas qualifiers separated by commas are dependent, qualifier branches separated by pipes are evaluated in parallel (this does not refer to any form of multithreadedness: it merely means that the branches are zipped).

[edit] XQuery and XPath

Like the original NPL use, these are fundamentally database access languages.

This makes the comprehension concept more important, because it is computationally infeasible to retrieve the entire list and operate on it (the initial 'entire list' may be an entire XML database).

In XPath, the expression:

/library/book//paragraph[@style='first-in-chapter']

is conceptually evaluated as a series of "steps" where each step produces a list and the next step applies a filter function to each element in the previous step's output.[4]

In XQuery, full XPath is available, but FLWOR statements are also used, which is a more powerful comprehension construct.[5]

for $b in //book
where $b[@pages < 400]
order by $b//title
return
  <shortBook>
    <title>{$b//title}</title>
    <firstPara>{($book//paragraph)[1]}</firstPara>
  </shortBook>

Here the XPath //book is evaluated to create a sequence (aka list); the where clause is a functional "filter", the order by sorts the result, and the <shortBook>...</shortBook> XML snippet is actually an anonymous function that builds/transforms XML for each element in the sequence using the 'map' approach found in other functional languages.

So, in another functional language the above FLWOR statement may be implemented like this:

map(
  newXML(shortBook, newXML(title, $1.title), newXML(firstPara, $1...))
  filter(
    lt($1.pages, 400), 
    xpath(//book)
  )
)

[edit] LINQ in C#

C# 3.0 has a group of related features called LINQ, which defines a set of query operators built to manipulate list-like structures (object enumerations, SQL datasets, …) which can be used in ways similar to list comprehension:

var s = from x in Enumerable.Range(0, 100) where x*x > 3 select x*2;

[edit] See also

[edit] Notes and references

  1. ^ Comprehensions, a query notation for DBPLs
  2. ^ The functional guts of the Kleisli query system
  3. ^ Warsaw, Barry (2 October 2008). "PEP 202 – List Comprehensions". python.org. http://www.python.org/dev/peps/pep-0202/. 
  4. ^ "2.1 Location Steps". XML Path Language (XPath). W3C. 16 November 1999. http://www.w3.org/TR/xpath#section-Location-Steps. 
  5. ^ "XQuery FLWOR Expressions". W3Schools. http://www.w3schools.com/XQuery/xquery_flwor.asp. 

[edit] Haskell

[edit] OCaml

[edit] Python

[edit] Common Lisp

[edit] Clojure

[edit] Axiom

[edit] External links

Retrieved from "http://en.wikipedia.org/wiki/List_comprehension"