Filter (higher-order function)

In functional programming, filter is a higher-order function that processes a data structure (typically a list) in some order to produce a new data structure containing exactly those elements of the original data structure for which a given predicate returns the boolean value true.

Example

In Haskell, the code example filter even [1..10] evaluates to the list 2, 4,…10 by applying the predicate even to every element of the list of integers 1, 2,… 10 in that order and creating a new list of those elements for which the predicate returns the boolean value true, thereby giving a list containing only the even members of that list. Conversely, the code example filter (not.even) [1..10] evaluates to the list 1, 3,…9 by collecting those elements of the list of integers 1, 2… 10 for which the predicate even returns the boolean value false (with . being the function composition operator).

Implementation

Filter is a standard function for many programming languages, e.g.Haskell, [http://haskell.org/onlinereport/standard-prelude.html#$vfilter filter] in the Haskell Standard Prelude]
Objective Caml, [http://caml.inria.fr/pub/docs/manual-ocaml/libref/List.html filter] in the Objective Caml standard library module list]
Standard ML, [cite web|url=http://www.standardml.org/Basis/list.html#SIG:LIST.filter:VAL|work=The Standard ML Basis Library|title=The List structure|accessdate=2007-09-25] ,or Erlang. [ [http://www.erlang.org/doc/doc-5.5.4/lib/stdlib-1.14.4/doc/html/lists.html#filter/2 filter/2] in the Erlang STDLIB Reference Manual documentation of the module lists]
Common Lisp provides the functions remove-if and remove-if-not. [http://www.lisp.org/HyperSpec/Body/fun_removecm__elete-if-not.html#remove-if-not remove-if-not] in the Common Lisp HyperSpec]
SRFI 1 provides an implementation of filter for the Scheme programming language. [http://srfi.schemers.org/srfi-1/srfi-1.html#FilteringPartitioning filter] in SRFI 1]
C++ provides the algorithms remove_if (mutating) and remove_copy_if (non-mutating). [http://www.sgi.com/tech/stl/remove_if.html remove_if] and [http://www.sgi.com/tech/stl/remove_copy_if.html remove_copy_if] in the SGI STL spec] Smalltalk provides the select: method for collections. Filter can also be realized using list comprehensions in languages that support them.

In Haskell, filter can be implemented like this: filter :: (a -> Bool) -> [a] -> [a] filter _ [] = [] filter p (x:xs) | p x = x : filter p xs
otherwise = filter p xs

Here, [] denotes the empty list, and : denotes the concatenation operator used to create a new list from a given value and an existing list.

Variants

Filter creates its result without modifying the original list. Many programming languages also provide variants that destructively modify the list argument instead for performance reasons. Other variants of filter (like e.g. [http://haskell.org/onlinereport/standard-prelude.html#$vdropWhile dropWhile] and [http://www.haskell.org/onlinereport/list.html#sect17.3 partition] ) are also common. A common memory optimization for purely functional programming languages is to have the input list and filtered result share the longest common tail (tail-sharing).

References

See also

* Map (higher-order function)
* List comprehension
* Guard (computing)


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