# 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

``` 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,[1] OCaml,[2] Standard ML,[3] or Erlang.[4] Common Lisp provides the functions `remove-if` and `remove-if-not`.[5] SRFI 1 provides an implementation of filter for the Scheme programming language.[6] C++ provides the algorithms `remove_if` (mutating) and `remove_copy_if` (non-mutating); C++11 additionally provides `copy_if` (non-mutating).[7] 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.

Filter in various languages
Language Filter Notes
C# 3.0 `ienum.Where(pred)` Where is an extension method
ienum is an IEnumerable
Similarly in all .NET languages
CFML `obj.filter(func)` Where `obj` is an array or a structure. The `func` receives as an argument each element's value.
Clojure `(filter predicate list)[8]` Or, via list comprehension: `(for [x list :when (pred x)] x)`
Common Lisp ```(remove-if inverted-pred list) (remove-if (complement pred) list) (remove-if-not pred list)``` The function `remove-if-not` has been deprecated[5] in favor of the equivalent `remove-if` where the predicate is complemented.[9] Thus the filter `(remove-if-not #'oddp '(0 1 2 3))` should be written `(remove-if (complement #'oddp) '(0 1 2 3))` or more simply: `(remove-if #'evenp '(0 1 2 3))` where `evenp` returns the inverted value of `oddp`.[10]
C++ ```std::remove_copy_if(begin, end, result, prednot) std::copy_if(begin, end, result, pred) (C++11)``` in header <algorithm>
begin, end, result are iterators
predicate is reversed
D `std.algorithm.filter!(pred)(list)`
Erlang `lists:filter(Fun, List)` Or, via list comprehension: `[ X || X <- List, Fun(X) ]`
Haskell `filter pred list` Or, via list comprehension: `[x | x <- list, pred x]`
Haxe `list.filter(pred)`
`Lambda.filter(list, pred)`
Or, via list comprehension: `[x | x <- list, pred x]`
J `(#~ pred) list` An example of a monadic hook. # is copy, ~ reverses arguments. `(f g) y = y f (g y)`
Java 8+ `stream.filter(pred)`
JavaScript 1.6 `array.filter(pred)`
Mathematica `Select[list, pred]`
Objective-C (Cocoa in Mac OS X 10.4+) `[array filteredArrayUsingPredicate:pred]` `pred` is an NSPredicate object, which may be limited in expressiveness
OCaml, Standard ML `List.filter pred list`
PARI/GP `select(expr, list)` The order of arguments is reversed in v. 2.4.2.
Perl ```grep block list grep expr, list```
PHP `array_filter(array, pred)`
Prolog `filter(+Closure,+List,-List)` Since ISO/IEC 13211-1:1995/Cor.2:2012[11] the core standard contains closure application via `call/N`[12]
Python `filter(func, list)` Or, via list comprehension: `[x for x in list if pred(x)]`. In Python 3.x, `filter` was changed to return an iterator rather than a list. The complementary functionality, returning an iterator over elements for which the predicate is false, is also available in the standard library as `filterfalse` in the `itertools` module.
Ruby ```enum.find_all {block} enum.select {block}``` `enum` is an Enumeration
S/R ```Filter(pred,array) array[pred(array)]``` In the second case, pred must be a vectorized function
Scala `list.filter(pred)` Or, via for-comprehension: `for(x <- list; if pred) yield x`
Scheme R6RS `(filter pred list)`
Smalltalk `aCollection select: aBlock`
Swift ```array.filter(pred) filter(sequence, pred)```

## 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. `dropWhile` and `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

1. ^ `filter` in the Haskell Standard Prelude
2. ^ `filter` in the OCaml standard library module `list`
3. ^ "The List structure". The Standard ML Basis Library. Retrieved 2007-09-25.
4. ^ `filter/2` in the Erlang STDLIB Reference Manual documentation of the module `lists`
5. ^ a b
6. ^ `filter` in SRFI 1
7. ^ `remove_if` and `remove_copy_if` in the SGI STL spec
8. ^ clojure.core/filter on ClojureDocs
9. ^
10. ^
11. ^ ISO/IEC 13211-1:1995/Cor 2:2012
12. ^ http://www.complang.tuwien.ac.at/ulrich/iso-prolog/dtc2#call