In many programming languages, map is the name of a higher-order function that applies a given function to a sequence of elements (such as a list) and returns a sequence of results. They are examples of both catamorphisms and anamorphisms.
For example, if we define a function square as follows:
square x = x * x
Then calling map square [1,2,3,4,5] will return [1,4,9,16,25].
Map itself may be defined recursively, like this code in Haskell:
map f [] = [] map f (x:xs) = f x : map f xs
Language comparison
The map function is especially common in functional programming languages, but some high-level procedural languages support it as well, and in others it may be defined. Common Lisp provides a whole family of map-like functions. The one that corresponds to the behavior described here is called mapcar, where the -car designation indicates access using the CAR operation. In C++'s Standard Template Library, the map function is called transform. In C# (3.0), the map function is provided as an extension method called Select. It is also frequently used as an array operation in scripting languages such as Perl, Python and Ruby; the operation is called map in Perl and Python and collect in Ruby (since it inherited the collect method from Smalltalk).
| Language | Map | Notes |
|---|---|---|
| Haskell | map func list | |
| OCaml | List.map func list Array.map func array |
|
| Python | map(func, list) | |
| Ruby | enum.collect {block} enum.map {block} |
enum is an Enumeration |
| C++ | std::transform(begin, end, result, func) | in header <algorithm> begin, end, & result are iterators result is written starting at result |
| Perl | map block list map expr, list |
|
| C# 3.0 | ienum.Select(func) | Select is an extension method ienum is an IEnumerable Similarly in all .NET languages |
| JavaScript 1.6 | array.map(func) | |
| Common Lisp | (map resulttype func list) | |
| Scheme | (map func list) |
Optimizations
The mathematical basis of maps allow for a number of optimizations. If one has map f . map g ('.' is function composition) then it is the same as the simpler map (f . g) xs; that is,
. This particular optimization eliminates an expensive second map by fusing it with the first map; thus it is a "map fusion"[1].
Map functions can and often are defined in terms of a fold such as foldr, which means one can do a "map-fold fusion": f z . map g is equivalent to foldr (f . g) z.
The implementation of map above on singly-linked lists is not tail-recursive, so may build up a lot of frames on the stack when called with a large list. Many languages alternately provide a "reverse map" function, which is equivalent to reversing a mapped list, but is tail-recursive. Here is an implementation which utilizes the fold-left function.
rev_map f = foldl (\ys x -> f x : ys) []
Since reversing a singly-linked list is also tail-recursive, reverse and reverse-map can be composed to perform normal map in a tail-recursive way.
Haskell's Functor class
In the Haskell programming language, map is generalized to a polymorphic function called fmap using the Functor type class. For every Functor instance, fmap must be defined such that it obeys the Functor laws:
fmap id = id -- identityfmap (f . g) = fmap f . fmap g -- composition