# Nested function

In computer programming, a nested function (or nested procedure/subroutine) is a function which is lexically (textually) encapsulated within another function, with lexical scope. Nested functions are used in many approaches to structured programming including early ones, such as ALGOL, Simula and Pascal, and also in many modern scripting and functional languages. However, they are typically not supported in the C-family of languages.

Due to nesting, the scope of the nested function is inside the enclosing function. This means that it can access local variables and other local functions (as well as local constants and types) in the enclosing function, while all of this is invisible outside the enclosing function.[1] The nesting is theoretically possible to any level of depth, although only a few levels are normally used in practical programs.

## Examples

An example using Pascal syntax (with Algol, Modula2, Oberon, Ada, etc. similar):

```function E(x: real): real;
function F(y: real): real;
begin
F := x + y
end;
begin
E := F(3) + F(4)
end;
```

The function `F` is nested within `E`. Note that `E`'s parameter `x` is visible also in `F` (as `F` is a part of `E`) while both `x` and `y` are invisible outside `E` and `F` respectively.

Similarly, in Standard ML:

```fun e (x : real) =
let
fun f y = x+y
in
f 3 + f 4
end;
```

One way to write the same example in Haskell syntax:

```e :: Float -> Float
e x = f 3 + f 4 where f y = x + y
```

The same example in GNU C syntax (C-extended with nested functions):

```float E(float x)
{
float F(float y)
{
return x + y;
}
return F(3) + F(4);
}
```

### Quicksort

A more realistic example is this implementation of quicksort:[2]

```void sort(int *a, int size)
{
void quickSort(int first, int last)
{
void swap(int p, int q) {int tmp=a[p]; a[p]=a[q]; a[q]=tmp;}

int partition()
{
int pivot=a[first], index=first;
swap (index,last);
for (int i=first; i<last; i++) if (a[i]<pivot) swap (index++,i);
swap (index,last);
return index;
}

if (first<last) {
int pivotIndex=partition();
quickSort (first,pivotIndex-1); quickSort (pivotIndex+1,last);
}
}
quickSort (0,size-1);
}
```

## Purpose

Lexically nested function definitions are a form of information hiding and are useful for dividing procedural tasks into subtasks which are only meaningful locally. This avoids cluttering other parts of the program with functions and variables that are unrelated to those parts.

They are typically used as helper functions or as recursive functions inside another function (as in the quicksort example above). This has the structural benefit of organizing the code, avoids polluting the scope, and also allows functions to share state easily.[3] As nested function can access local variables of the enclosing function, sharing of state is possible without passing parameters to the nested function or use a global variable, simplifying code.

In languages with nested functions, functions may normally also contain local constants, and types (in addition to local variables, parameters, and functions), encapsulated and hidden in the same nested manner, at any level of depth. This may further enhance the code structuring possibilities.

### Other uses

Nested functions can also be used for unstructured control flow, by using the return statement for general unstructured control flow. This can be used for finer-grained control than is possible with other built-in features of the language – for example, it can allow early termination of a for loop if `break` is not available, or early termination of a nested for loop if a multi-level `break` or exceptions are not available.

## Alternatives

The main alternative to nested functions in languages that lack support for them is to place all relevant functions and variables in a separate module (file) and expose only the top-level wrapper function publicly. In C this will generally be done by using static functions for encapsulation and static variables for communication.[4] This achieves encapsulation and sharing of state, though not the logical organization given by lexical nesting of functions, and comes at the cost of having a separate file. It is also not possible in more than a single level.

Another alternative is to share state between the functions through function parameters, most often passing references as arguments to avoid the cost of copying. In C this is generally implemented by a pointer to a structure containing the context.[4] This significantly increases the complexity of the function calls.[3]

## Languages

Well known languages supporting lexically nested functions include:

### Functional languages

In most functional programming languages, such as Scheme, nested functions are a common way of implementing algorithms with loops in them. A simple (tail) recursive inner function is created, which behaves as the algorithm's main loop, while the outer function performs startup actions that only need to be done once. In more complex cases, a number of mutually recursive functions may be created as inner functions.

### Some languages without direct support

Certain languages do not have straightforward syntactic and semantic support to implement nested functions. Nevertheless, for some of them the idea of nested functions can be simulated with some degree of difficulty through the use of other language constructs. The following languages can approximate nested functions through the respective strategies:

• C++ allows definition of classes within classes, providing the ability to use class methods in a way similar to nested functions in one level (see Function object in C++). C++11 additionally supports nested lambda functions.
• Eiffel explicitly disallows nesting of routines. This is to keep the language simple, and also allows the convention of using a special variable, Result, to denote the result of a (value-returning) function.
• Visual Basic and C#, by using anonymous methods or lambda expressions.
• Java, through a workaround that consists in an anonymous class containing a single method. A named class declared local to a method may also be used.

## Implementation

Implementation of nested functions can be more involved than it may appear, as a reference to a nested function that references non-local variables creates a closure. For this reason nested functions are not supported in some languages such as C, C++ or Java as this makes compilers more difficult to implement.[4][6] However, some compilers do support them, as a compiler specific extension. A well known example of this is the GNU C implementation of C which shares code with compilers for languages such as Pascal, Ada and Modula.

There are several ways to implement nested procedures, but the classic way is as follows:

Any non-local object, X, is reached via access-links in the activation frames on the machine stack. The caller, C, assists the called procedure, P, by pushing a direct link to the latest activation of P's immediate lexical encapsulation, (P), prior to the call itself. P may then quickly find the right activation for a certain X by following a fixed number (P.depth - X.depth) of links (normally a small number).
The caller creates this direct link by (itself) following C.depth - P.depth + 1 older links, leading up to the latest activation of (P), and then temporarily bridging over these with a direct link to that activation; the link later disappears together with P, whereby the older links beneath it may come into use again.
Note that P is visible for, and may therefore be called by, C if (P) = C / (C) / ((C)) / etc.

This original method is faster than it may seem, but it is nevertheless often optimized in practical modern compilers (using displays or similar techniques).

Another way to implement nested functions that is used by some compilers is to convert ("lift") nested functions into non-nested functions (where extra parameters replace the access links) using a process known as lambda lifting during an intermediate stage in the compilation.