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# Functions

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## Function Declaration Syntax

A function declaration is a sequence of function clauses separated by semicolons, and terminated by a period (`.`).

A function clause consists of a clause head and a clause body, separated by `->`.

A clause head consists of the function name, an argument list, and an optional guard sequence beginning with the keyword `when`:

    Name(Pattern11,...,Pattern1N) [when GuardSeq1] ->
        Body1;
    ...;
    Name(PatternK1,...,PatternKN) [when GuardSeqK] ->
        BodyK.

The function name is an atom. Each argument is a pattern.

The number of arguments `N` is the arity of the function. A function is uniquely defined by the module name, function name, and arity. That is, two functions with the same name and in the same module, but with different arities are two different functions.

A function named `f` in module `mod` and with arity `N` is often denoted as `mod:f/N`.

A clause body consists of a sequence of expressions separated by comma (`,`):

    Expr1,
    ...,
    ExprN

Valid Erlang expressions and guard sequences are described in Expressions.

Example:

    fact(N) when N > 0 ->  % first clause head
        N * fact(N-1);     % first clause body

    fact(0) ->             % second clause head
        1.                 % second clause body

## Function Evaluation

When a function `M:F/N` is called, first the code for the function is located. If the function cannot be found, an `undef` runtime error occurs. Notice that the function must be exported to be visible outside the module it is defined in.

If the function is found, the function clauses are scanned sequentially until a clause is found that fulfills both of the following two conditions:

1. The patterns in the clause head can be successfully matched against the given arguments.
2. The guard sequence, if any, is true.

If such a clause cannot be found, a `function_clause` runtime error occurs.

If such a clause is found, the corresponding clause body is evaluated. That is, the expressions in the body are evaluated sequentially and the value of the last expression is returned.

Consider the function `fact`:

    -module(mod).
    -export([fact/1]).

    fact(N) when N > 0 ->
        N * fact(N - 1);
    fact(0) ->
        1.

Assume that you want to calculate the factorial for 1:

    1> mod:fact(1).

Evaluation starts at the first clause. The pattern `N` is matched against argument 1. The matching succeeds and the guard (`N > 0`) is true, thus `N` is bound to 1, and the corresponding body is evaluated:

    N * fact(N-1) => (N is bound to 1)
    1 * fact(0)

Now, `fact(0)` is called, and the function clauses are scanned sequentially again. First, the pattern `N` is matched against 0. The matching succeeds, but the guard (`N > 0`) is false. Second, the pattern `0` is matched against the argument `0`. The matching succeeds and the body is evaluated:

    1 * fact(0) =>
    1 * 1 =>
    1

Evaluation has succeed and `mod:fact(1)` returns 1.

If `mod:fact/1` is called with a negative number as argument, no clause head matches. A `function_clause` runtime error occurs.

## Tail recursion

If the last expression of a function body is a function call, a tail-recursive call is done. This is to ensure that no system resources, for example, call stack, are consumed. This means that an infinite loop using tail-recursive calls will not exhaust the call stack and can (in principle) run forever.

Example:

    loop(N) ->
        io:format("~w~n", [N]),
        loop(N+1).

The earlier factorial example is a counter-example. It is not tail-recursive, since a multiplication is done on the result of the recursive call to `fact(N-1)`.

## Built-In Functions (BIFs)

Built-In Functions (BIFs) are implemented in C code in the runtime system. BIFs do things that are difficult or impossible to implement in Erlang. Most of the BIFs belong to module `erlang`, but there are also BIFs belonging to a few other modules, for example `lists` and `ets`.

The most commonly used BIFs belonging to `erlang` are auto-imported. They do not need to be prefixed with the module name. Which BIFs that are auto-imported is specified in the `erlang` module in ERTS. For example, standard-type conversion BIFs like `atom_to_list` and BIFs allowed in guards can be called without specifying the module name.

Examples:

    1> tuple_size({a,b,c}).
    3
    2> atom_to_list('Erlang').
    "Erlang"

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