To define a function with optional parameters, after the names of any required parameters, place the symbol **&optional** followed by the names of the optional parameters. A simple example looks like this:

When the function is called, arguments are first bound to the required parameters. After all the required parameters have been given values, if there are any arguments left, their values are assigned to the optional parameters. If the arguments run out before the optional parameters do, the remaining optional parameters are bound to the value **NIL**. Thus, the function defined previously gives the following results:

(foo 1 2)     ==> (1 2 NIL NIL)

Of course, you’ll often want a different default value than **NIL**. You can specify the default value by replacing the parameter name with a list containing a name and an expression. The expression will be evaluated only if the caller doesn’t pass enough arguments to provide a value for the optional parameter. The common case is simply to provide a value as the expression.

This function requires one argument that will be bound to the parameter a. The second parameter, b, will take either the value of the second argument, if there is one, or 10.

which would cause the height parameter to take the same value as the width parameter unless explicitly specified.

Occasionally, it’s useful to know whether the value of an optional argument was supplied by the caller or is the default value. Rather than writing code to check whether the value of the parameter is the default (which doesn’t work anyway, if the caller happens to explicitly pass the default value), you can add another variable name to the parameter specifier after the default-value expression. This variable will be bound to true if the caller actually supplied an argument for this parameter and **NIL** otherwise. By convention, these variables are usually named the same as the actual parameter with a “-supplied-p” on the end. For example: