A Sample Function Description - GNU Emacs Lisp Reference Manual

In a function description, the name of the function being described appears first. It is followed on the same line by a list of argument names. These names are also used in the body of the description, to stand for the values of the arguments.

The appearance of the keyword &optional in the argument list indicates that the subsequent arguments may be omitted (omitted arguments default to nil). Do not write &optional when you call the function.

The keyword &rest (which must be followed by a single argument name) indicates that any number of arguments can follow. The single following argument name will have a value, as a variable, which is a list of all these remaining arguments. Do not write &rest when you call the function.

— Function: foo integer1 &optional integer2 &rest integers

The function foo subtracts integer1 from integer2, then adds all the rest of the arguments to the result. If integer2 is not supplied, then the number 19 is used by default.
          (foo 1 5 3 9)
               => 16
          (foo 5)
               => 14
     
More generally,
          (foo w x y...)
          ==
          (+ (- x w) y...)
     

Any argument whose name contains the name of a type (e.g., integer, integer1 or buffer) is expected to be of that type. A plural of a type (such as buffers) often means a list of objects of that type. Arguments named object may be of any type. (See Lisp Data Types, for a list of Emacs object types.) Arguments with other sorts of names (e.g., new-file) are discussed specifically in the description of the function. In some sections, features common to the arguments of several functions are described at the beginning.

See Lambda Expressions, for a more complete description of optional and rest arguments.

Command, macro, and special form descriptions have the same format, but the word `Function' is replaced by `Command', `Macro', or `Special Form', respectively. Commands are simply functions that may be called interactively; macros process their arguments differently from functions (the arguments are not evaluated), but are presented the same way.

Special form descriptions use a more complex notation to specify optional and repeated arguments because they can break the argument list down into separate arguments in more complicated ways. ‘[optional-arg]’ means that optional-arg is optional and ‘repeated-args...’ stands for zero or more arguments. Parentheses are used when several arguments are grouped into additional levels of list structure. Here is an example:

— Special Form: count-loop (var [from to [inc]]) body...

This imaginary special form implements a loop that executes the body forms and then increments the variable var on each iteration. On the first iteration, the variable has the value from; on subsequent iterations, it is incremented by one (or by inc if that is given). The loop exits before executing body if var equals to. Here is an example:
          (count-loop (i 0 10)
            (prin1 i) (princ " ")
            (prin1 (aref vector i))
            (terpri))
     
If from and to are omitted, var is bound to nil before the loop begins, and the loop exits if var is non-nil at the beginning of an iteration. Here is an example:
          (count-loop (done)
            (if (pending)
                (fixit)
              (setq done t)))
     
In this special form, the arguments from and to are optional, but must both be present or both absent. If they are present, inc may optionally be specified as well. These arguments are grouped with the argument var into a list, to distinguish them from body, which includes all remaining elements of the form.

1.3.7.1 A Sample Function Description