Calling Functions - SXEmacs Lisp Reference Manual

Defining functions is only half the battle. Functions don't do anything until you call them, i.e., tell them to run. Calling a function is also known as invocation.

The most common way of invoking a function is by evaluating a list. For example, evaluating the list (concat "a" "b") calls the function concat with arguments "a" and "b". See Evaluation, for a description of evaluation.

When you write a list as an expression in your program, the function name is part of the program. This means that you choose which function to call, and how many arguments to give it, when you write the program. Usually that's just what you want. Occasionally you need to decide at run time which function to call. To do that, use the functions funcall and apply.

— Function: funcall function &rest arguments

funcall calls function with arguments, and returns whatever function returns.
Since funcall is a function, all of its arguments, including function, are evaluated before funcall is called. This means that you can use any expression to obtain the function to be called. It also means that funcall does not see the expressions you write for the arguments, only their values. These values are not evaluated a second time in the act of calling function; funcall enters the normal procedure for calling a function at the place where the arguments have already been evaluated.
The argument function must be either a Lisp function or a primitive function. Special forms and macros are not allowed, because they make sense only when given the “unevaluated” argument expressions. funcall cannot provide these because, as we saw above, it never knows them in the first place.
          (setq f 'list)
               ⇒ list
          (funcall f 'x 'y 'z)
               ⇒ (x y z)
          (funcall f 'x 'y '(z))
               ⇒ (x y (z))
          (funcall 'and t nil)
          error--> Invalid function: #<subr and>
Compare these example with the examples of apply.

— Function: apply function &rest arguments

apply calls function with arguments, just like funcall but with one difference: the last of arguments is a list of arguments to give to function, rather than a single argument. We also say that apply spreads this list so that each individual element becomes an argument.
apply returns the result of calling function. As with funcall, function must either be a Lisp function or a primitive function; special forms and macros do not make sense in apply.
          (setq f 'list)
               ⇒ list
          (apply f 'x 'y 'z)
          error--> Wrong type argument: listp, z
          (apply '+ 1 2 '(3 4))
               ⇒ 10
          (apply '+ '(1 2 3 4))
               ⇒ 10
          
          (apply 'append '((a b c) nil (x y z) nil))
               ⇒ (a b c x y z)
For an interesting example of using apply, see the description of mapcar, in Mapping Functions.

It is common for Lisp functions to accept functions as arguments or find them in data structures (especially in hook variables and property lists) and call them using funcall or apply. Functions that accept function arguments are often called functionals.

Sometimes, when you call a functional, it is useful to supply a no-op function as the argument. Here are two different kinds of no-op function:

17.5 Calling Functions