Putting the function definition together

We have created the parts for the function definition; now we need to put them together.

First, the contents of the while expression:

(while (<= row-number number-of-rows)   ; true-or-false-test
  (setq total (+ total row-number))
  (setq row-number (1+ row-number)))    ; incrementer

Along with the let expression varlist, this very nearly completes the body of the function definition. However, it requires one final element, the need for which is somewhat subtle.

The final touch is to place the variable total on a line by itself after the while expression. Otherwise, the value returned by the whole function is the value of the last expression that is evaluated in the body of the let, and this is the value returned by the while, which is always nil.

This may not be evident at first sight. It almost looks as if the incrementing expression is the last expression of the whole function. But that expression is part of the body of the while; it is the last element of the list that starts with the symbol while. Moreover, the whole of the while loop is a list within the body of the let.

In outline, the function will look like this:

(defun name-of-function (argument-list)
  "documentation…"
  (let (varlist)
    (while (true-or-false-test)
      body-of-while… )
    … ))                    ; Need final expression here.

The result of evaluating the let is what is going to be returned by the defun since the let is not embedded within any containing list, except for the defun as a whole. However, if the while is the last element of the let expression, the function will always return nil. This is not what we want! Instead, what we want is the value of the variable total. This is returned by simply placing the symbol as the last element of the list starting with let. It gets evaluated after the preceding elements of the list are evaluated, which means it gets evaluated after it has been assigned the correct value for the total.

It may be easier to see this by printing the list starting with let all on one line. This format makes it evident that the varlist and while expressions are the second and third elements of the list starting with let, and the total is the last element:

(let (varlist) (while (true-or-false-test) body-of-while… ) total)

Putting everything together, the triangle function definition looks like this:

(defun triangle (number-of-rows)    ; Version with
                                    ;   incrementing counter.
  "Add up the number of pebbles in a triangle.
The first row has one pebble, the second row two pebbles,
the third row three pebbles, and so on.
The argument is NUMBER-OF-ROWS."

  (let ((total 0)
        (row-number 1))
    (while (<= row-number number-of-rows)
      (setq total (+ total row-number))
      (setq row-number (1+ row-number)))
    total))

After you have installed triangle by evaluating the function, you can try it out. Here are two examples:

(triangle 4)

(triangle 7)

The sum of the first four numbers is 10 and the sum of the first seven numbers is 28.