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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:

(defunname-of-function(argument-list) "documentation@dots{}" (let (varlist) (while (true-or-false-test)body-of-while@dots{} ) @dots{} ) ; 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@dots{} ) 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.

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