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#### Putting the function definition together

We can put these expressions together to create a function definition
that works. However, on examination, we find that one of the local
variables is unneeded!

The function definition looks like this:

;;; First subtractive version.
(defun triangle (number-of-rows)
"Add up the number of pebbles in a triangle."
(let ((total 0)
(number-of-pebbles-in-row number-of-rows))
(while (> number-of-pebbles-in-row 0)
(setq total (+ total number-of-pebbles-in-row))
(setq number-of-pebbles-in-row
(1- number-of-pebbles-in-row)))
total))

As written, this function works.

However, we do not need `number-of-pebbles-in-row`

.

When the `triangle`

function is evaluated, the symbol
`number-of-rows`

will be bound to a number, giving it an initial
value. That number can be changed in the body of the function as if
it were a local variable, without any fear that such a change will
effect the value of the variable outside of the function. This is a
very useful characteristic of Lisp; it means that the variable
`number-of-rows`

can be used anywhere in the function where
`number-of-pebbles-in-row`

is used.

Here is a second version of the function written a bit more cleanly:

(defun triangle (number) ; Second version.
"Return sum of numbers 1 through NUMBER inclusive."
(let ((total 0))
(while (> number 0)
(setq total (+ total number))
(setq number (1- number)))
total))

In brief, a properly written `while`

loop will consist of three parts:

- A test that will return false after the loop has repeated itself the
correct number of times.
- An expression the evaluation of which will return the value desired
after being repeatedly evaluated.
- An expression to change the value passed to the true-or-false-test so
that the test returns false after the loop has repeated itself the right
number of times.