The `triangle`

function described in a previous section can also
be written recursively. It looks like this:

(defun triangle-recursively (number) "Return the sum of the numbers 1 through NUMBER inclusive. Uses recursion." (if (= number 1) ; do-again-test 1 ; then-part (+ number ; else-part (triangle-recursively ; recursive call (1- number))))) ; next-step-expression (triangle-recursively 7)

You can install this function by evaluating it and then try it by
evaluating `(triangle-recursively 7)`

. (Remember to put your
cursor immediately after the last parenthesis of the function
definition, before the comment.)

To understand how this function works, let's consider what happens in the various cases when the function is passed 1, 2, 3, or 4 as the value of its argument.

First, what happens if the value of the argument is 1?

The function has an `if`

expression after the documentation
string. It tests whether the value of `number`

is equal to 1; if
so, Emacs evaluates the then-part of the `if`

expression, which
returns the number 1 as the value of the function. (A triangle with
one row has one pebble in it.)

Suppose, however, that the value of the argument is 2. In this case,
Emacs evaluates the else-part of the `if`

expression.

The else-part consists of an addition, the recursive call to
`triangle-recursively`

and a decrementing action; and it looks like
this:

(+ number (triangle-recursively (1- number)))

When Emacs evaluates this expression, the innermost expression is evaluated first; then the other parts in sequence. Here are the steps in detail:

*Step 1 Evaluate the innermost expression.*-
The innermost expression is
`(1- number)`

so Emacs decrements the value of`number`

from 2 to 1. *Step 2 Evaluate the*`triangle-recursively`

function.-
It does not matter that this function is contained within itself.
Emacs passes the result Step 1 as the argument used by this instance
of the
`triangle-recursively`

function In this case, Emacs evaluates`triangle-recursively`

with an argument of 1. This means that this evaluation of`triangle-recursively`

returns 1. *Step 3 Evaluate the value of*`number`

.-
The variable
`number`

is the second element of the list that starts with`+`

; its value is 2. *Step 4 Evaluate the*`+`

expression.-
The
`+`

expression receives two arguments, the first from the evaluation of`number`

(Step 3) and the second from the evaluation of`triangle-recursively`

(Step 2). The result of the addition is the sum of 2 plus 1, and the number 3 is returned, which is correct. A triangle with two rows has three pebbles in it.

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