eintr: Recursive Example arg of 1 or 2
An argument of 1 or 2
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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.
The Lisp interpreter creates an individual instance of
‘triangle-recursively’. 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.
Info Catalog
eintr: Recursive triangle function
eintr: Recursive Example arg of 3 or 4