I am having trouble writing a tail-recursive power function in scheme. I want to write the function using a helper function. I know that I need to have a parameter to hold an accumulated value, but I am stuck after that. My code is as follows.
(define (pow-tr a b)
(define (pow-tr-h result)
(if (= b 0)
result
pow-tr a (- b 1))(* result a)) pow-tr-h 1)
I edited my code, and now it works. It is as follows:
(define (pow-tr2 a b)
(define (pow-tr2-h a b result)
(if (= 0 b)
result
(pow-tr2-h a (- b 1) (* result a))))
(pow-tr2-h a b 1))
Can someone explain to me why the helper function should have the same parameters as the main function. I am having a hard time trying to think of why this is necessary.
It's not correct to state that "the helper function should have the same parameters as the main function". You only need to pass the parameters that are going to change in each iteration - in the example, the exponent and the accumulated result. For instance, this will work fine without passing the base as a parameter:
(define (pow-tr2 a b)
(define (pow-tr2-h b result)
(if (= b 0)
result
(pow-tr2-h (- b 1) (* result a))))
(pow-tr2-h b 1))
It works because the inner, helper procedure can "see" the a parameter defined in the outer, main procedure. And because the base is never going to change, we don't have to pass it around. To read more about this, take a look at the section titled "Internal definitions and block structure" in the wonderful SICP book.
Now that you're using helper procedures, it'd be a good idea to start using named let, a very handy syntax for writing helpers without explicitly coding an inner procedure. The above code is equivalent to this:
(define (pow-tr2 a b)
(let pow-tr2-h [(b b) (result 1)]
(if (= b 0)
result
(pow-tr2-h (- b 1) (* result a)))))