Question

I’m trying to write a function which accumulates the value interval with the given operator and adds the initial value. Example:

(accumulate-interval + 0 2 4) :
2 + 3 + 4 + 0 = 9

(accumulate-interval * 1 2 5) :
2 * 3 * 4 * 5 * 1 = 120

Note: Only (+) and (*) to work is enough for me.

My code is:

(define accumulate-interval
  (lambda (op init lower upper) (if (= upper lower)
   (lambda (x) (op x init))
    (lambda (x)
      (op
      ((accumulate-interval op init lower (- upper 1)) x))))     ))

It returns a procedure instead of a value.
I’d really appreciate if you can help.

Answer 1

It returns a function because that is what you are returning. lambda is a function which creates an anonymous function and returns a reference to it. When your code does

(define accumulate-interval (lambda (op init lower upper) ......))

It is using lambda to create an anonymous function, return the reference to it and assign that reference as the value of accumulate-interval. accumulate-interval is thus associated with that function and that function is run whenever accumulate-interval is evaluated in the function position in a list.

Now, your accumulate-interval function consists of a single if expression which does

(if (= upper lower) (lambda (x) ...) (lambda (x) ...))

So if upper and lower are equal, it returns a reference to one anonymous function, otherwise it returns a different one. This is what you have told it to do.

I don’t know what you are trying to do, here, but I suspect you just want to execute the code which you are mistakenly wrapping in a function and returning. So I think your code is meant to look more like

(if (= upper lower)
  (op upper init) (op lower (accumulate-interval op init (+ lower 1) upper)))

Which should work, although I think you need to rethink your arguments because that recursive call is not in tail position.

Thinking about it,

(if (= upper lower)
   (op upper init)
   (accumulate-interval (op upper init) lower (- upper 1)))

Would work and be tail-recursive.

Note: I don’t normally do people’s homework for them, but I think you may have more than one misconception about Scheme syntax and showing working code was easier than exploring each of those possible misunderstandings separately and in combination.