Understanding how recursive functions work

Question

As the title explains I have a very fundamental programming question which I have just not been able to grok yet. Filtering out all of the (extremely clever) \"In order to

Answer 1

I think the confusion is stemming from thinking of it as "the same function" being called many times. If you think of it as "many copies of the same function being called", then it may be clearer:

Only one copy of the function ever returns 0, and it's not the first one (it's the last one). So the result of calling the first one is not 0.

For the second bit of confusion, I think it will be easier to spell out the recursion in English. Read this line:

return a + sumInts(a + 1, b: b)

as "return the value of 'a' plus (the return value of another copy of the function, which is the copy's value of 'a' plus (the return value of another copy of the function, which is the second copy's value of 'a' plus (...", with each copy of the function spawning a new copy of itself with a increased by 1, until the a > b condition is met.

By the time you reach the the a > b condition being true, you have a (potentially arbitrarily) long stack of copies of the function all in the middle of being run, all waiting on the result of the next copy to find out what they should add to 'a'.

(edit: also, something to be aware of is that the stack of copies of the function I mention is a real thing that takes up real memory, and will crash your program if it gets too large. The compiler can optimize it out in some cases, but exhausting stack space is a significant and unfortunate limitation of recursive functions in many languages)