She was too young for sentences. For her, "up" was not some standard library function she could call from a loop. It was the very procedure she was in the middle of defining.
That's certainly a way of representing it. But surely it's equivalent in practice (as long as the next step can't be a nested flight of stairs) to the iterative approach:
while there are stairs in front of me
climb one stair
I guess it's just not as clear to me as it is to you that the "up" utterance is associated with the "climb the stairs" procedure rather than the "climb one stair" procedure.
I agree that it's equivalent in practice; both programs could compile to the same machine code. Where it's different is the human thinking represented by the two programs.
The word "while" implies thinking about a range of time from beginning to end. In contrast, the non-"while" version lets you stay in the moment. It's a conceptually simpler program, up until the point we use that fancy mathematical r-word to describe it.
The word "while" implies thinking about a range of time from beginning to end. In contrast, the non-"while" version lets you stay in the moment.
I disagree. The word "while" does connote time, but it's just the word chosen by early programmers to describe a process of performing an action immediately depending on current conditions, with no knowledge of history. Recursion amounts to the same thing -- after you make the mental leap of a tail-recursive optimization. When you climb the next step, you're climbing it because it's part of the definition of climbing the rest of the steps, which was part of the definition of climbing the rest of the steps when you were on the previous step. As I pointed out in another comment, when you're climbing the last step of a twelve-step staircase, you're actually performing twelve "climb up the steps" operations that are nested like Russian dolls. Thinking recursively is only simple when you learn to mentally simplify all of that, basically to think in terms of the "same machine code" you mention in your comment. I don't think we arrive at that "machine code" starting from a recursive definition of climbing the stairs. It seems much more likely that we figure out the implementation (the while loop) long before we figure out (if we ever do) that we can derive that implementation from a recursive definition of the task.
They are only nested given the common assumption (among programmers, at least) that recursion a stack-like model. From the young child's perspective this is probably tail-recursive operation:
def up():
if not at top stair:
up()
Think of recursion in terms of induction. No nested state required.
You're still talking about state, yes? In either case you see a flight of stairs, you start executing "climb the stairs" and that continues until you are no longer climbing stairs.
It seems to me that "climb one stair as long as there are stairs" is a conceptually simpler definition than "climb one stair and then climb the stairs if there are still stairs."
I think my point still is I don't see how you're differentiating between these procedures in your daughter's mind— why you're assuming that "up" means "I need to climb all of these stairs" rather than "I need to climb this one stair in front of me."
(If indeed it makes sense to model human behavior either way at all; it probably makes the most sense to think of it more as an event loop...)
