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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Wed, 18 May 2011 09:43:24 -0600
Subject: Re: English Idiom in Unix: Directory Recursively
To: rusi <rustompmody@gmail.com>
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On Wed, May 18, 2011 at 9:15 AM, rusi <rustompmody@gmail.com> wrote:
>> What you're failing to explain is why you would consider that function
>> to be recursive from a programming standpoint.
>
> As for putting + under the format of primitive recursion, it would go
> something like this (I guess)
>
> Matching up that definition
> Put
> h is what is being defined ie + (or plus)
> k = 1
> f = id
> g(y, ic, x) = S(ic) #ignore y and x, ic is internal (recursive) call
>
> Gives
>
> plus(0, x) = x
> plus((S y), x) = S(plus(y, x))

You're still arguing mathematics.  I am not disputing that the
addition function is primitive recursive (in fact, I asserted that in
my original reply).  What I am saying is that this *implementation* of
the addition function:

def add(x, y):
  return y if x == 0 else add(x-1, y) + 1

is recursive in the programming sense (i.e. it uses the programming
technique of recursion), while this implementation is not:

def add(x, y):
  return x + y