English Idiom in Unix: Directory Recursively

[rusi]

On May 18, 7:32 pm, Ian Kelly <ian.g.ke... at gmail.com> wrote:
> On Wed, May 18, 2011 at 1:10 AM, rusi <rustompm... at gmail.com> wrote:
> >> Um, it is.  Consider the simple function (lambda x, y: x + y).
> >> Mathematically, this function is recursive.  Algorithmically, it is
> >> not.  Do you disagree?
>
> > See the definition of primitive recursion eg.
>
> >http://en.wikipedia.org/wiki/Primitive_recursive_function#Definition
>
> > (2 of the second set of "more complex" definitions) from where the
> > name 'primitive recursion' is presumably derived)
>
> > And for the more general (wider) class of 'recursive' functions (in
> > the math sense aka computable functions) see a little below:
>
> >http://en.wikipedia.org/wiki/Primitive_recursive_function#Relationshi...
>
> I know what primitive recursive and computable functions are, thanks.

Myself, my memory of things studied badly decades ago may be
fuzzy :D )

Anyhow taking those links to be authoritative, what I am saying is:
Coming from the computability side, there are 3 related but distinct
definitions of recursive:

1. Anything computable is recursive  -- general recursive or partial
recursive
  (evidently there is some dispute re these definitions
  http://mathworld.wolfram.com/RecursiveFunction.html
2. Primitive recursive -- ie any function that is defined using
 - constant
 - successor
 - projection
 - composition
 - primitive recursion
[This definition is recursive in a bad sense but let that be... The
first use of the term is for the set of functions such that...
The second is for a specific operation. Comes to the third use:

3. The *operation* of primitive recursion is exactly what programmers
call recursion.

In other words one specific and characteristic operation is used to
give the name to the set being defined.

> 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))