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Re: Atoms, Identifiers, and Primaries

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On Wed, Apr 17, 2013 at 5:33 PM, Ian Kelly <ian.g.kelly@gmail.com> wrote:
> On Wed, Apr 17, 2013 at 5:40 PM, Mark Janssen <dreamingforward@gmail.com> wrote:
>> Rercursion the "bedrock" of language-design.  I don't think so.  From
>> what I know, a well-defined language ends at its symbols.  It makes no
>> use of "infinities".
>
> From what I know, you can't have a Turing-complete language without
> some form of recursion.  So yeah, it's pretty damn important in
> language design.

A Turing-complete language generally has items that are defined in
terms of other, simpler items, but this is not called recursion in any
C.S. paper I know.
In C.S. of my world, recursion is a specific term that is related to
functional calculii.  This type of recursion is sometimes often found
in imperative/iterative languages, but is rooted in the fomer.

>> Conflating a programming
>> language ("an infinite object such as python language") with a program
>> written in that language ("there are an infinite number of python
>> programs").   These two are entirely separate (at least anything
>> implemented on a real computer).
>
> Mathematically, a language (e.g. a programming language) is a set of
> well-formed strings (i.e. programs) constructed from the symbols of an
> alphabet (i.e. tokens).

Mathematically, perhaps, but from C.S. theory, a language is a
fully-specified set of expressions and tokens which are considered
valid -- it's grammar.

> For most languages, this set is infinite;

This set is always finite, as you can see on the specification for
Python's language.

> saying "the Python language is infinite" is equivalent to saying
> "there are an infinite number of Python programs".

I don't think Guido would agree that "the Python language is
infinite", but then perhaps he doesn't care either.

> A finite, non-recursive grammar can only hope to accept a finite
> number of strings.

Is the language we're speaking in now one with a finite, non-recursive grammar?

-- 
MarkJ
Tacoma, Washington

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Atoms, Identifiers, and Primaries Bruce McGoveran <bruce.mcgoveran@gmail.com> - 2013-04-16 19:57 -0700
  Re: Atoms, Identifiers, and Primaries rusi <rustompmody@gmail.com> - 2013-04-16 20:55 -0700
    Re: Atoms, Identifiers, and Primaries Mark Janssen <dreamingforward@gmail.com> - 2013-04-17 16:40 -0700
      Re: Atoms, Identifiers, and Primaries alex23 <wuwei23@gmail.com> - 2013-04-17 17:29 -0700
        Re: Atoms, Identifiers, and Primaries Mark Janssen <dreamingforward@gmail.com> - 2013-04-17 17:41 -0700
        Re: Atoms, Identifiers, and Primaries Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-04-18 02:04 +0100
      Re: Atoms, Identifiers, and Primaries rusi <rustompmody@gmail.com> - 2013-04-18 00:40 -0700
    Re: Atoms, Identifiers, and Primaries Ian Kelly <ian.g.kelly@gmail.com> - 2013-04-17 18:33 -0600
      Re: Atoms, Identifiers, and Primaries Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-04-18 02:14 +0000
        Re: Atoms, Identifiers, and Primaries Ian Kelly <ian.g.kelly@gmail.com> - 2013-04-17 21:12 -0600
    Re: Atoms, Identifiers, and Primaries Mark Janssen <dreamingforward@gmail.com> - 2013-04-17 18:04 -0700
    Re: Atoms, Identifiers, and Primaries Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-04-18 02:08 +0100
    Re: Atoms, Identifiers, and Primaries Chris Angelico <rosuav@gmail.com> - 2013-04-18 11:56 +1000
    Re: Atoms, Identifiers, and Primaries Ian Kelly <ian.g.kelly@gmail.com> - 2013-04-17 21:10 -0600
  Re: Atoms, Identifiers, and Primaries Ian Kelly <ian.g.kelly@gmail.com> - 2013-04-17 01:21 -0600
    Re: Atoms, Identifiers, and Primaries 88888 Dihedral <dihedral88888@googlemail.com> - 2013-04-17 21:29 -0700
    Re: Atoms, Identifiers, and Primaries 88888 Dihedral <dihedral88888@googlemail.com> - 2013-04-17 21:29 -0700
  Re: Atoms, Identifiers, and Primaries Dave Angel <davea@davea.name> - 2013-04-17 07:07 -0400
  Re: Atoms, Identifiers, and Primaries Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-04-17 11:43 +0000
  Re: Atoms, Identifiers, and Primaries Bruce McGoveran <bruce.mcgoveran@gmail.com> - 2013-04-17 10:15 -0700
    Re: Atoms, Identifiers, and Primaries Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-04-18 04:43 +1000
      Re: Atoms, Identifiers, and Primaries rusi <rustompmody@gmail.com> - 2013-04-18 10:04 -0700

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