On 18/04/2013 02:04, Mark Janssen wrote:
On Wed, Apr 17, 2013 at 5:33 PM, Ian Kelly <ian.g.ke...@gmail.com> wrote:
On Wed, Apr 17, 2013 at 5:40 PM, Mark Janssen <dreamingforw...@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?
Thanks for reminding me that I must add food for the trolls to the
bottom of my shopping list.
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Mark Lawrence
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