Re: [stack] language hierarchy

On Dec 10, 2007, at 19:44 , William Tanksley, Jr wrote:

> Don Groves <[email protected]> wrote:
>> William Tanksley, Jr wrote:
>>> My definition, however, is now *very* specific to syntax. Perhaps  
>>> I'd
>>> better phrase it as: "A language's syntax is concatenative if the
>>> language it accepts is its own Kleene closure." Then, your  
>>> definition
>>> rephrased to be parallel to mine would be: "A language's  
>>> semantics is
>>> concatenative if every term denotes a function, and every
>>> concatenation of terms denotes an associative operation on those
>>> functions." (Hmm, is the word "semantics" plural?)
>
>> Function composition is associative. The phasing "every concatenation
>> of terms denotes an associative operation on those functions" begs  
>> the
>> question of what associative operations on functions other than
>> composition are we talking about?
>
> It's intended to raise the question rather than begging it.
>
>> Is it sufficient to say, as Manfred defined it for Joy, that
>> concatenation denotes function composition?
>
> That would be begging the question: assuming the answer which we  
> seek to prove.

Yes, I misused my terms quite well, didn't I?


> I'm not certain you're wrong, though. It may be that my definition
> could be satisfied by a language which we would all reject as entirely
> non-concatenative. I've attempted to test that by inventing a language
> which uses a different operation; for example, the language which
> looks like Joy syntactically but which uses 'null' as its
> concatenation operator (i.e. all programs do nothing). Although this
> language is extremely uninteresting, it seems to me that it remains
> concatenative... Just in a very boring way.

I was in no way trying to prove you wrong William -- note that mine
are questions, not statements. I'm completely in favor of the term
"concatenative" so long as we can pin it down with reasonable rigor.

I think you, Christopher, and the others have done quite well so far
in working toward that conclusion.
--
Don


> There are tons of nontrivial associative operators on functions. For
> example, let "+" be the operation which, given a pair of functions,
> produces the function defined by the sum of the values of the
> functions evaluated at a single, fixed value (which must be a number).
> The resulting language is, of course, commutative, and less
> interesting than Joy... But it seems like a real language to me,
> perhaps slightly useful, and -- from the results of Manfred's work --
> I'd even say it's concatenative, although there are many additional
> transformations possible to it, since it's commutative.
>
> Perhaps I'm starting to get a grasp on some way to prove my idea
> false... I need to come up with a associative operator which produces
> a language that I can't accept as concatenative. If I can do this I'll
> be very happy; of course, if I can't I won't have proven you wrong.
> I'm going to try doing this with a non-commutative operator... Let me
> think about this.
>
>> Don
>
> -Wm
>
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