Re: [stack] language hierarchy

On Dec 10, 2007, at 19:17 , William Tanksley, Jr wrote:

> I'm going to do something that's VERY unusual for me. I'm going to
> say, "let's skip the arguments and cut straight to the agreement."
>
> We've got a LOT of misunderstandings going in this thread... But
> you've come up with a refinement of the "standard" definition which is
> IMO beautiful.
>
> So, let's skip the arguments and cut straight to the agreement. THEN
> we can start arguing again more efficiently.
>
> Christopher Diggins <[email protected]> wrote:
>> Here is a new suggestion for the definition of
>> concatenative language:
>> "A concatenative language is a programming language where the
>> concatenation (i.e. the sequencing or juxtaposition) of terms
>> corresponds to an associative operation on functions."
>
> I like it. It actually reveals something to me that our original
> standard definition failed to do; specifically, it explains how my
> idea of "flatness" is related to the standard idea of concatenativity.
> I think you've discovered something very important.
>
> Let me paste in my phrasing of the "standard definition": "A
> concatenative programming language is a language in which the
> concatenation of any two valid programs is a valid program."
>
> Your definition is superior in that it expressly requires
> associativity, which (come to think of it) was part of what I was
> assuming all along. Therefore, I like it and second your vote to make
> it the new standard definition.
>
> I do have a question, though. Does the old standard definition
> covertly imply associativity? It does rule out application (contrary
> to your earlier statement), since application doesn't work between
> "any two programs". I think there's a clear implication that the
> properties of concatenation should apply, but I think the old
> definition is incomplete and erroneous because it does NOT clearly
> state that all programs in a concatenative language can be built using
> only composition.
>
> I did, earlier in this thread, post a definition which included that
> requirement: "A concatenative programming language is a language in
> which the concatenation of any two valid programs is a valid program,
> and the entire language can be generated by the concatenation of a
> finite set of primitive programs." In other words, the language must
> be closed under concatenation (which rules out application as the
> meaning of concatenation) and must consist only of primitives and the
> concatenation of valid programs. This requirement in turn implies that
> the semantics of the language must follow the properties of
> concatenation, including associativity.
>
> I believe that this is exactly equivalent to your definition: HOWEVER,
> I believe that your definition is useful when discussing semantics,
> since it makes a direct semantic requirement which my definition
> leaves implied.
>
> Hmm. My definition still has a flaw: it demands a finite set of
> primitives, which ignores the fact that literals (such as quotations)
> may be infinite. How about this: "A concatenative programming language
> is a programming language which is identical to its own Kleene
> closure." I found that term on Wikipedia while trying to sort out the
> idea of closure. A Kleene closure of a language is the set containing
> all concatenations of all terms in the language. It's the meaning of
> the Regexp symbol "*".
>
> In other words, although Haskell isn't concatenative, Haskell* would
> be (by my definition). :-) This suggests (jokingly) that C* would be
> the new concatenative version of C, just as C++ is the object-oriented
> version. (No, I don't want to see C++*. I suspect C*++ would be less
> complex than C++ alone.)
>
> 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?

Is it sufficient to say, as Manfred defined it for Joy, that  
concatenation
denotes function composition?
--
Don



> Now I *really* like your definition!!! This rephrase makes it VERY
> clear to me that even my new version is inadequate -- it was PURELY
> syntactic. I'm not sure whether your definition is sufficient by
> itself -- but it's clearly *necessary*.
>
> What do you think?
>> Thanks for hammering out these issues William,
>
> Hey, it's fun. Thanks for persisting.
>
>> Christopher
>
> -Wm
>
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