[SCL] two comments

[Tanel Tammet]

Hi,

Chris Menzel wrote:

>On Tue, Nov 04
>
>>
>>When you speak about the "purely abstract algebraic structure"
>>etc then I honestly do not understand what do you exactly mean.
>>    
>>
>
>Do you not think that the current spec in terms of syntactic function is
>a specification of purely abstract structure, Tanel?
>
>-chris
>  
>
The core of  this matter is the unanswerable philosophical question
 "what is abstract?" or "what does it mean to be abstract?"

Reading Pat's mail gave me an impression that he was thinking about 
something
more abstract than we have had so far, and  I became worried since
I did not understand what he meant. From the things I probably understood
it looked like does not like defining, say, lexicon as a set of primitive
lexical items, but something more abstract (categories of some kind?).

Citing Pat:

 >For example, in an AS, there is no such thing as a quantifier symbol, 
since
 >some concrete syntax forms indicate quantification diagrammatically.
 >The use of a quantifier symbol is only one style of indicating a 
quantified sentence
 > form in a concrete syntax.

I agree that there in some sense there is no concrete quantifier string
representation in abstract syntax (we are not specifying which
symbol table we use, can we put quotes around the string etc),
but there still has to be a name for universal and existential
quantifer symbols so that we can express SCL formulas
in abstract syntax, for example as:
Forall((x,y), Atom_2(x,y))

In that view there is a a quantifier symbol "Forall" in abstract
syntax, which may in each concrete syntax be represented in
different ways. "Forall" is abstract in the sense that
we do not treat the ascii etc symbol table aspects and
it would be easy to rewrite the spec using "A" instead
of "Forall", for example. But is it "purely abstract"?
I do not have a clue.

Similarly, the lexical item  "while "  in the C  language
may be considered as either concrete (a concrete
string) or abstract  in the sense "Kernighan and Ritchie
do not speak about ASCII and UNICODE differences,
so what about "while" in UNICODE" or abstract
in the sense "really there are voltages in the transistors
of processors, and ink dots on paper, not ascii strings", etc.

I was imagining that if we would remove the quantifier
symbols from abstract syntax, then we should use the
abstract syntax like this:
Exists symb. isforallquantifier(symb). symb((x,y), Atom_2(x,y)))
where we get an additional layer of language for representation
(Exists would be an "abstract" exists, "isforallquantifier" is
an "abstract" category) etc which would be quite unnecessarily
complicated.

Again, observe that when we write down formulas in abstract
syntax (and we have to do that in many places in the spec)
then the abstract syntax is used as a concrete syntax of
a special kind, which we happen to call "abstract",
since we have not defined the ascii etc aspects of
that language.

Pat's letter gave me an impression that he'd
like to AVOID the possibility of using abstract
syntax in a concrete way for writing examples
and algorithms. If that is so, then the spec
will become real hard to understand.

Since the suggestion was hard to understand,
I became worried about the outcome being hard
to grasp or taking the SCL group a long time
to digest or both.

Regards,
         Tanel



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