[SCL] two comments

[Murray Altheim]

pat hayes wrote:
[...]
> Guys, I was using the term 'abstract syntax' in a precise sense. It is a 
> technical term introduced by John McCarthy; its not just a handy English 
> phrase. See http://www-formal.stanford.edu/jmc/towards/node12.html
> for a succinct introduction.  This approach was later formalized and 
> systematized in the specification literature as 'term algebras', I 
> believe, but we don't really need to get that formal.

Pat,

I understand what you're saying. But are you *absolutely sure* that
there is such a thing? That *perhaps* that even within the concept of
an 'abstract syntax' there may be more levels/gradations of meta? All
of the programming languages I know have various levels of meta-ness,
but what is a primitive at one level (at what McCarthy would call the
"abstract syntax") may often be further broken down once you look at
it in a different context.

I don't want to sideline the conversation down this road, but I think
we may rely too heavily on the existence or possibility of some 'ur'
level. (I'm not really even so sure that there any *actual* distinctions
between meta-levels that exist absent any context, that it may be more
a continuum than true levels). I think that both "meta" and "context"
are recursively defined.

 > The key motivational point is stated economically there:
 >
 > " The predicates and functions whose existence and relations define the
 > syntax, are precisely those needed to translate from the language, or to
 > define the semantics. That is why we need not care whether sums are
 > represented by a+b, or + ab, or (PLUS A B), or even by Gödel numbers 7a11b."
 >
 > which is exactly the utility for us, since we want to allow things like
 > CG diagrams to count as logical syntax. In Murray's terminology, the AS
 > is the highest meta-level anyone needs to go to in order to define a
 > syntax and a model theory.  (Splicing together documents, now, is
 > another matter....)

The problem here is that the link between the "abstract" and the "concrete"
is always one of interpretation at some level/context, and I think I'd
have to take it on faith that there is a mode in which one can define a
*true* abstract syntax, something absent of context. But I suppose this
road has a lot of potholes (or I've got it all wrong), so perhaps it's
better we just stick to driving.

Murray

...........................................................................
Murray Altheim                         http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK                    .

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