[SCL] Proposed additions to the SCL draft standard

[John F. Sowa]

Chris,

I agree with most of your comments on Tanel's note, but I would
think that we can do more to accommodate comments (or annotations).

TT>>- Annotations (might be called also comments or documentation
>>  strings). Free text (strings) may be attached to terms
>>  and formulas.
> 
CM> I see the need for annotations in SCL implementations, but the suggested
> approach won't work.  You propose including them as terms.  But the
> underlying logic/semantics of SCL is classical, and in a classical
> semantics all terms must have a semantic value.

All terms, yes.  But the abstract syntax can specify things which
are not terms and which do not have a semantic value.  I think that
it would be better to adopt the principle that for every syntactic
rule there is a corresponding semantic rule.

For an example using BNF rules, a language might have a rule that
defines a constituent X as an A followed by a B:

    X -> A B

Then if we wanted to annotate X, we could extend that rule by saying

    X -> A B [ Comment ]

This says that X could be annotated with an optional comment
following the constituent B.  But the semantic interpretation would
be identical to the interpretation of the rule without the comment.

I used BNF notation to illustrate the principle, but we could also
say something similar in the unordered abstract syntax.  Then one
concrete language could enclose the comment in "/*" and "*/" while
another language could enclose it in curly braces "{" and "}", but
in any language the comment would be ignored by the semantics.

CM> If some sort of annotating facility is going to be added, it must be
> thought of as some sort metalinguistic device.  Hence, if we agree some
> notion of annotation is important, then we need to have a section of SCL
> that describes such a device, and offers counsel about how to implement
> it.

I think that comments could be supported by the SCL abstract syntax
by just adding a category called "Comment" to the rules that define
those categories that can be annotated -- by an approach similar to
the one sketched out above.

I agree with you on the following point:

CM> I don't think the semantics for predicate-bounded quantifiers will be
> genearalizable to a semantics for numerical quantifiers.  But it will be
> easy enough to implement an appropriate semantics.

I also agree with your comments about identity.  But there are other
features of the "wild-west syntax" that illustrate points that are
easily confusing to people who are familiar with more common notations
for logic.  So we do need a definition of a subset language with
restricted quantification.

John