[SCL] Re: Formal_Semantics of SCL & Z

[Jon Awbrey]

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John,

Thanks, that is very helpful.

But the next question that occurs to me is this:

If what we really mean by "formal semantics for X" is something like
the assumption of LOS -- for now let's leave a bit wobbly the latitude
of saying axiomatic LOS or naive LOS -- as a universal target language
in the category-theoretic sense, along with the provision of a mapping
f : X -> LOS, then why not just cut to the chase and work in LOS itself?

And the next question after that would be this:

Since there are evidently so many "universal languages in principal",
what further considerations of a practical nature would induce us
to select one of them over all others?

Jon Awbrey

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John F. Sowa wrote:
> 
> Jon,
> 
> I just want to address one point:
> 
> JA> I am unclear, from the discussions that I have seen
>  > so far on this and the CL list, what exactly Z has
>  > to do with S/CL.
> 
> Very little according to Pat, and a quite a bit
> according to me.  I'll let Pat speak for himself,
> but following is my position:
> 
>   1. Z is an example of a logic-based language that
>      was designed for a different purpose, but it has
>      a model-theoretic semantics that covers a large
>      subset of the SCL M-T semantics.
> 
>   2. Although Z was defined for specification rather
>      than interchange, it is a well-defined example of
>      a language that can be shown to be CL-conformant
>      according to the methods we are defining for the
>      CL standard.  Therefore, it would be a good example
>      to use because many people have heard of Z and
>      it would not require much work on our part to
>      demonstrate its conformance to the SCL semantics.
>      Other languages, such as UML, would require a
>      great deal more work because there is no definition
>      of UML that is as precise as the Z standard.
> 
>   3. The Z "toolkit" includes a formal definition of
>      some theories that would be very useful for many
>      users of CL languages:  sets, bags, sequences,
>      and integers.  When we demonstrate that Z is
>      a CL-conformant language, we can recommend the
>      Z toolkit as a convenient source of axioms and
>      definitions that can be imported into other
>      CL-conformant languages.
> 
>   4. Since the Z document has been formally approved
>      by the ISO procedures, it can serve as a useful
>      example of the expected style of an ISO standard
>      document.  By using that document as an example,
>      we can help ensure that we have covered everything
>      that people would expect to find in a standard.
> 
>   5. Finally, many people have been asking questions about the relationship
>      between Z and CL.  In particular, they have asked why we can't use Z
>      instead of CL as an interchange language.  By giving an explicit
>      demonstration of how CL relates to Z, we would show (a) that
>      CL has broader coverage than Z and (b) that Z and CL are
>      logically equivalent on the Z subset.
> 
> John

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