Ali, (01)
I just wanted to comment on the following point: (02)
> It's been difficult to find papers which discus the model theoretic
> implications of I guess what amounts to procedural attachment. (03)
The term "procedural attachment" was usually used by the "scruffies",
who avoid formal methods. The "neats" were very critical of that
work. So none of them would use that term in theoretical papers. (04)
My recommendation for handling procedures in a formal way is to
look at the literature on formal specifications of software.
They specify each procedure by its preconditions and postconditions. (05)
On the procedural side, any kind of scruffy code is permitted,
as long as it is constrained by the preconditions at the beginning
and the postconditions at the end. In between, all bets are off. (06)
Mathematica is probably the most extensive practical development
of these techniques. They use formal axioms, do symbolic reasoning,
and keep track of the preconditions and postconditions. (07)
But when you need efficient code, Mathematica will compile the
specifications into executable programs in FORTRAN or C. (08)
John (09)
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