Hi Rob,

>Given a Z specification it could generate a set of proof
>obligations called domain conditions. The idea was that
>if the domain conditions were true, then the specification
>was insensitive to the interpretation of undefined terms.

This is exactly what I was trying to describe, and the way
things currently work in B as well, I think.  (Of course
B is very closely related to Z).

>It ought to be feasible to do something similar for HOL.

Ah, that sounds good!  So I just am looking for a principled
account of what a reasonable definition of those "domain
conditions" are in the HOL logic.  I think.

Given that in HOL the logical connectives are defined in
terms of more primitive notions like equality, you would
like to have a calculus that gives you reasonable domain
conditions for those logical connectives, based on how
they are defined for terms that are just written in terms
of equality.

Freek

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