Here's one possible approach to the set-axiomatization/typedef issue: As a new primitive, we could have something like a "pred_typedef" operation that uses predicates. This would work just like the new_type_definition facility of HOL4, etc.
The type "'a set" could be introduced definitionally using "pred_typedef". After type "'a set" has been defined, we can implement the "typedef" command, preserving its current behavior, as a thin wrapper on top of "pred_typedef". This approach would let us avoid having to axiomatize the 'a set type. Also, for those of us who like predicates, "pred_typedef" might be rather useful as a user-level command. - Brian On Fri, Aug 26, 2011 at 12:06 AM, Lawrence Paulson <l...@cam.ac.uk> wrote: > indeed yes I'm the person who decided that this primitive should introduce a > type as a copy of an existing non-empty set. I have always preferred sets to > predicates and the examples I have looked at lately have only strengthened my > view. Not to mention numerous occasions when people have re-invented the > notion of an image. > Larry > > On 25 Aug 2011, at 23:24, Michael Norrish wrote: > >> On 26/08/11 7:26 AM, Florian Haftmann wrote: >>> Hi Andreas, >>> >>>> Let me ask something stupid: >>>> why exactly do you guys axiomatize 'a set? >>>> Sure it's admissable and all, but why not do this definitionally >>>> via the obvious typedef? >>> >>> the answer is rather technical: »typedef« in its current implementation >>> needs set syntax / set type as prerequisite. Of course you could change >>> »typedef« to be based on predicates, but there is some kind of unspoken >>> agreement not to set one's hand on that ancient and time-honoured Gordon >>> HOL primitive. >> >> HOL88, hol90, hol98 and HOL4 all have new_type_definition. This >> principle takes a theorem of the form >> >> ?x. P x >> >> HOL Light takes a theorem of the form P x (removing the dependency on >> the existential quantifier). >> >> To the best of my knowledge, none of these systems ever used sets in >> this role. >> >> Michael >> >> >> _______________________________________________ >> isabelle-dev mailing list >> isabelle-...@in.tum.de >> https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev > > _______________________________________________ > isabelle-dev mailing list > isabelle-...@in.tum.de > https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev > _______________________________________________ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev