You see: even with just aesthetic and software engineering considerations you are eventually lead to topos logic... -- Till Mossakowski Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3054 University of Bremen till@tzi.de P.O.Box 330440, D-28334 Bremen http://www.tzi.de/~till Message-Id: <200305270616.h4R6G3w8008134@plxc2089.pdx.intel.com> To: Randy Pollack <rap@inf.ed.ac.uk> cc: John Harrison <johnh@ichips.intel.com>, isabelle-users@cl.cam.ac.uk Subject: Re: HOL without description operators Date: Mon, 26 May 2003 23:16:03 -0700 From: John R Harrison <johnh@ichips.intel.com> Sender: Larry Paulson <Larry.Paulson@cl.cam.ac.uk> Hi Randy, | Perhaps more usefully, how do you suggest I do this task of developing HOL | without description operators. You might find it interesting to look at HOL Light. This gives a different axiomatization of the HOL logic, developed precisely because I was dissatisfied with the one in the original HOL system, on which I believe the Isabelle/HOL logic is based. Although I do eventually introduce the description operator, quite a lot of the basic logic --- including the automation of inductive definitions --- is developed without it (and indeed without excluded middle or extensionality). You may find it a more congenial starting-point. As Konrad Slind later pointed out, what I settled on is remarkably close to the internal logic of a topos, as presented for example in Lambek and Scott's book. This was a surprise to me since at that time I knew next to nothing about toposes and was motivated by a mixture of aesthetic and software engineering considerations. Cheers, John.