*To*: Makarius <makarius at sketis.net>*Subject*: Re: [isabelle] Experimental tweaks to make HOL intuitionistic-by-default*From*: Josh Tilles <merelyapseudonym at gmail.com>*Date*: Sat, 20 Dec 2014 21:06:26 -0500*Cc*: isabelle-users <isabelle-users at cl.cam.ac.uk>*In-reply-to*: <alpine.LNX.2.00.1412152100540.30515@lxbroy10.informatik.tu-muenchen.de>*References*: <CAGTcTFw5QbLPQ_YaSzmT5uXLgVjuyo6vnKNrmEJcGrzfEYCh=A@mail.gmail.com> <425E3845-D343-40DD-ADCA-81E49E4C6375@cam.ac.uk> <CAGTcTFzPk4XsjKFcQenDqPR5xE84VO9ihb8uEEQSKSzU1vkT=A@mail.gmail.com> <alpine.LNX.2.00.1412152100540.30515@lxbroy10.informatik.tu-muenchen.de>

On Mon, Dec 15, 2014 at 3:13 PM, Makarius <makarius at sketis.net> wrote: > > > As far as I can tell, there is nobody on this planet who is familiar with > all of Isabelle's internals. In fact the situation is better imagined like > this: http://toplowridersites.com/you-are-here-milky-way-galaxy/ Ha! Interesting. > > > > On Fri, 21 Nov 2014, Josh Tilles wrote: > > P.S. I'm about a hundred pages into *ML for the Working Programmer*, so I >> apologize if all of my questions are just a result of my not yet having >> read the chapter about constructing a tactical theorem prover [?] >> > > There is certainly something to learn from it: how proof assistants were > implemented in the early 1990-ies. See also the famous Handbook article by > Larry Paulson "Designing a theorem prover": http://www.cl.cam.ac.uk/ > techreports/UCAM-CL-TR-192.html Are you being tongue-in-cheek? I can't tell. Like, I wouldn't have guessed that implementation techniques from twenty years ago are relevant now... > > > The newer "Handbook of Practical Logic and Automated Reasoning" by John > Harrison also has a chapter on "Interactive theorem proving", see also > http://www.cl.cam.ac.uk/~jrh13/atp --- it describes HOL-Light, so the > prover architecture is very minimalistic. > Thank you for pointing that out! I might take a closer look at that later. > > > That won't help in the project to remove the classical principle from > Isabelle/HOL, which I would consider futile. You all would certainly know better than I. That said, shouldn't Isabelle be *able* to function with the classical axiom (HOL.True_or_False) made into a locale-assumption? I don't mean that as a criticism of anybody's work; just that if all that's needed is a bunch of tedious updates to proof automation tools, I think I'd be up to the task as long as I would still be welcome to ask questions on the mailing list when I run into difficulties. > Why change the logic anyway? The primary reason is actually a sequence of ideas: - I try to prove things in Isabelle (versus proving them on paper) as much as possible; - I'm reading John L. Bell's *A Primer of Infinitesimal Analysis *and would like to do the exercises (in Isabelle); - and (apparently) Infinitesimal Analysis is *incompatible* with classical logic. - For example, a fundamental principle is that "The set of magnitudes 𝜀 for which 𝜀^2 = 0 —the *nilsquare infinitesimals*— does not reduce to {0}." And yet the following lemma is easily provable in Isabelle/HOL (having imported only Fields and Set): lemma "{0} = {x::'a::field. x * x = 0}" by simp So, to *my* understanding, there's no way to do the exercises in Isabelle without introducing inconsistency. > Better use it (and its many ad-on tools) to model your own language and > logic inside it. > I'm not sure what you mean. Could you elaborate? Or perhaps point me toward some examples or explanations by other people?

**Follow-Ups**:**Re: [isabelle] Experimental tweaks to make HOL intuitionistic-by-default***From:*Elsa L. Gunter

**Re: [isabelle] Experimental tweaks to make HOL intuitionistic-by-default***From:*Lawrence Paulson

**Re: [isabelle] Experimental tweaks to make HOL intuitionistic-by-default***From:*Makarius

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