From Ramana.Kumar at cl.cam.ac.uk Thu Sep 17 11:11:49 2015 From: Ramana.Kumar at cl.cam.ac.uk (Ramana Kumar) Date: Thu, 17 Sep 2015 21:11:49 +1000 Subject: [opentheory-users] lambda terms vs articles Message-ID: Hi OpenTheory list! I have a question about the fundamental proof representation format used by OpenTheory: Why not lambda terms? I am inspired by the proof terms available in the Isabelle theorem prover. If one reads Berghofer and Nipkow's work on proof terms, they recount a number of reasons to prefer lambda terms to a flat unstructured sequence of commands for a virtual machine. Mostly these advantages come in the form of being able to re-use results from areas such as type checking and term rewriting more easily in the compression of proofs. (Apart from technical reasons, there are probably also social reasons for making things appealing to a wide group of smart people.) Now, it may be that in practice these supposed advantages of proof terms don't show up. Was the OpenTheory design chosen after a careful comparison, or was it just a matter of using something familiar and straightforward? Cheers, Ramana -------------- next part -------------- An HTML attachment was scrubbed... URL: From ai.robert.wangshuai at gmail.com Thu Sep 17 18:18:49 2015 From: ai.robert.wangshuai at gmail.com (Robert White) Date: Thu, 17 Sep 2015 20:18:49 +0200 Subject: [opentheory-users] packages that are not exported in hol.ml? Message-ID: Dear Joe, Sorry for not been "alive" for a while. I noticed that there are some files (in hol.ml) not exported to the base.art (mostly things about real numbers). I wonder if there is any reason for that. Also, I found there is problem downloading opentheory's hol-light. $ git clone http://src.gilith.com/hol-light Cloning into 'hol-light'... error: Unable to get pack file http://src.gilith.com/hol-light/objects/pack/pack-05098adefd7d57e51bb015ec2ec1cdb8e262856f.pack Recv failure: Connection reset by peer error: Unable to find 78e7e5d91a3b45ac7bd2f32939fe575fe0f18a64 under http://src.gilith.com/hol-light Cannot obtain needed tree 78e7e5d91a3b45ac7bd2f32939fe575fe0f18a64 while processing commit 9991514634d6ecea96ff4ea3985b069d3c4279ca. error: fetch failed. Thanks! Regards, Robert -------------- next part -------------- An HTML attachment was scrubbed... URL: From joe at gilith.com Thu Sep 17 19:04:38 2015 From: joe at gilith.com (Joe Leslie-Hurd) Date: Thu, 17 Sep 2015 12:04:38 -0700 Subject: [opentheory-users] packages that are not exported in hol.ml? In-Reply-To: References: Message-ID: Hi Robert, > Sorry for not been "alive" for a while. Good to have you back :-) > I noticed that there are some files (in hol.ml) not exported to the base.art > (mostly things about real numbers). I wonder if there is any reason for > that. The simple answer is that these files have not yet been ported to OpenTheory, which involves going through each theorem and making sure that it is provable using the modified HOL Light standard library that precedes it. I tend to do this kind of work lazily, when someone has a demand for it. > Also, I found there is problem downloading opentheory's hol-light. > > $ git clone http://src.gilith.com/hol-light It may have been a temporary connectivity issue - could you please retry and let me know if you get the same result? Cheers, Joe From ai.robert.wangshuai at gmail.com Thu Sep 17 19:21:51 2015 From: ai.robert.wangshuai at gmail.com (Robert White) Date: Thu, 17 Sep 2015 21:21:51 +0200 Subject: [opentheory-users] packages that are not exported in hol.ml? In-Reply-To: References: Message-ID: Dear Joe, > I tend to do this kind of work lazily, when someone has a demand for it. Okay, now I have demand :) Regards, Robert On 17 September 2015 at 21:04, Joe Leslie-Hurd wrote: > Hi Robert, > > > Sorry for not been "alive" for a while. > > Good to have you back :-) > > > I noticed that there are some files (in hol.ml) not exported to the > base.art > > (mostly things about real numbers). I wonder if there is any reason for > > that. > > The simple answer is that these files have not yet been ported to > OpenTheory, which involves going through each theorem and making sure > that it is provable using the modified HOL Light standard library that > precedes it. I tend to do this kind of work lazily, when someone has a > demand for it. > > > Also, I found there is problem downloading opentheory's hol-light. > > > > $ git clone http://src.gilith.com/hol-light > > It may have been a temporary connectivity issue - could you please > retry and let me know if you get the same result? > > Cheers, > > Joe > > _______________________________________________ > opentheory-users mailing list > opentheory-users at gilith.com > http://www.gilith.com/mailman/listinfo/opentheory-users > -- Regards, Robert New homepage at Github: https://airobert.github.io/ New email address at ILLC: shuai.wang at student.uva.nl Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 -------------- next part -------------- An HTML attachment was scrubbed... URL: From ai.robert.wangshuai at gmail.com Thu Sep 17 19:25:52 2015 From: ai.robert.wangshuai at gmail.com (Robert White) Date: Thu, 17 Sep 2015 21:25:52 +0200 Subject: [opentheory-users] packages that are not exported in hol.ml? In-Reply-To: References: Message-ID: Dear Joe, One of the things that I found was that the quotient type (in short, `:real`) can't get exported. I am suffering from that right now. Can you help? Thanks Robert On 17 September 2015 at 21:21, Robert White wrote: > Dear Joe, > > > I tend to do this kind of work lazily, when someone has a > demand for it. > > Okay, now I have demand :) > > Regards, > Robert > > > On 17 September 2015 at 21:04, Joe Leslie-Hurd wrote: > >> Hi Robert, >> >> > Sorry for not been "alive" for a while. >> >> Good to have you back :-) >> >> > I noticed that there are some files (in hol.ml) not exported to the >> base.art >> > (mostly things about real numbers). I wonder if there is any reason for >> > that. >> >> The simple answer is that these files have not yet been ported to >> OpenTheory, which involves going through each theorem and making sure >> that it is provable using the modified HOL Light standard library that >> precedes it. I tend to do this kind of work lazily, when someone has a >> demand for it. >> >> > Also, I found there is problem downloading opentheory's hol-light. >> > >> > $ git clone http://src.gilith.com/hol-light >> >> It may have been a temporary connectivity issue - could you please >> retry and let me know if you get the same result? >> >> Cheers, >> >> Joe >> >> _______________________________________________ >> opentheory-users mailing list >> opentheory-users at gilith.com >> http://www.gilith.com/mailman/listinfo/opentheory-users >> > > > > -- > > Regards, > Robert > > New homepage at Github: https://airobert.github.io/ > New email address at ILLC: shuai.wang at student.uva.nl > Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 > > -- Regards, Robert New homepage at Github: https://airobert.github.io/ New email address at ILLC: shuai.wang at student.uva.nl Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 -------------- next part -------------- An HTML attachment was scrubbed... URL: From joe at gilith.com Thu Sep 17 20:10:57 2015 From: joe at gilith.com (Joe Leslie-Hurd) Date: Thu, 17 Sep 2015 13:10:57 -0700 Subject: [opentheory-users] packages that are not exported in hol.ml? In-Reply-To: References: Message-ID: Hi Robert, I don't quite understand what doesn't work - can you give an example of something that fails? Cheers, Joe On Thu, Sep 17, 2015 at 12:25 PM, Robert White wrote: > Dear Joe, > > One of the things that I found was that the quotient type (in short, > `:real`) can't get exported. > I am suffering from that right now. > > Can you help? > > Thanks > Robert > > On 17 September 2015 at 21:21, Robert White > wrote: >> >> Dear Joe, >> >> > I tend to do this kind of work lazily, when someone has a >> demand for it. >> >> Okay, now I have demand :) >> >> Regards, >> Robert >> >> >> On 17 September 2015 at 21:04, Joe Leslie-Hurd wrote: >>> >>> Hi Robert, >>> >>> > Sorry for not been "alive" for a while. >>> >>> Good to have you back :-) >>> >>> > I noticed that there are some files (in hol.ml) not exported to the >>> > base.art >>> > (mostly things about real numbers). I wonder if there is any reason for >>> > that. >>> >>> The simple answer is that these files have not yet been ported to >>> OpenTheory, which involves going through each theorem and making sure >>> that it is provable using the modified HOL Light standard library that >>> precedes it. I tend to do this kind of work lazily, when someone has a >>> demand for it. >>> >>> > Also, I found there is problem downloading opentheory's hol-light. >>> > >>> > $ git clone http://src.gilith.com/hol-light >>> >>> It may have been a temporary connectivity issue - could you please >>> retry and let me know if you get the same result? >>> >>> Cheers, >>> >>> Joe >>> >>> _______________________________________________ >>> opentheory-users mailing list >>> opentheory-users at gilith.com >>> http://www.gilith.com/mailman/listinfo/opentheory-users >> >> >> >> >> -- >> >> Regards, >> Robert >> >> New homepage at Github: https://airobert.github.io/ >> New email address at ILLC: shuai.wang at student.uva.nl >> Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 >> > > > > -- > > Regards, > Robert > > New homepage at Github: https://airobert.github.io/ > New email address at ILLC: shuai.wang at student.uva.nl > Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 > > > _______________________________________________ > opentheory-users mailing list > opentheory-users at gilith.com > http://www.gilith.com/mailman/listinfo/opentheory-users > From ai.robert.wangshuai at gmail.com Thu Sep 17 20:39:07 2015 From: ai.robert.wangshuai at gmail.com (Robert White) Date: Thu, 17 Sep 2015 22:39:07 +0200 Subject: [opentheory-users] packages that are not exported in hol.ml? In-Reply-To: References: Message-ID: Dear Joe, Thanks for the reply. So basically I am trying to verify thing about reals. I am trying to get the files from "calc_int.ml" to the end of hol.ml exported and verified, as well as the libraries at /Library and /Multivariate folder. Thanks Robert On 17 September 2015 at 22:10, Joe Leslie-Hurd wrote: > Hi Robert, > > I don't quite understand what doesn't work - can you give an example > of something that fails? > > Cheers, > > Joe > > On Thu, Sep 17, 2015 at 12:25 PM, Robert White > wrote: > > Dear Joe, > > > > One of the things that I found was that the quotient type (in short, > > `:real`) can't get exported. > > I am suffering from that right now. > > > > Can you help? > > > > Thanks > > Robert > > > > On 17 September 2015 at 21:21, Robert White < > ai.robert.wangshuai at gmail.com> > > wrote: > >> > >> Dear Joe, > >> > >> > I tend to do this kind of work lazily, when someone has a > >> demand for it. > >> > >> Okay, now I have demand :) > >> > >> Regards, > >> Robert > >> > >> > >> On 17 September 2015 at 21:04, Joe Leslie-Hurd wrote: > >>> > >>> Hi Robert, > >>> > >>> > Sorry for not been "alive" for a while. > >>> > >>> Good to have you back :-) > >>> > >>> > I noticed that there are some files (in hol.ml) not exported to the > >>> > base.art > >>> > (mostly things about real numbers). I wonder if there is any reason > for > >>> > that. > >>> > >>> The simple answer is that these files have not yet been ported to > >>> OpenTheory, which involves going through each theorem and making sure > >>> that it is provable using the modified HOL Light standard library that > >>> precedes it. I tend to do this kind of work lazily, when someone has a > >>> demand for it. > >>> > >>> > Also, I found there is problem downloading opentheory's hol-light. > >>> > > >>> > $ git clone http://src.gilith.com/hol-light > >>> > >>> It may have been a temporary connectivity issue - could you please > >>> retry and let me know if you get the same result? > >>> > >>> Cheers, > >>> > >>> Joe > >>> > >>> _______________________________________________ > >>> opentheory-users mailing list > >>> opentheory-users at gilith.com > >>> http://www.gilith.com/mailman/listinfo/opentheory-users > >> > >> > >> > >> > >> -- > >> > >> Regards, > >> Robert > >> > >> New homepage at Github: https://airobert.github.io/ > >> New email address at ILLC: shuai.wang at student.uva.nl > >> Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 > >> > > > > > > > > -- > > > > Regards, > > Robert > > > > New homepage at Github: https://airobert.github.io/ > > New email address at ILLC: shuai.wang at student.uva.nl > > Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 > > > > > > _______________________________________________ > > opentheory-users mailing list > > opentheory-users at gilith.com > > http://www.gilith.com/mailman/listinfo/opentheory-users > > > > _______________________________________________ > opentheory-users mailing list > opentheory-users at gilith.com > http://www.gilith.com/mailman/listinfo/opentheory-users > -- Regards, Robert New homepage at Github: https://airobert.github.io/ New email address at ILLC: shuai.wang at student.uva.nl Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 -------------- next part -------------- An HTML attachment was scrubbed... URL: From joe at gilith.com Thu Sep 17 20:56:45 2015 From: joe at gilith.com (Joe Leslie-Hurd) Date: Thu, 17 Sep 2015 13:56:45 -0700 Subject: [opentheory-users] lambda terms vs articles In-Reply-To: References: Message-ID: Hi Ramana, > Was the OpenTheory design chosen after a careful comparison, > or was it just a matter of using something familiar and straightforward? I wish I could say that was true, but actually I have never compared the current design against any other. During design of the article format my number one priority was to make it easy to read in proofs, both in terms of reducing the implementation complexity of a reader and also reducing the maximum memory required to read in a proof. Given well-specified commands there are known techniques for implementing a virtual machine, and indeed by now there exist several implementations of readers for OpenTheory articles. In addition, a natural implementation will free objects (such as terms or theorems) for garbage collection as soon as they are no longer required, minimizing the memory required to read in a proof. It would definitely be cleaner to represent higher order logic proofs using lambda calculus, but I would hope these practical considerations are also taken into account in the design of an alternative format. Cheers, Joe From joe at gilith.com Thu Sep 17 20:59:11 2015 From: joe at gilith.com (Joe Leslie-Hurd) Date: Thu, 17 Sep 2015 13:59:11 -0700 Subject: [opentheory-users] packages that are not exported in hol.ml? In-Reply-To: References: Message-ID: Hi Robert, I suspected that was your plan, but I didn't understand what you meant by saying that the `:real` type couldn't be exported. The type of real numbers is defined and exported in the realax.ml file, which is already ported to OpenTheory. Cheers, Joe On Thu, Sep 17, 2015 at 1:39 PM, Robert White wrote: > Dear Joe, > > Thanks for the reply. > > So basically I am trying to verify thing about reals. I am trying to get the > files from "calc_int.ml" to the end of hol.ml exported and verified, as well > as the libraries at /Library and /Multivariate folder. > > Thanks > > Robert > > > > > On 17 September 2015 at 22:10, Joe Leslie-Hurd wrote: >> >> Hi Robert, >> >> I don't quite understand what doesn't work - can you give an example >> of something that fails? >> >> Cheers, >> >> Joe >> >> On Thu, Sep 17, 2015 at 12:25 PM, Robert White >> wrote: >> > Dear Joe, >> > >> > One of the things that I found was that the quotient type (in short, >> > `:real`) can't get exported. >> > I am suffering from that right now. >> > >> > Can you help? >> > >> > Thanks >> > Robert >> > >> > On 17 September 2015 at 21:21, Robert White >> > >> > wrote: >> >> >> >> Dear Joe, >> >> >> >> > I tend to do this kind of work lazily, when someone has a >> >> demand for it. >> >> >> >> Okay, now I have demand :) >> >> >> >> Regards, >> >> Robert >> >> >> >> >> >> On 17 September 2015 at 21:04, Joe Leslie-Hurd wrote: >> >>> >> >>> Hi Robert, >> >>> >> >>> > Sorry for not been "alive" for a while. >> >>> >> >>> Good to have you back :-) >> >>> >> >>> > I noticed that there are some files (in hol.ml) not exported to the >> >>> > base.art >> >>> > (mostly things about real numbers). I wonder if there is any reason >> >>> > for >> >>> > that. >> >>> >> >>> The simple answer is that these files have not yet been ported to >> >>> OpenTheory, which involves going through each theorem and making sure >> >>> that it is provable using the modified HOL Light standard library that >> >>> precedes it. I tend to do this kind of work lazily, when someone has a >> >>> demand for it. >> >>> >> >>> > Also, I found there is problem downloading opentheory's hol-light. >> >>> > >> >>> > $ git clone http://src.gilith.com/hol-light >> >>> >> >>> It may have been a temporary connectivity issue - could you please >> >>> retry and let me know if you get the same result? >> >>> >> >>> Cheers, >> >>> >> >>> Joe >> >>> >> >>> _______________________________________________ >> >>> opentheory-users mailing list >> >>> opentheory-users at gilith.com >> >>> http://www.gilith.com/mailman/listinfo/opentheory-users >> >> >> >> >> >> >> >> >> >> -- >> >> >> >> Regards, >> >> Robert >> >> >> >> New homepage at Github: https://airobert.github.io/ >> >> New email address at ILLC: shuai.wang at student.uva.nl >> >> Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 >> >> >> > >> > >> > >> > -- >> > >> > Regards, >> > Robert >> > >> > New homepage at Github: https://airobert.github.io/ >> > New email address at ILLC: shuai.wang at student.uva.nl >> > Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 >> > >> > >> > _______________________________________________ >> > opentheory-users mailing list >> > opentheory-users at gilith.com >> > http://www.gilith.com/mailman/listinfo/opentheory-users >> > >> >> _______________________________________________ >> opentheory-users mailing list >> opentheory-users at gilith.com >> http://www.gilith.com/mailman/listinfo/opentheory-users > > > > > -- > > Regards, > Robert > > New homepage at Github: https://airobert.github.io/ > New email address at ILLC: shuai.wang at student.uva.nl > Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 > > > _______________________________________________ > opentheory-users mailing list > opentheory-users at gilith.com > http://www.gilith.com/mailman/listinfo/opentheory-users > From ai.robert.wangshuai at gmail.com Fri Sep 18 15:44:04 2015 From: ai.robert.wangshuai at gmail.com (Robert White) Date: Fri, 18 Sep 2015 17:44:04 +0200 Subject: [opentheory-users] opentheory-users Digest, Vol 38, Issue 3 In-Reply-To: References: Message-ID: Dear Joe, Here is the error I get when I try to export things from real.ml: Exception: Failure "abs const out of type op definition scope: real". Error in included file /Users/robertwhite/Projects/hol-light/real.ml Another question is that. I noticed that you changed real_div to !x y. ~(y = &0) ==> x / y = x * inv y It was fun to see the original HOL Light version allowing y to be &0. So how is that possible? Finally, I don't know how to prove ~(&0 = &1) I find it hard to prove from ~(0 = 1). Can you give me some hint? Is that actually a subtyping or something cos I noticed that they are of different type: 0 : num & 0 : int inv (&0) : real Then how do I play with these types to get REAL_DIV_1 proved? Thanks! Robert -------------- next part -------------- An HTML attachment was scrubbed... URL: From joe at gilith.com Tue Sep 22 18:16:37 2015 From: joe at gilith.com (Joe Leslie-Hurd) Date: Tue, 22 Sep 2015 11:16:37 -0700 Subject: [opentheory-users] opentheory-users Digest, Vol 38, Issue 3 In-Reply-To: References: Message-ID: Hi Robert, Sorry about the delay in responding to your email. On Fri, Sep 18, 2015 at 8:44 AM, Robert White wrote: > Dear Joe, > > Here is the error I get when I try to export things from real.ml: > > Exception: Failure "abs const out of type op definition scope: real". > > Error in included file /Users/robertwhite/Projects/hol-light/real.ml This probably happens because there is a reference to a theorem in realax.ml that hasn't been exported, either deliberately or accidentally. Which theorem specifically produces this error? > Another question is that. I noticed that you changed real_div to !x y. ~(y = > &0) ==> x / y = x * inv y > > It was fun to see the original HOL Light version allowing y to be &0. So how > is that possible? It is not logically inconsistent to define 1/0 = 0, as HOL Light does. But since other theorem provers leave 1/0 underspecified, for the OpenTheory standard library I must take the weakest view and also leave it underspecified (hence the deviation from the standard distribution of HOL Light). This will likely entail some changes in theorems involving inv or div (extra side-conditions, or extra cases in the proof). I needed to do the same kind of thing with natural number subtraction (standard HOL Light sets 0 - n = 0 for all n). > Finally, I don't know how to prove ~(&0 = &1) I find it hard to prove from > ~(0 = 1). Can you give me some hint? Is that actually a subtyping or > something cos I noticed that they are of different type: > > 0 : num > > & 0 : int > > inv (&0) : real The default type for the symbol '&' in HOL Light is :num -> int, not :num->real as you want. The simplest way to deal with this is to add type annotations where necessary, like this: !m n. (&m : real) = &n ==> m = n Incidentally, this theorem will help you prove ~(&0 = &1). Hope that helps, Joe From ai.robert.wangshuai at gmail.com Wed Sep 23 08:27:02 2015 From: ai.robert.wangshuai at gmail.com (Robert White) Date: Wed, 23 Sep 2015 10:27:02 +0200 Subject: [opentheory-users] opentheory-users Digest, Vol 38, Issue 3 In-Reply-To: References: Message-ID: Dear Joe, Thanks for the reply. I will look into it again. Robert On 22 September 2015 at 20:16, Joe Leslie-Hurd wrote: > Hi Robert, > > Sorry about the delay in responding to your email. > > On Fri, Sep 18, 2015 at 8:44 AM, Robert White > wrote: > > Dear Joe, > > > > Here is the error I get when I try to export things from real.ml: > > > > Exception: Failure "abs const out of type op definition scope: real". > > > > Error in included file /Users/robertwhite/Projects/hol-light/real.ml > > This probably happens because there is a reference to a theorem in > realax.ml that hasn't been exported, either deliberately or > accidentally. Which theorem specifically produces this error? > > > Another question is that. I noticed that you changed real_div to !x y. > ~(y = > > &0) ==> x / y = x * inv y > > > > It was fun to see the original HOL Light version allowing y to be &0. So > how > > is that possible? > > It is not logically inconsistent to define 1/0 = 0, as HOL Light does. > But since other theorem provers leave 1/0 underspecified, for the > OpenTheory standard library I must take the weakest view and also > leave it underspecified (hence the deviation from the standard > distribution of HOL Light). This will likely entail some changes in > theorems involving inv or div (extra side-conditions, or extra cases > in the proof). I needed to do the same kind of thing with natural > number subtraction (standard HOL Light sets 0 - n = 0 for all n). > > > Finally, I don't know how to prove ~(&0 = &1) I find it hard to prove > from > > ~(0 = 1). Can you give me some hint? Is that actually a subtyping or > > something cos I noticed that they are of different type: > > > > 0 : num > > > > & 0 : int > > > > inv (&0) : real > > The default type for the symbol '&' in HOL Light is :num -> int, not > :num->real as you want. The simplest way to deal with this is to add > type annotations where necessary, like this: > > !m n. (&m : real) = &n ==> m = n > > Incidentally, this theorem will help you prove ~(&0 = &1). > > Hope that helps, > > Joe > > _______________________________________________ > opentheory-users mailing list > opentheory-users at gilith.com > http://www.gilith.com/mailman/listinfo/opentheory-users > -- Regards, Robert New homepage at Github: https://airobert.github.io/ New email address at ILLC: shuai.wang at student.uva.nl Carolina MacGillavrylaan 2246 , 1098 XK AMSTERDAM HP: 0652691901 -------------- next part -------------- An HTML attachment was scrubbed... URL: