Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
Hi Ramana, sure, I'll do it asap.
Le 11/02/2013 10:15, Ramana Kumar a écrit :
Any chance you'll check this in to the HOL4 repository, Vincent?
On Sat, Dec 29, 2012 at 12:35 AM, Vincent Aravantinos
vincent.aravanti...@gmail.com mailto:vincent.aravanti...@gmail.com
wrote:
Le 28/12/12 08:20, Michael Norrish a écrit :
I think my first reaction to a clean implementation with test
cases (in a selftest.sml file, say) and documentation (a .doc
file) would be to accept first and ask questions later. If it
turns out that something really is redundant or otherwise
unloved given other facilities in the system it can always be
removed. Michael
Ok. For now, here is a fast translation of HINT_EXISTS_TAC for HOL4:
fun HINT_EXISTS_TAC g =
let
val (hs,c) = g
val (v,c') = dest_exists c
val (vs,c') = strip_exists c'
fun hyp_match c h =
if exists (C mem vs) (free_vars c)
then fail ()
else (match_term c h,h)
val ((subs,_),h) = tryfind (C tryfind hs o hyp_match)
(strip_conj c')
val witness =
case subs of
[] = v
|[{redex = u, residue = t}] =
if u = v then t else failwith GEN_HINT_EXISTS_TAC not
applicable
|_ = failwith GEN_HINT_EXISTS_TAC not applicable
in
(EXISTS_TAC witness THEN ASM_REWRITE_TAC[]) g
end;
Cheers,
V.
--
Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University,
Hardware
Verification Group
http://users.encs.concordia.ca/~vincent/
http://users.encs.concordia.ca/%7Evincent/
--
Vincent Aravantinos
Postdoctoral Fellow, Concordia University, Hardware Verification Group
http://users.encs.concordia.ca/~vincent
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Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
Hi Thomas, Le 27/12/12 07:30, Thomas Tuerk a écrit : On Thu, 2012-12-27 at 19:55 +0800, Ramana Kumar wrote: There might be something in quantHeuristicsLib that can help, but I'm not sure. quantHeuristicsLib can do it (see below), but has other restrictions. SATISFY_ss allows to instantiate multiple variables at the same time. So, it can for example handle: ?x y. P x y /\ Q y x - 0. P 1 2 1. !x. Q 2 x Notice, assumption 1. SATISFY_ss does not use matching but unification with restriction to the variables occurring all-quantified in an assumption or existentially in the current goal. quantHeuristicsLib can currently only handle one variable at a time. I thought of this problem (handling more than 1 variable at a time) while writing HINT_EXISTS_TAC but came to the conclusion that I just wanted a pragmatic solution that does not claim to solve all the problems but just to be useful in many situations. Therefore, solving for one variable only seemed sufficient to me. However, using consequence conversions it can do your kind of instantiation guessing also at subpositions. Getting quantHeuristicLib to do what you want requires writing some ML-code, though. By default, it only searches for guesses with justification, i.e. it only instantiates a quantifier, if it can prove that the resulting term is really equivalent. For example: ?x. P x /\ Q x --- P 2 would not be instantated with 2, because Q 2 might be false, but there may still be a x that satisfies both. In order to get it working for your case, you need to tell it to use unjustified guesses for conjunction. Given ?x. X x /\ Y x, it should search for guesses for X x and Y x and return all found guesses, even if it can't prove that they are not guesses for the overall conjunct. implication_concl_qp in src/quantHeuristicsLib/quantHeuristicsParameter does this for the right hand side of implications. One could use that code as a basis or generalise it. I see. I'll have a look for my culture, but I think in the end that it will be simpler, if I need it, to just translate my current HINT_EXISTS_TAC to HOL4 (roughly nothing more than Ocaml-SML). I'll have a look at quantHeuristicsLib when I get the time though, because maybe the my problem will actually happen to be useless in the end. Thanks, V. -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group http://users.encs.concordia.ca/~vincent/ -- Master HTML5, CSS3, ASP.NET, MVC, AJAX, Knockout.js, Web API and much more. Get web development skills now with LearnDevNow - 350+ hours of step-by-step video tutorials by Microsoft MVPs and experts. SALE $99.99 this month only -- learn more at: http://p.sf.net/sfu/learnmore_122812 ___ hol-info mailing list hol-info@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/hol-info
Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
Le 28/12/12 08:20, Michael Norrish a écrit :
I think my first reaction to a clean implementation with test cases
(in a selftest.sml file, say) and documentation (a .doc file) would be
to accept first and ask questions later. If it turns out that
something really is redundant or otherwise unloved given other
facilities in the system it can always be removed. Michael
Ok. For now, here is a fast translation of HINT_EXISTS_TAC for HOL4:
fun HINT_EXISTS_TAC g =
let
val (hs,c) = g
val (v,c') = dest_exists c
val (vs,c') = strip_exists c'
fun hyp_match c h =
if exists (C mem vs) (free_vars c)
then fail ()
else (match_term c h,h)
val ((subs,_),h) = tryfind (C tryfind hs o hyp_match) (strip_conj c')
val witness =
case subs of
[] = v
|[{redex = u, residue = t}] =
if u = v then t else failwith GEN_HINT_EXISTS_TAC not
applicable
|_ = failwith GEN_HINT_EXISTS_TAC not applicable
in
(EXISTS_TAC witness THEN ASM_REWRITE_TAC[]) g
end;
Cheers,
V.
--
Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware
Verification Group
http://users.encs.concordia.ca/~vincent/
--
Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS,
MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current
with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft
MVPs and experts. SALE $99.99 this month only -- learn more at:
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Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
Hi Michael, I'm regularly amazed by the pearls that HOL4 contains... I did not know about the SatisfySimps module! Now, from my first tests, this can only be used to conclude a goal. Concretely, if I have a goal of the following form: ?x. P x /\ Q x 0. P t ... where Q x cannot be solved immediatly (assume it can be solved from other theorems or the other assumptions, but not automatically). Then SATISFY_ss won't do anything because of Q x. On the other hand, HINT_EXISTS_TAC will instantiate x by t, just leaving Q t as a new goal to prove (of course the new goal is not equivalent to the previous one, but the purpose of the tactic is just to make some progress and help the user reducing parts of the goal easily). Am I right about this behaviour of SATISFY_ss or did I miss something? V. Le 26/12/12 23:17, Michael Norrish a écrit : HOL4’s SATISFY_ss (from SatisfySimps) should solve this problem (particularly now that Thomas Türk has fixed a bug in its code). Michael On 27/12/2012, at 11:42, Ramana Kumar ram...@member.fsf.org mailto:ram...@member.fsf.org wrote: For what it's worth, my usual move in this situation is to do qmatch_assum_abbrev_tac 'P t' qexists_tac 't' simp[Abbr'X'] Note that P is a metavariable, i.e. I have to type it out, but I avoid typing the large term abbreviated by t. The X stands for pieces of P I want unabbreviated after. HINT_EXISTS_TAC might still be an improvement. Sorry for no proper backquotes, using my phone. On Dec 26, 2012 10:57 PM, Vincent Aravantinos vincent.aravanti...@gmail.com mailto:vincent.aravanti...@gmail.com wrote: Hi list, here is another situation which I don't like and often meet (both in HOL-Light and HOL4), and a potential solution. Please tell me if you also often meet the situation, if you agree that it is annoying, and if there is already a solution which I don't know of (I'm pretty sure there is no solution in HOL-Light, but I'm not familiar with all its extensions over there). SITUATION: goal of the form `?x. ... /\ P x /\ ...` + one of the assumptions is of the form `P t` (t is a big a term) + one wants to use t as the witness for x USUAL MOVE: e (EXISTS_TAC `t`) (*Then rewrite with the assumptions in order to remove the now trivial P t:*) e(ASM_REWRITE_TAC[]) PROBLEM WITH THIS: Annoying to write explicitly the big term t. Plus the subsequent ASM_REWRITE_TAC is trivial and can thus be systematized. Not really annoying if it only appears from time to time, but I personally often face this situation. SOLUTION: A tactic HINT_EXISTS_TAC which looks for an assumption matching one (or more) of the conjuncts in the conclusion and applies EXISTS_TAC with the corresponding term. EXAMPLE IN HOL-LIGHT: (* Consider the following goal:*) 0 [`P m`] 1 [`!x. P x == x = m`] `?x. P x` (* Usual move: *) # e (EXISTS_TAC `m:num`);; val it : goalstack = 1 subgoal (1 total) 0 [`P m`] 1 [`!x. P x == x = m`] `P m` # e (ASM_REWRITE_TAC[]);; val it : goalstack = No subgoals (* New solution, which finds the witness automatically and removes the trivial conjunct : *) # b (); b (); e HINT_EXISTS_TAC;; val it : goalstack = No subgoals (* Notes: * - The use case gets more interesting when m is actually a big term. * - Though, in this example, the tactic allows to conclude the goal, it can also be used just to make progress in the proof without necessary concluding. *) A HOL-Light implementation for HINT_EXISTS_TAC is provided below the signature. One for HOL4 can easily be implemented if anyone expresses some interest for it. Cheers, V. -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group http://users.encs.concordia.ca/~vincent/ http://users.encs.concordia.ca/%7Evincent/ let HINT_EXISTS_TAC (hs,c as g) = let hs = map snd hs in let v,c' = dest_exists c in let vs,c' = strip_exists c' in let hyp_match c h = ignore (check (not o exists (C mem vs) o frees) c); term_match (subtract (frees c) [v]) c (concl h), h in let (_,subs,_),h = tryfind (C tryfind hs o hyp_match) (binops `/\` c') in let witness = match subs with |[] - v |[t,u] when u = v - t |_ - failwith HINT_EXISTS_TAC not applicable in (EXISTS_TAC witness THEN REWRITE_TAC hs) g;; -- LogMeIn Rescue: Anywhere, Anytime Remote support for IT. Free Trial Remotely access PCs and mobile devices and provide instant support
Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
FYI. Somewhat related functionality is in Q.REFINE_EXISTS_TAC, which can be used to partially instantiate an existential. But you have to supply a witness, instead of saying find a witness in the assumptions. Konrad. On Thu, Dec 27, 2012 at 5:55 AM, Ramana Kumar ram...@member.fsf.org wrote: Dear Vincent, I think you are right about SATISFY_ss - it can only prove a goal, not refine it. There might be something in quantHeuristicsLib that can help, but I'm not sure. Do you have a clone of the HOL4 git repository? You could make a pull request on github after adding HINT_EXISTS_TAC in an appropriate place. In addition to match_assum_abbrev_tac, there is match_assum_rename_tac. Both of them could do with some improvement, e.g. see https://github.com/mn200/HOL/issues/81. If you happen to delve into this code, your patches would be warmly welcomed :) Ramana On Thu, Dec 27, 2012 at 6:48 PM, Vincent Aravantinos vincent.aravanti...@gmail.com wrote: Hi Michael, I'm regularly amazed by the pearls that HOL4 contains... I did not know about the SatisfySimps module! Now, from my first tests, this can only be used to conclude a goal. Concretely, if I have a goal of the following form: ?x. P x /\ Q x 0. P t ... where Q x cannot be solved immediatly (assume it can be solved from other theorems or the other assumptions, but not automatically). Then SATISFY_ss won't do anything because of Q x. On the other hand, HINT_EXISTS_TAC will instantiate x by t, just leaving Q t as a new goal to prove (of course the new goal is not equivalent to the previous one, but the purpose of the tactic is just to make some progress and help the user reducing parts of the goal easily). Am I right about this behaviour of SATISFY_ss or did I miss something? V. Le 26/12/12 23:17, Michael Norrish a écrit : HOL4’s SATISFY_ss (from SatisfySimps) should solve this problem (particularly now that Thomas Türk has fixed a bug in its code). Michael On 27/12/2012, at 11:42, Ramana Kumar ram...@member.fsf.org wrote: For what it's worth, my usual move in this situation is to do qmatch_assum_abbrev_tac 'P t' qexists_tac 't' simp[Abbr'X'] Note that P is a metavariable, i.e. I have to type it out, but I avoid typing the large term abbreviated by t. The X stands for pieces of P I want unabbreviated after. HINT_EXISTS_TAC might still be an improvement. Sorry for no proper backquotes, using my phone. On Dec 26, 2012 10:57 PM, Vincent Aravantinos vincent.aravanti...@gmail.com wrote: Hi list, here is another situation which I don't like and often meet (both in HOL-Light and HOL4), and a potential solution. Please tell me if you also often meet the situation, if you agree that it is annoying, and if there is already a solution which I don't know of (I'm pretty sure there is no solution in HOL-Light, but I'm not familiar with all its extensions over there). SITUATION: goal of the form `?x. ... /\ P x /\ ...` + one of the assumptions is of the form `P t` (t is a big a term) + one wants to use t as the witness for x USUAL MOVE: e (EXISTS_TAC `t`) (*Then rewrite with the assumptions in order to remove the now trivial P t:*) e(ASM_REWRITE_TAC[]) PROBLEM WITH THIS: Annoying to write explicitly the big term t. Plus the subsequent ASM_REWRITE_TAC is trivial and can thus be systematized. Not really annoying if it only appears from time to time, but I personally often face this situation. SOLUTION: A tactic HINT_EXISTS_TAC which looks for an assumption matching one (or more) of the conjuncts in the conclusion and applies EXISTS_TAC with the corresponding term. EXAMPLE IN HOL-LIGHT: (* Consider the following goal:*) 0 [`P m`] 1 [`!x. P x == x = m`] `?x. P x` (* Usual move: *) # e (EXISTS_TAC `m:num`);; val it : goalstack = 1 subgoal (1 total) 0 [`P m`] 1 [`!x. P x == x = m`] `P m` # e (ASM_REWRITE_TAC[]);; val it : goalstack = No subgoals (* New solution, which finds the witness automatically and removes the trivial conjunct : *) # b (); b (); e HINT_EXISTS_TAC;; val it : goalstack = No subgoals (* Notes: * - The use case gets more interesting when m is actually a big term. * - Though, in this example, the tactic allows to conclude the goal, it can also be used just to make progress in the proof without necessary concluding. *) A HOL-Light implementation for HINT_EXISTS_TAC is provided below the signature. One for HOL4 can easily be implemented if anyone expresses some interest for it. Cheers, V. -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group http://users.encs.concordia.ca/~vincent/ let HINT_EXISTS_TAC (hs,c as g) = let hs = map snd hs in let v,c' = dest_exists c in let vs,c' = strip_exists c' in let hyp_match c h =
Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
For what it's worth, my usual move in this situation is to do qmatch_assum_abbrev_tac 'P t' qexists_tac 't' simp[Abbr'X'] Note that P is a metavariable, i.e. I have to type it out, but I avoid typing the large term abbreviated by t. The X stands for pieces of P I want unabbreviated after. HINT_EXISTS_TAC might still be an improvement. Sorry for no proper backquotes, using my phone. On Dec 26, 2012 10:57 PM, Vincent Aravantinos vincent.aravanti...@gmail.com wrote: Hi list, here is another situation which I don't like and often meet (both in HOL-Light and HOL4), and a potential solution. Please tell me if you also often meet the situation, if you agree that it is annoying, and if there is already a solution which I don't know of (I'm pretty sure there is no solution in HOL-Light, but I'm not familiar with all its extensions over there). SITUATION: goal of the form `?x. ... /\ P x /\ ...` + one of the assumptions is of the form `P t` (t is a big a term) + one wants to use t as the witness for x USUAL MOVE: e (EXISTS_TAC `t`) (*Then rewrite with the assumptions in order to remove the now trivial P t:*) e(ASM_REWRITE_TAC[]) PROBLEM WITH THIS: Annoying to write explicitly the big term t. Plus the subsequent ASM_REWRITE_TAC is trivial and can thus be systematized. Not really annoying if it only appears from time to time, but I personally often face this situation. SOLUTION: A tactic HINT_EXISTS_TAC which looks for an assumption matching one (or more) of the conjuncts in the conclusion and applies EXISTS_TAC with the corresponding term. EXAMPLE IN HOL-LIGHT: (* Consider the following goal:*) 0 [`P m`] 1 [`!x. P x == x = m`] `?x. P x` (* Usual move: *) # e (EXISTS_TAC `m:num`);; val it : goalstack = 1 subgoal (1 total) 0 [`P m`] 1 [`!x. P x == x = m`] `P m` # e (ASM_REWRITE_TAC[]);; val it : goalstack = No subgoals (* New solution, which finds the witness automatically and removes the trivial conjunct : *) # b (); b (); e HINT_EXISTS_TAC;; val it : goalstack = No subgoals (* Notes: * - The use case gets more interesting when m is actually a big term. * - Though, in this example, the tactic allows to conclude the goal, it can also be used just to make progress in the proof without necessary concluding. *) A HOL-Light implementation for HINT_EXISTS_TAC is provided below the signature. One for HOL4 can easily be implemented if anyone expresses some interest for it. Cheers, V. -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group http://users.encs.concordia.ca/~vincent/ let HINT_EXISTS_TAC (hs,c as g) = let hs = map snd hs in let v,c' = dest_exists c in let vs,c' = strip_exists c' in let hyp_match c h = ignore (check (not o exists (C mem vs) o frees) c); term_match (subtract (frees c) [v]) c (concl h), h in let (_,subs,_),h = tryfind (C tryfind hs o hyp_match) (binops `/\` c') in let witness = match subs with |[] - v |[t,u] when u = v - t |_ - failwith HINT_EXISTS_TAC not applicable in (EXISTS_TAC witness THEN REWRITE_TAC hs) g;; -- LogMeIn Rescue: Anywhere, Anytime Remote support for IT. Free Trial Remotely access PCs and mobile devices and provide instant support Improve your efficiency, and focus on delivering more value-add services Discover what IT Professionals Know. Rescue delivers http://p.sf.net/sfu/logmein_12329d2d ___ hol-info mailing list hol-info@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/hol-info -- Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS, MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft MVPs and experts. ON SALE this month only -- learn more at: http://p.sf.net/sfu/learnmore_122712___ hol-info mailing list hol-info@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/hol-info
Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
Hi Ramana, HINT_EXISTS_TAC allows not to type `P` explicitly. Indeed the good thing about this tactic, in my opinion, is that you don't need to type any term explicitly and just let the prover find them for you. And it's shorter of course. On the other hand, it has maybe the disdvantage of being specialized: one might prefer the more general mechanism provided by MATCH_ASSUM_ABBREV_TAC. In any case, thanks a lot, you taught me some HOL4 commands I was not aware of :-) (namely, MATCH_ASSUM_ABBREV_TAC and Abbr); I'm more familiar with HOL Light... Cheers, V. Le 26/12/12 19:42, Ramana Kumar a écrit : For what it's worth, my usual move in this situation is to do qmatch_assum_abbrev_tac 'P t' qexists_tac 't' simp[Abbr'X'] Note that P is a metavariable, i.e. I have to type it out, but I avoid typing the large term abbreviated by t. The X stands for pieces of P I want unabbreviated after. HINT_EXISTS_TAC might still be an improvement. Sorry for no proper backquotes, using my phone. On Dec 26, 2012 10:57 PM, Vincent Aravantinos vincent.aravanti...@gmail.com mailto:vincent.aravanti...@gmail.com wrote: Hi list, here is another situation which I don't like and often meet (both in HOL-Light and HOL4), and a potential solution. Please tell me if you also often meet the situation, if you agree that it is annoying, and if there is already a solution which I don't know of (I'm pretty sure there is no solution in HOL-Light, but I'm not familiar with all its extensions over there). SITUATION: goal of the form `?x. ... /\ P x /\ ...` + one of the assumptions is of the form `P t` (t is a big a term) + one wants to use t as the witness for x USUAL MOVE: e (EXISTS_TAC `t`) (*Then rewrite with the assumptions in order to remove the now trivial P t:*) e(ASM_REWRITE_TAC[]) PROBLEM WITH THIS: Annoying to write explicitly the big term t. Plus the subsequent ASM_REWRITE_TAC is trivial and can thus be systematized. Not really annoying if it only appears from time to time, but I personally often face this situation. SOLUTION: A tactic HINT_EXISTS_TAC which looks for an assumption matching one (or more) of the conjuncts in the conclusion and applies EXISTS_TAC with the corresponding term. EXAMPLE IN HOL-LIGHT: (* Consider the following goal:*) 0 [`P m`] 1 [`!x. P x == x = m`] `?x. P x` (* Usual move: *) # e (EXISTS_TAC `m:num`);; val it : goalstack = 1 subgoal (1 total) 0 [`P m`] 1 [`!x. P x == x = m`] `P m` # e (ASM_REWRITE_TAC[]);; val it : goalstack = No subgoals (* New solution, which finds the witness automatically and removes the trivial conjunct : *) # b (); b (); e HINT_EXISTS_TAC;; val it : goalstack = No subgoals (* Notes: * - The use case gets more interesting when m is actually a big term. * - Though, in this example, the tactic allows to conclude the goal, it can also be used just to make progress in the proof without necessary concluding. *) A HOL-Light implementation for HINT_EXISTS_TAC is provided below the signature. One for HOL4 can easily be implemented if anyone expresses some interest for it. Cheers, V. -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group http://users.encs.concordia.ca/~vincent/ http://users.encs.concordia.ca/%7Evincent/ let HINT_EXISTS_TAC (hs,c as g) = let hs = map snd hs in let v,c' = dest_exists c in let vs,c' = strip_exists c' in let hyp_match c h = ignore (check (not o exists (C mem vs) o frees) c); term_match (subtract (frees c) [v]) c (concl h), h in let (_,subs,_),h = tryfind (C tryfind hs o hyp_match) (binops `/\` c') in let witness = match subs with |[] - v |[t,u] when u = v - t |_ - failwith HINT_EXISTS_TAC not applicable in (EXISTS_TAC witness THEN REWRITE_TAC hs) g;; -- LogMeIn Rescue: Anywhere, Anytime Remote support for IT. Free Trial Remotely access PCs and mobile devices and provide instant support Improve your efficiency, and focus on delivering more value-add services Discover what IT Professionals Know. Rescue delivers http://p.sf.net/sfu/logmein_12329d2d ___ hol-info mailing list hol-info@lists.sourceforge.net mailto:hol-info@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/hol-info -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group
