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Re: [Hol-info] Improve EXISTS_TAC with by taking hints from the assumption list
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From: Vincent A. <vin...@gm...> - 2012-12-27 10:48:44
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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 <ra...@me... > <mailto:ra...@me...>> 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" >> <vin...@gm... >> <mailto:vin...@gm...>> 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...@li... >> <mailto:hol...@li...> >> https://lists.sourceforge.net/lists/listinfo/hol-info >> >> ------------------------------------------------------------------------------ >> Master Visual Studio, SharePoint, SQL, ASP.NET <http://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...@li... <mailto:hol...@li...> >> https://lists.sourceforge.net/lists/listinfo/hol-info -- Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware Verification Group http://users.encs.concordia.ca/~vincent/ |
