### Re: [isabelle-dev] simplifier and subgoaler not transitive

I am amazedby you and the simplifier! Yes, indeed one rule in question was added by mksimps. You were spot on. I never knew that they have some more-than-special meaning. ;o) The reason why I prefer to keep the freshness constraints together is that atom a # (x1, x2, x3, x4, x5) would expand to atom a # x1 /\ atom a # x2 /\ ... thus bloating the goal state. Poring over the trace again and again, and adding probes, like the ones below (in case somebody is interested), actually the trace information is quite instructive. It is just a lot of pain to piece everything together...but I guess that is what one has to love when working with Isabelle. ;o) In conclusion, I need to implement a special solver for solving the type of goals I want to solve...quite a sophisticated piece of code the simplifier, but good that it lets me do that. Thanks again for all replies! Christian ML {* val test_solver = mk_solver test solver (fn ss = fn n = print_tac (TEST SOLVER)) fun test_subgoaler ss n = print_tac (SUBGOALER TEST) THEN asm_simp_tac ss n *} declaration {* fn _ = Simplifier.map_ss (fn ss = Simplifier.set_subgoaler test_subgoaler (ss addSolver test_solver)) *} On Wednesday, May 23, 2012 at 11:39:53 (+1000), Thomas Sewell wrote: Question: it looks to me like (atom v # (x, y)) = (atom v # x atom v # y) It also looks like what you're trying to do is allow the system to reason with the above equality without actually giving it that equality. It looks like you've provided the equality in one direction as a rewrite rule and in the other direction by adjusting mksimps (just guessing here, but that's what it looks like). Did I guess right? If so, I know why that won't work :-) The new rewrite rules created by mksimps aren't themselves candidates for simplification, so the system won't apply Nominal2_Base.fresh_at_base_2 to them, which was what resulted in further progress on goal #2. Those are all giant guesses. Am I anywhere near the mark? More directly, why not just add the rewrite at the top of this email to the simpset? This will reduce all of these sharp statements to trivial inequalities. This is the approach that fits with the general design of the simplifier. Not the structure you want? Too many inequalities? In that case you really need a guided solver - giving the simplifier opportunities for wild exploration will just slow everything down. Yours, Thomas. On 23/05/12 02:23, Christian Urban wrote: Dear All, Assuming that this is about the bowels of the simplifier, I hope this is the right place to ask the following question. The simplifier has a subgoaler, which helps with rewriting conditional lemmas. This simplifiying/subgoaling process seems to be not transitive (probably is not meant to be). The problem that arises for me is the following: I have set up the simplifier to automatically solve the first two lemmas: lemma atom v # (x1, x2) == atom v # x1 apply(simp) done lemma atom v # x1 == v \noteq x1 apply(simp) done but it chokes, if I am trying to string both lemmas together lemma atom v # (x1, x2) == v \noteq x1 apply(simp) --fails Is there some magic that I can make the simplifier to deal also with the latter goal? The cool thing about jEdit is that I have the simplifier traces of all three goals next to each other (the trick is to disable the auto update). Unfortunately, I am not very good at reading these traces. The only thing I can say is that the simplifier starts off with goal 1 and 3 in the same direction, but then things start to diverge. Is there a place where one can read up about the tracing information of the simplifier? The traces are attached for reference. Best wishes and thanks for any help, Christian GOAL 1 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ (x1, x2) ⟹ atom v ♯ x1 [1]Applying instance of rewrite rule ??.unknown: ?a1 ♯ ?x1.1 ⟹ ?a1 ♯ ?x2.1 ⟹ ?a1 ♯ (?x1.1, ?x2.1) ≡ True [1]Trying to rewrite: atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [2]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 [1]FAILED atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ t ≡ True [1]Applying instance of rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Rewriting: atom v ♯ x1 ≡ True proof (prove): step 1 goal: No subgoals! GOAL 2 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 ⟹ v ≠ x1 [1]Applying instance of rewrite rule Nominal2_Base.fresh_at_base_2: ?a1 ♯ ?b1 ≡ ?a1 ≠ atom ?b1 [1]Rewriting: atom v ♯ x1 ≡ atom v ≠ atom x1 [1]Applying instance of rewrite rule

### Re: [isabelle-dev] simplifier and subgoaler not transitive

On Tue, 22 May 2012, Christian Urban wrote: Assuming that this is about the bowels of the simplifier, I hope this is the right place to ask the following question. From what I've seen on the thread so far, it is all perfectly normal Isabelle user-space. You did not propose to re-implement the simplifier, so it could just as well be discussed on the larger audience of isabelle-users. The experts are out there, and they are using Isabelle Professional Edition (aka release). Makarius ___ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev

### Re: [isabelle-dev] simplifier and subgoaler not transitive

Am 22/05/2012 18:23, schrieb Christian Urban: Dear All, Assuming that this is about the bowels of the simplifier, I hope this is the right place to ask the following question. The simplifier has a subgoaler, which helps with rewriting conditional lemmas. This simplifiying/subgoaling process seems to be not transitive (probably is not meant to be). Indeed, there is no guarantee. Hence it is unclear of it is cost effective to figure out why exactly it did not work in your example. I took a look ... The problem that arises for me is the following: I have set up the simplifier to automatically solve the first two lemmas: lemma atom v # (x1, x2) == atom v # x1 apply(simp) done lemma atom v # x1 == v \noteq x1 apply(simp) done but it chokes, if I am trying to string both lemmas together lemma atom v # (x1, x2) == v \noteq x1 apply(simp) --fails Is there some magic that I can make the simplifier to deal also with the latter goal? The cool thing about jEdit is that I have the simplifier traces of all three goals next to each other (the trick is to disable the auto update). Unfortunately, I am not very good at reading these traces. The only thing I can say is that the simplifier starts off with goal 1 and 3 in the same direction, but then things start to diverge. Is there a place where one can read up about the tracing information of the simplifier? The traces are attached for reference. Best wishes and thanks for any help, Christian GOAL 1 == but am at least as confused as you are: [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ (x1, x2) ⟹ atom v ♯ x1 [1]Applying instance of rewrite rule ??.unknown: ?a1 ♯ ?x1.1 ⟹ ?a1 ♯ ?x2.1 ⟹ ?a1 ♯ (?x1.1, ?x2.1) ≡ True Where does this rewrite rule come from? Its name suggests it was created during the simp process, but there is no indication of that. [1]Trying to rewrite: atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True This should be an instance of the above rule, but it is not, there is a funny t. I have no idea where that comes from. I'm confused. With ATPs, and the simplifier is one, it is best not to spend much time on figuring out why they failed but to accept it when they fail. [A typical problem for the simplifier are rules of the form P x y == Q x, which can be applied if a premise P a b is present but not if it needs another conidtional rule R x y == P x y first.] Tobias [2]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 [1]FAILED atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ t ≡ True [1]Applying instance of rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Rewriting: atom v ♯ x1 ≡ True proof (prove): step 1 goal: No subgoals! GOAL 2 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 ⟹ v ≠ x1 [1]Applying instance of rewrite rule Nominal2_Base.fresh_at_base_2: ?a1 ♯ ?b1 ≡ ?a1 ≠ atom ?b1 [1]Rewriting: atom v ♯ x1 ≡ atom v ≠ atom x1 [1]Applying instance of rewrite rule Nominal2_Base.at_base_class.atom_eq_iff: atom ?a1 = atom ?b1 ≡ ?a1 = ?b1 [1]Rewriting: atom v = atom x1 ≡ v = x1 [1]Adding rewrite rule ??.unknown: v = x1 ≡ False [1]Applying instance of rewrite rule ??.unknown: v = x1 ≡ False [1]Rewriting: v = x1 ≡ False [1]Applying instance of rewrite rule HOL.simp_thms_8: ¬ False ≡ True [1]Rewriting: ¬ False ≡ True proof (prove): step 1 goal: No subgoals! Goal 3 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ (x1, x2) ⟹ v ≠ x1 [1]Applying instance of rewrite rule ??.unknown: ?a1 ♯ ?x1.1 ⟹ ?a1 ♯ ?x2.1 ⟹ ?a1 ♯ (?x1.1, ?x2.1) ≡ True [1]Trying to rewrite: atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [2]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 [2]Applying instance of rewrite rule Nominal2_Base.fresh_at_base_2: ?a1 ♯ ?b1 ≡ ?a1 ≠ atom ?b1 [2]Rewriting: atom v ♯ x1 ≡ atom v ≠ atom x1 [2]Applying instance of rewrite rule Nominal2_Base.at_base_class.atom_eq_iff: atom ?a1 = atom ?b1 ≡ ?a1 = ?b1 [2]Rewriting: atom v = atom x1 ≡ v = x1 [1]FAILED atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ t ≡ True empty result sequence -- proof command failed ___ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev ___ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev

### Re: [isabelle-dev] simplifier and subgoaler not transitive

On Tuesday, May 22, 2012 at 20:59:28 (+0200), Tobias Nipkow wrote: but am at least as confused as you are: [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ (x1, x2) ⟹ atom v ♯ x1 [1]Applying instance of rewrite rule ??.unknown: ?a1 ♯ ?x1.1 ⟹ ?a1 ♯ ?x2.1 ⟹ ?a1 ♯ (?x1.1, ?x2.1) ≡ True Where does this rewrite rule come from? Its name suggests it was created during the simp process, but there is no indication of that. [1]Trying to rewrite: atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True This should be an instance of the above rule, but it is not, there is a funny t. I have no idea where that comes from. I'm confused. Sorry, this was because of my postediting of the trace. It should be a x2. Not sure whether this improves things. Christian ___ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev

### Re: [isabelle-dev] simplifier and subgoaler not transitive

Question: it looks to me like (atom v # (x, y)) = (atom v # x atom v # y) It also looks like what you're trying to do is allow the system to reason with the above equality without actually giving it that equality. It looks like you've provided the equality in one direction as a rewrite rule and in the other direction by adjusting mksimps (just guessing here, but that's what it looks like). Did I guess right? If so, I know why that won't work :-) The new rewrite rules created by mksimps aren't themselves candidates for simplification, so the system won't apply Nominal2_Base.fresh_at_base_2 to them, which was what resulted in further progress on goal #2. Those are all giant guesses. Am I anywhere near the mark? More directly, why not just add the rewrite at the top of this email to the simpset? This will reduce all of these sharp statements to trivial inequalities. This is the approach that fits with the general design of the simplifier. Not the structure you want? Too many inequalities? In that case you really need a guided solver - giving the simplifier opportunities for wild exploration will just slow everything down. Yours, Thomas. On 23/05/12 02:23, Christian Urban wrote: Dear All, Assuming that this is about the bowels of the simplifier, I hope this is the right place to ask the following question. The simplifier has a subgoaler, which helps with rewriting conditional lemmas. This simplifiying/subgoaling process seems to be not transitive (probably is not meant to be). The problem that arises for me is the following: I have set up the simplifier to automatically solve the first two lemmas: lemma atom v # (x1, x2) == atom v # x1 apply(simp) done lemma atom v # x1 == v \noteq x1 apply(simp) done but it chokes, if I am trying to string both lemmas together lemma atom v # (x1, x2) == v \noteq x1 apply(simp) --fails Is there some magic that I can make the simplifier to deal also with the latter goal? The cool thing about jEdit is that I have the simplifier traces of all three goals next to each other (the trick is to disable the auto update). Unfortunately, I am not very good at reading these traces. The only thing I can say is that the simplifier starts off with goal 1 and 3 in the same direction, but then things start to diverge. Is there a place where one can read up about the tracing information of the simplifier? The traces are attached for reference. Best wishes and thanks for any help, Christian GOAL 1 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ (x1, x2) ⟹ atom v ♯ x1 [1]Applying instance of rewrite rule ??.unknown: ?a1 ♯ ?x1.1 ⟹ ?a1 ♯ ?x2.1 ⟹ ?a1 ♯ (?x1.1, ?x2.1) ≡ True [1]Trying to rewrite: atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [2]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 [1]FAILED atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ t ≡ True [1]Applying instance of rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Rewriting: atom v ♯ x1 ≡ True proof (prove): step 1 goal: No subgoals! GOAL 2 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 ⟹ v ≠ x1 [1]Applying instance of rewrite rule Nominal2_Base.fresh_at_base_2: ?a1 ♯ ?b1 ≡ ?a1 ≠ atom ?b1 [1]Rewriting: atom v ♯ x1 ≡ atom v ≠ atom x1 [1]Applying instance of rewrite rule Nominal2_Base.at_base_class.atom_eq_iff: atom ?a1 = atom ?b1 ≡ ?a1 = ?b1 [1]Rewriting: atom v = atom x1 ≡ v = x1 [1]Adding rewrite rule ??.unknown: v = x1 ≡ False [1]Applying instance of rewrite rule ??.unknown: v = x1 ≡ False [1]Rewriting: v = x1 ≡ False [1]Applying instance of rewrite rule HOL.simp_thms_8: ¬ False ≡ True [1]Rewriting: ¬ False ≡ True proof (prove): step 1 goal: No subgoals! Goal 3 == [1]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ (x1, x2) ⟹ v ≠ x1 [1]Applying instance of rewrite rule ??.unknown: ?a1 ♯ ?x1.1 ⟹ ?a1 ♯ ?x2.1 ⟹ ?a1 ♯ (?x1.1, ?x2.1) ≡ True [1]Trying to rewrite: atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [2]SIMPLIFIER INVOKED ON THE FOLLOWING TERM: atom v ♯ x1 [2]Applying instance of rewrite rule Nominal2_Base.fresh_at_base_2: ?a1 ♯ ?b1 ≡ ?a1 ≠ atom ?b1 [2]Rewriting: atom v ♯ x1 ≡ atom v ≠ atom x1 [2]Applying instance of rewrite rule Nominal2_Base.at_base_class.atom_eq_iff: atom ?a1 = atom ?b1 ≡ ?a1 = ?b1 [2]Rewriting: atom v = atom x1 ≡ v = x1 [1]FAILED atom v ♯ x1 ⟹ atom v ♯ t ⟹ atom v ♯ (x1, x2) ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ x1 ≡ True [1]Adding rewrite rule ??.unknown: atom v ♯ t ≡ True empty result sequence -- proof command failed ___ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev ___ isabelle-dev mailing list isabelle-...@in.tum.de