author | wenzelm |
Thu, 08 Aug 2019 11:40:42 +0200 | |
changeset 70489 | 12d1e6e2c1d0 |
parent 70488 | c7ef6685c943 |
child 70513 | dc749e0dc6b2 |
permissions | -rw-r--r-- |
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renamed "Metis_Tactics" to "Metis_Tactic", now that there is only one Metis tactic ("metisFT" is legacy)
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(* Title: HOL/Tools/Metis/metis_tactic.ML |
38027 | 2 |
Author: Kong W. Susanto, Cambridge University Computer Laboratory |
3 |
Author: Lawrence C. Paulson, Cambridge University Computer Laboratory |
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Author: Jasmin Blanchette, TU Muenchen |
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The Metis prover (slightly modified version from Larry);
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Copyright Cambridge University 2007 |
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HOL setup for the Metis prover. |
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The Metis prover (slightly modified version from Larry);
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*) |
028e39e5e8f3
The Metis prover (slightly modified version from Larry);
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parents:
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|
44651
5d6a11e166cf
renamed "Metis_Tactics" to "Metis_Tactic", now that there is only one Metis tactic ("metisFT" is legacy)
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signature METIS_TACTIC = |
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The Metis prover (slightly modified version from Larry);
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sig |
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val trace : bool Config.T |
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val verbose : bool Config.T |
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use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
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val new_skolem : bool Config.T |
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added "metis_advisory_simp" option to orient as many equations as possible in Metis the right way (cf. "More SPASS with Isabelle")
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val advisory_simp : bool Config.T |
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added a version of the Metis tactic that returns the unused facts
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val metis_tac_unused : string list -> string -> Proof.context -> thm list -> int -> thm -> |
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thm list * thm Seq.seq |
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val metis_tac : string list -> string -> Proof.context -> thm list -> int -> tactic |
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val metis_method : (string list option * string option) * thm list -> Proof.context -> thm list -> |
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tactic |
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val metis_lam_transs : string list |
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val parse_metis_options : (string list option * string option) parser |
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The Metis prover (slightly modified version from Larry);
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end |
028e39e5e8f3
The Metis prover (slightly modified version from Larry);
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parents:
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|
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renamed "Metis_Tactics" to "Metis_Tactic", now that there is only one Metis tactic ("metisFT" is legacy)
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structure Metis_Tactic : METIS_TACTIC = |
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The Metis prover (slightly modified version from Larry);
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struct |
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open ATP_Problem_Generate |
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open ATP_Proof_Reconstruct |
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open Metis_Generate |
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open Metis_Reconstruct |
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val new_skolem = Attrib.setup_config_bool \<^binding>\<open>metis_new_skolem\<close> (K false) |
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val advisory_simp = Attrib.setup_config_bool \<^binding>\<open>metis_advisory_simp\<close> (K true) |
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The Metis prover (slightly modified version from Larry);
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make sure no warnings are given for polymorphic facts where we use a monomorphic instance
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(* Designed to work also with monomorphic instances of polymorphic theorems. *) |
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fun have_common_thm ctxt ths1 ths2 = |
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exists (member (Term.aconv_untyped o apply2 Thm.prop_of) ths1) |
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(map (Meson.make_meta_clause ctxt) ths2) |
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The Metis prover (slightly modified version from Larry);
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(*Determining which axiom clauses are actually used*) |
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"Metis." -> "Metis_" to reflect change in "metis.ML"
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fun used_axioms axioms (th, Metis_Proof.Axiom _) = SOME (lookth axioms th) |
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| used_axioms _ _ = NONE |
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(* Lightweight predicate type information comes in two flavors, "t = t'" and |
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"t => t'", where "t" and "t'" are the same term modulo type tags. |
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In Isabelle, type tags are stripped away, so we are left with "t = t" or |
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added support for helpers in new Metis, so far only for polymorphic type encodings
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"t => t". Type tag idempotence is also handled this way. *) |
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fun reflexive_or_trivial_of_metis ctxt type_enc sym_tab concealed mth = |
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(case hol_clause_of_metis ctxt type_enc sym_tab concealed mth of |
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Const (\<^const_name>\<open>HOL.eq\<close>, _) $ _ $ t => |
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let |
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val ct = Thm.cterm_of ctxt t |
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val cT = Thm.ctyp_of_cterm ct |
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in refl |> Thm.instantiate' [SOME cT] [SOME ct] end |
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| Const (\<^const_name>\<open>disj\<close>, _) $ t1 $ t2 => |
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(if can HOLogic.dest_not t1 then t2 else t1) |
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|> HOLogic.mk_Trueprop |> Thm.cterm_of ctxt |> Thm.trivial |
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| _ => raise Fail "expected reflexive or trivial clause") |
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|> Meson.make_meta_clause ctxt |
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fun lam_lifted_of_metis ctxt type_enc sym_tab concealed mth = |
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let |
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val tac = rewrite_goals_tac ctxt @{thms lambda_def [abs_def]} THEN resolve_tac ctxt [refl] 1 |
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val t = hol_clause_of_metis ctxt type_enc sym_tab concealed mth |
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val ct = Thm.cterm_of ctxt (HOLogic.mk_Trueprop t) |
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in |
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Goal.prove_internal ctxt [] ct (K tac) |
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|> Meson.make_meta_clause ctxt |
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end |
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|
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fun add_vars_and_frees (t $ u) = fold (add_vars_and_frees) [t, u] |
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| add_vars_and_frees (Abs (_, _, t)) = add_vars_and_frees t |
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| add_vars_and_frees (t as Var _) = insert (op =) t |
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| add_vars_and_frees (t as Free _) = insert (op =) t |
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pull variables (Var) out of lambdas, so that the Isabelle theorems closely mirror the Metis lambda-lifted ones
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| add_vars_and_frees _ = I |
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fun introduce_lam_wrappers ctxt th = |
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if Meson_Clausify.is_quasi_lambda_free (Thm.prop_of th) then th |
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else |
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let |
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fun conv first ctxt ct = |
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if Meson_Clausify.is_quasi_lambda_free (Thm.term_of ct) then Thm.reflexive ct |
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else |
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(case Thm.term_of ct of |
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Abs (_, _, u) => |
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if first then |
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(case add_vars_and_frees u [] of |
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[] => |
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Conv.abs_conv (conv false o snd) ctxt ct |
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|> (fn th => Meson.first_order_resolve ctxt th @{thm Metis.eq_lambdaI}) |
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| v :: _ => |
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Abs (Name.uu, fastype_of v, abstract_over (v, Thm.term_of ct)) $ v |
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|> Thm.cterm_of ctxt |
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|> Conv.comb_conv (conv true ctxt)) |
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else Conv.abs_conv (conv false o snd) ctxt ct |
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| Const (\<^const_name>\<open>Meson.skolem\<close>, _) $ _ => Thm.reflexive ct |
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| _ => Conv.comb_conv (conv true ctxt) ct) |
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val eq_th = conv true ctxt (Thm.cprop_of th) |
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(* We replace the equation's left-hand side with a beta-equivalent term |
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so that "Thm.equal_elim" works below. *) |
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val t0 $ _ $ t2 = Thm.prop_of eq_th |
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val eq_ct = t0 $ Thm.prop_of th $ t2 |> Thm.cterm_of ctxt |
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val eq_th' = Goal.prove_internal ctxt [] eq_ct (K (resolve_tac ctxt [eq_th] 1)) |
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in Thm.equal_elim eq_th' th end |
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|
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fun clause_params ordering = |
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{ordering = ordering, |
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orderLiterals = Metis_Clause.UnsignedLiteralOrder, |
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orderTerms = true} |
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fun active_params ordering = |
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{clause = clause_params ordering, |
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prefactor = #prefactor Metis_Active.default, |
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postfactor = #postfactor Metis_Active.default} |
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val waiting_params = |
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{symbolsWeight = 1.0, |
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variablesWeight = 0.05, |
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literalsWeight = 0.01, |
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models = []} |
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added "metis_advisory_simp" option to orient as many equations as possible in Metis the right way (cf. "More SPASS with Isabelle")
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fun resolution_params ordering = |
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{active = active_params ordering, waiting = waiting_params} |
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|
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fun kbo_advisory_simp_ordering ord_info = |
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let |
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fun weight (m, _) = |
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AList.lookup (op =) ord_info (Metis_Name.toString m) |> the_default 1 |
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fun precedence p = |
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(case int_ord (apply2 weight p) of |
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added "metis_advisory_simp" option to orient as many equations as possible in Metis the right way (cf. "More SPASS with Isabelle")
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EQUAL => #precedence Metis_KnuthBendixOrder.default p |
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| ord => ord) |
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in {weight = weight, precedence = precedence} end |
37573 | 132 |
|
55285 | 133 |
fun metis_call type_enc lam_trans = |
134 |
let |
|
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val type_enc = |
|
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(case AList.find (fn (enc, encs) => enc = hd encs) type_enc_aliases type_enc of |
|
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[alias] => alias |
|
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| _ => type_enc) |
|
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val opts = |
|
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[] |> type_enc <> partial_typesN ? cons type_enc |
|
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|> lam_trans <> default_metis_lam_trans ? cons lam_trans |
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in metisN ^ (if null opts then "" else " (" ^ commas opts ^ ")") end |
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||
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exception METIS_UNPROVABLE of unit |
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have "metis" method and "metis_tac" fall back on "metisFT" upon failure, following a suggestion by Larry
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(* Main function to start Metis proof and reconstruction *) |
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fun FOL_SOLVE unused type_encs lam_trans ctxt cls ths0 = |
70489 | 148 |
let |
149 |
val thy = Proof_Context.theory_of ctxt |
|
150 |
||
151 |
val new_skolem = Config.get ctxt new_skolem orelse null (Meson.choice_theorems thy) |
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val do_lams = |
|
153 |
(lam_trans = liftingN orelse lam_trans = lam_liftingN) ? introduce_lam_wrappers ctxt |
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val th_cls_pairs = |
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map2 (fn j => fn th => |
|
156 |
(Thm.get_name_hint th, |
|
157 |
th |
|
158 |
|> Drule.eta_contraction_rule |
|
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|> Meson_Clausify.cnf_axiom ctxt new_skolem (lam_trans = combsN) j |
|
160 |
||> map do_lams)) |
|
161 |
(0 upto length ths0 - 1) ths0 |
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162 |
val ths = maps (snd o snd) th_cls_pairs |
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val dischargers = map (fst o snd) th_cls_pairs |
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val cls = cls |> map (Drule.eta_contraction_rule #> do_lams) |
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val _ = trace_msg ctxt (K "FOL_SOLVE: CONJECTURE CLAUSES") |
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val _ = List.app (fn th => trace_msg ctxt (fn () => Thm.string_of_thm ctxt th)) cls |
|
167 |
||
168 |
val type_enc :: fallback_type_encs = type_encs |
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169 |
val _ = trace_msg ctxt (fn () => "type_enc = " ^ type_enc) |
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170 |
val type_enc = type_enc_of_string Strict type_enc |
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||
172 |
val (sym_tab, axioms, ord_info, concealed) = |
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173 |
generate_metis_problem ctxt type_enc lam_trans cls ths |
|
174 |
fun get_isa_thm mth Isa_Reflexive_or_Trivial = |
|
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reflexive_or_trivial_of_metis ctxt type_enc sym_tab concealed mth |
70489 | 176 |
| get_isa_thm mth Isa_Lambda_Lifted = |
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177 |
lam_lifted_of_metis ctxt type_enc sym_tab concealed mth |
70489 | 178 |
| get_isa_thm _ (Isa_Raw ith) = ith |
179 |
val axioms = axioms |> map (fn (mth, ith) => (mth, get_isa_thm mth ith)) |
|
180 |
val _ = trace_msg ctxt (K "ISABELLE CLAUSES") |
|
181 |
val _ = List.app (fn (_, ith) => trace_msg ctxt (fn () => Thm.string_of_thm ctxt ith)) axioms |
|
182 |
val _ = trace_msg ctxt (K "METIS CLAUSES") |
|
183 |
val _ = List.app (fn (mth, _) => trace_msg ctxt (fn () => Metis_Thm.toString mth)) axioms |
|
184 |
||
185 |
val _ = trace_msg ctxt (K "START METIS PROVE PROCESS") |
|
186 |
val ordering = |
|
187 |
if Config.get ctxt advisory_simp |
|
188 |
then kbo_advisory_simp_ordering (ord_info ()) |
|
189 |
else Metis_KnuthBendixOrder.default |
|
190 |
||
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191 |
fun fall_back () = |
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192 |
(verbose_warning ctxt |
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("Falling back on " ^ quote (metis_call (hd fallback_type_encs) lam_trans) ^ "..."); |
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194 |
FOL_SOLVE unused fallback_type_encs lam_trans ctxt cls ths0) |
32956 | 195 |
in |
69593 | 196 |
(case filter (fn t => Thm.prop_of t aconv \<^prop>\<open>False\<close>) cls of |
70489 | 197 |
false_th :: _ => [false_th RS @{thm FalseE}] |
198 |
| [] => |
|
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(case Metis_Resolution.loop (Metis_Resolution.new (resolution_params ordering) |
|
200 |
{axioms = axioms |> map fst, conjecture = []}) of |
|
201 |
Metis_Resolution.Contradiction mth => |
|
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let |
|
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val _ = trace_msg ctxt (fn () => "METIS RECONSTRUCTION START: " ^ Metis_Thm.toString mth) |
|
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val ctxt' = fold Variable.declare_constraints (map Thm.prop_of cls) ctxt |
|
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(*add constraints arising from converting goal to clause form*) |
|
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val proof = Metis_Proof.proof mth |
|
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val result = fold (replay_one_inference ctxt' type_enc concealed sym_tab) proof axioms |
|
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val used = map_filter (used_axioms axioms) proof |
|
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val _ = trace_msg ctxt (K "METIS COMPLETED; clauses actually used:") |
|
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val _ = List.app (fn th => trace_msg ctxt (fn () => Thm.string_of_thm ctxt th)) used |
|
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val (used_th_cls_pairs, unused_th_cls_pairs) = |
|
212 |
List.partition (have_common_thm ctxt used o snd o snd) th_cls_pairs |
|
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val unused_ths = maps (snd o snd) unused_th_cls_pairs |
|
214 |
val unused_names = map fst unused_th_cls_pairs |
|
215 |
||
216 |
val _ = unused := unused_ths; |
|
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val _ = |
|
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if not (null unused_names) then |
|
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verbose_warning ctxt ("Unused theorems: " ^ commas_quote unused_names) |
|
220 |
else (); |
|
221 |
val _ = |
|
222 |
if not (null cls) andalso not (have_common_thm ctxt used cls) then |
|
223 |
verbose_warning ctxt "The assumptions are inconsistent" |
|
224 |
else (); |
|
225 |
in |
|
226 |
(case result of |
|
227 |
(_, ith) :: _ => |
|
228 |
(trace_msg ctxt (fn () => "Success: " ^ Thm.string_of_thm ctxt ith); |
|
229 |
[discharge_skolem_premises ctxt dischargers ith]) |
|
230 |
| _ => (trace_msg ctxt (K "Metis: No result"); [])) |
|
231 |
end |
|
232 |
| Metis_Resolution.Satisfiable _ => |
|
233 |
(trace_msg ctxt (K "Metis: No first-order proof with the supplied lemmas"); |
|
234 |
raise METIS_UNPROVABLE ())) |
|
235 |
handle METIS_UNPROVABLE () => if null fallback_type_encs then [] else fall_back () |
|
236 |
| METIS_RECONSTRUCT (loc, msg) => |
|
237 |
if null fallback_type_encs then |
|
238 |
(verbose_warning ctxt ("Failed to replay Metis proof\n" ^ loc ^ ": " ^ msg); []) |
|
239 |
else fall_back ()) |
|
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|
240 |
end |
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The Metis prover (slightly modified version from Larry);
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|
241 |
|
45508 | 242 |
fun neg_clausify ctxt combinators = |
38028 | 243 |
single |
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|
244 |
#> Meson.make_clauses_unsorted ctxt |
55236 | 245 |
#> combinators ? map (Meson_Clausify.introduce_combinators_in_theorem ctxt) |
38028 | 246 |
#> Meson.finish_cnf |
247 |
||
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|
248 |
fun preskolem_tac ctxt st0 = |
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changeset
|
249 |
(if exists (Meson.has_too_many_clauses ctxt) |
59582 | 250 |
(Logic.prems_of_goal (Thm.prop_of st0) 1) then |
51717
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simplifier uses proper Proof.context instead of historic type simpset;
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diff
changeset
|
251 |
Simplifier.full_simp_tac (Meson_Clausify.ss_only @{thms not_all not_ex} ctxt) 1 |
55239 | 252 |
THEN CNF.cnfx_rewrite_tac ctxt 1 |
39269
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changeset
|
253 |
else |
c2795d8a2461
use definitional CNF for the goal if at least one of the premisses would lead to too many clauses in Meson
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parents:
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changeset
|
254 |
all_tac) st0 |
c2795d8a2461
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parents:
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changeset
|
255 |
|
55521
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added a version of the Metis tactic that returns the unused facts
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parents:
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diff
changeset
|
256 |
fun metis_tac_unused type_encs0 lam_trans ctxt ths i st0 = |
37926
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|
257 |
let |
55521
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added a version of the Metis tactic that returns the unused facts
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diff
changeset
|
258 |
val unused = Unsynchronized.ref [] |
55520 | 259 |
val type_encs = if null type_encs0 then partial_type_encs else type_encs0 |
39978
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parents:
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changeset
|
260 |
val _ = trace_msg ctxt (fn () => |
61268 | 261 |
"Metis called with theorems\n" ^ cat_lines (map (Thm.string_of_thm ctxt) ths)) |
45519
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blanchet
parents:
45514
diff
changeset
|
262 |
val type_encs = type_encs |> maps unalias_type_enc |
55521
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added a version of the Metis tactic that returns the unused facts
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parents:
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diff
changeset
|
263 |
val combs = (lam_trans = combsN) |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59058
diff
changeset
|
264 |
fun tac clause = resolve_tac ctxt (FOL_SOLVE unused type_encs lam_trans ctxt clause ths) 1 |
55521
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added a version of the Metis tactic that returns the unused facts
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parents:
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diff
changeset
|
265 |
val seq = Meson.MESON (preskolem_tac ctxt) (maps (neg_clausify ctxt combs)) tac ctxt i st0 |
32956 | 266 |
in |
55521
241c6a2fdda1
added a version of the Metis tactic that returns the unused facts
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parents:
55520
diff
changeset
|
267 |
(!unused, seq) |
32956 | 268 |
end |
23442
028e39e5e8f3
The Metis prover (slightly modified version from Larry);
wenzelm
parents:
diff
changeset
|
269 |
|
55521
241c6a2fdda1
added a version of the Metis tactic that returns the unused facts
blanchet
parents:
55520
diff
changeset
|
270 |
fun metis_tac type_encs lam_trans ctxt ths i = snd o metis_tac_unused type_encs lam_trans ctxt ths i |
241c6a2fdda1
added a version of the Metis tactic that returns the unused facts
blanchet
parents:
55520
diff
changeset
|
271 |
|
55520 | 272 |
(* Whenever "X" has schematic type variables, we treat "using X by metis" as "by (metis X)" to |
273 |
prevent "Subgoal.FOCUS" from freezing the type variables. We don't do it for nonschematic facts |
|
274 |
"X" because this breaks a few proofs (in the rare and subtle case where a proof relied on |
|
275 |
extensionality not being applied) and brings few benefits. *) |
|
59582 | 276 |
val has_tvar = exists_type (exists_subtype (fn TVar _ => true | _ => false)) o Thm.prop_of |
43034
18259246abb5
try both "metis" and (on failure) "metisFT" in replay
blanchet
parents:
42847
diff
changeset
|
277 |
|
55315 | 278 |
fun metis_method ((override_type_encs, lam_trans), ths) ctxt facts = |
55520 | 279 |
let val (schem_facts, nonschem_facts) = List.partition has_tvar facts in |
61841
4d3527b94f2a
more general types Proof.method / context_tactic;
wenzelm
parents:
61302
diff
changeset
|
280 |
HEADGOAL (Method.insert_tac ctxt nonschem_facts THEN' |
55520 | 281 |
CHANGED_PROP o metis_tac (these override_type_encs) |
282 |
(the_default default_metis_lam_trans lam_trans) ctxt (schem_facts @ ths)) |
|
43099 | 283 |
end |
43100 | 284 |
|
46365 | 285 |
val metis_lam_transs = [hide_lamsN, liftingN, combsN] |
45519
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
286 |
|
45578 | 287 |
fun set_opt _ x NONE = SOME x |
288 |
| set_opt get x (SOME x0) = |
|
55523
9429e7b5b827
removed final periods in messages for proof methods
blanchet
parents:
55521
diff
changeset
|
289 |
error ("Cannot specify both " ^ quote (get x0) ^ " and " ^ quote (get x)) |
54756 | 290 |
|
45519
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
291 |
fun consider_opt s = |
54756 | 292 |
if member (op =) metis_lam_transs s then apsnd (set_opt I s) else apfst (set_opt hd [s]) |
45514 | 293 |
|
45519
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
294 |
val parse_metis_options = |
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
295 |
Scan.optional |
69593 | 296 |
(Args.parens (Args.name -- Scan.option (\<^keyword>\<open>,\<close> |-- Args.name)) |
45519
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
297 |
>> (fn (s, s') => |
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
298 |
(NONE, NONE) |> consider_opt s |
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
299 |
|> (case s' of SOME s' => consider_opt s' | _ => I))) |
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
300 |
(NONE, NONE) |
cd6e78cb6ee8
make metis reconstruction handling more flexible
blanchet
parents:
45514
diff
changeset
|
301 |
|
58818 | 302 |
val _ = |
303 |
Theory.setup |
|
69593 | 304 |
(Method.setup \<^binding>\<open>metis\<close> |
58818 | 305 |
(Scan.lift parse_metis_options -- Attrib.thms >> (METHOD oo metis_method)) |
306 |
"Metis for FOL and HOL problems") |
|
23442
028e39e5e8f3
The Metis prover (slightly modified version from Larry);
wenzelm
parents:
diff
changeset
|
307 |
|
028e39e5e8f3
The Metis prover (slightly modified version from Larry);
wenzelm
parents:
diff
changeset
|
308 |
end; |