--- a/src/HOL/Tools/meson.ML Mon Oct 04 20:55:55 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,712 +0,0 @@
-(* Title: HOL/Tools/meson.ML
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
-
-The MESON resolution proof procedure for HOL.
-When making clauses, avoids using the rewriter -- instead uses RS recursively.
-*)
-
-signature MESON =
-sig
- val trace: bool Unsynchronized.ref
- val term_pair_of: indexname * (typ * 'a) -> term * 'a
- val size_of_subgoals: thm -> int
- val has_too_many_clauses: Proof.context -> term -> bool
- val make_cnf: thm list -> thm -> Proof.context -> thm list * Proof.context
- val finish_cnf: thm list -> thm list
- val presimplify: thm -> thm
- val make_nnf: Proof.context -> thm -> thm
- val skolemize_with_choice_thms : Proof.context -> thm list -> thm -> thm
- val skolemize : Proof.context -> thm -> thm
- val is_fol_term: theory -> term -> bool
- val make_clauses_unsorted: thm list -> thm list
- val make_clauses: thm list -> thm list
- val make_horns: thm list -> thm list
- val best_prolog_tac: (thm -> int) -> thm list -> tactic
- val depth_prolog_tac: thm list -> tactic
- val gocls: thm list -> thm list
- val skolemize_prems_tac : Proof.context -> thm list -> int -> tactic
- val MESON:
- tactic -> (thm list -> thm list) -> (thm list -> tactic) -> Proof.context
- -> int -> tactic
- val best_meson_tac: (thm -> int) -> Proof.context -> int -> tactic
- val safe_best_meson_tac: Proof.context -> int -> tactic
- val depth_meson_tac: Proof.context -> int -> tactic
- val prolog_step_tac': thm list -> int -> tactic
- val iter_deepen_prolog_tac: thm list -> tactic
- val iter_deepen_meson_tac: Proof.context -> thm list -> int -> tactic
- val make_meta_clause: thm -> thm
- val make_meta_clauses: thm list -> thm list
- val meson_tac: Proof.context -> thm list -> int -> tactic
- val setup: theory -> theory
-end
-
-structure Meson : MESON =
-struct
-
-val trace = Unsynchronized.ref false;
-fun trace_msg msg = if ! trace then tracing (msg ()) else ();
-
-val max_clauses_default = 60;
-val (max_clauses, setup) = Attrib.config_int "meson_max_clauses" (K max_clauses_default);
-
-(*No known example (on 1-5-2007) needs even thirty*)
-val iter_deepen_limit = 50;
-
-val disj_forward = @{thm disj_forward};
-val disj_forward2 = @{thm disj_forward2};
-val make_pos_rule = @{thm make_pos_rule};
-val make_pos_rule' = @{thm make_pos_rule'};
-val make_pos_goal = @{thm make_pos_goal};
-val make_neg_rule = @{thm make_neg_rule};
-val make_neg_rule' = @{thm make_neg_rule'};
-val make_neg_goal = @{thm make_neg_goal};
-val conj_forward = @{thm conj_forward};
-val all_forward = @{thm all_forward};
-val ex_forward = @{thm ex_forward};
-
-val not_conjD = @{thm meson_not_conjD};
-val not_disjD = @{thm meson_not_disjD};
-val not_notD = @{thm meson_not_notD};
-val not_allD = @{thm meson_not_allD};
-val not_exD = @{thm meson_not_exD};
-val imp_to_disjD = @{thm meson_imp_to_disjD};
-val not_impD = @{thm meson_not_impD};
-val iff_to_disjD = @{thm meson_iff_to_disjD};
-val not_iffD = @{thm meson_not_iffD};
-val conj_exD1 = @{thm meson_conj_exD1};
-val conj_exD2 = @{thm meson_conj_exD2};
-val disj_exD = @{thm meson_disj_exD};
-val disj_exD1 = @{thm meson_disj_exD1};
-val disj_exD2 = @{thm meson_disj_exD2};
-val disj_assoc = @{thm meson_disj_assoc};
-val disj_comm = @{thm meson_disj_comm};
-val disj_FalseD1 = @{thm meson_disj_FalseD1};
-val disj_FalseD2 = @{thm meson_disj_FalseD2};
-
-
-(**** Operators for forward proof ****)
-
-
-(** First-order Resolution **)
-
-fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t);
-
-(*FIXME: currently does not "rename variables apart"*)
-fun first_order_resolve thA thB =
- (case
- try (fn () =>
- let val thy = theory_of_thm thA
- val tmA = concl_of thA
- val Const("==>",_) $ tmB $ _ = prop_of thB
- val tenv =
- Pattern.first_order_match thy (tmB, tmA)
- (Vartab.empty, Vartab.empty) |> snd
- val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv)
- in thA RS (cterm_instantiate ct_pairs thB) end) () of
- SOME th => th
- | NONE => raise THM ("first_order_resolve", 0, [thA, thB]))
-
-(* Applying "choice" swaps the bound variable names. We tweak
- "Thm.rename_boundvars"'s input to get the desired names. *)
-fun fix_bounds (_ $ (Const (@{const_name Ex}, _)
- $ Abs (_, _, Const (@{const_name All}, _) $ _)))
- (t0 $ (Const (@{const_name All}, T1)
- $ Abs (a1, T1', Const (@{const_name Ex}, T2)
- $ Abs (a2, T2', t')))) =
- t0 $ (Const (@{const_name All}, T1)
- $ Abs (a2, T1', Const (@{const_name Ex}, T2) $ Abs (a1, T2', t')))
- | fix_bounds _ t = t
-
-(* Hack to make it less likely that we lose our precious bound variable names in
- "rename_bvs_RS" below, because of a clash. *)
-val protect_prefix = "_"
-
-fun protect_bounds (t $ u) = protect_bounds t $ protect_bounds u
- | protect_bounds (Abs (s, T, t')) =
- Abs (protect_prefix ^ s, T, protect_bounds t')
- | protect_bounds t = t
-
-(* Forward proof while preserving bound variables names*)
-fun rename_bvs_RS th rl =
- let
- val t = concl_of th
- val r = concl_of rl
- val th' = th RS Thm.rename_boundvars r (protect_bounds r) rl
- val t' = concl_of th'
- in Thm.rename_boundvars t' (fix_bounds t' t) th' end
-
-(*raises exception if no rules apply*)
-fun tryres (th, rls) =
- let fun tryall [] = raise THM("tryres", 0, th::rls)
- | tryall (rl::rls) = (rename_bvs_RS th rl handle THM _ => tryall rls)
- in tryall rls end;
-
-(*Permits forward proof from rules that discharge assumptions. The supplied proof state st,
- e.g. from conj_forward, should have the form
- "[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q"
- and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*)
-fun forward_res ctxt nf st =
- let fun forward_tacf [prem] = rtac (nf prem) 1
- | forward_tacf prems =
- error (cat_lines
- ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:" ::
- Display.string_of_thm ctxt st ::
- "Premises:" :: map (Display.string_of_thm ctxt) prems))
- in
- case Seq.pull (ALLGOALS (Misc_Legacy.METAHYPS forward_tacf) st)
- of SOME(th,_) => th
- | NONE => raise THM("forward_res", 0, [st])
- end;
-
-(*Are any of the logical connectives in "bs" present in the term?*)
-fun has_conns bs =
- let fun has (Const _) = false
- | has (Const(@{const_name Trueprop},_) $ p) = has p
- | has (Const(@{const_name Not},_) $ p) = has p
- | has (Const(@{const_name HOL.disj},_) $ p $ q) = member (op =) bs @{const_name HOL.disj} orelse has p orelse has q
- | has (Const(@{const_name HOL.conj},_) $ p $ q) = member (op =) bs @{const_name HOL.conj} orelse has p orelse has q
- | has (Const(@{const_name All},_) $ Abs(_,_,p)) = member (op =) bs @{const_name All} orelse has p
- | has (Const(@{const_name Ex},_) $ Abs(_,_,p)) = member (op =) bs @{const_name Ex} orelse has p
- | has _ = false
- in has end;
-
-
-(**** Clause handling ****)
-
-fun literals (Const(@{const_name Trueprop},_) $ P) = literals P
- | literals (Const(@{const_name HOL.disj},_) $ P $ Q) = literals P @ literals Q
- | literals (Const(@{const_name Not},_) $ P) = [(false,P)]
- | literals P = [(true,P)];
-
-(*number of literals in a term*)
-val nliterals = length o literals;
-
-
-(*** Tautology Checking ***)
-
-fun signed_lits_aux (Const (@{const_name HOL.disj}, _) $ P $ Q) (poslits, neglits) =
- signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
- | signed_lits_aux (Const(@{const_name Not},_) $ P) (poslits, neglits) = (poslits, P::neglits)
- | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
-
-fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
-
-(*Literals like X=X are tautologous*)
-fun taut_poslit (Const(@{const_name HOL.eq},_) $ t $ u) = t aconv u
- | taut_poslit (Const(@{const_name True},_)) = true
- | taut_poslit _ = false;
-
-fun is_taut th =
- let val (poslits,neglits) = signed_lits th
- in exists taut_poslit poslits
- orelse
- exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
- end
- handle TERM _ => false; (*probably dest_Trueprop on a weird theorem*)
-
-
-(*** To remove trivial negated equality literals from clauses ***)
-
-(*They are typically functional reflexivity axioms and are the converses of
- injectivity equivalences*)
-
-val not_refl_disj_D = @{thm meson_not_refl_disj_D};
-
-(*Is either term a Var that does not properly occur in the other term?*)
-fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
- | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
- | eliminable _ = false;
-
-fun refl_clause_aux 0 th = th
- | refl_clause_aux n th =
- case HOLogic.dest_Trueprop (concl_of th) of
- (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _) =>
- refl_clause_aux n (th RS disj_assoc) (*isolate an atom as first disjunct*)
- | (Const (@{const_name HOL.disj}, _) $ (Const(@{const_name Not},_) $ (Const(@{const_name HOL.eq},_) $ t $ u)) $ _) =>
- if eliminable(t,u)
- then refl_clause_aux (n-1) (th RS not_refl_disj_D) (*Var inequation: delete*)
- else refl_clause_aux (n-1) (th RS disj_comm) (*not between Vars: ignore*)
- | (Const (@{const_name HOL.disj}, _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
- | _ => (*not a disjunction*) th;
-
-fun notequal_lits_count (Const (@{const_name HOL.disj}, _) $ P $ Q) =
- notequal_lits_count P + notequal_lits_count Q
- | notequal_lits_count (Const(@{const_name Not},_) $ (Const(@{const_name HOL.eq},_) $ _ $ _)) = 1
- | notequal_lits_count _ = 0;
-
-(*Simplify a clause by applying reflexivity to its negated equality literals*)
-fun refl_clause th =
- let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
- in zero_var_indexes (refl_clause_aux neqs th) end
- handle TERM _ => th; (*probably dest_Trueprop on a weird theorem*)
-
-
-(*** Removal of duplicate literals ***)
-
-(*Forward proof, passing extra assumptions as theorems to the tactic*)
-fun forward_res2 nf hyps st =
- case Seq.pull
- (REPEAT
- (Misc_Legacy.METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
- st)
- of SOME(th,_) => th
- | NONE => raise THM("forward_res2", 0, [st]);
-
-(*Remove duplicates in P|Q by assuming ~P in Q
- rls (initially []) accumulates assumptions of the form P==>False*)
-fun nodups_aux ctxt rls th = nodups_aux ctxt rls (th RS disj_assoc)
- handle THM _ => tryres(th,rls)
- handle THM _ => tryres(forward_res2 (nodups_aux ctxt) rls (th RS disj_forward2),
- [disj_FalseD1, disj_FalseD2, asm_rl])
- handle THM _ => th;
-
-(*Remove duplicate literals, if there are any*)
-fun nodups ctxt th =
- if has_duplicates (op =) (literals (prop_of th))
- then nodups_aux ctxt [] th
- else th;
-
-
-(*** The basic CNF transformation ***)
-
-fun estimated_num_clauses bound t =
- let
- fun sum x y = if x < bound andalso y < bound then x+y else bound
- fun prod x y = if x < bound andalso y < bound then x*y else bound
-
- (*Estimate the number of clauses in order to detect infeasible theorems*)
- fun signed_nclauses b (Const(@{const_name Trueprop},_) $ t) = signed_nclauses b t
- | signed_nclauses b (Const(@{const_name Not},_) $ t) = signed_nclauses (not b) t
- | signed_nclauses b (Const(@{const_name HOL.conj},_) $ t $ u) =
- if b then sum (signed_nclauses b t) (signed_nclauses b u)
- else prod (signed_nclauses b t) (signed_nclauses b u)
- | signed_nclauses b (Const(@{const_name HOL.disj},_) $ t $ u) =
- if b then prod (signed_nclauses b t) (signed_nclauses b u)
- else sum (signed_nclauses b t) (signed_nclauses b u)
- | signed_nclauses b (Const(@{const_name HOL.implies},_) $ t $ u) =
- if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
- else sum (signed_nclauses (not b) t) (signed_nclauses b u)
- | signed_nclauses b (Const(@{const_name HOL.eq}, Type ("fun", [T, _])) $ t $ u) =
- if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
- if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
- (prod (signed_nclauses (not b) u) (signed_nclauses b t))
- else sum (prod (signed_nclauses b t) (signed_nclauses b u))
- (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
- else 1
- | signed_nclauses b (Const(@{const_name Ex}, _) $ Abs (_,_,t)) = signed_nclauses b t
- | signed_nclauses b (Const(@{const_name All},_) $ Abs (_,_,t)) = signed_nclauses b t
- | signed_nclauses _ _ = 1; (* literal *)
- in signed_nclauses true t end
-
-fun has_too_many_clauses ctxt t =
- let val max_cl = Config.get ctxt max_clauses in
- estimated_num_clauses (max_cl + 1) t > max_cl
- end
-
-(*Replaces universally quantified variables by FREE variables -- because
- assumptions may not contain scheme variables. Later, generalize using Variable.export. *)
-local
- val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
- val spec_varT = #T (Thm.rep_cterm spec_var);
- fun name_of (Const (@{const_name All}, _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
-in
- fun freeze_spec th ctxt =
- let
- val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
- val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
- val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
- in (th RS spec', ctxt') end
-end;
-
-(*Used with METAHYPS below. There is one assumption, which gets bound to prem
- and then normalized via function nf. The normal form is given to resolve_tac,
- instantiate a Boolean variable created by resolution with disj_forward. Since
- (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
-fun resop nf [prem] = resolve_tac (nf prem) 1;
-
-(* Any need to extend this list with "HOL.type_class", "HOL.eq_class",
- and "Pure.term"? *)
-val has_meta_conn = exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
-
-fun apply_skolem_theorem (th, rls) =
- let
- fun tryall [] = raise THM ("apply_skolem_theorem", 0, th::rls)
- | tryall (rl :: rls) =
- first_order_resolve th rl handle THM _ => tryall rls
- in tryall rls end
-
-(* Conjunctive normal form, adding clauses from th in front of ths (for foldr).
- Strips universal quantifiers and breaks up conjunctions.
- Eliminates existential quantifiers using Skolemization theorems. *)
-fun cnf old_skolem_ths ctxt (th, ths) =
- let val ctxtr = Unsynchronized.ref ctxt (* FIXME ??? *)
- fun cnf_aux (th,ths) =
- if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
- else if not (has_conns [@{const_name All}, @{const_name Ex}, @{const_name HOL.conj}] (prop_of th))
- then nodups ctxt th :: ths (*no work to do, terminate*)
- else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
- Const (@{const_name HOL.conj}, _) => (*conjunction*)
- cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
- | Const (@{const_name All}, _) => (*universal quantifier*)
- let val (th',ctxt') = freeze_spec th (!ctxtr)
- in ctxtr := ctxt'; cnf_aux (th', ths) end
- | Const (@{const_name Ex}, _) =>
- (*existential quantifier: Insert Skolem functions*)
- cnf_aux (apply_skolem_theorem (th, old_skolem_ths), ths)
- | Const (@{const_name HOL.disj}, _) =>
- (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
- all combinations of converting P, Q to CNF.*)
- let val tac =
- Misc_Legacy.METAHYPS (resop cnf_nil) 1 THEN
- (fn st' => st' |> Misc_Legacy.METAHYPS (resop cnf_nil) 1)
- in Seq.list_of (tac (th RS disj_forward)) @ ths end
- | _ => nodups ctxt th :: ths (*no work to do*)
- and cnf_nil th = cnf_aux (th,[])
- val cls =
- if has_too_many_clauses ctxt (concl_of th)
- then (trace_msg (fn () => "cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
- else cnf_aux (th,ths)
- in (cls, !ctxtr) end;
-
-fun make_cnf old_skolem_ths th ctxt = cnf old_skolem_ths ctxt (th, [])
-
-(*Generalization, removal of redundant equalities, removal of tautologies.*)
-fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
-
-
-(**** Generation of contrapositives ****)
-
-fun is_left (Const (@{const_name Trueprop}, _) $
- (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _)) = true
- | is_left _ = false;
-
-(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
-fun assoc_right th =
- if is_left (prop_of th) then assoc_right (th RS disj_assoc)
- else th;
-
-(*Must check for negative literal first!*)
-val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
-
-(*For ordinary resolution. *)
-val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
-
-(*Create a goal or support clause, conclusing False*)
-fun make_goal th = (*Must check for negative literal first!*)
- make_goal (tryres(th, clause_rules))
- handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
-
-(*Sort clauses by number of literals*)
-fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
-
-fun sort_clauses ths = sort (make_ord fewerlits) ths;
-
-fun has_bool @{typ bool} = true
- | has_bool (Type (_, Ts)) = exists has_bool Ts
- | has_bool _ = false
-
-fun has_fun (Type (@{type_name fun}, _)) = true
- | has_fun (Type (_, Ts)) = exists has_fun Ts
- | has_fun _ = false
-
-(*Is the string the name of a connective? Really only | and Not can remain,
- since this code expects to be called on a clause form.*)
-val is_conn = member (op =)
- [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
- @{const_name HOL.implies}, @{const_name Not},
- @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex}];
-
-(*True if the term contains a function--not a logical connective--where the type
- of any argument contains bool.*)
-val has_bool_arg_const =
- exists_Const
- (fn (c,T) => not(is_conn c) andalso exists has_bool (binder_types T));
-
-(*A higher-order instance of a first-order constant? Example is the definition of
- one, 1, at a function type in theory Function_Algebras.*)
-fun higher_inst_const thy (c,T) =
- case binder_types T of
- [] => false (*not a function type, OK*)
- | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
-
-(*Returns false if any Vars in the theorem mention type bool.
- Also rejects functions whose arguments are Booleans or other functions.*)
-fun is_fol_term thy t =
- Term.is_first_order ["all", @{const_name All}, @{const_name Ex}] t andalso
- not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
- | _ => false) t orelse
- has_bool_arg_const t orelse
- exists_Const (higher_inst_const thy) t orelse
- has_meta_conn t);
-
-fun rigid t = not (is_Var (head_of t));
-
-fun ok4horn (Const (@{const_name Trueprop},_) $ (Const (@{const_name HOL.disj}, _) $ t $ _)) = rigid t
- | ok4horn (Const (@{const_name Trueprop},_) $ t) = rigid t
- | ok4horn _ = false;
-
-(*Create a meta-level Horn clause*)
-fun make_horn crules th =
- if ok4horn (concl_of th)
- then make_horn crules (tryres(th,crules)) handle THM _ => th
- else th;
-
-(*Generate Horn clauses for all contrapositives of a clause. The input, th,
- is a HOL disjunction.*)
-fun add_contras crules th hcs =
- let fun rots (0,_) = hcs
- | rots (k,th) = zero_var_indexes (make_horn crules th) ::
- rots(k-1, assoc_right (th RS disj_comm))
- in case nliterals(prop_of th) of
- 1 => th::hcs
- | n => rots(n, assoc_right th)
- end;
-
-(*Use "theorem naming" to label the clauses*)
-fun name_thms label =
- let fun name1 th (k, ths) =
- (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
- in fn ths => #2 (fold_rev name1 ths (length ths, [])) end;
-
-(*Is the given disjunction an all-negative support clause?*)
-fun is_negative th = forall (not o #1) (literals (prop_of th));
-
-val neg_clauses = filter is_negative;
-
-
-(***** MESON PROOF PROCEDURE *****)
-
-fun rhyps (Const("==>",_) $ (Const(@{const_name Trueprop},_) $ A) $ phi,
- As) = rhyps(phi, A::As)
- | rhyps (_, As) = As;
-
-(** Detecting repeated assumptions in a subgoal **)
-
-(*The stringtree detects repeated assumptions.*)
-fun ins_term t net = Net.insert_term (op aconv) (t, t) net;
-
-(*detects repetitions in a list of terms*)
-fun has_reps [] = false
- | has_reps [_] = false
- | has_reps [t,u] = (t aconv u)
- | has_reps ts = (fold ins_term ts Net.empty; false) handle Net.INSERT => true;
-
-(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
-fun TRYING_eq_assume_tac 0 st = Seq.single st
- | TRYING_eq_assume_tac i st =
- TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
- handle THM _ => TRYING_eq_assume_tac (i-1) st;
-
-fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
-
-(*Loop checking: FAIL if trying to prove the same thing twice
- -- if *ANY* subgoal has repeated literals*)
-fun check_tac st =
- if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
- then Seq.empty else Seq.single st;
-
-
-(* net_resolve_tac actually made it slower... *)
-fun prolog_step_tac horns i =
- (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
- TRYALL_eq_assume_tac;
-
-(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
-fun addconcl prem sz = size_of_term (Logic.strip_assums_concl prem) + sz;
-
-fun size_of_subgoals st = fold_rev addconcl (prems_of st) 0;
-
-
-(*Negation Normal Form*)
-val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
- not_impD, not_iffD, not_allD, not_exD, not_notD];
-
-fun ok4nnf (Const (@{const_name Trueprop},_) $ (Const (@{const_name Not}, _) $ t)) = rigid t
- | ok4nnf (Const (@{const_name Trueprop},_) $ t) = rigid t
- | ok4nnf _ = false;
-
-fun make_nnf1 ctxt th =
- if ok4nnf (concl_of th)
- then make_nnf1 ctxt (tryres(th, nnf_rls))
- handle THM ("tryres", _, _) =>
- forward_res ctxt (make_nnf1 ctxt)
- (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
- handle THM ("tryres", _, _) => th
- else th
-
-(*The simplification removes defined quantifiers and occurrences of True and False.
- nnf_ss also includes the one-point simprocs,
- which are needed to avoid the various one-point theorems from generating junk clauses.*)
-val nnf_simps =
- @{thms simp_implies_def Ex1_def Ball_def Bex_def if_True if_False if_cancel
- if_eq_cancel cases_simp}
-val nnf_extra_simps = @{thms split_ifs ex_simps all_simps simp_thms}
-
-val nnf_ss =
- HOL_basic_ss addsimps nnf_extra_simps
- addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
-
-val presimplify =
- rewrite_rule (map safe_mk_meta_eq nnf_simps) #> simplify nnf_ss
-
-fun make_nnf ctxt th = case prems_of th of
- [] => th |> presimplify |> make_nnf1 ctxt
- | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
-
-(* Pull existential quantifiers to front. This accomplishes Skolemization for
- clauses that arise from a subgoal. *)
-fun skolemize_with_choice_thms ctxt choice_ths =
- let
- fun aux th =
- if not (has_conns [@{const_name Ex}] (prop_of th)) then
- th
- else
- tryres (th, choice_ths @
- [conj_exD1, conj_exD2, disj_exD, disj_exD1, disj_exD2])
- |> aux
- handle THM ("tryres", _, _) =>
- tryres (th, [conj_forward, disj_forward, all_forward])
- |> forward_res ctxt aux
- |> aux
- handle THM ("tryres", _, _) =>
- rename_bvs_RS th ex_forward
- |> forward_res ctxt aux
- in aux o make_nnf ctxt end
-
-fun skolemize ctxt = skolemize_with_choice_thms ctxt (Meson_Choices.get ctxt)
-
-(* "RS" can fail if "unify_search_bound" is too small. *)
-fun try_skolemize ctxt th =
- try (skolemize ctxt) th
- |> tap (fn NONE => trace_msg (fn () => "Failed to skolemize " ^
- Display.string_of_thm ctxt th)
- | _ => ())
-
-fun add_clauses th cls =
- let val ctxt0 = Variable.global_thm_context th
- val (cnfs, ctxt) = make_cnf [] th ctxt0
- in Variable.export ctxt ctxt0 cnfs @ cls end;
-
-(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
- The resulting clauses are HOL disjunctions.*)
-fun make_clauses_unsorted ths = fold_rev add_clauses ths [];
-val make_clauses = sort_clauses o make_clauses_unsorted;
-
-(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
-fun make_horns ths =
- name_thms "Horn#"
- (distinct Thm.eq_thm_prop (fold_rev (add_contras clause_rules) ths []));
-
-(*Could simply use nprems_of, which would count remaining subgoals -- no
- discrimination as to their size! With BEST_FIRST, fails for problem 41.*)
-
-fun best_prolog_tac sizef horns =
- BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
-
-fun depth_prolog_tac horns =
- DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
-
-(*Return all negative clauses, as possible goal clauses*)
-fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
-
-fun skolemize_prems_tac ctxt prems =
- cut_facts_tac (map_filter (try_skolemize ctxt) prems) THEN' REPEAT o etac exE
-
-(*Basis of all meson-tactics. Supplies cltac with clauses: HOL disjunctions.
- Function mkcl converts theorems to clauses.*)
-fun MESON preskolem_tac mkcl cltac ctxt i st =
- SELECT_GOAL
- (EVERY [Object_Logic.atomize_prems_tac 1,
- rtac ccontr 1,
- preskolem_tac,
- Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
- EVERY1 [skolemize_prems_tac ctxt negs,
- Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
- handle THM _ => no_tac st; (*probably from make_meta_clause, not first-order*)
-
-
-(** Best-first search versions **)
-
-(*ths is a list of additional clauses (HOL disjunctions) to use.*)
-fun best_meson_tac sizef =
- MESON all_tac make_clauses
- (fn cls =>
- THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
- (has_fewer_prems 1, sizef)
- (prolog_step_tac (make_horns cls) 1));
-
-(*First, breaks the goal into independent units*)
-fun safe_best_meson_tac ctxt =
- SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
- TRYALL (best_meson_tac size_of_subgoals ctxt));
-
-(** Depth-first search version **)
-
-val depth_meson_tac =
- MESON all_tac make_clauses
- (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
-
-
-(** Iterative deepening version **)
-
-(*This version does only one inference per call;
- having only one eq_assume_tac speeds it up!*)
-fun prolog_step_tac' horns =
- let val (horn0s, _) = (*0 subgoals vs 1 or more*)
- take_prefix Thm.no_prems horns
- val nrtac = net_resolve_tac horns
- in fn i => eq_assume_tac i ORELSE
- match_tac horn0s i ORELSE (*no backtracking if unit MATCHES*)
- ((assume_tac i APPEND nrtac i) THEN check_tac)
- end;
-
-fun iter_deepen_prolog_tac horns =
- ITER_DEEPEN iter_deepen_limit (has_fewer_prems 1) (prolog_step_tac' horns);
-
-fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON all_tac make_clauses
- (fn cls =>
- (case (gocls (cls @ ths)) of
- [] => no_tac (*no goal clauses*)
- | goes =>
- let
- val horns = make_horns (cls @ ths)
- val _ = trace_msg (fn () =>
- cat_lines ("meson method called:" ::
- map (Display.string_of_thm ctxt) (cls @ ths) @
- ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
- in
- THEN_ITER_DEEPEN iter_deepen_limit
- (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
- end));
-
-fun meson_tac ctxt ths =
- SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
-
-
-(**** Code to support ordinary resolution, rather than Model Elimination ****)
-
-(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
- with no contrapositives, for ordinary resolution.*)
-
-(*Rules to convert the head literal into a negated assumption. If the head
- literal is already negated, then using notEfalse instead of notEfalse'
- prevents a double negation.*)
-val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
-val notEfalse' = rotate_prems 1 notEfalse;
-
-fun negated_asm_of_head th =
- th RS notEfalse handle THM _ => th RS notEfalse';
-
-(*Converting one theorem from a disjunction to a meta-level clause*)
-fun make_meta_clause th =
- let val (fth,thaw) = Drule.legacy_freeze_thaw_robust th
- in
- (zero_var_indexes o Thm.varifyT_global o thaw 0 o
- negated_asm_of_head o make_horn resolution_clause_rules) fth
- end;
-
-fun make_meta_clauses ths =
- name_thms "MClause#"
- (distinct Thm.eq_thm_prop (map make_meta_clause ths));
-
-end;