# HG changeset patch
# User blanchet
# Date 1286221062 -7200
# Node ID 1f01c9b2b76b8f929b13ad59e5435209e82cb12a
# Parent  6e9aff5ee9b5d90e979ee1ebee2715ec57498280
move MESON files together

diff -r 6e9aff5ee9b5 -r 1f01c9b2b76b src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Mon Oct 04 20:55:55 2010 +0200
+++ b/src/HOL/IsaMakefile	Mon Oct 04 21:37:42 2010 +0200
@@ -201,6 +201,8 @@
   Tools/inductive_realizer.ML \
   Tools/inductive_set.ML \
   Tools/lin_arith.ML \
+  Tools/Meson/meson.ML \
+  Tools/Meson/meson_clausify.ML \
   Tools/nat_arith.ML \
   Tools/primrec.ML \
   Tools/prop_logic.ML \
@@ -275,7 +277,6 @@
   Tools/int_arith.ML \
   Tools/groebner.ML \
   Tools/list_code.ML \
-  Tools/meson.ML \
   Tools/nat_numeral_simprocs.ML \
   Tools/Nitpick/kodkod.ML \
   Tools/Nitpick/kodkod_sat.ML \
@@ -315,7 +316,6 @@
   Tools/recdef.ML \
   Tools/record.ML \
   Tools/semiring_normalizer.ML \
-  Tools/Sledgehammer/meson_clausify.ML \
   Tools/Sledgehammer/metis_reconstruct.ML \
   Tools/Sledgehammer/metis_translate.ML \
   Tools/Sledgehammer/metis_tactics.ML \
diff -r 6e9aff5ee9b5 -r 1f01c9b2b76b src/HOL/Tools/Meson/meson.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Meson/meson.ML	Mon Oct 04 21:37:42 2010 +0200
@@ -0,0 +1,712 @@
+(*  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;
diff -r 6e9aff5ee9b5 -r 1f01c9b2b76b src/HOL/Tools/Meson/meson_clausify.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Meson/meson_clausify.ML	Mon Oct 04 21:37:42 2010 +0200
@@ -0,0 +1,376 @@
+(*  Title:      HOL/Tools/Sledgehammer/meson_clausify.ML
+    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
+    Author:     Jasmin Blanchette, TU Muenchen
+
+Transformation of axiom rules (elim/intro/etc) into CNF forms.
+*)
+
+signature MESON_CLAUSIFY =
+sig
+  val new_skolem_var_prefix : string
+  val extensionalize_theorem : thm -> thm
+  val introduce_combinators_in_cterm : cterm -> thm
+  val introduce_combinators_in_theorem : thm -> thm
+  val to_definitional_cnf_with_quantifiers : theory -> thm -> thm
+  val cluster_of_zapped_var_name : string -> (int * (int * int)) * bool
+  val cnf_axiom :
+    Proof.context -> bool -> int -> thm -> (thm * term) option * thm list
+  val meson_general_tac : Proof.context -> thm list -> int -> tactic
+  val setup: theory -> theory
+end;
+
+structure Meson_Clausify : MESON_CLAUSIFY =
+struct
+
+(* the extra "?" helps prevent clashes *)
+val new_skolem_var_prefix = "?SK"
+val new_nonskolem_var_prefix = "?V"
+
+(**** Transformation of Elimination Rules into First-Order Formulas****)
+
+val cfalse = cterm_of @{theory HOL} HOLogic.false_const;
+val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const);
+
+(* Converts an elim-rule into an equivalent theorem that does not have the
+   predicate variable. Leaves other theorems unchanged. We simply instantiate
+   the conclusion variable to False. (Cf. "transform_elim_term" in
+   "Sledgehammer_Util".) *)
+fun transform_elim_theorem th =
+  case concl_of th of    (*conclusion variable*)
+       @{const Trueprop} $ (v as Var (_, @{typ bool})) =>
+           Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th
+    | v as Var(_, @{typ prop}) =>
+           Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th
+    | _ => th
+
+
+(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
+
+fun mk_old_skolem_term_wrapper t =
+  let val T = fastype_of t in
+    Const (@{const_name skolem}, T --> T) $ t
+  end
+
+fun beta_eta_in_abs_body (Abs (s, T, t')) = Abs (s, T, beta_eta_in_abs_body t')
+  | beta_eta_in_abs_body t = Envir.beta_eta_contract t
+
+(*Traverse a theorem, accumulating Skolem function definitions.*)
+fun old_skolem_defs th =
+  let
+    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (_, T, p))) rhss =
+        (*Existential: declare a Skolem function, then insert into body and continue*)
+        let
+          val args = OldTerm.term_frees body
+          (* Forms a lambda-abstraction over the formal parameters *)
+          val rhs =
+            list_abs_free (map dest_Free args,
+                           HOLogic.choice_const T $ beta_eta_in_abs_body body)
+            |> mk_old_skolem_term_wrapper
+          val comb = list_comb (rhs, args)
+        in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end
+      | dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) rhss =
+        (*Universal quant: insert a free variable into body and continue*)
+        let val fname = Name.variant (OldTerm.add_term_names (p,[])) a
+        in dec_sko (subst_bound (Free(fname,T), p)) rhss end
+      | dec_sko (@{const conj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q
+      | dec_sko (@{const disj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q
+      | dec_sko (@{const Trueprop} $ p) rhss = dec_sko p rhss
+      | dec_sko _ rhss = rhss
+  in  dec_sko (prop_of th) []  end;
+
+
+(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
+
+val fun_cong_all = @{thm fun_eq_iff [THEN iffD1]}
+
+(* Removes the lambdas from an equation of the form "t = (%x. u)".
+   (Cf. "extensionalize_term" in "Sledgehammer_Translate".) *)
+fun extensionalize_theorem th =
+  case prop_of th of
+    _ $ (Const (@{const_name HOL.eq}, Type (_, [Type (@{type_name fun}, _), _]))
+         $ _ $ Abs _) => extensionalize_theorem (th RS fun_cong_all)
+  | _ => th
+
+fun is_quasi_lambda_free (Const (@{const_name skolem}, _) $ _) = true
+  | is_quasi_lambda_free (t1 $ t2) =
+    is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2
+  | is_quasi_lambda_free (Abs _) = false
+  | is_quasi_lambda_free _ = true
+
+val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B}));
+val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
+val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
+
+(* FIXME: Requires more use of cterm constructors. *)
+fun abstract ct =
+  let
+      val thy = theory_of_cterm ct
+      val Abs(x,_,body) = term_of ct
+      val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct)
+      val cxT = ctyp_of thy xT
+      val cbodyT = ctyp_of thy bodyT
+      fun makeK () =
+        instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)]
+                     @{thm abs_K}
+  in
+      case body of
+          Const _ => makeK()
+        | Free _ => makeK()
+        | Var _ => makeK()  (*though Var isn't expected*)
+        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
+        | rator$rand =>
+            if loose_bvar1 (rator,0) then (*C or S*)
+               if loose_bvar1 (rand,0) then (*S*)
+                 let val crator = cterm_of thy (Abs(x,xT,rator))
+                     val crand = cterm_of thy (Abs(x,xT,rand))
+                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
+                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
+                 in
+                   Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
+                 end
+               else (*C*)
+                 let val crator = cterm_of thy (Abs(x,xT,rator))
+                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
+                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
+                 in
+                   Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
+                 end
+            else if loose_bvar1 (rand,0) then (*B or eta*)
+               if rand = Bound 0 then Thm.eta_conversion ct
+               else (*B*)
+                 let val crand = cterm_of thy (Abs(x,xT,rand))
+                     val crator = cterm_of thy rator
+                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
+                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
+                 in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end
+            else makeK()
+        | _ => raise Fail "abstract: Bad term"
+  end;
+
+(* Traverse a theorem, remplacing lambda-abstractions with combinators. *)
+fun introduce_combinators_in_cterm ct =
+  if is_quasi_lambda_free (term_of ct) then
+    Thm.reflexive ct
+  else case term_of ct of
+    Abs _ =>
+    let
+      val (cv, cta) = Thm.dest_abs NONE ct
+      val (v, _) = dest_Free (term_of cv)
+      val u_th = introduce_combinators_in_cterm cta
+      val cu = Thm.rhs_of u_th
+      val comb_eq = abstract (Thm.cabs cv cu)
+    in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end
+  | _ $ _ =>
+    let val (ct1, ct2) = Thm.dest_comb ct in
+        Thm.combination (introduce_combinators_in_cterm ct1)
+                        (introduce_combinators_in_cterm ct2)
+    end
+
+fun introduce_combinators_in_theorem th =
+  if is_quasi_lambda_free (prop_of th) then
+    th
+  else
+    let
+      val th = Drule.eta_contraction_rule th
+      val eqth = introduce_combinators_in_cterm (cprop_of th)
+    in Thm.equal_elim eqth th end
+    handle THM (msg, _, _) =>
+           (warning ("Error in the combinator translation of " ^
+                     Display.string_of_thm_without_context th ^
+                     "\nException message: " ^ msg ^ ".");
+            (* A type variable of sort "{}" will make abstraction fail. *)
+            TrueI)
+
+(*cterms are used throughout for efficiency*)
+val cTrueprop = cterm_of @{theory HOL} HOLogic.Trueprop;
+
+(*Given an abstraction over n variables, replace the bound variables by free
+  ones. Return the body, along with the list of free variables.*)
+fun c_variant_abs_multi (ct0, vars) =
+      let val (cv,ct) = Thm.dest_abs NONE ct0
+      in  c_variant_abs_multi (ct, cv::vars)  end
+      handle CTERM _ => (ct0, rev vars);
+
+val skolem_def_raw = @{thms skolem_def_raw}
+
+(* Given the definition of a Skolem function, return a theorem to replace
+   an existential formula by a use of that function.
+   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
+fun old_skolem_theorem_from_def thy rhs0 =
+  let
+    val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> cterm_of thy
+    val rhs' = rhs |> Thm.dest_comb |> snd
+    val (ch, frees) = c_variant_abs_multi (rhs', [])
+    val (hilbert, cabs) = ch |> Thm.dest_comb |>> term_of
+    val T =
+      case hilbert of
+        Const (@{const_name Eps}, Type (@{type_name fun}, [_, T])) => T
+      | _ => raise TERM ("old_skolem_theorem_from_def: expected \"Eps\"",
+                         [hilbert])
+    val cex = cterm_of thy (HOLogic.exists_const T)
+    val ex_tm = Thm.capply cTrueprop (Thm.capply cex cabs)
+    val conc =
+      Drule.list_comb (rhs, frees)
+      |> Drule.beta_conv cabs |> Thm.capply cTrueprop
+    fun tacf [prem] =
+      rewrite_goals_tac skolem_def_raw
+      THEN rtac ((prem |> rewrite_rule skolem_def_raw) RS @{thm someI_ex}) 1
+  in
+    Goal.prove_internal [ex_tm] conc tacf
+    |> forall_intr_list frees
+    |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
+    |> Thm.varifyT_global
+  end
+
+fun to_definitional_cnf_with_quantifiers thy th =
+  let
+    val eqth = cnf.make_cnfx_thm thy (HOLogic.dest_Trueprop (prop_of th))
+    val eqth = eqth RS @{thm eq_reflection}
+    val eqth = eqth RS @{thm TruepropI}
+  in Thm.equal_elim eqth th end
+
+fun zapped_var_name ((ax_no, cluster_no), skolem) index_no s =
+  (if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^
+  "_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^
+  string_of_int index_no ^ "_" ^ s
+
+fun cluster_of_zapped_var_name s =
+  let val get_int = the o Int.fromString o nth (space_explode "_" s) in
+    ((get_int 1, (get_int 2, get_int 3)),
+     String.isPrefix new_skolem_var_prefix s)
+  end
+
+fun zap (cluster as (cluster_no, cluster_skolem)) index_no pos ct =
+  ct
+  |> (case term_of ct of
+        Const (s, _) $ Abs (s', _, _) =>
+        if s = @{const_name all} orelse s = @{const_name All} orelse
+           s = @{const_name Ex} then
+          let
+            val skolem = (pos = (s = @{const_name Ex}))
+            val (cluster, index_no) =
+              if skolem = cluster_skolem then (cluster, index_no)
+              else ((cluster_no ||> cluster_skolem ? Integer.add 1, skolem), 0)
+          in
+            Thm.dest_comb #> snd
+            #> Thm.dest_abs (SOME (zapped_var_name cluster index_no s'))
+            #> snd #> zap cluster (index_no + 1) pos
+          end
+        else
+          Conv.all_conv
+      | Const (s, _) $ _ $ _ =>
+        if s = @{const_name "==>"} orelse s = @{const_name implies} then
+          Conv.combination_conv (Conv.arg_conv (zap cluster index_no (not pos)))
+                                (zap cluster index_no pos)
+        else if s = @{const_name conj} orelse s = @{const_name disj} then
+          Conv.combination_conv (Conv.arg_conv (zap cluster index_no pos))
+                                (zap cluster index_no pos)
+        else
+          Conv.all_conv
+      | Const (s, _) $ _ =>
+        if s = @{const_name Trueprop} then
+          Conv.arg_conv (zap cluster index_no pos)
+        else if s = @{const_name Not} then
+          Conv.arg_conv (zap cluster index_no (not pos))
+        else
+          Conv.all_conv
+      | _ => Conv.all_conv)
+
+fun ss_only ths = MetaSimplifier.clear_ss HOL_basic_ss addsimps ths
+
+val no_choice =
+  @{prop "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)"}
+  |> Logic.varify_global
+  |> Skip_Proof.make_thm @{theory}
+
+(* Converts an Isabelle theorem into NNF. *)
+fun nnf_axiom choice_ths new_skolemizer ax_no th ctxt =
+  let
+    val thy = ProofContext.theory_of ctxt
+    val th =
+      th |> transform_elim_theorem
+         |> zero_var_indexes
+         |> new_skolemizer ? forall_intr_vars
+    val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single
+    val th = th |> Conv.fconv_rule Object_Logic.atomize
+                |> extensionalize_theorem
+                |> Meson.make_nnf ctxt
+  in
+    if new_skolemizer then
+      let
+        fun skolemize choice_ths =
+          Meson.skolemize_with_choice_thms ctxt choice_ths
+          #> simplify (ss_only @{thms all_simps[symmetric]})
+        val pull_out =
+          simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]})
+        val (discharger_th, fully_skolemized_th) =
+          if null choice_ths then
+            th |> `I |>> pull_out ||> skolemize [no_choice]
+          else
+            th |> skolemize choice_ths |> `I
+        val t =
+          fully_skolemized_th |> cprop_of
+          |> zap ((ax_no, 0), true) 0 true |> Drule.export_without_context
+          |> cprop_of |> Thm.dest_equals |> snd |> term_of
+      in
+        if exists_subterm (fn Var ((s, _), _) =>
+                              String.isPrefix new_skolem_var_prefix s
+                            | _ => false) t then
+          let
+            val (ct, ctxt) =
+              Variable.import_terms true [t] ctxt
+              |>> the_single |>> cterm_of thy
+          in (SOME (discharger_th, ct), Thm.assume ct, ctxt) end
+       else
+         (NONE, th, ctxt)
+      end
+    else
+      (NONE, th, ctxt)
+  end
+
+(* Convert a theorem to CNF, with additional premises due to skolemization. *)
+fun cnf_axiom ctxt0 new_skolemizer ax_no th =
+  let
+    val thy = ProofContext.theory_of ctxt0
+    val choice_ths = Meson_Choices.get ctxt0
+    val (opt, nnf_th, ctxt) = nnf_axiom choice_ths new_skolemizer ax_no th ctxt0
+    fun clausify th =
+      Meson.make_cnf (if new_skolemizer then
+                        []
+                      else
+                        map (old_skolem_theorem_from_def thy)
+                            (old_skolem_defs th)) th ctxt
+    val (cnf_ths, ctxt) =
+      clausify nnf_th
+      |> (fn ([], _) =>
+             clausify (to_definitional_cnf_with_quantifiers thy nnf_th)
+           | p => p)
+    fun intr_imp ct th =
+      Thm.instantiate ([], map (pairself (cterm_of @{theory}))
+                               [(Var (("i", 1), @{typ nat}),
+                                 HOLogic.mk_nat ax_no)])
+                      @{thm skolem_COMBK_D}
+      RS Thm.implies_intr ct th
+  in
+    (opt |> Option.map (I #>> singleton (Variable.export ctxt ctxt0)
+                        ##> (term_of #> HOLogic.dest_Trueprop
+                             #> singleton (Variable.export_terms ctxt ctxt0))),
+     cnf_ths |> map (introduce_combinators_in_theorem
+                     #> (case opt of SOME (_, ct) => intr_imp ct | NONE => I))
+             |> Variable.export ctxt ctxt0
+             |> Meson.finish_cnf
+             |> map Thm.close_derivation)
+  end
+  handle THM _ => (NONE, [])
+
+fun meson_general_tac ctxt ths =
+  let val ctxt = Classical.put_claset HOL_cs ctxt in
+    Meson.meson_tac ctxt (maps (snd o cnf_axiom ctxt false 0) ths)
+  end
+
+val setup =
+  Method.setup @{binding meson} (Attrib.thms >> (fn ths => fn ctxt =>
+     SIMPLE_METHOD' (CHANGED_PROP o meson_general_tac ctxt ths)))
+     "MESON resolution proof procedure"
+
+end;
diff -r 6e9aff5ee9b5 -r 1f01c9b2b76b src/HOL/Tools/Sledgehammer/meson_clausify.ML
--- a/src/HOL/Tools/Sledgehammer/meson_clausify.ML	Mon Oct 04 20:55:55 2010 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,376 +0,0 @@
-(*  Title:      HOL/Tools/Sledgehammer/meson_clausify.ML
-    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
-    Author:     Jasmin Blanchette, TU Muenchen
-
-Transformation of axiom rules (elim/intro/etc) into CNF forms.
-*)
-
-signature MESON_CLAUSIFY =
-sig
-  val new_skolem_var_prefix : string
-  val extensionalize_theorem : thm -> thm
-  val introduce_combinators_in_cterm : cterm -> thm
-  val introduce_combinators_in_theorem : thm -> thm
-  val to_definitional_cnf_with_quantifiers : theory -> thm -> thm
-  val cluster_of_zapped_var_name : string -> (int * (int * int)) * bool
-  val cnf_axiom :
-    Proof.context -> bool -> int -> thm -> (thm * term) option * thm list
-  val meson_general_tac : Proof.context -> thm list -> int -> tactic
-  val setup: theory -> theory
-end;
-
-structure Meson_Clausify : MESON_CLAUSIFY =
-struct
-
-(* the extra "?" helps prevent clashes *)
-val new_skolem_var_prefix = "?SK"
-val new_nonskolem_var_prefix = "?V"
-
-(**** Transformation of Elimination Rules into First-Order Formulas****)
-
-val cfalse = cterm_of @{theory HOL} HOLogic.false_const;
-val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const);
-
-(* Converts an elim-rule into an equivalent theorem that does not have the
-   predicate variable. Leaves other theorems unchanged. We simply instantiate
-   the conclusion variable to False. (Cf. "transform_elim_term" in
-   "Sledgehammer_Util".) *)
-fun transform_elim_theorem th =
-  case concl_of th of    (*conclusion variable*)
-       @{const Trueprop} $ (v as Var (_, @{typ bool})) =>
-           Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th
-    | v as Var(_, @{typ prop}) =>
-           Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th
-    | _ => th
-
-
-(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
-
-fun mk_old_skolem_term_wrapper t =
-  let val T = fastype_of t in
-    Const (@{const_name skolem}, T --> T) $ t
-  end
-
-fun beta_eta_in_abs_body (Abs (s, T, t')) = Abs (s, T, beta_eta_in_abs_body t')
-  | beta_eta_in_abs_body t = Envir.beta_eta_contract t
-
-(*Traverse a theorem, accumulating Skolem function definitions.*)
-fun old_skolem_defs th =
-  let
-    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (_, T, p))) rhss =
-        (*Existential: declare a Skolem function, then insert into body and continue*)
-        let
-          val args = OldTerm.term_frees body
-          (* Forms a lambda-abstraction over the formal parameters *)
-          val rhs =
-            list_abs_free (map dest_Free args,
-                           HOLogic.choice_const T $ beta_eta_in_abs_body body)
-            |> mk_old_skolem_term_wrapper
-          val comb = list_comb (rhs, args)
-        in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end
-      | dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) rhss =
-        (*Universal quant: insert a free variable into body and continue*)
-        let val fname = Name.variant (OldTerm.add_term_names (p,[])) a
-        in dec_sko (subst_bound (Free(fname,T), p)) rhss end
-      | dec_sko (@{const conj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q
-      | dec_sko (@{const disj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q
-      | dec_sko (@{const Trueprop} $ p) rhss = dec_sko p rhss
-      | dec_sko _ rhss = rhss
-  in  dec_sko (prop_of th) []  end;
-
-
-(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
-
-val fun_cong_all = @{thm fun_eq_iff [THEN iffD1]}
-
-(* Removes the lambdas from an equation of the form "t = (%x. u)".
-   (Cf. "extensionalize_term" in "Sledgehammer_Translate".) *)
-fun extensionalize_theorem th =
-  case prop_of th of
-    _ $ (Const (@{const_name HOL.eq}, Type (_, [Type (@{type_name fun}, _), _]))
-         $ _ $ Abs _) => extensionalize_theorem (th RS fun_cong_all)
-  | _ => th
-
-fun is_quasi_lambda_free (Const (@{const_name skolem}, _) $ _) = true
-  | is_quasi_lambda_free (t1 $ t2) =
-    is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2
-  | is_quasi_lambda_free (Abs _) = false
-  | is_quasi_lambda_free _ = true
-
-val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B}));
-val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
-val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
-
-(* FIXME: Requires more use of cterm constructors. *)
-fun abstract ct =
-  let
-      val thy = theory_of_cterm ct
-      val Abs(x,_,body) = term_of ct
-      val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct)
-      val cxT = ctyp_of thy xT
-      val cbodyT = ctyp_of thy bodyT
-      fun makeK () =
-        instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)]
-                     @{thm abs_K}
-  in
-      case body of
-          Const _ => makeK()
-        | Free _ => makeK()
-        | Var _ => makeK()  (*though Var isn't expected*)
-        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
-        | rator$rand =>
-            if loose_bvar1 (rator,0) then (*C or S*)
-               if loose_bvar1 (rand,0) then (*S*)
-                 let val crator = cterm_of thy (Abs(x,xT,rator))
-                     val crand = cterm_of thy (Abs(x,xT,rand))
-                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
-                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
-                 in
-                   Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
-                 end
-               else (*C*)
-                 let val crator = cterm_of thy (Abs(x,xT,rator))
-                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
-                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
-                 in
-                   Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
-                 end
-            else if loose_bvar1 (rand,0) then (*B or eta*)
-               if rand = Bound 0 then Thm.eta_conversion ct
-               else (*B*)
-                 let val crand = cterm_of thy (Abs(x,xT,rand))
-                     val crator = cterm_of thy rator
-                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
-                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
-                 in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end
-            else makeK()
-        | _ => raise Fail "abstract: Bad term"
-  end;
-
-(* Traverse a theorem, remplacing lambda-abstractions with combinators. *)
-fun introduce_combinators_in_cterm ct =
-  if is_quasi_lambda_free (term_of ct) then
-    Thm.reflexive ct
-  else case term_of ct of
-    Abs _ =>
-    let
-      val (cv, cta) = Thm.dest_abs NONE ct
-      val (v, _) = dest_Free (term_of cv)
-      val u_th = introduce_combinators_in_cterm cta
-      val cu = Thm.rhs_of u_th
-      val comb_eq = abstract (Thm.cabs cv cu)
-    in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end
-  | _ $ _ =>
-    let val (ct1, ct2) = Thm.dest_comb ct in
-        Thm.combination (introduce_combinators_in_cterm ct1)
-                        (introduce_combinators_in_cterm ct2)
-    end
-
-fun introduce_combinators_in_theorem th =
-  if is_quasi_lambda_free (prop_of th) then
-    th
-  else
-    let
-      val th = Drule.eta_contraction_rule th
-      val eqth = introduce_combinators_in_cterm (cprop_of th)
-    in Thm.equal_elim eqth th end
-    handle THM (msg, _, _) =>
-           (warning ("Error in the combinator translation of " ^
-                     Display.string_of_thm_without_context th ^
-                     "\nException message: " ^ msg ^ ".");
-            (* A type variable of sort "{}" will make abstraction fail. *)
-            TrueI)
-
-(*cterms are used throughout for efficiency*)
-val cTrueprop = cterm_of @{theory HOL} HOLogic.Trueprop;
-
-(*Given an abstraction over n variables, replace the bound variables by free
-  ones. Return the body, along with the list of free variables.*)
-fun c_variant_abs_multi (ct0, vars) =
-      let val (cv,ct) = Thm.dest_abs NONE ct0
-      in  c_variant_abs_multi (ct, cv::vars)  end
-      handle CTERM _ => (ct0, rev vars);
-
-val skolem_def_raw = @{thms skolem_def_raw}
-
-(* Given the definition of a Skolem function, return a theorem to replace
-   an existential formula by a use of that function.
-   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
-fun old_skolem_theorem_from_def thy rhs0 =
-  let
-    val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> cterm_of thy
-    val rhs' = rhs |> Thm.dest_comb |> snd
-    val (ch, frees) = c_variant_abs_multi (rhs', [])
-    val (hilbert, cabs) = ch |> Thm.dest_comb |>> term_of
-    val T =
-      case hilbert of
-        Const (@{const_name Eps}, Type (@{type_name fun}, [_, T])) => T
-      | _ => raise TERM ("old_skolem_theorem_from_def: expected \"Eps\"",
-                         [hilbert])
-    val cex = cterm_of thy (HOLogic.exists_const T)
-    val ex_tm = Thm.capply cTrueprop (Thm.capply cex cabs)
-    val conc =
-      Drule.list_comb (rhs, frees)
-      |> Drule.beta_conv cabs |> Thm.capply cTrueprop
-    fun tacf [prem] =
-      rewrite_goals_tac skolem_def_raw
-      THEN rtac ((prem |> rewrite_rule skolem_def_raw) RS @{thm someI_ex}) 1
-  in
-    Goal.prove_internal [ex_tm] conc tacf
-    |> forall_intr_list frees
-    |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
-    |> Thm.varifyT_global
-  end
-
-fun to_definitional_cnf_with_quantifiers thy th =
-  let
-    val eqth = cnf.make_cnfx_thm thy (HOLogic.dest_Trueprop (prop_of th))
-    val eqth = eqth RS @{thm eq_reflection}
-    val eqth = eqth RS @{thm TruepropI}
-  in Thm.equal_elim eqth th end
-
-fun zapped_var_name ((ax_no, cluster_no), skolem) index_no s =
-  (if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^
-  "_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^
-  string_of_int index_no ^ "_" ^ s
-
-fun cluster_of_zapped_var_name s =
-  let val get_int = the o Int.fromString o nth (space_explode "_" s) in
-    ((get_int 1, (get_int 2, get_int 3)),
-     String.isPrefix new_skolem_var_prefix s)
-  end
-
-fun zap (cluster as (cluster_no, cluster_skolem)) index_no pos ct =
-  ct
-  |> (case term_of ct of
-        Const (s, _) $ Abs (s', _, _) =>
-        if s = @{const_name all} orelse s = @{const_name All} orelse
-           s = @{const_name Ex} then
-          let
-            val skolem = (pos = (s = @{const_name Ex}))
-            val (cluster, index_no) =
-              if skolem = cluster_skolem then (cluster, index_no)
-              else ((cluster_no ||> cluster_skolem ? Integer.add 1, skolem), 0)
-          in
-            Thm.dest_comb #> snd
-            #> Thm.dest_abs (SOME (zapped_var_name cluster index_no s'))
-            #> snd #> zap cluster (index_no + 1) pos
-          end
-        else
-          Conv.all_conv
-      | Const (s, _) $ _ $ _ =>
-        if s = @{const_name "==>"} orelse s = @{const_name implies} then
-          Conv.combination_conv (Conv.arg_conv (zap cluster index_no (not pos)))
-                                (zap cluster index_no pos)
-        else if s = @{const_name conj} orelse s = @{const_name disj} then
-          Conv.combination_conv (Conv.arg_conv (zap cluster index_no pos))
-                                (zap cluster index_no pos)
-        else
-          Conv.all_conv
-      | Const (s, _) $ _ =>
-        if s = @{const_name Trueprop} then
-          Conv.arg_conv (zap cluster index_no pos)
-        else if s = @{const_name Not} then
-          Conv.arg_conv (zap cluster index_no (not pos))
-        else
-          Conv.all_conv
-      | _ => Conv.all_conv)
-
-fun ss_only ths = MetaSimplifier.clear_ss HOL_basic_ss addsimps ths
-
-val no_choice =
-  @{prop "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)"}
-  |> Logic.varify_global
-  |> Skip_Proof.make_thm @{theory}
-
-(* Converts an Isabelle theorem into NNF. *)
-fun nnf_axiom choice_ths new_skolemizer ax_no th ctxt =
-  let
-    val thy = ProofContext.theory_of ctxt
-    val th =
-      th |> transform_elim_theorem
-         |> zero_var_indexes
-         |> new_skolemizer ? forall_intr_vars
-    val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single
-    val th = th |> Conv.fconv_rule Object_Logic.atomize
-                |> extensionalize_theorem
-                |> Meson.make_nnf ctxt
-  in
-    if new_skolemizer then
-      let
-        fun skolemize choice_ths =
-          Meson.skolemize_with_choice_thms ctxt choice_ths
-          #> simplify (ss_only @{thms all_simps[symmetric]})
-        val pull_out =
-          simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]})
-        val (discharger_th, fully_skolemized_th) =
-          if null choice_ths then
-            th |> `I |>> pull_out ||> skolemize [no_choice]
-          else
-            th |> skolemize choice_ths |> `I
-        val t =
-          fully_skolemized_th |> cprop_of
-          |> zap ((ax_no, 0), true) 0 true |> Drule.export_without_context
-          |> cprop_of |> Thm.dest_equals |> snd |> term_of
-      in
-        if exists_subterm (fn Var ((s, _), _) =>
-                              String.isPrefix new_skolem_var_prefix s
-                            | _ => false) t then
-          let
-            val (ct, ctxt) =
-              Variable.import_terms true [t] ctxt
-              |>> the_single |>> cterm_of thy
-          in (SOME (discharger_th, ct), Thm.assume ct, ctxt) end
-       else
-         (NONE, th, ctxt)
-      end
-    else
-      (NONE, th, ctxt)
-  end
-
-(* Convert a theorem to CNF, with additional premises due to skolemization. *)
-fun cnf_axiom ctxt0 new_skolemizer ax_no th =
-  let
-    val thy = ProofContext.theory_of ctxt0
-    val choice_ths = Meson_Choices.get ctxt0
-    val (opt, nnf_th, ctxt) = nnf_axiom choice_ths new_skolemizer ax_no th ctxt0
-    fun clausify th =
-      Meson.make_cnf (if new_skolemizer then
-                        []
-                      else
-                        map (old_skolem_theorem_from_def thy)
-                            (old_skolem_defs th)) th ctxt
-    val (cnf_ths, ctxt) =
-      clausify nnf_th
-      |> (fn ([], _) =>
-             clausify (to_definitional_cnf_with_quantifiers thy nnf_th)
-           | p => p)
-    fun intr_imp ct th =
-      Thm.instantiate ([], map (pairself (cterm_of @{theory}))
-                               [(Var (("i", 1), @{typ nat}),
-                                 HOLogic.mk_nat ax_no)])
-                      @{thm skolem_COMBK_D}
-      RS Thm.implies_intr ct th
-  in
-    (opt |> Option.map (I #>> singleton (Variable.export ctxt ctxt0)
-                        ##> (term_of #> HOLogic.dest_Trueprop
-                             #> singleton (Variable.export_terms ctxt ctxt0))),
-     cnf_ths |> map (introduce_combinators_in_theorem
-                     #> (case opt of SOME (_, ct) => intr_imp ct | NONE => I))
-             |> Variable.export ctxt ctxt0
-             |> Meson.finish_cnf
-             |> map Thm.close_derivation)
-  end
-  handle THM _ => (NONE, [])
-
-fun meson_general_tac ctxt ths =
-  let val ctxt = Classical.put_claset HOL_cs ctxt in
-    Meson.meson_tac ctxt (maps (snd o cnf_axiom ctxt false 0) ths)
-  end
-
-val setup =
-  Method.setup @{binding meson} (Attrib.thms >> (fn ths => fn ctxt =>
-     SIMPLE_METHOD' (CHANGED_PROP o meson_general_tac ctxt ths)))
-     "MESON resolution proof procedure"
-
-end;
diff -r 6e9aff5ee9b5 -r 1f01c9b2b76b src/HOL/Tools/meson.ML
--- 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;