src/HOL/Tools/meson.ML
author blanchet
Fri Oct 01 15:34:09 2010 +0200 (2010-10-01)
changeset 39901 75d792edf634
parent 39900 549c00e0e89b
child 39904 f9e89d36a31a
permissions -rw-r--r--
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
wenzelm@9869
     1
(*  Title:      HOL/Tools/meson.ML
paulson@9840
     2
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
paulson@9840
     3
wenzelm@9869
     4
The MESON resolution proof procedure for HOL.
wenzelm@29267
     5
When making clauses, avoids using the rewriter -- instead uses RS recursively.
paulson@9840
     6
*)
paulson@9840
     7
wenzelm@24300
     8
signature MESON =
paulson@15579
     9
sig
wenzelm@32955
    10
  val trace: bool Unsynchronized.ref
wenzelm@24300
    11
  val term_pair_of: indexname * (typ * 'a) -> term * 'a
wenzelm@24300
    12
  val size_of_subgoals: thm -> int
blanchet@39269
    13
  val has_too_many_clauses: Proof.context -> term -> bool
paulson@24937
    14
  val make_cnf: thm list -> thm -> Proof.context -> thm list * Proof.context
wenzelm@24300
    15
  val finish_cnf: thm list -> thm list
blanchet@38089
    16
  val presimplify: thm -> thm
wenzelm@32262
    17
  val make_nnf: Proof.context -> thm -> thm
blanchet@39901
    18
  val skolemize : Proof.context -> thm list -> thm -> thm
wenzelm@24300
    19
  val is_fol_term: theory -> term -> bool
blanchet@35869
    20
  val make_clauses_unsorted: thm list -> thm list
wenzelm@24300
    21
  val make_clauses: thm list -> thm list
wenzelm@24300
    22
  val make_horns: thm list -> thm list
wenzelm@24300
    23
  val best_prolog_tac: (thm -> int) -> thm list -> tactic
wenzelm@24300
    24
  val depth_prolog_tac: thm list -> tactic
wenzelm@24300
    25
  val gocls: thm list -> thm list
blanchet@39900
    26
  val skolemize_prems_tac : Proof.context -> thm list -> int -> tactic
blanchet@39037
    27
  val MESON:
blanchet@39269
    28
    tactic -> (thm list -> thm list) -> (thm list -> tactic) -> Proof.context
blanchet@39269
    29
    -> int -> tactic
wenzelm@32262
    30
  val best_meson_tac: (thm -> int) -> Proof.context -> int -> tactic
wenzelm@32262
    31
  val safe_best_meson_tac: Proof.context -> int -> tactic
wenzelm@32262
    32
  val depth_meson_tac: Proof.context -> int -> tactic
wenzelm@24300
    33
  val prolog_step_tac': thm list -> int -> tactic
wenzelm@24300
    34
  val iter_deepen_prolog_tac: thm list -> tactic
wenzelm@32262
    35
  val iter_deepen_meson_tac: Proof.context -> thm list -> int -> tactic
wenzelm@24300
    36
  val make_meta_clause: thm -> thm
wenzelm@24300
    37
  val make_meta_clauses: thm list -> thm list
wenzelm@32262
    38
  val meson_tac: Proof.context -> thm list -> int -> tactic
wenzelm@32262
    39
  val setup: theory -> theory
paulson@15579
    40
end
paulson@9840
    41
blanchet@39901
    42
structure Meson : MESON =
paulson@15579
    43
struct
paulson@9840
    44
wenzelm@32955
    45
val trace = Unsynchronized.ref false;
wenzelm@32955
    46
fun trace_msg msg = if ! trace then tracing (msg ()) else ();
wenzelm@32955
    47
paulson@26562
    48
val max_clauses_default = 60;
wenzelm@38806
    49
val (max_clauses, setup) = Attrib.config_int "meson_max_clauses" (K max_clauses_default);
paulson@26562
    50
wenzelm@38802
    51
(*No known example (on 1-5-2007) needs even thirty*)
wenzelm@38802
    52
val iter_deepen_limit = 50;
wenzelm@38802
    53
haftmann@31454
    54
val disj_forward = @{thm disj_forward};
haftmann@31454
    55
val disj_forward2 = @{thm disj_forward2};
haftmann@31454
    56
val make_pos_rule = @{thm make_pos_rule};
haftmann@31454
    57
val make_pos_rule' = @{thm make_pos_rule'};
haftmann@31454
    58
val make_pos_goal = @{thm make_pos_goal};
haftmann@31454
    59
val make_neg_rule = @{thm make_neg_rule};
haftmann@31454
    60
val make_neg_rule' = @{thm make_neg_rule'};
haftmann@31454
    61
val make_neg_goal = @{thm make_neg_goal};
haftmann@31454
    62
val conj_forward = @{thm conj_forward};
haftmann@31454
    63
val all_forward = @{thm all_forward};
haftmann@31454
    64
val ex_forward = @{thm ex_forward};
haftmann@31454
    65
wenzelm@39159
    66
val not_conjD = @{thm meson_not_conjD};
wenzelm@39159
    67
val not_disjD = @{thm meson_not_disjD};
wenzelm@39159
    68
val not_notD = @{thm meson_not_notD};
wenzelm@39159
    69
val not_allD = @{thm meson_not_allD};
wenzelm@39159
    70
val not_exD = @{thm meson_not_exD};
wenzelm@39159
    71
val imp_to_disjD = @{thm meson_imp_to_disjD};
wenzelm@39159
    72
val not_impD = @{thm meson_not_impD};
wenzelm@39159
    73
val iff_to_disjD = @{thm meson_iff_to_disjD};
wenzelm@39159
    74
val not_iffD = @{thm meson_not_iffD};
wenzelm@39159
    75
val conj_exD1 = @{thm meson_conj_exD1};
wenzelm@39159
    76
val conj_exD2 = @{thm meson_conj_exD2};
wenzelm@39159
    77
val disj_exD = @{thm meson_disj_exD};
wenzelm@39159
    78
val disj_exD1 = @{thm meson_disj_exD1};
wenzelm@39159
    79
val disj_exD2 = @{thm meson_disj_exD2};
wenzelm@39159
    80
val disj_assoc = @{thm meson_disj_assoc};
wenzelm@39159
    81
val disj_comm = @{thm meson_disj_comm};
wenzelm@39159
    82
val disj_FalseD1 = @{thm meson_disj_FalseD1};
wenzelm@39159
    83
val disj_FalseD2 = @{thm meson_disj_FalseD2};
paulson@9840
    84
paulson@9840
    85
paulson@15579
    86
(**** Operators for forward proof ****)
paulson@15579
    87
paulson@20417
    88
paulson@20417
    89
(** First-order Resolution **)
paulson@20417
    90
paulson@20417
    91
fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t);
paulson@20417
    92
paulson@20417
    93
(*FIXME: currently does not "rename variables apart"*)
paulson@20417
    94
fun first_order_resolve thA thB =
wenzelm@32262
    95
  (case
wenzelm@32262
    96
    try (fn () =>
wenzelm@32262
    97
      let val thy = theory_of_thm thA
wenzelm@32262
    98
          val tmA = concl_of thA
wenzelm@32262
    99
          val Const("==>",_) $ tmB $ _ = prop_of thB
blanchet@37398
   100
          val tenv =
blanchet@37410
   101
            Pattern.first_order_match thy (tmB, tmA)
blanchet@37410
   102
                                          (Vartab.empty, Vartab.empty) |> snd
wenzelm@32262
   103
          val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv)
wenzelm@32262
   104
      in  thA RS (cterm_instantiate ct_pairs thB)  end) () of
wenzelm@32262
   105
    SOME th => th
blanchet@37398
   106
  | NONE => raise THM ("first_order_resolve", 0, [thA, thB]))
paulson@18175
   107
paulson@24937
   108
(*Forward proof while preserving bound variables names*)
paulson@24937
   109
fun rename_bvs_RS th rl =
paulson@24937
   110
  let val th' = th RS rl
paulson@24937
   111
  in  Thm.rename_boundvars (concl_of th') (concl_of th) th' end;
paulson@24937
   112
paulson@24937
   113
(*raises exception if no rules apply*)
wenzelm@24300
   114
fun tryres (th, rls) =
paulson@18141
   115
  let fun tryall [] = raise THM("tryres", 0, th::rls)
paulson@24937
   116
        | tryall (rl::rls) = (rename_bvs_RS th rl handle THM _ => tryall rls)
paulson@18141
   117
  in  tryall rls  end;
wenzelm@24300
   118
paulson@21050
   119
(*Permits forward proof from rules that discharge assumptions. The supplied proof state st,
paulson@21050
   120
  e.g. from conj_forward, should have the form
paulson@21050
   121
    "[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q"
paulson@21050
   122
  and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*)
wenzelm@32262
   123
fun forward_res ctxt nf st =
paulson@21050
   124
  let fun forward_tacf [prem] = rtac (nf prem) 1
wenzelm@24300
   125
        | forward_tacf prems =
wenzelm@32091
   126
            error (cat_lines
wenzelm@32091
   127
              ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:" ::
wenzelm@32262
   128
                Display.string_of_thm ctxt st ::
wenzelm@32262
   129
                "Premises:" :: map (Display.string_of_thm ctxt) prems))
paulson@21050
   130
  in
wenzelm@37781
   131
    case Seq.pull (ALLGOALS (Misc_Legacy.METAHYPS forward_tacf) st)
paulson@21050
   132
    of SOME(th,_) => th
paulson@21050
   133
     | NONE => raise THM("forward_res", 0, [st])
paulson@21050
   134
  end;
paulson@15579
   135
paulson@20134
   136
(*Are any of the logical connectives in "bs" present in the term?*)
paulson@20134
   137
fun has_conns bs =
blanchet@39328
   138
  let fun has (Const _) = false
haftmann@38557
   139
        | has (Const(@{const_name Trueprop},_) $ p) = has p
haftmann@38557
   140
        | has (Const(@{const_name Not},_) $ p) = has p
haftmann@38795
   141
        | has (Const(@{const_name HOL.disj},_) $ p $ q) = member (op =) bs @{const_name HOL.disj} orelse has p orelse has q
haftmann@38795
   142
        | has (Const(@{const_name HOL.conj},_) $ p $ q) = member (op =) bs @{const_name HOL.conj} orelse has p orelse has q
haftmann@38557
   143
        | has (Const(@{const_name All},_) $ Abs(_,_,p)) = member (op =) bs @{const_name All} orelse has p
haftmann@38557
   144
        | has (Const(@{const_name Ex},_) $ Abs(_,_,p)) = member (op =) bs @{const_name Ex} orelse has p
wenzelm@24300
   145
        | has _ = false
paulson@15579
   146
  in  has  end;
wenzelm@24300
   147
paulson@9840
   148
paulson@15579
   149
(**** Clause handling ****)
paulson@9840
   150
haftmann@38557
   151
fun literals (Const(@{const_name Trueprop},_) $ P) = literals P
haftmann@38795
   152
  | literals (Const(@{const_name HOL.disj},_) $ P $ Q) = literals P @ literals Q
haftmann@38557
   153
  | literals (Const(@{const_name Not},_) $ P) = [(false,P)]
paulson@15579
   154
  | literals P = [(true,P)];
paulson@9840
   155
paulson@15579
   156
(*number of literals in a term*)
paulson@15579
   157
val nliterals = length o literals;
paulson@9840
   158
paulson@18389
   159
paulson@18389
   160
(*** Tautology Checking ***)
paulson@18389
   161
haftmann@38795
   162
fun signed_lits_aux (Const (@{const_name HOL.disj}, _) $ P $ Q) (poslits, neglits) =
paulson@18389
   163
      signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
haftmann@38557
   164
  | signed_lits_aux (Const(@{const_name Not},_) $ P) (poslits, neglits) = (poslits, P::neglits)
paulson@18389
   165
  | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
wenzelm@24300
   166
paulson@18389
   167
fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
paulson@18389
   168
paulson@18389
   169
(*Literals like X=X are tautologous*)
haftmann@38864
   170
fun taut_poslit (Const(@{const_name HOL.eq},_) $ t $ u) = t aconv u
haftmann@38557
   171
  | taut_poslit (Const(@{const_name True},_)) = true
paulson@18389
   172
  | taut_poslit _ = false;
paulson@18389
   173
paulson@18389
   174
fun is_taut th =
paulson@18389
   175
  let val (poslits,neglits) = signed_lits th
paulson@18389
   176
  in  exists taut_poslit poslits
paulson@18389
   177
      orelse
wenzelm@20073
   178
      exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
paulson@19894
   179
  end
wenzelm@24300
   180
  handle TERM _ => false;       (*probably dest_Trueprop on a weird theorem*)
paulson@18389
   181
paulson@18389
   182
paulson@18389
   183
(*** To remove trivial negated equality literals from clauses ***)
paulson@18389
   184
paulson@18389
   185
(*They are typically functional reflexivity axioms and are the converses of
paulson@18389
   186
  injectivity equivalences*)
wenzelm@24300
   187
wenzelm@39159
   188
val not_refl_disj_D = @{thm meson_not_refl_disj_D};
paulson@18389
   189
paulson@20119
   190
(*Is either term a Var that does not properly occur in the other term?*)
paulson@20119
   191
fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
paulson@20119
   192
  | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
paulson@20119
   193
  | eliminable _ = false;
paulson@20119
   194
paulson@18389
   195
fun refl_clause_aux 0 th = th
paulson@18389
   196
  | refl_clause_aux n th =
paulson@18389
   197
       case HOLogic.dest_Trueprop (concl_of th) of
haftmann@38795
   198
          (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _) =>
paulson@18389
   199
            refl_clause_aux n (th RS disj_assoc)    (*isolate an atom as first disjunct*)
haftmann@38864
   200
        | (Const (@{const_name HOL.disj}, _) $ (Const(@{const_name Not},_) $ (Const(@{const_name HOL.eq},_) $ t $ u)) $ _) =>
wenzelm@24300
   201
            if eliminable(t,u)
wenzelm@24300
   202
            then refl_clause_aux (n-1) (th RS not_refl_disj_D)  (*Var inequation: delete*)
wenzelm@24300
   203
            else refl_clause_aux (n-1) (th RS disj_comm)  (*not between Vars: ignore*)
haftmann@38795
   204
        | (Const (@{const_name HOL.disj}, _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
wenzelm@24300
   205
        | _ => (*not a disjunction*) th;
paulson@18389
   206
haftmann@38795
   207
fun notequal_lits_count (Const (@{const_name HOL.disj}, _) $ P $ Q) =
paulson@18389
   208
      notequal_lits_count P + notequal_lits_count Q
haftmann@38864
   209
  | notequal_lits_count (Const(@{const_name Not},_) $ (Const(@{const_name HOL.eq},_) $ _ $ _)) = 1
paulson@18389
   210
  | notequal_lits_count _ = 0;
paulson@18389
   211
paulson@18389
   212
(*Simplify a clause by applying reflexivity to its negated equality literals*)
wenzelm@24300
   213
fun refl_clause th =
paulson@18389
   214
  let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
paulson@19894
   215
  in  zero_var_indexes (refl_clause_aux neqs th)  end
wenzelm@24300
   216
  handle TERM _ => th;  (*probably dest_Trueprop on a weird theorem*)
paulson@18389
   217
paulson@18389
   218
paulson@24937
   219
(*** Removal of duplicate literals ***)
paulson@24937
   220
paulson@24937
   221
(*Forward proof, passing extra assumptions as theorems to the tactic*)
blanchet@39328
   222
fun forward_res2 nf hyps st =
paulson@24937
   223
  case Seq.pull
paulson@24937
   224
        (REPEAT
wenzelm@37781
   225
         (Misc_Legacy.METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
paulson@24937
   226
         st)
paulson@24937
   227
  of SOME(th,_) => th
paulson@24937
   228
   | NONE => raise THM("forward_res2", 0, [st]);
paulson@24937
   229
paulson@24937
   230
(*Remove duplicates in P|Q by assuming ~P in Q
paulson@24937
   231
  rls (initially []) accumulates assumptions of the form P==>False*)
wenzelm@32262
   232
fun nodups_aux ctxt rls th = nodups_aux ctxt rls (th RS disj_assoc)
paulson@24937
   233
    handle THM _ => tryres(th,rls)
blanchet@39328
   234
    handle THM _ => tryres(forward_res2 (nodups_aux ctxt) rls (th RS disj_forward2),
paulson@24937
   235
                           [disj_FalseD1, disj_FalseD2, asm_rl])
paulson@24937
   236
    handle THM _ => th;
paulson@24937
   237
paulson@24937
   238
(*Remove duplicate literals, if there are any*)
wenzelm@32262
   239
fun nodups ctxt th =
paulson@24937
   240
  if has_duplicates (op =) (literals (prop_of th))
wenzelm@32262
   241
    then nodups_aux ctxt [] th
paulson@24937
   242
    else th;
paulson@24937
   243
paulson@24937
   244
paulson@18389
   245
(*** The basic CNF transformation ***)
paulson@18389
   246
blanchet@39328
   247
fun estimated_num_clauses bound t =
paulson@26562
   248
 let
blanchet@39269
   249
  fun sum x y = if x < bound andalso y < bound then x+y else bound
blanchet@39269
   250
  fun prod x y = if x < bound andalso y < bound then x*y else bound
paulson@26562
   251
  
paulson@26562
   252
  (*Estimate the number of clauses in order to detect infeasible theorems*)
haftmann@38557
   253
  fun signed_nclauses b (Const(@{const_name Trueprop},_) $ t) = signed_nclauses b t
haftmann@38557
   254
    | signed_nclauses b (Const(@{const_name Not},_) $ t) = signed_nclauses (not b) t
haftmann@38795
   255
    | signed_nclauses b (Const(@{const_name HOL.conj},_) $ t $ u) =
wenzelm@32960
   256
        if b then sum (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   257
             else prod (signed_nclauses b t) (signed_nclauses b u)
haftmann@38795
   258
    | signed_nclauses b (Const(@{const_name HOL.disj},_) $ t $ u) =
wenzelm@32960
   259
        if b then prod (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   260
             else sum (signed_nclauses b t) (signed_nclauses b u)
haftmann@38786
   261
    | signed_nclauses b (Const(@{const_name HOL.implies},_) $ t $ u) =
wenzelm@32960
   262
        if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
wenzelm@32960
   263
             else sum (signed_nclauses (not b) t) (signed_nclauses b u)
haftmann@38864
   264
    | signed_nclauses b (Const(@{const_name HOL.eq}, Type ("fun", [T, _])) $ t $ u) =
wenzelm@32960
   265
        if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
wenzelm@32960
   266
            if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
wenzelm@32960
   267
                          (prod (signed_nclauses (not b) u) (signed_nclauses b t))
wenzelm@32960
   268
                 else sum (prod (signed_nclauses b t) (signed_nclauses b u))
wenzelm@32960
   269
                          (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
wenzelm@32960
   270
        else 1
haftmann@38557
   271
    | signed_nclauses b (Const(@{const_name Ex}, _) $ Abs (_,_,t)) = signed_nclauses b t
haftmann@38557
   272
    | signed_nclauses b (Const(@{const_name All},_) $ Abs (_,_,t)) = signed_nclauses b t
paulson@26562
   273
    | signed_nclauses _ _ = 1; (* literal *)
blanchet@39269
   274
 in signed_nclauses true t end
blanchet@39269
   275
blanchet@39269
   276
fun has_too_many_clauses ctxt t =
blanchet@39269
   277
  let val max_cl = Config.get ctxt max_clauses in
blanchet@39328
   278
    estimated_num_clauses (max_cl + 1) t > max_cl
blanchet@39269
   279
  end
paulson@19894
   280
paulson@15579
   281
(*Replaces universally quantified variables by FREE variables -- because
paulson@24937
   282
  assumptions may not contain scheme variables.  Later, generalize using Variable.export. *)
paulson@24937
   283
local  
paulson@24937
   284
  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
paulson@24937
   285
  val spec_varT = #T (Thm.rep_cterm spec_var);
haftmann@38557
   286
  fun name_of (Const (@{const_name All}, _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
paulson@24937
   287
in  
paulson@24937
   288
  fun freeze_spec th ctxt =
paulson@24937
   289
    let
paulson@24937
   290
      val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
paulson@24937
   291
      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
paulson@24937
   292
      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
paulson@24937
   293
    in (th RS spec', ctxt') end
paulson@24937
   294
end;
paulson@9840
   295
paulson@15998
   296
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   297
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@22515
   298
  instantiate a Boolean variable created by resolution with disj_forward. Since
paulson@22515
   299
  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
paulson@15579
   300
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   301
blanchet@39037
   302
(* Any need to extend this list with "HOL.type_class", "HOL.eq_class",
blanchet@39037
   303
   and "Pure.term"? *)
haftmann@38557
   304
val has_meta_conn = exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
paulson@20417
   305
blanchet@37410
   306
fun apply_skolem_theorem (th, rls) =
blanchet@37398
   307
  let
blanchet@37410
   308
    fun tryall [] = raise THM ("apply_skolem_theorem", 0, th::rls)
blanchet@37398
   309
      | tryall (rl :: rls) =
blanchet@37398
   310
        first_order_resolve th rl handle THM _ => tryall rls
blanchet@37398
   311
  in tryall rls end
paulson@22515
   312
blanchet@37410
   313
(* Conjunctive normal form, adding clauses from th in front of ths (for foldr).
blanchet@37410
   314
   Strips universal quantifiers and breaks up conjunctions.
blanchet@37410
   315
   Eliminates existential quantifiers using Skolemization theorems. *)
blanchet@39886
   316
fun cnf old_skolem_ths ctxt (th, ths) =
wenzelm@33222
   317
  let val ctxtr = Unsynchronized.ref ctxt   (* FIXME ??? *)
paulson@24937
   318
      fun cnf_aux (th,ths) =
wenzelm@24300
   319
        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
haftmann@38795
   320
        else if not (has_conns [@{const_name All}, @{const_name Ex}, @{const_name HOL.conj}] (prop_of th))
wenzelm@32262
   321
        then nodups ctxt th :: ths (*no work to do, terminate*)
wenzelm@24300
   322
        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
haftmann@38795
   323
            Const (@{const_name HOL.conj}, _) => (*conjunction*)
wenzelm@24300
   324
                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
haftmann@38557
   325
          | Const (@{const_name All}, _) => (*universal quantifier*)
paulson@24937
   326
                let val (th',ctxt') = freeze_spec th (!ctxtr)
paulson@24937
   327
                in  ctxtr := ctxt'; cnf_aux (th', ths) end
haftmann@38557
   328
          | Const (@{const_name Ex}, _) =>
wenzelm@24300
   329
              (*existential quantifier: Insert Skolem functions*)
blanchet@39886
   330
              cnf_aux (apply_skolem_theorem (th, old_skolem_ths), ths)
haftmann@38795
   331
          | Const (@{const_name HOL.disj}, _) =>
wenzelm@24300
   332
              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
wenzelm@24300
   333
                all combinations of converting P, Q to CNF.*)
wenzelm@24300
   334
              let val tac =
wenzelm@37781
   335
                  Misc_Legacy.METAHYPS (resop cnf_nil) 1 THEN
wenzelm@37781
   336
                   (fn st' => st' |> Misc_Legacy.METAHYPS (resop cnf_nil) 1)
wenzelm@24300
   337
              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
wenzelm@32262
   338
          | _ => nodups ctxt th :: ths  (*no work to do*)
paulson@19154
   339
      and cnf_nil th = cnf_aux (th,[])
blanchet@39269
   340
      val cls =
blanchet@39269
   341
            if has_too_many_clauses ctxt (concl_of th)
wenzelm@32960
   342
            then (trace_msg (fn () => "cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
wenzelm@32960
   343
            else cnf_aux (th,ths)
paulson@24937
   344
  in  (cls, !ctxtr)  end;
paulson@22515
   345
blanchet@39886
   346
fun make_cnf old_skolem_ths th ctxt = cnf old_skolem_ths ctxt (th, [])
paulson@20417
   347
paulson@20417
   348
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@24937
   349
fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
paulson@9840
   350
paulson@9840
   351
paulson@15579
   352
(**** Generation of contrapositives ****)
paulson@9840
   353
haftmann@38557
   354
fun is_left (Const (@{const_name Trueprop}, _) $
haftmann@38795
   355
               (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _)) = true
paulson@21102
   356
  | is_left _ = false;
wenzelm@24300
   357
paulson@15579
   358
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
wenzelm@24300
   359
fun assoc_right th =
paulson@21102
   360
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   361
  else th;
paulson@9840
   362
paulson@15579
   363
(*Must check for negative literal first!*)
paulson@15579
   364
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   365
paulson@15579
   366
(*For ordinary resolution. *)
paulson@15579
   367
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   368
paulson@15579
   369
(*Create a goal or support clause, conclusing False*)
paulson@15579
   370
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   371
    make_goal (tryres(th, clause_rules))
paulson@15579
   372
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   373
paulson@15579
   374
(*Sort clauses by number of literals*)
paulson@15579
   375
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   376
paulson@18389
   377
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   378
blanchet@38099
   379
fun has_bool @{typ bool} = true
blanchet@38099
   380
  | has_bool (Type (_, Ts)) = exists has_bool Ts
blanchet@38099
   381
  | has_bool _ = false
blanchet@38099
   382
blanchet@38099
   383
fun has_fun (Type (@{type_name fun}, _)) = true
blanchet@38099
   384
  | has_fun (Type (_, Ts)) = exists has_fun Ts
blanchet@38099
   385
  | has_fun _ = false
wenzelm@24300
   386
wenzelm@24300
   387
(*Is the string the name of a connective? Really only | and Not can remain,
wenzelm@24300
   388
  since this code expects to be called on a clause form.*)
wenzelm@19875
   389
val is_conn = member (op =)
haftmann@38795
   390
    [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
haftmann@38786
   391
     @{const_name HOL.implies}, @{const_name Not},
haftmann@38557
   392
     @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex}];
paulson@15613
   393
wenzelm@24300
   394
(*True if the term contains a function--not a logical connective--where the type
paulson@20524
   395
  of any argument contains bool.*)
wenzelm@24300
   396
val has_bool_arg_const =
paulson@15613
   397
    exists_Const
blanchet@38099
   398
      (fn (c,T) => not(is_conn c) andalso exists has_bool (binder_types T));
paulson@22381
   399
wenzelm@24300
   400
(*A higher-order instance of a first-order constant? Example is the definition of
haftmann@38622
   401
  one, 1, at a function type in theory Function_Algebras.*)
wenzelm@24300
   402
fun higher_inst_const thy (c,T) =
paulson@22381
   403
  case binder_types T of
paulson@22381
   404
      [] => false (*not a function type, OK*)
paulson@22381
   405
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
paulson@22381
   406
paulson@24742
   407
(*Returns false if any Vars in the theorem mention type bool.
paulson@21102
   408
  Also rejects functions whose arguments are Booleans or other functions.*)
paulson@22381
   409
fun is_fol_term thy t =
haftmann@38557
   410
    Term.is_first_order ["all", @{const_name All}, @{const_name Ex}] t andalso
blanchet@38099
   411
    not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
blanchet@38099
   412
                           | _ => false) t orelse
blanchet@38099
   413
         has_bool_arg_const t orelse
wenzelm@24300
   414
         exists_Const (higher_inst_const thy) t orelse
wenzelm@24300
   415
         has_meta_conn t);
paulson@19204
   416
paulson@21102
   417
fun rigid t = not (is_Var (head_of t));
paulson@21102
   418
haftmann@38795
   419
fun ok4horn (Const (@{const_name Trueprop},_) $ (Const (@{const_name HOL.disj}, _) $ t $ _)) = rigid t
haftmann@38557
   420
  | ok4horn (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   421
  | ok4horn _ = false;
paulson@21102
   422
paulson@15579
   423
(*Create a meta-level Horn clause*)
wenzelm@24300
   424
fun make_horn crules th =
wenzelm@24300
   425
  if ok4horn (concl_of th)
paulson@21102
   426
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   427
  else th;
paulson@9840
   428
paulson@16563
   429
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   430
  is a HOL disjunction.*)
wenzelm@33339
   431
fun add_contras crules th hcs =
blanchet@39328
   432
  let fun rots (0,_) = hcs
wenzelm@24300
   433
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
wenzelm@24300
   434
                        rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   435
  in case nliterals(prop_of th) of
wenzelm@24300
   436
        1 => th::hcs
paulson@15579
   437
      | n => rots(n, assoc_right th)
paulson@15579
   438
  end;
paulson@9840
   439
paulson@15579
   440
(*Use "theorem naming" to label the clauses*)
paulson@15579
   441
fun name_thms label =
wenzelm@33339
   442
    let fun name1 th (k, ths) =
wenzelm@27865
   443
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
wenzelm@33339
   444
    in  fn ths => #2 (fold_rev name1 ths (length ths, []))  end;
paulson@9840
   445
paulson@16563
   446
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   447
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   448
wenzelm@33317
   449
val neg_clauses = filter is_negative;
paulson@9840
   450
paulson@9840
   451
paulson@15579
   452
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   453
haftmann@38557
   454
fun rhyps (Const("==>",_) $ (Const(@{const_name Trueprop},_) $ A) $ phi,
wenzelm@24300
   455
           As) = rhyps(phi, A::As)
paulson@15579
   456
  | rhyps (_, As) = As;
paulson@9840
   457
paulson@15579
   458
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   459
paulson@15579
   460
(*The stringtree detects repeated assumptions.*)
wenzelm@33245
   461
fun ins_term t net = Net.insert_term (op aconv) (t, t) net;
paulson@9840
   462
paulson@15579
   463
(*detects repetitions in a list of terms*)
paulson@15579
   464
fun has_reps [] = false
paulson@15579
   465
  | has_reps [_] = false
paulson@15579
   466
  | has_reps [t,u] = (t aconv u)
wenzelm@33245
   467
  | has_reps ts = (fold ins_term ts Net.empty; false) handle Net.INSERT => true;
paulson@9840
   468
paulson@15579
   469
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   470
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   471
  | TRYING_eq_assume_tac i st =
wenzelm@31945
   472
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
paulson@18508
   473
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   474
paulson@18508
   475
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   476
paulson@15579
   477
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   478
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   479
fun check_tac st =
paulson@15579
   480
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   481
  then  Seq.empty  else  Seq.single st;
paulson@9840
   482
paulson@9840
   483
paulson@15579
   484
(* net_resolve_tac actually made it slower... *)
paulson@15579
   485
fun prolog_step_tac horns i =
paulson@15579
   486
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   487
    TRYALL_eq_assume_tac;
paulson@9840
   488
paulson@9840
   489
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
wenzelm@33339
   490
fun addconcl prem sz = size_of_term (Logic.strip_assums_concl prem) + sz;
paulson@15579
   491
wenzelm@33339
   492
fun size_of_subgoals st = fold_rev addconcl (prems_of st) 0;
paulson@15579
   493
paulson@9840
   494
paulson@9840
   495
(*Negation Normal Form*)
paulson@9840
   496
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   497
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   498
haftmann@38557
   499
fun ok4nnf (Const (@{const_name Trueprop},_) $ (Const (@{const_name Not}, _) $ t)) = rigid t
haftmann@38557
   500
  | ok4nnf (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   501
  | ok4nnf _ = false;
paulson@21102
   502
wenzelm@32262
   503
fun make_nnf1 ctxt th =
wenzelm@24300
   504
  if ok4nnf (concl_of th)
wenzelm@32262
   505
  then make_nnf1 ctxt (tryres(th, nnf_rls))
paulson@28174
   506
    handle THM ("tryres", _, _) =>
wenzelm@32262
   507
        forward_res ctxt (make_nnf1 ctxt)
wenzelm@9869
   508
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@28174
   509
    handle THM ("tryres", _, _) => th
blanchet@38608
   510
  else th
paulson@9840
   511
wenzelm@24300
   512
(*The simplification removes defined quantifiers and occurrences of True and False.
paulson@20018
   513
  nnf_ss also includes the one-point simprocs,
paulson@18405
   514
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   515
val nnf_simps =
blanchet@37539
   516
  @{thms simp_implies_def Ex1_def Ball_def Bex_def if_True if_False if_cancel
blanchet@37539
   517
         if_eq_cancel cases_simp}
blanchet@37539
   518
val nnf_extra_simps = @{thms split_ifs ex_simps all_simps simp_thms}
paulson@18405
   519
paulson@18405
   520
val nnf_ss =
wenzelm@24300
   521
  HOL_basic_ss addsimps nnf_extra_simps
wenzelm@24040
   522
    addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
paulson@15872
   523
blanchet@38089
   524
val presimplify =
blanchet@39900
   525
  rewrite_rule (map safe_mk_meta_eq nnf_simps) #> simplify nnf_ss
blanchet@38089
   526
wenzelm@32262
   527
fun make_nnf ctxt th = case prems_of th of
blanchet@38606
   528
    [] => th |> presimplify |> make_nnf1 ctxt
paulson@21050
   529
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   530
blanchet@39900
   531
(* Pull existential quantifiers to front. This accomplishes Skolemization for
blanchet@39900
   532
   clauses that arise from a subgoal. *)
blanchet@39901
   533
fun skolemize ctxt choice_ths =
blanchet@39900
   534
  let
blanchet@39900
   535
    fun aux th =
blanchet@39900
   536
      if not (has_conns [@{const_name Ex}] (prop_of th)) then
blanchet@39900
   537
        th
blanchet@39900
   538
      else
blanchet@39901
   539
        tryres (th, choice_ths @
blanchet@39900
   540
                    [conj_exD1, conj_exD2, disj_exD, disj_exD1, disj_exD2])
blanchet@39900
   541
        |> aux
blanchet@39900
   542
        handle THM ("tryres", _, _) =>
blanchet@39900
   543
               tryres (th, [conj_forward, disj_forward, all_forward])
blanchet@39900
   544
               |> forward_res ctxt aux
blanchet@39900
   545
               |> aux
blanchet@39900
   546
               handle THM ("tryres", _, _) =>
blanchet@39900
   547
                      rename_bvs_RS th ex_forward
blanchet@39900
   548
                      |> forward_res ctxt aux
blanchet@39900
   549
  in aux o make_nnf ctxt end
paulson@29684
   550
blanchet@39900
   551
(* "RS" can fail if "unify_search_bound" is too small. *)
blanchet@39900
   552
fun try_skolemize ctxt th =
blanchet@39901
   553
  try (skolemize ctxt (Meson_Choices.get ctxt)) th
blanchet@39900
   554
  |> tap (fn NONE => trace_msg (fn () => "Failed to skolemize " ^
blanchet@39900
   555
                                         Display.string_of_thm ctxt th)
blanchet@39900
   556
           | _ => ())
paulson@25694
   557
wenzelm@33339
   558
fun add_clauses th cls =
wenzelm@36603
   559
  let val ctxt0 = Variable.global_thm_context th
wenzelm@33339
   560
      val (cnfs, ctxt) = make_cnf [] th ctxt0
paulson@24937
   561
  in Variable.export ctxt ctxt0 cnfs @ cls end;
paulson@9840
   562
paulson@9840
   563
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   564
  The resulting clauses are HOL disjunctions.*)
wenzelm@39235
   565
fun make_clauses_unsorted ths = fold_rev add_clauses ths [];
blanchet@35869
   566
val make_clauses = sort_clauses o make_clauses_unsorted;
quigley@15773
   567
paulson@16563
   568
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   569
fun make_horns ths =
paulson@9840
   570
    name_thms "Horn#"
wenzelm@33339
   571
      (distinct Thm.eq_thm_prop (fold_rev (add_contras clause_rules) ths []));
paulson@9840
   572
paulson@9840
   573
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   574
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   575
wenzelm@9869
   576
fun best_prolog_tac sizef horns =
paulson@9840
   577
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   578
wenzelm@9869
   579
fun depth_prolog_tac horns =
paulson@9840
   580
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   581
paulson@9840
   582
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   583
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   584
wenzelm@32262
   585
fun skolemize_prems_tac ctxt prems =
blanchet@39900
   586
  cut_facts_tac (map_filter (try_skolemize ctxt) prems) THEN' REPEAT o etac exE
paulson@9840
   587
paulson@22546
   588
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
paulson@22546
   589
  Function mkcl converts theorems to clauses.*)
blanchet@39037
   590
fun MESON preskolem_tac mkcl cltac ctxt i st =
paulson@16588
   591
  SELECT_GOAL
wenzelm@35625
   592
    (EVERY [Object_Logic.atomize_prems_tac 1,
paulson@23552
   593
            rtac ccontr 1,
blanchet@39269
   594
            preskolem_tac,
wenzelm@32283
   595
            Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
blanchet@39269
   596
                      EVERY1 [skolemize_prems_tac ctxt negs,
wenzelm@32283
   597
                              Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
wenzelm@24300
   598
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
paulson@9840
   599
blanchet@39037
   600
paulson@9840
   601
(** Best-first search versions **)
paulson@9840
   602
paulson@16563
   603
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
wenzelm@9869
   604
fun best_meson_tac sizef =
blanchet@39269
   605
  MESON all_tac make_clauses
paulson@22546
   606
    (fn cls =>
paulson@9840
   607
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   608
                         (has_fewer_prems 1, sizef)
paulson@9840
   609
                         (prolog_step_tac (make_horns cls) 1));
paulson@9840
   610
paulson@9840
   611
(*First, breaks the goal into independent units*)
wenzelm@32262
   612
fun safe_best_meson_tac ctxt =
wenzelm@32262
   613
     SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
wenzelm@32262
   614
                  TRYALL (best_meson_tac size_of_subgoals ctxt));
paulson@9840
   615
paulson@9840
   616
(** Depth-first search version **)
paulson@9840
   617
paulson@9840
   618
val depth_meson_tac =
blanchet@39269
   619
  MESON all_tac make_clauses
paulson@22546
   620
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
paulson@9840
   621
paulson@9840
   622
paulson@9840
   623
(** Iterative deepening version **)
paulson@9840
   624
paulson@9840
   625
(*This version does only one inference per call;
paulson@9840
   626
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   627
fun prolog_step_tac' horns =
blanchet@39328
   628
    let val (horn0s, _) = (*0 subgoals vs 1 or more*)
paulson@9840
   629
            take_prefix Thm.no_prems horns
paulson@9840
   630
        val nrtac = net_resolve_tac horns
paulson@9840
   631
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   632
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   633
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   634
    end;
paulson@9840
   635
wenzelm@9869
   636
fun iter_deepen_prolog_tac horns =
wenzelm@38802
   637
    ITER_DEEPEN iter_deepen_limit (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   638
blanchet@39269
   639
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON all_tac make_clauses
wenzelm@32091
   640
  (fn cls =>
wenzelm@32091
   641
    (case (gocls (cls @ ths)) of
wenzelm@32091
   642
      [] => no_tac  (*no goal clauses*)
wenzelm@32091
   643
    | goes =>
wenzelm@32091
   644
        let
wenzelm@32091
   645
          val horns = make_horns (cls @ ths)
wenzelm@32955
   646
          val _ = trace_msg (fn () =>
wenzelm@32091
   647
            cat_lines ("meson method called:" ::
wenzelm@32262
   648
              map (Display.string_of_thm ctxt) (cls @ ths) @
wenzelm@32262
   649
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
wenzelm@38802
   650
        in
wenzelm@38802
   651
          THEN_ITER_DEEPEN iter_deepen_limit
wenzelm@38802
   652
            (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
wenzelm@38802
   653
        end));
paulson@9840
   654
wenzelm@32262
   655
fun meson_tac ctxt ths =
wenzelm@32262
   656
  SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
wenzelm@9869
   657
wenzelm@9869
   658
paulson@14813
   659
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   660
wenzelm@24300
   661
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
paulson@15008
   662
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   663
paulson@14744
   664
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   665
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   666
  prevents a double negation.*)
wenzelm@27239
   667
val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
paulson@14744
   668
val notEfalse' = rotate_prems 1 notEfalse;
paulson@14744
   669
wenzelm@24300
   670
fun negated_asm_of_head th =
paulson@14744
   671
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   672
paulson@26066
   673
(*Converting one theorem from a disjunction to a meta-level clause*)
paulson@26066
   674
fun make_meta_clause th =
wenzelm@33832
   675
  let val (fth,thaw) = Drule.legacy_freeze_thaw_robust th
paulson@26066
   676
  in  
wenzelm@35845
   677
      (zero_var_indexes o Thm.varifyT_global o thaw 0 o 
paulson@26066
   678
       negated_asm_of_head o make_horn resolution_clause_rules) fth
paulson@26066
   679
  end;
wenzelm@24300
   680
paulson@14744
   681
fun make_meta_clauses ths =
paulson@14744
   682
    name_thms "MClause#"
wenzelm@22360
   683
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   684
paulson@9840
   685
end;