src/HOL/Tools/meson.ML
author wenzelm
Fri Aug 27 16:29:12 2010 +0200 (2010-08-27)
changeset 38802 a925c0ee42f7
parent 38795 848be46708dc
child 38806 0aafc7e81056
permissions -rw-r--r--
clarified iter_deepen_limit vs meson (cf. 7c5896919eb8) -- eliminated global ref;
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 flexflex_first_order: thm -> thm
wenzelm@24300
    13
  val size_of_subgoals: thm -> int
paulson@26562
    14
  val too_many_clauses: Proof.context option -> term -> bool
paulson@24937
    15
  val make_cnf: thm list -> thm -> Proof.context -> thm list * Proof.context
wenzelm@24300
    16
  val finish_cnf: thm list -> thm list
blanchet@38089
    17
  val presimplify: thm -> thm
wenzelm@32262
    18
  val make_nnf: Proof.context -> thm -> thm
wenzelm@32262
    19
  val skolemize: Proof.context -> thm -> thm
wenzelm@24300
    20
  val is_fol_term: theory -> term -> bool
blanchet@35869
    21
  val make_clauses_unsorted: thm list -> thm list
wenzelm@24300
    22
  val make_clauses: thm list -> thm list
wenzelm@24300
    23
  val make_horns: thm list -> thm list
wenzelm@24300
    24
  val best_prolog_tac: (thm -> int) -> thm list -> tactic
wenzelm@24300
    25
  val depth_prolog_tac: thm list -> tactic
wenzelm@24300
    26
  val gocls: thm list -> thm list
wenzelm@32262
    27
  val skolemize_prems_tac: Proof.context -> thm list -> int -> tactic
wenzelm@32262
    28
  val MESON: (thm list -> thm list) -> (thm list -> tactic) -> Proof.context -> int -> tactic
wenzelm@32262
    29
  val best_meson_tac: (thm -> int) -> Proof.context -> int -> tactic
wenzelm@32262
    30
  val safe_best_meson_tac: Proof.context -> int -> tactic
wenzelm@32262
    31
  val depth_meson_tac: Proof.context -> int -> tactic
wenzelm@24300
    32
  val prolog_step_tac': thm list -> int -> tactic
wenzelm@24300
    33
  val iter_deepen_prolog_tac: thm list -> tactic
wenzelm@32262
    34
  val iter_deepen_meson_tac: Proof.context -> thm list -> int -> tactic
wenzelm@24300
    35
  val make_meta_clause: thm -> thm
wenzelm@24300
    36
  val make_meta_clauses: thm list -> thm list
wenzelm@32262
    37
  val meson_tac: Proof.context -> thm list -> int -> tactic
wenzelm@24300
    38
  val negate_head: thm -> thm
wenzelm@24300
    39
  val select_literal: int -> thm -> thm
wenzelm@32262
    40
  val skolemize_tac: Proof.context -> int -> tactic
wenzelm@32262
    41
  val setup: theory -> theory
paulson@15579
    42
end
paulson@9840
    43
wenzelm@24300
    44
structure Meson: MESON =
paulson@15579
    45
struct
paulson@9840
    46
wenzelm@32955
    47
val trace = Unsynchronized.ref false;
wenzelm@32955
    48
fun trace_msg msg = if ! trace then tracing (msg ()) else ();
wenzelm@32955
    49
paulson@26562
    50
val max_clauses_default = 60;
wenzelm@36001
    51
val (max_clauses, setup) = Attrib.config_int "max_clauses" (K max_clauses_default);
paulson@26562
    52
wenzelm@38802
    53
(*No known example (on 1-5-2007) needs even thirty*)
wenzelm@38802
    54
val iter_deepen_limit = 50;
wenzelm@38802
    55
haftmann@31454
    56
val disj_forward = @{thm disj_forward};
haftmann@31454
    57
val disj_forward2 = @{thm disj_forward2};
haftmann@31454
    58
val make_pos_rule = @{thm make_pos_rule};
haftmann@31454
    59
val make_pos_rule' = @{thm make_pos_rule'};
haftmann@31454
    60
val make_pos_goal = @{thm make_pos_goal};
haftmann@31454
    61
val make_neg_rule = @{thm make_neg_rule};
haftmann@31454
    62
val make_neg_rule' = @{thm make_neg_rule'};
haftmann@31454
    63
val make_neg_goal = @{thm make_neg_goal};
haftmann@31454
    64
val conj_forward = @{thm conj_forward};
haftmann@31454
    65
val all_forward = @{thm all_forward};
haftmann@31454
    66
val ex_forward = @{thm ex_forward};
haftmann@31454
    67
val choice = @{thm choice};
haftmann@31454
    68
paulson@15579
    69
val not_conjD = thm "meson_not_conjD";
paulson@15579
    70
val not_disjD = thm "meson_not_disjD";
paulson@15579
    71
val not_notD = thm "meson_not_notD";
paulson@15579
    72
val not_allD = thm "meson_not_allD";
paulson@15579
    73
val not_exD = thm "meson_not_exD";
paulson@15579
    74
val imp_to_disjD = thm "meson_imp_to_disjD";
paulson@15579
    75
val not_impD = thm "meson_not_impD";
paulson@15579
    76
val iff_to_disjD = thm "meson_iff_to_disjD";
paulson@15579
    77
val not_iffD = thm "meson_not_iffD";
paulson@15579
    78
val conj_exD1 = thm "meson_conj_exD1";
paulson@15579
    79
val conj_exD2 = thm "meson_conj_exD2";
paulson@15579
    80
val disj_exD = thm "meson_disj_exD";
paulson@15579
    81
val disj_exD1 = thm "meson_disj_exD1";
paulson@15579
    82
val disj_exD2 = thm "meson_disj_exD2";
paulson@15579
    83
val disj_assoc = thm "meson_disj_assoc";
paulson@15579
    84
val disj_comm = thm "meson_disj_comm";
paulson@15579
    85
val disj_FalseD1 = thm "meson_disj_FalseD1";
paulson@15579
    86
val disj_FalseD2 = thm "meson_disj_FalseD2";
paulson@9840
    87
paulson@9840
    88
paulson@15579
    89
(**** Operators for forward proof ****)
paulson@15579
    90
paulson@20417
    91
paulson@20417
    92
(** First-order Resolution **)
paulson@20417
    93
paulson@20417
    94
fun typ_pair_of (ix, (sort,ty)) = (TVar (ix,sort), ty);
paulson@20417
    95
fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t);
paulson@20417
    96
paulson@20417
    97
(*FIXME: currently does not "rename variables apart"*)
paulson@20417
    98
fun first_order_resolve thA thB =
wenzelm@32262
    99
  (case
wenzelm@32262
   100
    try (fn () =>
wenzelm@32262
   101
      let val thy = theory_of_thm thA
wenzelm@32262
   102
          val tmA = concl_of thA
wenzelm@32262
   103
          val Const("==>",_) $ tmB $ _ = prop_of thB
blanchet@37398
   104
          val tenv =
blanchet@37410
   105
            Pattern.first_order_match thy (tmB, tmA)
blanchet@37410
   106
                                          (Vartab.empty, Vartab.empty) |> snd
wenzelm@32262
   107
          val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv)
wenzelm@32262
   108
      in  thA RS (cterm_instantiate ct_pairs thB)  end) () of
wenzelm@32262
   109
    SOME th => th
blanchet@37398
   110
  | NONE => raise THM ("first_order_resolve", 0, [thA, thB]))
paulson@18175
   111
wenzelm@24300
   112
fun flexflex_first_order th =
wenzelm@38709
   113
  case Thm.tpairs_of th of
paulson@23440
   114
      [] => th
paulson@23440
   115
    | pairs =>
wenzelm@24300
   116
        let val thy = theory_of_thm th
wenzelm@32032
   117
            val (tyenv, tenv) =
wenzelm@32032
   118
              fold (Pattern.first_order_match thy) pairs (Vartab.empty, Vartab.empty)
wenzelm@24300
   119
            val t_pairs = map term_pair_of (Vartab.dest tenv)
wenzelm@24300
   120
            val th' = Thm.instantiate ([], map (pairself (cterm_of thy)) t_pairs) th
wenzelm@24300
   121
        in  th'  end
wenzelm@24300
   122
        handle THM _ => th;
paulson@23440
   123
paulson@24937
   124
(*Forward proof while preserving bound variables names*)
paulson@24937
   125
fun rename_bvs_RS th rl =
paulson@24937
   126
  let val th' = th RS rl
paulson@24937
   127
  in  Thm.rename_boundvars (concl_of th') (concl_of th) th' end;
paulson@24937
   128
paulson@24937
   129
(*raises exception if no rules apply*)
wenzelm@24300
   130
fun tryres (th, rls) =
paulson@18141
   131
  let fun tryall [] = raise THM("tryres", 0, th::rls)
paulson@24937
   132
        | tryall (rl::rls) = (rename_bvs_RS th rl handle THM _ => tryall rls)
paulson@18141
   133
  in  tryall rls  end;
wenzelm@24300
   134
paulson@21050
   135
(*Permits forward proof from rules that discharge assumptions. The supplied proof state st,
paulson@21050
   136
  e.g. from conj_forward, should have the form
paulson@21050
   137
    "[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q"
paulson@21050
   138
  and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*)
wenzelm@32262
   139
fun forward_res ctxt nf st =
paulson@21050
   140
  let fun forward_tacf [prem] = rtac (nf prem) 1
wenzelm@24300
   141
        | forward_tacf prems =
wenzelm@32091
   142
            error (cat_lines
wenzelm@32091
   143
              ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:" ::
wenzelm@32262
   144
                Display.string_of_thm ctxt st ::
wenzelm@32262
   145
                "Premises:" :: map (Display.string_of_thm ctxt) prems))
paulson@21050
   146
  in
wenzelm@37781
   147
    case Seq.pull (ALLGOALS (Misc_Legacy.METAHYPS forward_tacf) st)
paulson@21050
   148
    of SOME(th,_) => th
paulson@21050
   149
     | NONE => raise THM("forward_res", 0, [st])
paulson@21050
   150
  end;
paulson@15579
   151
paulson@20134
   152
(*Are any of the logical connectives in "bs" present in the term?*)
paulson@20134
   153
fun has_conns bs =
paulson@20134
   154
  let fun has (Const(a,_)) = false
haftmann@38557
   155
        | has (Const(@{const_name Trueprop},_) $ p) = has p
haftmann@38557
   156
        | has (Const(@{const_name Not},_) $ p) = has p
haftmann@38795
   157
        | has (Const(@{const_name HOL.disj},_) $ p $ q) = member (op =) bs @{const_name HOL.disj} orelse has p orelse has q
haftmann@38795
   158
        | has (Const(@{const_name HOL.conj},_) $ p $ q) = member (op =) bs @{const_name HOL.conj} orelse has p orelse has q
haftmann@38557
   159
        | has (Const(@{const_name All},_) $ Abs(_,_,p)) = member (op =) bs @{const_name All} orelse has p
haftmann@38557
   160
        | has (Const(@{const_name Ex},_) $ Abs(_,_,p)) = member (op =) bs @{const_name Ex} orelse has p
wenzelm@24300
   161
        | has _ = false
paulson@15579
   162
  in  has  end;
wenzelm@24300
   163
paulson@9840
   164
paulson@15579
   165
(**** Clause handling ****)
paulson@9840
   166
haftmann@38557
   167
fun literals (Const(@{const_name Trueprop},_) $ P) = literals P
haftmann@38795
   168
  | literals (Const(@{const_name HOL.disj},_) $ P $ Q) = literals P @ literals Q
haftmann@38557
   169
  | literals (Const(@{const_name Not},_) $ P) = [(false,P)]
paulson@15579
   170
  | literals P = [(true,P)];
paulson@9840
   171
paulson@15579
   172
(*number of literals in a term*)
paulson@15579
   173
val nliterals = length o literals;
paulson@9840
   174
paulson@18389
   175
paulson@18389
   176
(*** Tautology Checking ***)
paulson@18389
   177
haftmann@38795
   178
fun signed_lits_aux (Const (@{const_name HOL.disj}, _) $ P $ Q) (poslits, neglits) =
paulson@18389
   179
      signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
haftmann@38557
   180
  | signed_lits_aux (Const(@{const_name Not},_) $ P) (poslits, neglits) = (poslits, P::neglits)
paulson@18389
   181
  | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
wenzelm@24300
   182
paulson@18389
   183
fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
paulson@18389
   184
paulson@18389
   185
(*Literals like X=X are tautologous*)
haftmann@38549
   186
fun taut_poslit (Const(@{const_name "op ="},_) $ t $ u) = t aconv u
haftmann@38557
   187
  | taut_poslit (Const(@{const_name True},_)) = true
paulson@18389
   188
  | taut_poslit _ = false;
paulson@18389
   189
paulson@18389
   190
fun is_taut th =
paulson@18389
   191
  let val (poslits,neglits) = signed_lits th
paulson@18389
   192
  in  exists taut_poslit poslits
paulson@18389
   193
      orelse
wenzelm@20073
   194
      exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
paulson@19894
   195
  end
wenzelm@24300
   196
  handle TERM _ => false;       (*probably dest_Trueprop on a weird theorem*)
paulson@18389
   197
paulson@18389
   198
paulson@18389
   199
(*** To remove trivial negated equality literals from clauses ***)
paulson@18389
   200
paulson@18389
   201
(*They are typically functional reflexivity axioms and are the converses of
paulson@18389
   202
  injectivity equivalences*)
wenzelm@24300
   203
paulson@18389
   204
val not_refl_disj_D = thm"meson_not_refl_disj_D";
paulson@18389
   205
paulson@20119
   206
(*Is either term a Var that does not properly occur in the other term?*)
paulson@20119
   207
fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
paulson@20119
   208
  | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
paulson@20119
   209
  | eliminable _ = false;
paulson@20119
   210
paulson@18389
   211
fun refl_clause_aux 0 th = th
paulson@18389
   212
  | refl_clause_aux n th =
paulson@18389
   213
       case HOLogic.dest_Trueprop (concl_of th) of
haftmann@38795
   214
          (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _) =>
paulson@18389
   215
            refl_clause_aux n (th RS disj_assoc)    (*isolate an atom as first disjunct*)
haftmann@38795
   216
        | (Const (@{const_name HOL.disj}, _) $ (Const(@{const_name Not},_) $ (Const(@{const_name "op ="},_) $ t $ u)) $ _) =>
wenzelm@24300
   217
            if eliminable(t,u)
wenzelm@24300
   218
            then refl_clause_aux (n-1) (th RS not_refl_disj_D)  (*Var inequation: delete*)
wenzelm@24300
   219
            else refl_clause_aux (n-1) (th RS disj_comm)  (*not between Vars: ignore*)
haftmann@38795
   220
        | (Const (@{const_name HOL.disj}, _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
wenzelm@24300
   221
        | _ => (*not a disjunction*) th;
paulson@18389
   222
haftmann@38795
   223
fun notequal_lits_count (Const (@{const_name HOL.disj}, _) $ P $ Q) =
paulson@18389
   224
      notequal_lits_count P + notequal_lits_count Q
haftmann@38557
   225
  | notequal_lits_count (Const(@{const_name Not},_) $ (Const(@{const_name "op ="},_) $ _ $ _)) = 1
paulson@18389
   226
  | notequal_lits_count _ = 0;
paulson@18389
   227
paulson@18389
   228
(*Simplify a clause by applying reflexivity to its negated equality literals*)
wenzelm@24300
   229
fun refl_clause th =
paulson@18389
   230
  let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
paulson@19894
   231
  in  zero_var_indexes (refl_clause_aux neqs th)  end
wenzelm@24300
   232
  handle TERM _ => th;  (*probably dest_Trueprop on a weird theorem*)
paulson@18389
   233
paulson@18389
   234
paulson@24937
   235
(*** Removal of duplicate literals ***)
paulson@24937
   236
paulson@24937
   237
(*Forward proof, passing extra assumptions as theorems to the tactic*)
wenzelm@32262
   238
fun forward_res2 ctxt nf hyps st =
paulson@24937
   239
  case Seq.pull
paulson@24937
   240
        (REPEAT
wenzelm@37781
   241
         (Misc_Legacy.METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
paulson@24937
   242
         st)
paulson@24937
   243
  of SOME(th,_) => th
paulson@24937
   244
   | NONE => raise THM("forward_res2", 0, [st]);
paulson@24937
   245
paulson@24937
   246
(*Remove duplicates in P|Q by assuming ~P in Q
paulson@24937
   247
  rls (initially []) accumulates assumptions of the form P==>False*)
wenzelm@32262
   248
fun nodups_aux ctxt rls th = nodups_aux ctxt rls (th RS disj_assoc)
paulson@24937
   249
    handle THM _ => tryres(th,rls)
wenzelm@32262
   250
    handle THM _ => tryres(forward_res2 ctxt (nodups_aux ctxt) rls (th RS disj_forward2),
paulson@24937
   251
                           [disj_FalseD1, disj_FalseD2, asm_rl])
paulson@24937
   252
    handle THM _ => th;
paulson@24937
   253
paulson@24937
   254
(*Remove duplicate literals, if there are any*)
wenzelm@32262
   255
fun nodups ctxt th =
paulson@24937
   256
  if has_duplicates (op =) (literals (prop_of th))
wenzelm@32262
   257
    then nodups_aux ctxt [] th
paulson@24937
   258
    else th;
paulson@24937
   259
paulson@24937
   260
paulson@18389
   261
(*** The basic CNF transformation ***)
paulson@18389
   262
paulson@26562
   263
fun too_many_clauses ctxto t = 
paulson@26562
   264
 let
paulson@26562
   265
  val max_cl = case ctxto of SOME ctxt => Config.get ctxt max_clauses
paulson@26562
   266
                           | NONE => max_clauses_default
paulson@26562
   267
  
paulson@26562
   268
  fun sum x y = if x < max_cl andalso y < max_cl then x+y else max_cl;
paulson@26562
   269
  fun prod x y = if x < max_cl andalso y < max_cl then x*y else max_cl;
paulson@26562
   270
  
paulson@26562
   271
  (*Estimate the number of clauses in order to detect infeasible theorems*)
haftmann@38557
   272
  fun signed_nclauses b (Const(@{const_name Trueprop},_) $ t) = signed_nclauses b t
haftmann@38557
   273
    | signed_nclauses b (Const(@{const_name Not},_) $ t) = signed_nclauses (not b) t
haftmann@38795
   274
    | signed_nclauses b (Const(@{const_name HOL.conj},_) $ t $ u) =
wenzelm@32960
   275
        if b then sum (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   276
             else prod (signed_nclauses b t) (signed_nclauses b u)
haftmann@38795
   277
    | signed_nclauses b (Const(@{const_name HOL.disj},_) $ t $ u) =
wenzelm@32960
   278
        if b then prod (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   279
             else sum (signed_nclauses b t) (signed_nclauses b u)
haftmann@38786
   280
    | signed_nclauses b (Const(@{const_name HOL.implies},_) $ t $ u) =
wenzelm@32960
   281
        if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
wenzelm@32960
   282
             else sum (signed_nclauses (not b) t) (signed_nclauses b u)
haftmann@38549
   283
    | signed_nclauses b (Const(@{const_name "op ="}, Type ("fun", [T, _])) $ t $ u) =
wenzelm@32960
   284
        if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
wenzelm@32960
   285
            if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
wenzelm@32960
   286
                          (prod (signed_nclauses (not b) u) (signed_nclauses b t))
wenzelm@32960
   287
                 else sum (prod (signed_nclauses b t) (signed_nclauses b u))
wenzelm@32960
   288
                          (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
wenzelm@32960
   289
        else 1
haftmann@38557
   290
    | signed_nclauses b (Const(@{const_name Ex}, _) $ Abs (_,_,t)) = signed_nclauses b t
haftmann@38557
   291
    | signed_nclauses b (Const(@{const_name All},_) $ Abs (_,_,t)) = signed_nclauses b t
paulson@26562
   292
    | signed_nclauses _ _ = 1; (* literal *)
paulson@26562
   293
 in 
paulson@26562
   294
  signed_nclauses true t >= max_cl
paulson@26562
   295
 end;
paulson@19894
   296
paulson@15579
   297
(*Replaces universally quantified variables by FREE variables -- because
paulson@24937
   298
  assumptions may not contain scheme variables.  Later, generalize using Variable.export. *)
paulson@24937
   299
local  
paulson@24937
   300
  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
paulson@24937
   301
  val spec_varT = #T (Thm.rep_cterm spec_var);
haftmann@38557
   302
  fun name_of (Const (@{const_name All}, _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
paulson@24937
   303
in  
paulson@24937
   304
  fun freeze_spec th ctxt =
paulson@24937
   305
    let
paulson@24937
   306
      val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
paulson@24937
   307
      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
paulson@24937
   308
      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
paulson@24937
   309
    in (th RS spec', ctxt') end
paulson@24937
   310
end;
paulson@9840
   311
paulson@15998
   312
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   313
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@22515
   314
  instantiate a Boolean variable created by resolution with disj_forward. Since
paulson@22515
   315
  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
paulson@15579
   316
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   317
wenzelm@24300
   318
(*Any need to extend this list with
wenzelm@26424
   319
  "HOL.type_class","HOL.eq_class","Pure.term"?*)
haftmann@38557
   320
val has_meta_conn = exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
paulson@20417
   321
blanchet@37410
   322
fun apply_skolem_theorem (th, rls) =
blanchet@37398
   323
  let
blanchet@37410
   324
    fun tryall [] = raise THM ("apply_skolem_theorem", 0, th::rls)
blanchet@37398
   325
      | tryall (rl :: rls) =
blanchet@37398
   326
        first_order_resolve th rl handle THM _ => tryall rls
blanchet@37398
   327
  in tryall rls end
paulson@22515
   328
blanchet@37410
   329
(* Conjunctive normal form, adding clauses from th in front of ths (for foldr).
blanchet@37410
   330
   Strips universal quantifiers and breaks up conjunctions.
blanchet@37410
   331
   Eliminates existential quantifiers using Skolemization theorems. *)
blanchet@37410
   332
fun cnf skolem_ths ctxt (th, ths) =
wenzelm@33222
   333
  let val ctxtr = Unsynchronized.ref ctxt   (* FIXME ??? *)
paulson@24937
   334
      fun cnf_aux (th,ths) =
wenzelm@24300
   335
        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
haftmann@38795
   336
        else if not (has_conns [@{const_name All}, @{const_name Ex}, @{const_name HOL.conj}] (prop_of th))
wenzelm@32262
   337
        then nodups ctxt th :: ths (*no work to do, terminate*)
wenzelm@24300
   338
        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
haftmann@38795
   339
            Const (@{const_name HOL.conj}, _) => (*conjunction*)
wenzelm@24300
   340
                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
haftmann@38557
   341
          | Const (@{const_name All}, _) => (*universal quantifier*)
paulson@24937
   342
                let val (th',ctxt') = freeze_spec th (!ctxtr)
paulson@24937
   343
                in  ctxtr := ctxt'; cnf_aux (th', ths) end
haftmann@38557
   344
          | Const (@{const_name Ex}, _) =>
wenzelm@24300
   345
              (*existential quantifier: Insert Skolem functions*)
blanchet@37410
   346
              cnf_aux (apply_skolem_theorem (th, skolem_ths), ths)
haftmann@38795
   347
          | Const (@{const_name HOL.disj}, _) =>
wenzelm@24300
   348
              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
wenzelm@24300
   349
                all combinations of converting P, Q to CNF.*)
wenzelm@24300
   350
              let val tac =
wenzelm@37781
   351
                  Misc_Legacy.METAHYPS (resop cnf_nil) 1 THEN
wenzelm@37781
   352
                   (fn st' => st' |> Misc_Legacy.METAHYPS (resop cnf_nil) 1)
wenzelm@24300
   353
              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
wenzelm@32262
   354
          | _ => nodups ctxt th :: ths  (*no work to do*)
paulson@19154
   355
      and cnf_nil th = cnf_aux (th,[])
paulson@24937
   356
      val cls = 
wenzelm@32960
   357
            if too_many_clauses (SOME ctxt) (concl_of th)
wenzelm@32960
   358
            then (trace_msg (fn () => "cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
wenzelm@32960
   359
            else cnf_aux (th,ths)
paulson@24937
   360
  in  (cls, !ctxtr)  end;
paulson@22515
   361
blanchet@37410
   362
fun make_cnf skolem_ths th ctxt = cnf skolem_ths ctxt (th, []);
paulson@20417
   363
paulson@20417
   364
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@24937
   365
fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
paulson@9840
   366
paulson@9840
   367
paulson@15579
   368
(**** Generation of contrapositives ****)
paulson@9840
   369
haftmann@38557
   370
fun is_left (Const (@{const_name Trueprop}, _) $
haftmann@38795
   371
               (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _)) = true
paulson@21102
   372
  | is_left _ = false;
wenzelm@24300
   373
paulson@15579
   374
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
wenzelm@24300
   375
fun assoc_right th =
paulson@21102
   376
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   377
  else th;
paulson@9840
   378
paulson@15579
   379
(*Must check for negative literal first!*)
paulson@15579
   380
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   381
paulson@15579
   382
(*For ordinary resolution. *)
paulson@15579
   383
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   384
paulson@15579
   385
(*Create a goal or support clause, conclusing False*)
paulson@15579
   386
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   387
    make_goal (tryres(th, clause_rules))
paulson@15579
   388
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   389
paulson@15579
   390
(*Sort clauses by number of literals*)
paulson@15579
   391
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   392
paulson@18389
   393
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   394
blanchet@38099
   395
fun has_bool @{typ bool} = true
blanchet@38099
   396
  | has_bool (Type (_, Ts)) = exists has_bool Ts
blanchet@38099
   397
  | has_bool _ = false
blanchet@38099
   398
blanchet@38099
   399
fun has_fun (Type (@{type_name fun}, _)) = true
blanchet@38099
   400
  | has_fun (Type (_, Ts)) = exists has_fun Ts
blanchet@38099
   401
  | has_fun _ = false
wenzelm@24300
   402
wenzelm@24300
   403
(*Is the string the name of a connective? Really only | and Not can remain,
wenzelm@24300
   404
  since this code expects to be called on a clause form.*)
wenzelm@19875
   405
val is_conn = member (op =)
haftmann@38795
   406
    [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
haftmann@38786
   407
     @{const_name HOL.implies}, @{const_name Not},
haftmann@38557
   408
     @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex}];
paulson@15613
   409
wenzelm@24300
   410
(*True if the term contains a function--not a logical connective--where the type
paulson@20524
   411
  of any argument contains bool.*)
wenzelm@24300
   412
val has_bool_arg_const =
paulson@15613
   413
    exists_Const
blanchet@38099
   414
      (fn (c,T) => not(is_conn c) andalso exists has_bool (binder_types T));
paulson@22381
   415
wenzelm@24300
   416
(*A higher-order instance of a first-order constant? Example is the definition of
haftmann@38622
   417
  one, 1, at a function type in theory Function_Algebras.*)
wenzelm@24300
   418
fun higher_inst_const thy (c,T) =
paulson@22381
   419
  case binder_types T of
paulson@22381
   420
      [] => false (*not a function type, OK*)
paulson@22381
   421
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
paulson@22381
   422
paulson@24742
   423
(*Returns false if any Vars in the theorem mention type bool.
paulson@21102
   424
  Also rejects functions whose arguments are Booleans or other functions.*)
paulson@22381
   425
fun is_fol_term thy t =
haftmann@38557
   426
    Term.is_first_order ["all", @{const_name All}, @{const_name Ex}] t andalso
blanchet@38099
   427
    not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
blanchet@38099
   428
                           | _ => false) t orelse
blanchet@38099
   429
         has_bool_arg_const t orelse
wenzelm@24300
   430
         exists_Const (higher_inst_const thy) t orelse
wenzelm@24300
   431
         has_meta_conn t);
paulson@19204
   432
paulson@21102
   433
fun rigid t = not (is_Var (head_of t));
paulson@21102
   434
haftmann@38795
   435
fun ok4horn (Const (@{const_name Trueprop},_) $ (Const (@{const_name HOL.disj}, _) $ t $ _)) = rigid t
haftmann@38557
   436
  | ok4horn (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   437
  | ok4horn _ = false;
paulson@21102
   438
paulson@15579
   439
(*Create a meta-level Horn clause*)
wenzelm@24300
   440
fun make_horn crules th =
wenzelm@24300
   441
  if ok4horn (concl_of th)
paulson@21102
   442
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   443
  else th;
paulson@9840
   444
paulson@16563
   445
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   446
  is a HOL disjunction.*)
wenzelm@33339
   447
fun add_contras crules th hcs =
paulson@15579
   448
  let fun rots (0,th) = hcs
wenzelm@24300
   449
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
wenzelm@24300
   450
                        rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   451
  in case nliterals(prop_of th) of
wenzelm@24300
   452
        1 => th::hcs
paulson@15579
   453
      | n => rots(n, assoc_right th)
paulson@15579
   454
  end;
paulson@9840
   455
paulson@15579
   456
(*Use "theorem naming" to label the clauses*)
paulson@15579
   457
fun name_thms label =
wenzelm@33339
   458
    let fun name1 th (k, ths) =
wenzelm@27865
   459
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
wenzelm@33339
   460
    in  fn ths => #2 (fold_rev name1 ths (length ths, []))  end;
paulson@9840
   461
paulson@16563
   462
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   463
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   464
wenzelm@33317
   465
val neg_clauses = filter is_negative;
paulson@9840
   466
paulson@9840
   467
paulson@15579
   468
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   469
haftmann@38557
   470
fun rhyps (Const("==>",_) $ (Const(@{const_name Trueprop},_) $ A) $ phi,
wenzelm@24300
   471
           As) = rhyps(phi, A::As)
paulson@15579
   472
  | rhyps (_, As) = As;
paulson@9840
   473
paulson@15579
   474
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   475
paulson@15579
   476
(*The stringtree detects repeated assumptions.*)
wenzelm@33245
   477
fun ins_term t net = Net.insert_term (op aconv) (t, t) net;
paulson@9840
   478
paulson@15579
   479
(*detects repetitions in a list of terms*)
paulson@15579
   480
fun has_reps [] = false
paulson@15579
   481
  | has_reps [_] = false
paulson@15579
   482
  | has_reps [t,u] = (t aconv u)
wenzelm@33245
   483
  | has_reps ts = (fold ins_term ts Net.empty; false) handle Net.INSERT => true;
paulson@9840
   484
paulson@15579
   485
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   486
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   487
  | TRYING_eq_assume_tac i st =
wenzelm@31945
   488
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
paulson@18508
   489
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   490
paulson@18508
   491
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   492
paulson@15579
   493
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   494
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   495
fun check_tac st =
paulson@15579
   496
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   497
  then  Seq.empty  else  Seq.single st;
paulson@9840
   498
paulson@9840
   499
paulson@15579
   500
(* net_resolve_tac actually made it slower... *)
paulson@15579
   501
fun prolog_step_tac horns i =
paulson@15579
   502
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   503
    TRYALL_eq_assume_tac;
paulson@9840
   504
paulson@9840
   505
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
wenzelm@33339
   506
fun addconcl prem sz = size_of_term (Logic.strip_assums_concl prem) + sz;
paulson@15579
   507
wenzelm@33339
   508
fun size_of_subgoals st = fold_rev addconcl (prems_of st) 0;
paulson@15579
   509
paulson@9840
   510
paulson@9840
   511
(*Negation Normal Form*)
paulson@9840
   512
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   513
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   514
haftmann@38557
   515
fun ok4nnf (Const (@{const_name Trueprop},_) $ (Const (@{const_name Not}, _) $ t)) = rigid t
haftmann@38557
   516
  | ok4nnf (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   517
  | ok4nnf _ = false;
paulson@21102
   518
wenzelm@32262
   519
fun make_nnf1 ctxt th =
wenzelm@24300
   520
  if ok4nnf (concl_of th)
wenzelm@32262
   521
  then make_nnf1 ctxt (tryres(th, nnf_rls))
paulson@28174
   522
    handle THM ("tryres", _, _) =>
wenzelm@32262
   523
        forward_res ctxt (make_nnf1 ctxt)
wenzelm@9869
   524
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@28174
   525
    handle THM ("tryres", _, _) => th
blanchet@38608
   526
  else th
paulson@9840
   527
wenzelm@24300
   528
(*The simplification removes defined quantifiers and occurrences of True and False.
paulson@20018
   529
  nnf_ss also includes the one-point simprocs,
paulson@18405
   530
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   531
val nnf_simps =
blanchet@37539
   532
  @{thms simp_implies_def Ex1_def Ball_def Bex_def if_True if_False if_cancel
blanchet@37539
   533
         if_eq_cancel cases_simp}
blanchet@37539
   534
val nnf_extra_simps = @{thms split_ifs ex_simps all_simps simp_thms}
paulson@18405
   535
paulson@18405
   536
val nnf_ss =
wenzelm@24300
   537
  HOL_basic_ss addsimps nnf_extra_simps
wenzelm@24040
   538
    addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
paulson@15872
   539
blanchet@38089
   540
val presimplify =
blanchet@38089
   541
  rewrite_rule (map safe_mk_meta_eq nnf_simps)
blanchet@38089
   542
  #> simplify nnf_ss
blanchet@38089
   543
wenzelm@32262
   544
fun make_nnf ctxt th = case prems_of th of
blanchet@38606
   545
    [] => th |> presimplify |> make_nnf1 ctxt
paulson@21050
   546
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   547
paulson@15965
   548
(*Pull existential quantifiers to front. This accomplishes Skolemization for
paulson@15965
   549
  clauses that arise from a subgoal.*)
wenzelm@32262
   550
fun skolemize1 ctxt th =
haftmann@38557
   551
  if not (has_conns [@{const_name Ex}] (prop_of th)) then th
wenzelm@32262
   552
  else (skolemize1 ctxt (tryres(th, [choice, conj_exD1, conj_exD2,
quigley@15679
   553
                              disj_exD, disj_exD1, disj_exD2])))
paulson@28174
   554
    handle THM ("tryres", _, _) =>
wenzelm@32262
   555
        skolemize1 ctxt (forward_res ctxt (skolemize1 ctxt)
wenzelm@9869
   556
                   (tryres (th, [conj_forward, disj_forward, all_forward])))
paulson@28174
   557
    handle THM ("tryres", _, _) => 
wenzelm@32262
   558
        forward_res ctxt (skolemize1 ctxt) (rename_bvs_RS th ex_forward);
paulson@29684
   559
wenzelm@32262
   560
fun skolemize ctxt th = skolemize1 ctxt (make_nnf ctxt th);
paulson@9840
   561
wenzelm@32262
   562
fun skolemize_nnf_list _ [] = []
wenzelm@32262
   563
  | skolemize_nnf_list ctxt (th::ths) =
wenzelm@32262
   564
      skolemize ctxt th :: skolemize_nnf_list ctxt ths
paulson@25710
   565
      handle THM _ => (*RS can fail if Unify.search_bound is too small*)
wenzelm@32955
   566
       (trace_msg (fn () => "Failed to Skolemize " ^ Display.string_of_thm ctxt th);
wenzelm@32262
   567
        skolemize_nnf_list ctxt ths);
paulson@25694
   568
wenzelm@33339
   569
fun add_clauses th cls =
wenzelm@36603
   570
  let val ctxt0 = Variable.global_thm_context th
wenzelm@33339
   571
      val (cnfs, ctxt) = make_cnf [] th ctxt0
paulson@24937
   572
  in Variable.export ctxt ctxt0 cnfs @ cls end;
paulson@9840
   573
paulson@9840
   574
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   575
  The resulting clauses are HOL disjunctions.*)
blanchet@35869
   576
fun make_clauses_unsorted ths = fold_rev add_clauses ths [];
blanchet@35869
   577
val make_clauses = sort_clauses o make_clauses_unsorted;
quigley@15773
   578
paulson@16563
   579
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   580
fun make_horns ths =
paulson@9840
   581
    name_thms "Horn#"
wenzelm@33339
   582
      (distinct Thm.eq_thm_prop (fold_rev (add_contras clause_rules) ths []));
paulson@9840
   583
paulson@9840
   584
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   585
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   586
wenzelm@9869
   587
fun best_prolog_tac sizef horns =
paulson@9840
   588
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   589
wenzelm@9869
   590
fun depth_prolog_tac horns =
paulson@9840
   591
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   592
paulson@9840
   593
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   594
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   595
wenzelm@32262
   596
fun skolemize_prems_tac ctxt prems =
blanchet@37926
   597
  cut_facts_tac (skolemize_nnf_list ctxt prems) THEN' REPEAT o etac exE
paulson@9840
   598
paulson@22546
   599
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
paulson@22546
   600
  Function mkcl converts theorems to clauses.*)
wenzelm@32262
   601
fun MESON mkcl cltac ctxt i st =
paulson@16588
   602
  SELECT_GOAL
wenzelm@35625
   603
    (EVERY [Object_Logic.atomize_prems_tac 1,
paulson@23552
   604
            rtac ccontr 1,
wenzelm@32283
   605
            Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
wenzelm@32262
   606
                      EVERY1 [skolemize_prems_tac ctxt negs,
wenzelm@32283
   607
                              Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
wenzelm@24300
   608
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
paulson@9840
   609
paulson@9840
   610
(** Best-first search versions **)
paulson@9840
   611
paulson@16563
   612
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
wenzelm@9869
   613
fun best_meson_tac sizef =
wenzelm@24300
   614
  MESON make_clauses
paulson@22546
   615
    (fn cls =>
paulson@9840
   616
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   617
                         (has_fewer_prems 1, sizef)
paulson@9840
   618
                         (prolog_step_tac (make_horns cls) 1));
paulson@9840
   619
paulson@9840
   620
(*First, breaks the goal into independent units*)
wenzelm@32262
   621
fun safe_best_meson_tac ctxt =
wenzelm@32262
   622
     SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
wenzelm@32262
   623
                  TRYALL (best_meson_tac size_of_subgoals ctxt));
paulson@9840
   624
paulson@9840
   625
(** Depth-first search version **)
paulson@9840
   626
paulson@9840
   627
val depth_meson_tac =
paulson@22546
   628
  MESON make_clauses
paulson@22546
   629
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
paulson@9840
   630
paulson@9840
   631
paulson@9840
   632
(** Iterative deepening version **)
paulson@9840
   633
paulson@9840
   634
(*This version does only one inference per call;
paulson@9840
   635
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   636
fun prolog_step_tac' horns =
paulson@9840
   637
    let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
paulson@9840
   638
            take_prefix Thm.no_prems horns
paulson@9840
   639
        val nrtac = net_resolve_tac horns
paulson@9840
   640
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   641
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   642
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   643
    end;
paulson@9840
   644
wenzelm@9869
   645
fun iter_deepen_prolog_tac horns =
wenzelm@38802
   646
    ITER_DEEPEN iter_deepen_limit (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   647
wenzelm@32262
   648
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON make_clauses
wenzelm@32091
   649
  (fn cls =>
wenzelm@32091
   650
    (case (gocls (cls @ ths)) of
wenzelm@32091
   651
      [] => no_tac  (*no goal clauses*)
wenzelm@32091
   652
    | goes =>
wenzelm@32091
   653
        let
wenzelm@32091
   654
          val horns = make_horns (cls @ ths)
wenzelm@32955
   655
          val _ = trace_msg (fn () =>
wenzelm@32091
   656
            cat_lines ("meson method called:" ::
wenzelm@32262
   657
              map (Display.string_of_thm ctxt) (cls @ ths) @
wenzelm@32262
   658
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
wenzelm@38802
   659
        in
wenzelm@38802
   660
          THEN_ITER_DEEPEN iter_deepen_limit
wenzelm@38802
   661
            (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
wenzelm@38802
   662
        end));
paulson@9840
   663
wenzelm@32262
   664
fun meson_tac ctxt ths =
wenzelm@32262
   665
  SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
wenzelm@9869
   666
wenzelm@9869
   667
paulson@14813
   668
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   669
wenzelm@24300
   670
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
paulson@15008
   671
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   672
paulson@14744
   673
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   674
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   675
  prevents a double negation.*)
wenzelm@27239
   676
val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
paulson@14744
   677
val notEfalse' = rotate_prems 1 notEfalse;
paulson@14744
   678
wenzelm@24300
   679
fun negated_asm_of_head th =
paulson@14744
   680
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   681
paulson@26066
   682
(*Converting one theorem from a disjunction to a meta-level clause*)
paulson@26066
   683
fun make_meta_clause th =
wenzelm@33832
   684
  let val (fth,thaw) = Drule.legacy_freeze_thaw_robust th
paulson@26066
   685
  in  
wenzelm@35845
   686
      (zero_var_indexes o Thm.varifyT_global o thaw 0 o 
paulson@26066
   687
       negated_asm_of_head o make_horn resolution_clause_rules) fth
paulson@26066
   688
  end;
wenzelm@24300
   689
paulson@14744
   690
fun make_meta_clauses ths =
paulson@14744
   691
    name_thms "MClause#"
wenzelm@22360
   692
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   693
paulson@14744
   694
(*Permute a rule's premises to move the i-th premise to the last position.*)
paulson@14744
   695
fun make_last i th =
wenzelm@24300
   696
  let val n = nprems_of th
wenzelm@24300
   697
  in  if 1 <= i andalso i <= n
paulson@14744
   698
      then Thm.permute_prems (i-1) 1 th
paulson@15118
   699
      else raise THM("select_literal", i, [th])
paulson@14744
   700
  end;
paulson@14744
   701
paulson@14744
   702
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
paulson@14744
   703
  double-negations.*)
wenzelm@35410
   704
val negate_head = rewrite_rule [@{thm atomize_not}, not_not RS eq_reflection];
paulson@14744
   705
paulson@14744
   706
(*Maps the clause  [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
paulson@14744
   707
fun select_literal i cl = negate_head (make_last i cl);
paulson@14744
   708
paulson@18508
   709
paulson@14813
   710
(*Top-level Skolemization. Allows part of the conversion to clauses to be
wenzelm@24300
   711
  expressed as a tactic (or Isar method).  Each assumption of the selected
paulson@14813
   712
  goal is converted to NNF and then its existential quantifiers are pulled
wenzelm@24300
   713
  to the front. Finally, all existential quantifiers are eliminated,
paulson@14813
   714
  leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
paulson@14813
   715
  might generate many subgoals.*)
mengj@18194
   716
wenzelm@32262
   717
fun skolemize_tac ctxt = SUBGOAL (fn (goal, i) =>
wenzelm@32262
   718
  let val ts = Logic.strip_assums_hyp goal
wenzelm@24300
   719
  in
wenzelm@32262
   720
    EVERY'
wenzelm@37781
   721
     [Misc_Legacy.METAHYPS (fn hyps =>
wenzelm@32262
   722
        (cut_facts_tac (skolemize_nnf_list ctxt hyps) 1
wenzelm@32262
   723
          THEN REPEAT (etac exE 1))),
wenzelm@32262
   724
      REPEAT_DETERM_N (length ts) o (etac thin_rl)] i
wenzelm@32262
   725
  end);
mengj@18194
   726
paulson@9840
   727
end;