src/HOL/Tools/Sledgehammer/meson_clausify.ML
author blanchet
Mon Oct 04 09:08:46 2010 +0200 (2010-10-04)
changeset 39931 97b8051033be
parent 39908 44cd24da1beb
child 39932 acde1b606b0e
permissions -rw-r--r--
renamed internal function
blanchet@39890
     1
(*  Title:      HOL/Tools/Sledgehammer/meson_clausify.ML
blanchet@38027
     2
    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
blanchet@36393
     3
    Author:     Jasmin Blanchette, TU Muenchen
paulson@15347
     4
wenzelm@20461
     5
Transformation of axiom rules (elim/intro/etc) into CNF forms.
paulson@15347
     6
*)
paulson@15347
     7
blanchet@39890
     8
signature MESON_CLAUSIFY =
wenzelm@21505
     9
sig
blanchet@39887
    10
  val new_skolem_var_prefix : string
blanchet@38632
    11
  val extensionalize_theorem : thm -> thm
blanchet@38001
    12
  val introduce_combinators_in_cterm : cterm -> thm
blanchet@38028
    13
  val introduce_combinators_in_theorem : thm -> thm
blanchet@39037
    14
  val to_definitional_cnf_with_quantifiers : theory -> thm -> thm
blanchet@39899
    15
  val cluster_of_zapped_var_name : string -> (int * int) * bool
blanchet@39897
    16
  val cnf_axiom :
blanchet@39901
    17
    Proof.context -> bool -> int -> thm -> (thm * term) option * thm list
blanchet@39720
    18
  val meson_general_tac : Proof.context -> thm list -> int -> tactic
blanchet@39720
    19
  val setup: theory -> theory
wenzelm@21505
    20
end;
mengj@19196
    21
blanchet@39890
    22
structure Meson_Clausify : MESON_CLAUSIFY =
paulson@15997
    23
struct
paulson@15347
    24
blanchet@39899
    25
(* the extra "?" helps prevent clashes *)
blanchet@39899
    26
val new_skolem_var_prefix = "?SK"
blanchet@39899
    27
val new_nonskolem_var_prefix = "?V"
blanchet@39887
    28
paulson@15997
    29
(**** Transformation of Elimination Rules into First-Order Formulas****)
paulson@15347
    30
wenzelm@29064
    31
val cfalse = cterm_of @{theory HOL} HOLogic.false_const;
wenzelm@29064
    32
val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const);
wenzelm@20461
    33
blanchet@38001
    34
(* Converts an elim-rule into an equivalent theorem that does not have the
blanchet@38001
    35
   predicate variable. Leaves other theorems unchanged. We simply instantiate
blanchet@38001
    36
   the conclusion variable to False. (Cf. "transform_elim_term" in
blanchet@38652
    37
   "Sledgehammer_Util".) *)
blanchet@38001
    38
fun transform_elim_theorem th =
paulson@21430
    39
  case concl_of th of    (*conclusion variable*)
blanchet@35963
    40
       @{const Trueprop} $ (v as Var (_, @{typ bool})) =>
wenzelm@29064
    41
           Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th
blanchet@35963
    42
    | v as Var(_, @{typ prop}) =>
wenzelm@29064
    43
           Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th
blanchet@38001
    44
    | _ => th
paulson@15997
    45
wenzelm@28544
    46
paulson@16009
    47
(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
paulson@16009
    48
blanchet@39886
    49
fun mk_old_skolem_term_wrapper t =
blanchet@37436
    50
  let val T = fastype_of t in
blanchet@39355
    51
    Const (@{const_name skolem}, T --> T) $ t
blanchet@37436
    52
  end
blanchet@37410
    53
blanchet@39931
    54
fun beta_eta_in_abs_body (Abs (s, T, t')) = Abs (s, T, beta_eta_in_abs_body t')
blanchet@39931
    55
  | beta_eta_in_abs_body t = Envir.beta_eta_contract t
blanchet@37512
    56
paulson@18141
    57
(*Traverse a theorem, accumulating Skolem function definitions.*)
blanchet@39886
    58
fun old_skolem_defs th =
blanchet@37399
    59
  let
blanchet@39376
    60
    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (_, T, p))) rhss =
blanchet@37399
    61
        (*Existential: declare a Skolem function, then insert into body and continue*)
blanchet@37399
    62
        let
blanchet@37617
    63
          val args = OldTerm.term_frees body
blanchet@37500
    64
          (* Forms a lambda-abstraction over the formal parameters *)
blanchet@37500
    65
          val rhs =
blanchet@37500
    66
            list_abs_free (map dest_Free args,
blanchet@39931
    67
                           HOLogic.choice_const T $ beta_eta_in_abs_body body)
blanchet@39886
    68
            |> mk_old_skolem_term_wrapper
blanchet@37518
    69
          val comb = list_comb (rhs, args)
blanchet@37617
    70
        in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end
blanchet@37617
    71
      | dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) rhss =
blanchet@37399
    72
        (*Universal quant: insert a free variable into body and continue*)
blanchet@37399
    73
        let val fname = Name.variant (OldTerm.add_term_names (p,[])) a
blanchet@37617
    74
        in dec_sko (subst_bound (Free(fname,T), p)) rhss end
blanchet@39906
    75
      | dec_sko (@{const conj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q
blanchet@39906
    76
      | dec_sko (@{const disj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q
blanchet@37617
    77
      | dec_sko (@{const Trueprop} $ p) rhss = dec_sko p rhss
blanchet@37617
    78
      | dec_sko _ rhss = rhss
paulson@20419
    79
  in  dec_sko (prop_of th) []  end;
paulson@20419
    80
paulson@20419
    81
paulson@24827
    82
(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
paulson@20419
    83
nipkow@39302
    84
val fun_cong_all = @{thm fun_eq_iff [THEN iffD1]}
paulson@20419
    85
blanchet@38001
    86
(* Removes the lambdas from an equation of the form "t = (%x. u)".
blanchet@38608
    87
   (Cf. "extensionalize_term" in "Sledgehammer_Translate".) *)
blanchet@38000
    88
fun extensionalize_theorem th =
blanchet@37540
    89
  case prop_of th of
haftmann@38864
    90
    _ $ (Const (@{const_name HOL.eq}, Type (_, [Type (@{type_name fun}, _), _]))
blanchet@39376
    91
         $ _ $ Abs _) => extensionalize_theorem (th RS fun_cong_all)
blanchet@37540
    92
  | _ => th
paulson@20419
    93
blanchet@39355
    94
fun is_quasi_lambda_free (Const (@{const_name skolem}, _) $ _) = true
blanchet@37416
    95
  | is_quasi_lambda_free (t1 $ t2) =
blanchet@37416
    96
    is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2
blanchet@37416
    97
  | is_quasi_lambda_free (Abs _) = false
blanchet@37416
    98
  | is_quasi_lambda_free _ = true
wenzelm@20461
    99
wenzelm@32010
   100
val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B}));
wenzelm@32010
   101
val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
wenzelm@32010
   102
val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
paulson@20863
   103
blanchet@38282
   104
(* FIXME: Requires more use of cterm constructors. *)
paulson@24827
   105
fun abstract ct =
wenzelm@28544
   106
  let
wenzelm@28544
   107
      val thy = theory_of_cterm ct
paulson@25256
   108
      val Abs(x,_,body) = term_of ct
blanchet@35963
   109
      val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct)
blanchet@38005
   110
      val cxT = ctyp_of thy xT
blanchet@38005
   111
      val cbodyT = ctyp_of thy bodyT
blanchet@38005
   112
      fun makeK () =
blanchet@38005
   113
        instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)]
blanchet@38005
   114
                     @{thm abs_K}
paulson@24827
   115
  in
paulson@24827
   116
      case body of
paulson@24827
   117
          Const _ => makeK()
paulson@24827
   118
        | Free _ => makeK()
paulson@24827
   119
        | Var _ => makeK()  (*though Var isn't expected*)
wenzelm@27184
   120
        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
paulson@24827
   121
        | rator$rand =>
wenzelm@27184
   122
            if loose_bvar1 (rator,0) then (*C or S*)
wenzelm@27179
   123
               if loose_bvar1 (rand,0) then (*S*)
wenzelm@27179
   124
                 let val crator = cterm_of thy (Abs(x,xT,rator))
wenzelm@27179
   125
                     val crand = cterm_of thy (Abs(x,xT,rand))
wenzelm@27184
   126
                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
wenzelm@27184
   127
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
wenzelm@27179
   128
                 in
wenzelm@27179
   129
                   Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
wenzelm@27179
   130
                 end
wenzelm@27179
   131
               else (*C*)
wenzelm@27179
   132
                 let val crator = cterm_of thy (Abs(x,xT,rator))
wenzelm@27184
   133
                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
wenzelm@27184
   134
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
wenzelm@27179
   135
                 in
wenzelm@27179
   136
                   Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
wenzelm@27179
   137
                 end
wenzelm@27184
   138
            else if loose_bvar1 (rand,0) then (*B or eta*)
wenzelm@36945
   139
               if rand = Bound 0 then Thm.eta_conversion ct
wenzelm@27179
   140
               else (*B*)
wenzelm@27179
   141
                 let val crand = cterm_of thy (Abs(x,xT,rand))
wenzelm@27179
   142
                     val crator = cterm_of thy rator
wenzelm@27184
   143
                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
wenzelm@27184
   144
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
blanchet@37349
   145
                 in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end
wenzelm@27179
   146
            else makeK()
blanchet@37349
   147
        | _ => raise Fail "abstract: Bad term"
paulson@24827
   148
  end;
paulson@20863
   149
blanchet@37349
   150
(* Traverse a theorem, remplacing lambda-abstractions with combinators. *)
blanchet@38001
   151
fun introduce_combinators_in_cterm ct =
blanchet@37416
   152
  if is_quasi_lambda_free (term_of ct) then
blanchet@37349
   153
    Thm.reflexive ct
blanchet@37349
   154
  else case term_of ct of
blanchet@37349
   155
    Abs _ =>
blanchet@37349
   156
    let
blanchet@37349
   157
      val (cv, cta) = Thm.dest_abs NONE ct
blanchet@37349
   158
      val (v, _) = dest_Free (term_of cv)
blanchet@38001
   159
      val u_th = introduce_combinators_in_cterm cta
blanchet@37349
   160
      val cu = Thm.rhs_of u_th
blanchet@37349
   161
      val comb_eq = abstract (Thm.cabs cv cu)
blanchet@37349
   162
    in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end
blanchet@37349
   163
  | _ $ _ =>
blanchet@37349
   164
    let val (ct1, ct2) = Thm.dest_comb ct in
blanchet@38001
   165
        Thm.combination (introduce_combinators_in_cterm ct1)
blanchet@38001
   166
                        (introduce_combinators_in_cterm ct2)
blanchet@37349
   167
    end
blanchet@37349
   168
blanchet@38001
   169
fun introduce_combinators_in_theorem th =
blanchet@37416
   170
  if is_quasi_lambda_free (prop_of th) then
blanchet@37349
   171
    th
paulson@24827
   172
  else
blanchet@37349
   173
    let
blanchet@37349
   174
      val th = Drule.eta_contraction_rule th
blanchet@38001
   175
      val eqth = introduce_combinators_in_cterm (cprop_of th)
blanchet@37349
   176
    in Thm.equal_elim eqth th end
blanchet@37349
   177
    handle THM (msg, _, _) =>
blanchet@37349
   178
           (warning ("Error in the combinator translation of " ^
blanchet@37349
   179
                     Display.string_of_thm_without_context th ^
blanchet@37349
   180
                     "\nException message: " ^ msg ^ ".");
blanchet@37349
   181
            (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@37349
   182
            TrueI)
paulson@16009
   183
paulson@16009
   184
(*cterms are used throughout for efficiency*)
blanchet@38280
   185
val cTrueprop = cterm_of @{theory HOL} HOLogic.Trueprop;
paulson@16009
   186
paulson@16009
   187
(*Given an abstraction over n variables, replace the bound variables by free
paulson@16009
   188
  ones. Return the body, along with the list of free variables.*)
wenzelm@20461
   189
fun c_variant_abs_multi (ct0, vars) =
paulson@16009
   190
      let val (cv,ct) = Thm.dest_abs NONE ct0
paulson@16009
   191
      in  c_variant_abs_multi (ct, cv::vars)  end
paulson@16009
   192
      handle CTERM _ => (ct0, rev vars);
paulson@16009
   193
blanchet@39355
   194
val skolem_def_raw = @{thms skolem_def_raw}
blanchet@37617
   195
blanchet@37617
   196
(* Given the definition of a Skolem function, return a theorem to replace
blanchet@37617
   197
   an existential formula by a use of that function.
paulson@18141
   198
   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
blanchet@39886
   199
fun old_skolem_theorem_from_def thy rhs0 =
blanchet@37399
   200
  let
blanchet@38280
   201
    val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> cterm_of thy
blanchet@37617
   202
    val rhs' = rhs |> Thm.dest_comb |> snd
blanchet@37617
   203
    val (ch, frees) = c_variant_abs_multi (rhs', [])
blanchet@37617
   204
    val (hilbert, cabs) = ch |> Thm.dest_comb |>> term_of
blanchet@37617
   205
    val T =
blanchet@37617
   206
      case hilbert of
blanchet@37617
   207
        Const (@{const_name Eps}, Type (@{type_name fun}, [_, T])) => T
blanchet@39886
   208
      | _ => raise TERM ("old_skolem_theorem_from_def: expected \"Eps\"",
blanchet@39886
   209
                         [hilbert])
blanchet@38280
   210
    val cex = cterm_of thy (HOLogic.exists_const T)
blanchet@37617
   211
    val ex_tm = Thm.capply cTrueprop (Thm.capply cex cabs)
blanchet@37629
   212
    val conc =
blanchet@37617
   213
      Drule.list_comb (rhs, frees)
blanchet@37617
   214
      |> Drule.beta_conv cabs |> Thm.capply cTrueprop
blanchet@37617
   215
    fun tacf [prem] =
blanchet@39355
   216
      rewrite_goals_tac skolem_def_raw
blanchet@39355
   217
      THEN rtac ((prem |> rewrite_rule skolem_def_raw) RS @{thm someI_ex}) 1
blanchet@37617
   218
  in
blanchet@37629
   219
    Goal.prove_internal [ex_tm] conc tacf
blanchet@37629
   220
    |> forall_intr_list frees
blanchet@37629
   221
    |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
blanchet@37629
   222
    |> Thm.varifyT_global
blanchet@37617
   223
  end
paulson@24742
   224
blanchet@39036
   225
fun to_definitional_cnf_with_quantifiers thy th =
blanchet@39036
   226
  let
blanchet@39036
   227
    val eqth = cnf.make_cnfx_thm thy (HOLogic.dest_Trueprop (prop_of th))
blanchet@39036
   228
    val eqth = eqth RS @{thm eq_reflection}
blanchet@39036
   229
    val eqth = eqth RS @{thm TruepropI}
blanchet@39036
   230
  in Thm.equal_elim eqth th end
blanchet@39036
   231
blanchet@39897
   232
fun zapped_var_name ax_no (cluster_no, skolem) s =
blanchet@39896
   233
  (if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^
blanchet@39899
   234
  "_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^ s
blanchet@39896
   235
blanchet@39899
   236
fun cluster_of_zapped_var_name s =
blanchet@39899
   237
  ((1, 2) |> pairself (the o Int.fromString o nth (space_explode "_" s)),
blanchet@39897
   238
   String.isPrefix new_skolem_var_prefix s)
blanchet@39897
   239
blanchet@39905
   240
fun rename_vars_to_be_zapped ax_no =
blanchet@39887
   241
  let
blanchet@39905
   242
    fun aux (cluster as (cluster_no, cluster_skolem)) pos t =
blanchet@39905
   243
      case t of
blanchet@39905
   244
        (t1 as Const (s, _)) $ Abs (s', T, t') =>
blanchet@39905
   245
        if s = @{const_name all} orelse s = @{const_name All} orelse
blanchet@39905
   246
           s = @{const_name Ex} then
blanchet@39905
   247
          let
blanchet@39905
   248
            val skolem = (pos = (s = @{const_name Ex}))
blanchet@39905
   249
            val cluster =
blanchet@39905
   250
              if skolem = cluster_skolem then cluster
blanchet@39905
   251
              else (cluster_no |> cluster_skolem ? Integer.add 1, skolem)
blanchet@39905
   252
            val s' = zapped_var_name ax_no cluster s'
blanchet@39905
   253
          in t1 $ Abs (s', T, aux cluster pos t') end
blanchet@39905
   254
        else
blanchet@39905
   255
          t
blanchet@39905
   256
      | (t1 as Const (s, _)) $ t2 $ t3 =>
blanchet@39906
   257
        if s = @{const_name "==>"} orelse s = @{const_name implies} then
blanchet@39905
   258
          t1 $ aux cluster (not pos) t2 $ aux cluster pos t3
blanchet@39906
   259
        else if s = @{const_name conj} orelse s = @{const_name disj} then
blanchet@39905
   260
          t1 $ aux cluster pos t2 $ aux cluster pos t3
blanchet@39905
   261
        else
blanchet@39905
   262
          t
blanchet@39905
   263
      | (t1 as Const (s, _)) $ t2 =>
blanchet@39905
   264
        if s = @{const_name Trueprop} then t1 $ aux cluster pos t2
blanchet@39905
   265
        else if s = @{const_name Not} then t1 $ aux cluster (not pos) t2
blanchet@39905
   266
        else t
blanchet@39905
   267
      | _ => t
blanchet@39905
   268
  in aux (0, true) true end
blanchet@39905
   269
blanchet@39906
   270
fun zap pos ct =
blanchet@39906
   271
  ct
blanchet@39906
   272
  |> (case term_of ct of
blanchet@39906
   273
        Const (s, _) $ Abs (s', _, _) =>
blanchet@39906
   274
        if s = @{const_name all} orelse s = @{const_name All} orelse
blanchet@39906
   275
           s = @{const_name Ex} then
blanchet@39906
   276
          Thm.dest_comb #> snd #> Thm.dest_abs (SOME s') #> snd #> zap pos
blanchet@39906
   277
        else
blanchet@39906
   278
          Conv.all_conv
blanchet@39906
   279
      | Const (s, _) $ _ $ _ =>
blanchet@39906
   280
        if s = @{const_name "==>"} orelse s = @{const_name implies} then
blanchet@39906
   281
          Conv.combination_conv (Conv.arg_conv (zap (not pos))) (zap pos)
blanchet@39906
   282
        else if s = @{const_name conj} orelse s = @{const_name disj} then
blanchet@39906
   283
          Conv.combination_conv (Conv.arg_conv (zap pos)) (zap pos)
blanchet@39906
   284
        else
blanchet@39906
   285
          Conv.all_conv
blanchet@39906
   286
      | Const (s, _) $ _ =>
blanchet@39906
   287
        if s = @{const_name Trueprop} then Conv.arg_conv (zap pos)
blanchet@39906
   288
        else if s = @{const_name Not} then Conv.arg_conv (zap (not pos))
blanchet@39906
   289
        else Conv.all_conv
blanchet@39906
   290
      | _ => Conv.all_conv)
blanchet@39887
   291
blanchet@39901
   292
fun ss_only ths = MetaSimplifier.clear_ss HOL_basic_ss addsimps ths
blanchet@39901
   293
blanchet@39901
   294
val no_choice =
blanchet@39901
   295
  @{prop "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)"}
blanchet@39901
   296
  |> Logic.varify_global
blanchet@39901
   297
  |> Skip_Proof.make_thm @{theory}
blanchet@39887
   298
blanchet@39887
   299
(* Converts an Isabelle theorem into NNF. *)
blanchet@39901
   300
fun nnf_axiom choice_ths new_skolemizer ax_no th ctxt =
blanchet@39887
   301
  let
blanchet@39887
   302
    val thy = ProofContext.theory_of ctxt
blanchet@39887
   303
    val th =
blanchet@39887
   304
      th |> transform_elim_theorem
blanchet@39887
   305
         |> zero_var_indexes
blanchet@39887
   306
         |> new_skolemizer ? forall_intr_vars
blanchet@39887
   307
    val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single
blanchet@39887
   308
    val th = th |> Conv.fconv_rule Object_Logic.atomize
blanchet@39887
   309
                |> extensionalize_theorem
blanchet@39887
   310
                |> Meson.make_nnf ctxt
blanchet@39887
   311
  in
blanchet@39887
   312
    if new_skolemizer then
blanchet@39887
   313
      let
blanchet@39907
   314
        fun rename_bound_vars th =
blanchet@39907
   315
          let val t = concl_of th in
blanchet@39907
   316
            th |> Thm.rename_boundvars t (rename_vars_to_be_zapped ax_no t)
blanchet@39907
   317
          end
blanchet@39901
   318
        fun skolemize choice_ths =
blanchet@39904
   319
          Meson.skolemize_with_choice_thms ctxt choice_ths
blanchet@39901
   320
          #> simplify (ss_only @{thms all_simps[symmetric]})
blanchet@39901
   321
        val pull_out =
blanchet@39901
   322
          simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]})
blanchet@39901
   323
        val (discharger_th, fully_skolemized_th) =
blanchet@39901
   324
          if null choice_ths then
blanchet@39907
   325
            th |> rename_bound_vars |> `I |>> pull_out ||> skolemize [no_choice]
blanchet@39901
   326
          else
blanchet@39907
   327
            th |> skolemize choice_ths |> rename_bound_vars |> `I
blanchet@39901
   328
        val t =
blanchet@39906
   329
          fully_skolemized_th |> cprop_of
blanchet@39906
   330
          |> zap true |> Drule.export_without_context
blanchet@39906
   331
          |> cprop_of |> Thm.dest_equals |> snd |> term_of
blanchet@39887
   332
      in
blanchet@39887
   333
        if exists_subterm (fn Var ((s, _), _) =>
blanchet@39887
   334
                              String.isPrefix new_skolem_var_prefix s
blanchet@39887
   335
                            | _ => false) t then
blanchet@39887
   336
          let
blanchet@39887
   337
            val (ct, ctxt) =
blanchet@39887
   338
              Variable.import_terms true [t] ctxt
blanchet@39887
   339
              |>> the_single |>> cterm_of thy
blanchet@39901
   340
          in (SOME (discharger_th, ct), Thm.assume ct, ctxt) end
blanchet@39887
   341
       else
blanchet@39908
   342
         (NONE, th, ctxt)
blanchet@39887
   343
      end
blanchet@39887
   344
    else
blanchet@39887
   345
      (NONE, th, ctxt)
blanchet@39887
   346
  end
blanchet@39887
   347
blanchet@39887
   348
(* Convert a theorem to CNF, with additional premises due to skolemization. *)
blanchet@39901
   349
fun cnf_axiom ctxt0 new_skolemizer ax_no th =
blanchet@37626
   350
  let
blanchet@39901
   351
    val thy = ProofContext.theory_of ctxt0
blanchet@39901
   352
    val choice_ths = Meson_Choices.get ctxt0
blanchet@39901
   353
    val (opt, nnf_th, ctxt) = nnf_axiom choice_ths new_skolemizer ax_no th ctxt0
blanchet@39894
   354
    fun clausify th =
blanchet@39887
   355
      Meson.make_cnf (if new_skolemizer then
blanchet@39887
   356
                        []
blanchet@39887
   357
                      else
blanchet@39887
   358
                        map (old_skolem_theorem_from_def thy)
blanchet@39887
   359
                            (old_skolem_defs th)) th ctxt
blanchet@39261
   360
    val (cnf_ths, ctxt) =
blanchet@39894
   361
      clausify nnf_th
blanchet@39894
   362
      |> (fn ([], _) =>
blanchet@39894
   363
             clausify (to_definitional_cnf_with_quantifiers thy nnf_th)
blanchet@39268
   364
           | p => p)
blanchet@39894
   365
    fun intr_imp ct th =
blanchet@39894
   366
      Thm.instantiate ([], map (pairself (cterm_of @{theory}))
blanchet@39894
   367
                               [(Var (("i", 1), @{typ nat}),
blanchet@39902
   368
                                 HOLogic.mk_nat ax_no)])
blanchet@39894
   369
                      @{thm skolem_COMBK_D}
blanchet@39894
   370
      RS Thm.implies_intr ct th
blanchet@37626
   371
  in
blanchet@39897
   372
    (opt |> Option.map (I #>> singleton (Variable.export ctxt ctxt0)
blanchet@39897
   373
                        ##> (term_of #> HOLogic.dest_Trueprop
blanchet@39897
   374
                             #> singleton (Variable.export_terms ctxt ctxt0))),
blanchet@39887
   375
     cnf_ths |> map (introduce_combinators_in_theorem
blanchet@39894
   376
                     #> (case opt of SOME (_, ct) => intr_imp ct | NONE => I))
blanchet@39897
   377
             |> Variable.export ctxt ctxt0
blanchet@39887
   378
             |> Meson.finish_cnf
blanchet@39887
   379
             |> map Thm.close_derivation)
blanchet@37626
   380
  end
blanchet@39887
   381
  handle THM _ => (NONE, [])
wenzelm@27184
   382
blanchet@39720
   383
fun meson_general_tac ctxt ths =
blanchet@39901
   384
  let val ctxt = Classical.put_claset HOL_cs ctxt in
blanchet@39901
   385
    Meson.meson_tac ctxt (maps (snd o cnf_axiom ctxt false 0) ths)
blanchet@39901
   386
  end
blanchet@39720
   387
blanchet@39720
   388
val setup =
blanchet@39891
   389
  Method.setup @{binding meson} (Attrib.thms >> (fn ths => fn ctxt =>
blanchet@39891
   390
     SIMPLE_METHOD' (CHANGED_PROP o meson_general_tac ctxt ths)))
blanchet@39891
   391
     "MESON resolution proof procedure"
blanchet@39720
   392
wenzelm@20461
   393
end;