src/HOL/Tools/Meson/meson_clausify.ML
author blanchet
Fri Oct 29 12:49:05 2010 +0200 (2010-10-29)
changeset 40262 8403085384eb
parent 40261 7a02144874f3
child 40263 51ed7a5ad4c5
permissions -rw-r--r--
ensure that MESON correctly preserves the name of variables (needed by the new Skolemizer)
blanchet@39941
     1
(*  Title:      HOL/Tools/Meson/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
blanchet@39941
     5
Transformation of HOL theorems 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@39932
    15
  val cluster_of_zapped_var_name : string -> (int * (int * int)) * bool
blanchet@39897
    16
  val cnf_axiom :
blanchet@39901
    17
    Proof.context -> bool -> int -> thm -> (thm * term) option * thm list
wenzelm@21505
    18
end;
mengj@19196
    19
blanchet@39890
    20
structure Meson_Clausify : MESON_CLAUSIFY =
paulson@15997
    21
struct
paulson@15347
    22
blanchet@39950
    23
open Meson
blanchet@39950
    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@39962
    51
    Const (@{const_name Meson.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@39962
    94
fun is_quasi_lambda_free (Const (@{const_name Meson.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@39941
   207
        Const (_, 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@39941
   217
      THEN rtac ((prem |> rewrite_rule skolem_def_raw)
blanchet@39949
   218
                 RS Global_Theory.get_thm thy "Hilbert_Choice.someI_ex") 1
blanchet@37617
   219
  in
blanchet@37629
   220
    Goal.prove_internal [ex_tm] conc tacf
blanchet@37629
   221
    |> forall_intr_list frees
blanchet@37629
   222
    |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
blanchet@37629
   223
    |> Thm.varifyT_global
blanchet@37617
   224
  end
paulson@24742
   225
blanchet@39036
   226
fun to_definitional_cnf_with_quantifiers thy th =
blanchet@39036
   227
  let
blanchet@39036
   228
    val eqth = cnf.make_cnfx_thm thy (HOLogic.dest_Trueprop (prop_of th))
blanchet@39036
   229
    val eqth = eqth RS @{thm eq_reflection}
blanchet@39036
   230
    val eqth = eqth RS @{thm TruepropI}
blanchet@39036
   231
  in Thm.equal_elim eqth th end
blanchet@39036
   232
blanchet@39932
   233
fun zapped_var_name ((ax_no, cluster_no), skolem) index_no s =
blanchet@39896
   234
  (if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^
blanchet@39932
   235
  "_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^
blanchet@40261
   236
  string_of_int index_no ^ "_" ^ Name.desymbolize false s
blanchet@39896
   237
blanchet@39899
   238
fun cluster_of_zapped_var_name s =
blanchet@39932
   239
  let val get_int = the o Int.fromString o nth (space_explode "_" s) in
blanchet@39932
   240
    ((get_int 1, (get_int 2, get_int 3)),
blanchet@39932
   241
     String.isPrefix new_skolem_var_prefix s)
blanchet@39932
   242
  end
blanchet@39897
   243
blanchet@40260
   244
fun rename_bound_vars_to_be_zapped ax_no =
blanchet@40260
   245
  let
blanchet@40260
   246
    fun aux (cluster as (cluster_no, cluster_skolem)) index_no pos t =
blanchet@40260
   247
      case t of
blanchet@40260
   248
        (t1 as Const (s, _)) $ Abs (s', T, t') =>
blanchet@39906
   249
        if s = @{const_name all} orelse s = @{const_name All} orelse
blanchet@39906
   250
           s = @{const_name Ex} then
blanchet@39932
   251
          let
blanchet@39932
   252
            val skolem = (pos = (s = @{const_name Ex}))
blanchet@39932
   253
            val (cluster, index_no) =
blanchet@39932
   254
              if skolem = cluster_skolem then (cluster, index_no)
blanchet@39932
   255
              else ((cluster_no ||> cluster_skolem ? Integer.add 1, skolem), 0)
blanchet@40260
   256
            val s' = zapped_var_name cluster index_no s'
blanchet@40260
   257
          in t1 $ Abs (s', T, aux cluster (index_no + 1) pos t') end
blanchet@40260
   258
        else
blanchet@40260
   259
          t
blanchet@40260
   260
      | (t1 as Const (s, _)) $ t2 $ t3 =>
blanchet@40260
   261
        if s = @{const_name "==>"} orelse s = @{const_name HOL.implies} then
blanchet@40260
   262
          t1 $ aux cluster index_no (not pos) t2 $ aux cluster index_no pos t3
blanchet@40260
   263
        else if s = @{const_name HOL.conj} orelse
blanchet@40260
   264
                s = @{const_name HOL.disj} then
blanchet@40260
   265
          t1 $ aux cluster index_no pos t2 $ aux cluster index_no pos t3
blanchet@40260
   266
        else
blanchet@40260
   267
          t
blanchet@40260
   268
      | (t1 as Const (s, _)) $ t2 =>
blanchet@40260
   269
        if s = @{const_name Trueprop} then
blanchet@40260
   270
          t1 $ aux cluster index_no pos t2
blanchet@40260
   271
        else if s = @{const_name Not} then
blanchet@40260
   272
          t1 $ aux cluster index_no (not pos) t2
blanchet@40260
   273
        else
blanchet@40260
   274
          t
blanchet@40260
   275
      | _ => t
blanchet@40260
   276
  in aux ((ax_no, 0), true) 0 true end
blanchet@40260
   277
blanchet@40260
   278
fun zap pos ct =
blanchet@40260
   279
  ct
blanchet@40260
   280
  |> (case term_of ct of
blanchet@40260
   281
        Const (s, _) $ Abs (s', _, _) =>
blanchet@40260
   282
        if s = @{const_name all} orelse s = @{const_name All} orelse
blanchet@40260
   283
           s = @{const_name Ex} then
blanchet@40260
   284
          Thm.dest_comb #> snd #> Thm.dest_abs (SOME s') #> snd #> zap pos
blanchet@39906
   285
        else
blanchet@39906
   286
          Conv.all_conv
blanchet@39906
   287
      | Const (s, _) $ _ $ _ =>
blanchet@39906
   288
        if s = @{const_name "==>"} orelse s = @{const_name implies} then
blanchet@40260
   289
          Conv.combination_conv (Conv.arg_conv (zap (not pos))) (zap pos)
blanchet@39906
   290
        else if s = @{const_name conj} orelse s = @{const_name disj} then
blanchet@40260
   291
          Conv.combination_conv (Conv.arg_conv (zap pos)) (zap pos)
blanchet@39906
   292
        else
blanchet@39906
   293
          Conv.all_conv
blanchet@39906
   294
      | Const (s, _) $ _ =>
blanchet@40260
   295
        if s = @{const_name Trueprop} then Conv.arg_conv (zap pos)
blanchet@40260
   296
        else if s = @{const_name Not} then Conv.arg_conv (zap (not pos))
blanchet@40260
   297
        else Conv.all_conv
blanchet@39906
   298
      | _ => Conv.all_conv)
blanchet@39887
   299
blanchet@39901
   300
fun ss_only ths = MetaSimplifier.clear_ss HOL_basic_ss addsimps ths
blanchet@39901
   301
blanchet@40261
   302
val cheat_choice =
blanchet@39901
   303
  @{prop "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)"}
blanchet@39901
   304
  |> Logic.varify_global
blanchet@39901
   305
  |> Skip_Proof.make_thm @{theory}
blanchet@39887
   306
blanchet@39887
   307
(* Converts an Isabelle theorem into NNF. *)
blanchet@39901
   308
fun nnf_axiom choice_ths new_skolemizer ax_no th ctxt =
blanchet@39887
   309
  let
blanchet@39887
   310
    val thy = ProofContext.theory_of ctxt
blanchet@39887
   311
    val th =
blanchet@39887
   312
      th |> transform_elim_theorem
blanchet@39887
   313
         |> zero_var_indexes
blanchet@39887
   314
         |> new_skolemizer ? forall_intr_vars
blanchet@39887
   315
    val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single
blanchet@39887
   316
    val th = th |> Conv.fconv_rule Object_Logic.atomize
blanchet@39887
   317
                |> extensionalize_theorem
blanchet@39950
   318
                |> make_nnf ctxt
blanchet@39887
   319
  in
blanchet@39887
   320
    if new_skolemizer then
blanchet@39887
   321
      let
blanchet@39901
   322
        fun skolemize choice_ths =
blanchet@39950
   323
          skolemize_with_choice_theorems ctxt choice_ths
blanchet@39901
   324
          #> simplify (ss_only @{thms all_simps[symmetric]})
blanchet@39901
   325
        val pull_out =
blanchet@39901
   326
          simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]})
blanchet@40261
   327
        val no_choice = null choice_ths
blanchet@40260
   328
        val discharger_th =
blanchet@40261
   329
          th |> (if no_choice then pull_out else skolemize choice_ths)
blanchet@40260
   330
        val fully_skolemized_t =
blanchet@40261
   331
          th |> prop_of
blanchet@40261
   332
             |> no_choice ? rename_bound_vars_to_be_zapped ax_no
blanchet@40261
   333
             |> Skip_Proof.make_thm thy |> skolemize [cheat_choice] |> cprop_of
blanchet@40261
   334
             |> not no_choice
blanchet@40261
   335
                ? (term_of #> rename_bound_vars_to_be_zapped ax_no
blanchet@40261
   336
                   #> cterm_of thy)
blanchet@40260
   337
             |> zap true |> Drule.export_without_context
blanchet@40260
   338
             |> cprop_of |> Thm.dest_equals |> snd |> term_of
blanchet@39887
   339
      in
blanchet@39887
   340
        if exists_subterm (fn Var ((s, _), _) =>
blanchet@39887
   341
                              String.isPrefix new_skolem_var_prefix s
blanchet@40260
   342
                            | _ => false) fully_skolemized_t then
blanchet@39887
   343
          let
blanchet@40260
   344
            val (fully_skolemized_ct, ctxt) =
blanchet@40260
   345
              Variable.import_terms true [fully_skolemized_t] ctxt
blanchet@39887
   346
              |>> the_single |>> cterm_of thy
blanchet@40260
   347
          in
blanchet@40260
   348
            (SOME (discharger_th, fully_skolemized_ct),
blanchet@40262
   349
             (Thm.assume fully_skolemized_ct, ctxt))
blanchet@40260
   350
          end
blanchet@39887
   351
       else
blanchet@40262
   352
         (NONE, (th, ctxt))
blanchet@39887
   353
      end
blanchet@39887
   354
    else
blanchet@40262
   355
      (NONE, (th, ctxt))
blanchet@39887
   356
  end
blanchet@39887
   357
blanchet@39887
   358
(* Convert a theorem to CNF, with additional premises due to skolemization. *)
blanchet@39901
   359
fun cnf_axiom ctxt0 new_skolemizer ax_no th =
blanchet@37626
   360
  let
blanchet@39901
   361
    val thy = ProofContext.theory_of ctxt0
blanchet@39950
   362
    val choice_ths = choice_theorems thy
blanchet@40262
   363
    val (opt, (nnf_th, ctxt)) =
blanchet@40262
   364
      nnf_axiom choice_ths new_skolemizer ax_no th ctxt0
blanchet@39894
   365
    fun clausify th =
blanchet@39950
   366
      make_cnf (if new_skolemizer orelse null choice_ths then
blanchet@39950
   367
                  []
blanchet@39950
   368
                else
blanchet@39950
   369
                  map (old_skolem_theorem_from_def thy)
blanchet@39950
   370
                      (old_skolem_defs th)) th ctxt
blanchet@39261
   371
    val (cnf_ths, ctxt) =
blanchet@39894
   372
      clausify nnf_th
blanchet@39894
   373
      |> (fn ([], _) =>
blanchet@40262
   374
             (* FIXME: This probably doesn't work with the new Skolemizer *)
blanchet@39894
   375
             clausify (to_definitional_cnf_with_quantifiers thy nnf_th)
blanchet@39268
   376
           | p => p)
blanchet@39894
   377
    fun intr_imp ct th =
blanchet@39950
   378
      Thm.instantiate ([], map (pairself (cterm_of thy))
blanchet@39962
   379
                               [(Var (("i", 0), @{typ nat}),
blanchet@39902
   380
                                 HOLogic.mk_nat ax_no)])
blanchet@39962
   381
                      (zero_var_indexes @{thm skolem_COMBK_D})
blanchet@39894
   382
      RS Thm.implies_intr ct th
blanchet@37626
   383
  in
blanchet@39897
   384
    (opt |> Option.map (I #>> singleton (Variable.export ctxt ctxt0)
blanchet@39897
   385
                        ##> (term_of #> HOLogic.dest_Trueprop
blanchet@39897
   386
                             #> singleton (Variable.export_terms ctxt ctxt0))),
blanchet@39887
   387
     cnf_ths |> map (introduce_combinators_in_theorem
blanchet@39894
   388
                     #> (case opt of SOME (_, ct) => intr_imp ct | NONE => I))
blanchet@39897
   389
             |> Variable.export ctxt ctxt0
blanchet@39950
   390
             |> finish_cnf
blanchet@39887
   391
             |> map Thm.close_derivation)
blanchet@37626
   392
  end
blanchet@39887
   393
  handle THM _ => (NONE, [])
wenzelm@27184
   394
wenzelm@20461
   395
end;