src/HOL/Tools/Sledgehammer/sledgehammer_fact_preprocessor.ML
author blanchet
Wed Apr 28 15:53:17 2010 +0200 (2010-04-28)
changeset 36492 60532b9bcd1c
parent 36478 1aba777a367f
child 36603 d5d6111761a6
permissions -rw-r--r--
save the name of Skolemized variables in Sledgehammer for use in the proof reconstruction code
blanchet@35826
     1
(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fact_preprocessor.ML
wenzelm@33311
     2
    Author:     Jia Meng, Cambridge University Computer Laboratory
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@35826
     8
signature SLEDGEHAMMER_FACT_PREPROCESSOR =
wenzelm@21505
     9
sig
wenzelm@32955
    10
  val trace: bool Unsynchronized.ref
wenzelm@32955
    11
  val trace_msg: (unit -> string) -> unit
blanchet@35865
    12
  val skolem_prefix: string
blanchet@36492
    13
  val skolem_infix: string
wenzelm@27179
    14
  val cnf_axiom: theory -> thm -> thm list
wenzelm@27184
    15
  val multi_base_blacklist: string list
paulson@25243
    16
  val bad_for_atp: thm -> bool
wenzelm@35568
    17
  val type_has_topsort: typ -> bool
wenzelm@27179
    18
  val cnf_rules_pairs: theory -> (string * thm) list -> (thm * (string * int)) list
wenzelm@32740
    19
  val suppress_endtheory: bool Unsynchronized.ref
wenzelm@32740
    20
    (*for emergency use where endtheory causes problems*)
blanchet@36478
    21
  val strip_subgoal : thm -> int -> (string * typ) list * term list * term
blanchet@36398
    22
  val neg_clausify: thm -> thm list
blanchet@36398
    23
  val neg_conjecture_clauses:
blanchet@36398
    24
    Proof.context -> thm -> int -> thm list list * (string * typ) list
blanchet@36394
    25
  val neg_clausify_tac: Proof.context -> int -> tactic
wenzelm@24669
    26
  val setup: theory -> theory
wenzelm@21505
    27
end;
mengj@19196
    28
blanchet@35826
    29
structure Sledgehammer_Fact_Preprocessor : SLEDGEHAMMER_FACT_PREPROCESSOR =
paulson@15997
    30
struct
paulson@15347
    31
blanchet@35865
    32
open Sledgehammer_FOL_Clause
blanchet@35865
    33
wenzelm@32955
    34
val trace = Unsynchronized.ref false;
blanchet@35865
    35
fun trace_msg msg = if !trace then tracing (msg ()) else ();
blanchet@35865
    36
blanchet@35865
    37
val skolem_prefix = "sko_"
blanchet@36492
    38
val skolem_infix = "$"
wenzelm@32955
    39
wenzelm@33832
    40
fun freeze_thm th = #1 (Drule.legacy_freeze_thaw th);
paulson@20863
    41
wenzelm@35568
    42
val type_has_topsort = Term.exists_subtype
wenzelm@35568
    43
  (fn TFree (_, []) => true
wenzelm@35568
    44
    | TVar (_, []) => true
wenzelm@35568
    45
    | _ => false);
wenzelm@27184
    46
wenzelm@28544
    47
paulson@15997
    48
(**** Transformation of Elimination Rules into First-Order Formulas****)
paulson@15347
    49
wenzelm@29064
    50
val cfalse = cterm_of @{theory HOL} HOLogic.false_const;
wenzelm@29064
    51
val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const);
wenzelm@20461
    52
paulson@21430
    53
(*Converts an elim-rule into an equivalent theorem that does not have the
paulson@21430
    54
  predicate variable.  Leaves other theorems unchanged.  We simply instantiate the
paulson@21430
    55
  conclusion variable to False.*)
paulson@16009
    56
fun transform_elim th =
paulson@21430
    57
  case concl_of th of    (*conclusion variable*)
blanchet@35963
    58
       @{const Trueprop} $ (v as Var (_, @{typ bool})) =>
wenzelm@29064
    59
           Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th
blanchet@35963
    60
    | v as Var(_, @{typ prop}) =>
wenzelm@29064
    61
           Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th
paulson@21430
    62
    | _ => th;
paulson@15997
    63
paulson@24742
    64
(*To enforce single-threading*)
paulson@24742
    65
exception Clausify_failure of theory;
wenzelm@20461
    66
wenzelm@28544
    67
paulson@16009
    68
(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
paulson@16009
    69
blanchet@36492
    70
(*Keep the full complexity of the original name*)
blanchet@36492
    71
fun flatten_name s = space_implode "_X" (Long_Name.explode s);
blanchet@36492
    72
blanchet@36492
    73
fun skolem_name thm_name nref var_name =
blanchet@36492
    74
  skolem_prefix ^ thm_name ^ "_" ^ Int.toString (Unsynchronized.inc nref) ^
blanchet@36492
    75
  skolem_infix ^ (if var_name = "" then "g" else flatten_name var_name)
blanchet@36492
    76
paulson@24742
    77
fun rhs_extra_types lhsT rhs =
paulson@24742
    78
  let val lhs_vars = Term.add_tfreesT lhsT []
paulson@24742
    79
      fun add_new_TFrees (TFree v) =
wenzelm@24821
    80
            if member (op =) lhs_vars v then I else insert (op =) (TFree v)
wenzelm@24821
    81
        | add_new_TFrees _ = I
paulson@24742
    82
      val rhs_consts = fold_aterms (fn Const c => insert (op =) c | _ => I) rhs []
paulson@24742
    83
  in fold (#2 #> Term.fold_atyps add_new_TFrees) rhs_consts [] end;
paulson@24742
    84
paulson@18141
    85
(*Traverse a theorem, declaring Skolem function definitions. String s is the suggested
wenzelm@27174
    86
  prefix for the Skolem constant.*)
wenzelm@27174
    87
fun declare_skofuns s th =
wenzelm@27174
    88
  let
wenzelm@33222
    89
    val nref = Unsynchronized.ref 0    (* FIXME ??? *)
blanchet@36492
    90
    fun dec_sko (Const (@{const_name Ex}, _) $ (xtp as Abs (s', T, p))) (axs, thy) =
wenzelm@27174
    91
          (*Existential: declare a Skolem function, then insert into body and continue*)
wenzelm@27174
    92
          let
blanchet@36492
    93
            val cname = skolem_name s nref s'
wenzelm@29265
    94
            val args0 = OldTerm.term_frees xtp  (*get the formal parameter list*)
wenzelm@27174
    95
            val Ts = map type_of args0
wenzelm@27174
    96
            val extraTs = rhs_extra_types (Ts ---> T) xtp
wenzelm@27174
    97
            val argsx = map (fn T => Free (gensym "vsk", T)) extraTs
wenzelm@27174
    98
            val args = argsx @ args0
wenzelm@27174
    99
            val cT = extraTs ---> Ts ---> T
wenzelm@27174
   100
            val rhs = list_abs_free (map dest_Free args, HOLogic.choice_const T $ xtp)
wenzelm@27174
   101
                    (*Forms a lambda-abstraction over the formal parameters*)
wenzelm@28110
   102
            val (c, thy') =
wenzelm@33173
   103
              Sign.declare_const ((Binding.conceal (Binding.name cname), cT), NoSyn) thy
wenzelm@27174
   104
            val cdef = cname ^ "_def"
wenzelm@36106
   105
            val ((_, ax), thy'') =
wenzelm@35984
   106
              Thm.add_def true false (Binding.name cdef, Logic.mk_equals (c, rhs)) thy'
wenzelm@35984
   107
            val ax' = Drule.export_without_context ax
wenzelm@35984
   108
          in dec_sko (subst_bound (list_comb (c, args), p)) (ax' :: axs, thy'') end
blanchet@35963
   109
      | dec_sko (Const (@{const_name All}, _) $ (Abs (a, T, p))) thx =
wenzelm@27174
   110
          (*Universal quant: insert a free variable into body and continue*)
wenzelm@29270
   111
          let val fname = Name.variant (OldTerm.add_term_names (p, [])) a
wenzelm@27174
   112
          in dec_sko (subst_bound (Free (fname, T), p)) thx end
blanchet@35963
   113
      | dec_sko (@{const "op &"} $ p $ q) thx = dec_sko q (dec_sko p thx)
blanchet@35963
   114
      | dec_sko (@{const "op |"} $ p $ q) thx = dec_sko q (dec_sko p thx)
blanchet@35963
   115
      | dec_sko (@{const Trueprop} $ p) thx = dec_sko p thx
wenzelm@27174
   116
      | dec_sko t thx = thx (*Do nothing otherwise*)
wenzelm@27174
   117
  in fn thy => dec_sko (Thm.prop_of th) ([], thy) end;
paulson@18141
   118
paulson@18141
   119
(*Traverse a theorem, accumulating Skolem function definitions.*)
paulson@22731
   120
fun assume_skofuns s th =
wenzelm@33222
   121
  let val sko_count = Unsynchronized.ref 0   (* FIXME ??? *)
blanchet@36492
   122
      fun dec_sko (Const (@{const_name Ex}, _) $ (xtp as Abs (s', T, p))) defs =
wenzelm@20461
   123
            (*Existential: declare a Skolem function, then insert into body and continue*)
wenzelm@20461
   124
            let val skos = map (#1 o Logic.dest_equals) defs  (*existing sko fns*)
haftmann@33040
   125
                val args = subtract (op =) skos (OldTerm.term_frees xtp) (*the formal parameters*)
wenzelm@20461
   126
                val Ts = map type_of args
wenzelm@20461
   127
                val cT = Ts ---> T
blanchet@36492
   128
                val id = skolem_name s sko_count s'
paulson@22731
   129
                val c = Free (id, cT)
wenzelm@20461
   130
                val rhs = list_abs_free (map dest_Free args,
wenzelm@20461
   131
                                         HOLogic.choice_const T $ xtp)
wenzelm@20461
   132
                      (*Forms a lambda-abstraction over the formal parameters*)
wenzelm@27330
   133
                val def = Logic.mk_equals (c, rhs)
wenzelm@20461
   134
            in dec_sko (subst_bound (list_comb(c,args), p))
wenzelm@20461
   135
                       (def :: defs)
wenzelm@20461
   136
            end
blanchet@35963
   137
        | dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) defs =
wenzelm@20461
   138
            (*Universal quant: insert a free variable into body and continue*)
wenzelm@29270
   139
            let val fname = Name.variant (OldTerm.add_term_names (p,[])) a
wenzelm@20461
   140
            in dec_sko (subst_bound (Free(fname,T), p)) defs end
blanchet@35963
   141
        | dec_sko (@{const "op &"} $ p $ q) defs = dec_sko q (dec_sko p defs)
blanchet@35963
   142
        | dec_sko (@{const "op |"} $ p $ q) defs = dec_sko q (dec_sko p defs)
blanchet@35963
   143
        | dec_sko (@{const Trueprop} $ p) defs = dec_sko p defs
wenzelm@20461
   144
        | dec_sko t defs = defs (*Do nothing otherwise*)
paulson@20419
   145
  in  dec_sko (prop_of th) []  end;
paulson@20419
   146
paulson@20419
   147
paulson@24827
   148
(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
paulson@20419
   149
paulson@20419
   150
(*Returns the vars of a theorem*)
paulson@20419
   151
fun vars_of_thm th =
wenzelm@22691
   152
  map (Thm.cterm_of (theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th []);
paulson@20419
   153
paulson@20419
   154
(*Make a version of fun_cong with a given variable name*)
paulson@20419
   155
local
paulson@20419
   156
    val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*)
paulson@20419
   157
    val cx = hd (vars_of_thm fun_cong');
paulson@20419
   158
    val ty = typ_of (ctyp_of_term cx);
paulson@20445
   159
    val thy = theory_of_thm fun_cong;
paulson@20419
   160
    fun mkvar a = cterm_of thy (Var((a,0),ty));
paulson@20419
   161
in
paulson@20419
   162
fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong'
paulson@20419
   163
end;
paulson@20419
   164
paulson@20863
   165
(*Removes the lambdas from an equation of the form t = (%x. u).  A non-negative n,
paulson@20863
   166
  serves as an upper bound on how many to remove.*)
paulson@20863
   167
fun strip_lambdas 0 th = th
wenzelm@24669
   168
  | strip_lambdas n th =
paulson@20863
   169
      case prop_of th of
blanchet@35963
   170
          _ $ (Const (@{const_name "op ="}, _) $ _ $ Abs (x, _, _)) =>
wenzelm@24669
   171
              strip_lambdas (n-1) (freeze_thm (th RS xfun_cong x))
wenzelm@24669
   172
        | _ => th;
paulson@20419
   173
wenzelm@24669
   174
val lambda_free = not o Term.has_abs;
wenzelm@20461
   175
wenzelm@32010
   176
val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B}));
wenzelm@32010
   177
val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
wenzelm@32010
   178
val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
paulson@20863
   179
paulson@24827
   180
(*FIXME: requires more use of cterm constructors*)
paulson@24827
   181
fun abstract ct =
wenzelm@28544
   182
  let
wenzelm@28544
   183
      val thy = theory_of_cterm ct
paulson@25256
   184
      val Abs(x,_,body) = term_of ct
blanchet@35963
   185
      val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct)
paulson@24827
   186
      val cxT = ctyp_of thy xT and cbodyT = ctyp_of thy bodyT
wenzelm@27184
   187
      fun makeK() = instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] @{thm abs_K}
paulson@24827
   188
  in
paulson@24827
   189
      case body of
paulson@24827
   190
          Const _ => makeK()
paulson@24827
   191
        | Free _ => makeK()
paulson@24827
   192
        | Var _ => makeK()  (*though Var isn't expected*)
wenzelm@27184
   193
        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
paulson@24827
   194
        | rator$rand =>
wenzelm@27184
   195
            if loose_bvar1 (rator,0) then (*C or S*)
wenzelm@27179
   196
               if loose_bvar1 (rand,0) then (*S*)
wenzelm@27179
   197
                 let val crator = cterm_of thy (Abs(x,xT,rator))
wenzelm@27179
   198
                     val crand = cterm_of thy (Abs(x,xT,rand))
wenzelm@27184
   199
                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
wenzelm@27184
   200
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
wenzelm@27179
   201
                 in
wenzelm@27179
   202
                   Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
wenzelm@27179
   203
                 end
wenzelm@27179
   204
               else (*C*)
wenzelm@27179
   205
                 let val crator = cterm_of thy (Abs(x,xT,rator))
wenzelm@27184
   206
                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
wenzelm@27184
   207
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
wenzelm@27179
   208
                 in
wenzelm@27179
   209
                   Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
wenzelm@27179
   210
                 end
wenzelm@27184
   211
            else if loose_bvar1 (rand,0) then (*B or eta*)
wenzelm@27179
   212
               if rand = Bound 0 then eta_conversion ct
wenzelm@27179
   213
               else (*B*)
wenzelm@27179
   214
                 let val crand = cterm_of thy (Abs(x,xT,rand))
wenzelm@27179
   215
                     val crator = cterm_of thy rator
wenzelm@27184
   216
                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
wenzelm@27184
   217
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
wenzelm@27179
   218
                 in
wenzelm@27179
   219
                   Thm.transitive abs_B' (Conv.arg_conv abstract rhs)
wenzelm@27179
   220
                 end
wenzelm@27179
   221
            else makeK()
paulson@24827
   222
        | _ => error "abstract: Bad term"
paulson@24827
   223
  end;
paulson@20863
   224
paulson@20419
   225
(*Traverse a theorem, declaring abstraction function definitions. String s is the suggested
wenzelm@28544
   226
  prefix for the constants.*)
paulson@24827
   227
fun combinators_aux ct =
paulson@24827
   228
  if lambda_free (term_of ct) then reflexive ct
paulson@24827
   229
  else
paulson@24827
   230
  case term_of ct of
paulson@24827
   231
      Abs _ =>
wenzelm@32994
   232
        let val (cv, cta) = Thm.dest_abs NONE ct
wenzelm@32994
   233
            val (v, _) = dest_Free (term_of cv)
wenzelm@27179
   234
            val u_th = combinators_aux cta
wenzelm@27179
   235
            val cu = Thm.rhs_of u_th
wenzelm@27179
   236
            val comb_eq = abstract (Thm.cabs cv cu)
wenzelm@28544
   237
        in transitive (abstract_rule v cv u_th) comb_eq end
wenzelm@32994
   238
    | _ $ _ =>
wenzelm@32994
   239
        let val (ct1, ct2) = Thm.dest_comb ct
wenzelm@27179
   240
        in  combination (combinators_aux ct1) (combinators_aux ct2)  end;
wenzelm@27184
   241
paulson@24827
   242
fun combinators th =
wenzelm@27184
   243
  if lambda_free (prop_of th) then th
paulson@24827
   244
  else
wenzelm@28544
   245
    let val th = Drule.eta_contraction_rule th
wenzelm@27179
   246
        val eqth = combinators_aux (cprop_of th)
paulson@25256
   247
    in  equal_elim eqth th   end
wenzelm@27184
   248
    handle THM (msg,_,_) =>
wenzelm@32091
   249
      (warning (cat_lines
wenzelm@32091
   250
        ["Error in the combinator translation of " ^ Display.string_of_thm_without_context th,
wenzelm@32091
   251
          "  Exception message: " ^ msg]);
paulson@25256
   252
       TrueI);  (*A type variable of sort {} will cause make abstraction fail.*)
paulson@16009
   253
paulson@16009
   254
(*cterms are used throughout for efficiency*)
wenzelm@29064
   255
val cTrueprop = Thm.cterm_of @{theory HOL} HOLogic.Trueprop;
paulson@16009
   256
paulson@16009
   257
(*cterm version of mk_cTrueprop*)
paulson@16009
   258
fun c_mkTrueprop A = Thm.capply cTrueprop A;
paulson@16009
   259
paulson@16009
   260
(*Given an abstraction over n variables, replace the bound variables by free
paulson@16009
   261
  ones. Return the body, along with the list of free variables.*)
wenzelm@20461
   262
fun c_variant_abs_multi (ct0, vars) =
paulson@16009
   263
      let val (cv,ct) = Thm.dest_abs NONE ct0
paulson@16009
   264
      in  c_variant_abs_multi (ct, cv::vars)  end
paulson@16009
   265
      handle CTERM _ => (ct0, rev vars);
paulson@16009
   266
wenzelm@20461
   267
(*Given the definition of a Skolem function, return a theorem to replace
wenzelm@20461
   268
  an existential formula by a use of that function.
paulson@18141
   269
   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
wenzelm@20461
   270
fun skolem_of_def def =
wenzelm@22902
   271
  let val (c,rhs) = Thm.dest_equals (cprop_of (freeze_thm def))
paulson@16009
   272
      val (ch, frees) = c_variant_abs_multi (rhs, [])
paulson@18141
   273
      val (chilbert,cabs) = Thm.dest_comb ch
wenzelm@26627
   274
      val thy = Thm.theory_of_cterm chilbert
wenzelm@26627
   275
      val t = Thm.term_of chilbert
blanchet@35963
   276
      val T = case t of
blanchet@35963
   277
                Const (@{const_name Eps}, Type (@{type_name fun},[_,T])) => T
blanchet@35963
   278
              | _ => raise THM ("skolem_of_def: expected Eps", 0, [def])
wenzelm@22596
   279
      val cex = Thm.cterm_of thy (HOLogic.exists_const T)
paulson@16009
   280
      val ex_tm = c_mkTrueprop (Thm.capply cex cabs)
paulson@16009
   281
      and conc =  c_mkTrueprop (Drule.beta_conv cabs (Drule.list_comb(c,frees)));
haftmann@31454
   282
      fun tacf [prem] = rewrite_goals_tac [def] THEN rtac (prem RS @{thm someI_ex}) 1
wenzelm@23352
   283
  in  Goal.prove_internal [ex_tm] conc tacf
paulson@18141
   284
       |> forall_intr_list frees
wenzelm@26653
   285
       |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
wenzelm@35845
   286
       |> Thm.varifyT_global
paulson@18141
   287
  end;
paulson@16009
   288
paulson@24742
   289
paulson@20863
   290
(*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)
paulson@24937
   291
fun to_nnf th ctxt0 =
wenzelm@27179
   292
  let val th1 = th |> transform_elim |> zero_var_indexes
wenzelm@32262
   293
      val ((_, [th2]), ctxt) = Variable.import true [th1] ctxt0
wenzelm@32262
   294
      val th3 = th2
wenzelm@35625
   295
        |> Conv.fconv_rule Object_Logic.atomize
wenzelm@32262
   296
        |> Meson.make_nnf ctxt |> strip_lambdas ~1
paulson@24937
   297
  in  (th3, ctxt)  end;
paulson@16009
   298
paulson@18141
   299
(*Generate Skolem functions for a theorem supplied in nnf*)
paulson@24937
   300
fun assume_skolem_of_def s th =
paulson@22731
   301
  map (skolem_of_def o assume o (cterm_of (theory_of_thm th))) (assume_skofuns s th);
paulson@18141
   302
paulson@25007
   303
blanchet@35963
   304
(*** Blacklisting (FIXME: duplicated in "Sledgehammer_Fact_Filter"?) ***)
paulson@25007
   305
paulson@25007
   306
val max_lambda_nesting = 3;
wenzelm@27184
   307
paulson@25007
   308
fun excessive_lambdas (f$t, k) = excessive_lambdas (f,k) orelse excessive_lambdas (t,k)
paulson@25007
   309
  | excessive_lambdas (Abs(_,_,t), k) = k=0 orelse excessive_lambdas (t,k-1)
paulson@25007
   310
  | excessive_lambdas _ = false;
paulson@25007
   311
paulson@25007
   312
fun is_formula_type T = (T = HOLogic.boolT orelse T = propT);
paulson@25007
   313
paulson@25007
   314
(*Don't count nested lambdas at the level of formulas, as they are quantifiers*)
paulson@25007
   315
fun excessive_lambdas_fm Ts (Abs(_,T,t)) = excessive_lambdas_fm (T::Ts) t
paulson@25007
   316
  | excessive_lambdas_fm Ts t =
paulson@25007
   317
      if is_formula_type (fastype_of1 (Ts, t))
paulson@25007
   318
      then exists (excessive_lambdas_fm Ts) (#2 (strip_comb t))
paulson@25007
   319
      else excessive_lambdas (t, max_lambda_nesting);
paulson@25007
   320
wenzelm@33027
   321
(*The max apply_depth of any metis call in Metis_Examples (on 31-10-2007) was 11.*)
paulson@25256
   322
val max_apply_depth = 15;
wenzelm@27184
   323
paulson@25256
   324
fun apply_depth (f$t) = Int.max (apply_depth f, apply_depth t + 1)
paulson@25256
   325
  | apply_depth (Abs(_,_,t)) = apply_depth t
paulson@25256
   326
  | apply_depth _ = 0;
paulson@25256
   327
wenzelm@27184
   328
fun too_complex t =
wenzelm@27184
   329
  apply_depth t > max_apply_depth orelse
paulson@26562
   330
  Meson.too_many_clauses NONE t orelse
paulson@25256
   331
  excessive_lambdas_fm [] t;
wenzelm@27184
   332
paulson@25243
   333
fun is_strange_thm th =
paulson@25243
   334
  case head_of (concl_of th) of
blanchet@35963
   335
      Const (a, _) => (a <> @{const_name Trueprop} andalso
blanchet@35963
   336
                       a <> @{const_name "=="})
paulson@25243
   337
    | _ => false;
paulson@25243
   338
wenzelm@27184
   339
fun bad_for_atp th =
wenzelm@33306
   340
  too_complex (prop_of th)
wenzelm@35568
   341
  orelse exists_type type_has_topsort (prop_of th)
paulson@25761
   342
  orelse is_strange_thm th;
paulson@25243
   343
blanchet@35963
   344
(* FIXME: put other record thms here, or declare as "no_atp" *)
paulson@25007
   345
val multi_base_blacklist =
blanchet@35963
   346
  ["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",
blanchet@35963
   347
   "split_asm", "cases", "ext_cases"];
paulson@25007
   348
paulson@22731
   349
fun fake_name th =
wenzelm@27865
   350
  if Thm.has_name_hint th then flatten_name (Thm.get_name_hint th)
paulson@22731
   351
  else gensym "unknown_thm_";
paulson@22731
   352
wenzelm@27184
   353
(*Skolemize a named theorem, with Skolem functions as additional premises.*)
wenzelm@27184
   354
fun skolem_thm (s, th) =
wenzelm@30364
   355
  if member (op =) multi_base_blacklist (Long_Name.base_name s) orelse bad_for_atp th then []
wenzelm@27184
   356
  else
wenzelm@27184
   357
    let
wenzelm@27184
   358
      val ctxt0 = Variable.thm_context th
wenzelm@27184
   359
      val (nnfth, ctxt1) = to_nnf th ctxt0
wenzelm@27184
   360
      val (cnfs, ctxt2) = Meson.make_cnf (assume_skolem_of_def s nnfth) nnfth ctxt1
wenzelm@27184
   361
    in  cnfs |> map combinators |> Variable.export ctxt2 ctxt0 |> Meson.finish_cnf  end
wenzelm@27184
   362
    handle THM _ => [];
wenzelm@27184
   363
paulson@24742
   364
(*The cache prevents repeated clausification of a theorem, and also repeated declaration of
paulson@24742
   365
  Skolem functions.*)
wenzelm@33522
   366
structure ThmCache = Theory_Data
wenzelm@22846
   367
(
wenzelm@28544
   368
  type T = thm list Thmtab.table * unit Symtab.table;
wenzelm@28544
   369
  val empty = (Thmtab.empty, Symtab.empty);
wenzelm@26618
   370
  val extend = I;
wenzelm@33522
   371
  fun merge ((cache1, seen1), (cache2, seen2)) : T =
wenzelm@27184
   372
    (Thmtab.merge (K true) (cache1, cache2), Symtab.merge (K true) (seen1, seen2));
wenzelm@22846
   373
);
paulson@22516
   374
wenzelm@27184
   375
val lookup_cache = Thmtab.lookup o #1 o ThmCache.get;
wenzelm@27184
   376
val already_seen = Symtab.defined o #2 o ThmCache.get;
wenzelm@20461
   377
wenzelm@27184
   378
val update_cache = ThmCache.map o apfst o Thmtab.update;
wenzelm@27184
   379
fun mark_seen name = ThmCache.map (apsnd (Symtab.update (name, ())));
paulson@25007
   380
blanchet@36228
   381
(* Convert Isabelle theorems into axiom clauses. *)
wenzelm@27179
   382
fun cnf_axiom thy th0 =
wenzelm@27184
   383
  let val th = Thm.transfer thy th0 in
wenzelm@27184
   384
    case lookup_cache thy th of
wenzelm@27184
   385
      NONE => map Thm.close_derivation (skolem_thm (fake_name th, th))
wenzelm@27184
   386
    | SOME cls => cls
paulson@22516
   387
  end;
paulson@15347
   388
paulson@18141
   389
paulson@22471
   390
(**** Translate a set of theorems into CNF ****)
paulson@15347
   391
paulson@19894
   392
fun pair_name_cls k (n, []) = []
paulson@19894
   393
  | pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss)
wenzelm@20461
   394
wenzelm@27179
   395
fun cnf_rules_pairs_aux _ pairs [] = pairs
wenzelm@27179
   396
  | cnf_rules_pairs_aux thy pairs ((name,th)::ths) =
wenzelm@27179
   397
      let val pairs' = (pair_name_cls 0 (name, cnf_axiom thy th)) @ pairs
blanchet@35826
   398
                       handle THM _ => pairs |
blanchet@35865
   399
                              CLAUSE _ => pairs
wenzelm@27179
   400
      in  cnf_rules_pairs_aux thy pairs' ths  end;
wenzelm@20461
   401
paulson@21290
   402
(*The combination of rev and tail recursion preserves the original order*)
wenzelm@27179
   403
fun cnf_rules_pairs thy l = cnf_rules_pairs_aux thy [] (rev l);
mengj@19353
   404
mengj@19196
   405
blanchet@35865
   406
(**** Convert all facts of the theory into FOL or HOL clauses ****)
paulson@15347
   407
wenzelm@28544
   408
local
wenzelm@28544
   409
wenzelm@28544
   410
fun skolem_def (name, th) thy =
wenzelm@28544
   411
  let val ctxt0 = Variable.thm_context th in
wenzelm@28544
   412
    (case try (to_nnf th) ctxt0 of
wenzelm@28544
   413
      NONE => (NONE, thy)
wenzelm@28544
   414
    | SOME (nnfth, ctxt1) =>
wenzelm@28544
   415
        let val (defs, thy') = declare_skofuns (flatten_name name) nnfth thy
wenzelm@28544
   416
        in (SOME (th, ctxt0, ctxt1, nnfth, defs), thy') end)
wenzelm@28544
   417
  end;
paulson@24742
   418
wenzelm@28544
   419
fun skolem_cnfs (th, ctxt0, ctxt1, nnfth, defs) =
wenzelm@28544
   420
  let
wenzelm@28544
   421
    val (cnfs, ctxt2) = Meson.make_cnf (map skolem_of_def defs) nnfth ctxt1;
wenzelm@28544
   422
    val cnfs' = cnfs
wenzelm@28544
   423
      |> map combinators
wenzelm@28544
   424
      |> Variable.export ctxt2 ctxt0
wenzelm@28544
   425
      |> Meson.finish_cnf
wenzelm@28544
   426
      |> map Thm.close_derivation;
wenzelm@28544
   427
    in (th, cnfs') end;
wenzelm@28544
   428
wenzelm@28544
   429
in
paulson@24742
   430
wenzelm@27184
   431
fun saturate_skolem_cache thy =
wenzelm@28544
   432
  let
wenzelm@33306
   433
    val facts = PureThy.facts_of thy;
wenzelm@33306
   434
    val new_facts = (facts, []) |-> Facts.fold_static (fn (name, ths) =>
wenzelm@33306
   435
      if Facts.is_concealed facts name orelse already_seen thy name then I
wenzelm@33306
   436
      else cons (name, ths));
wenzelm@28544
   437
    val new_thms = (new_facts, []) |-> fold (fn (name, ths) =>
wenzelm@30364
   438
      if member (op =) multi_base_blacklist (Long_Name.base_name name) then I
wenzelm@28544
   439
      else fold_index (fn (i, th) =>
wenzelm@28544
   440
        if bad_for_atp th orelse is_some (lookup_cache thy th) then I
wenzelm@28544
   441
        else cons (name ^ "_" ^ string_of_int (i + 1), Thm.transfer thy th)) ths);
wenzelm@28544
   442
  in
wenzelm@28544
   443
    if null new_facts then NONE
wenzelm@28544
   444
    else
wenzelm@28544
   445
      let
wenzelm@28544
   446
        val (defs, thy') = thy
wenzelm@28544
   447
          |> fold (mark_seen o #1) new_facts
wenzelm@28544
   448
          |> fold_map skolem_def (sort_distinct (Thm.thm_ord o pairself snd) new_thms)
wenzelm@28544
   449
          |>> map_filter I;
wenzelm@29368
   450
        val cache_entries = Par_List.map skolem_cnfs defs;
wenzelm@28544
   451
      in SOME (fold update_cache cache_entries thy') end
wenzelm@28544
   452
  end;
wenzelm@27184
   453
wenzelm@28544
   454
end;
paulson@24854
   455
wenzelm@32740
   456
val suppress_endtheory = Unsynchronized.ref false;
wenzelm@27184
   457
wenzelm@27184
   458
fun clause_cache_endtheory thy =
wenzelm@27184
   459
  if ! suppress_endtheory then NONE
wenzelm@27184
   460
  else saturate_skolem_cache thy;
wenzelm@27184
   461
paulson@20457
   462
paulson@22516
   463
(*The cache can be kept smaller by inspecting the prop of each thm. Can ignore all that are
paulson@22516
   464
  lambda_free, but then the individual theory caches become much bigger.*)
paulson@21071
   465
wenzelm@27179
   466
blanchet@36398
   467
fun strip_subgoal goal i =
blanchet@36398
   468
  let
blanchet@36398
   469
    val (t, frees) = Logic.goal_params (prop_of goal) i
blanchet@36398
   470
    val hyp_ts = t |> Logic.strip_assums_hyp |> map (curry subst_bounds frees)
blanchet@36398
   471
    val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees
blanchet@36478
   472
  in (rev (map dest_Free frees), hyp_ts, concl_t) end
blanchet@36398
   473
paulson@21999
   474
(*** Converting a subgoal into negated conjecture clauses. ***)
paulson@21999
   475
wenzelm@32262
   476
fun neg_skolemize_tac ctxt =
wenzelm@35625
   477
  EVERY' [rtac ccontr, Object_Logic.atomize_prems_tac, Meson.skolemize_tac ctxt];
paulson@22471
   478
blanchet@36398
   479
fun neg_skolemize_tac ctxt =
blanchet@36398
   480
  EVERY' [rtac ccontr, Object_Logic.atomize_prems_tac, Meson.skolemize_tac ctxt];
blanchet@36398
   481
blanchet@35869
   482
val neg_clausify =
blanchet@36398
   483
  single #> Meson.make_clauses_unsorted #> map combinators #> Meson.finish_cnf
paulson@21999
   484
wenzelm@32257
   485
fun neg_conjecture_clauses ctxt st0 n =
wenzelm@32257
   486
  let
wenzelm@32262
   487
    val st = Seq.hd (neg_skolemize_tac ctxt n st0)
wenzelm@32257
   488
    val ({params, prems, ...}, _) = Subgoal.focus (Variable.set_body false ctxt) n st
blanchet@36398
   489
  in
blanchet@36398
   490
    (map neg_clausify prems, map (Term.dest_Free o Thm.term_of o #2) params)
blanchet@36398
   491
  end
paulson@21999
   492
wenzelm@24669
   493
(*Conversion of a subgoal to conjecture clauses. Each clause has
paulson@21999
   494
  leading !!-bound universal variables, to express generality. *)
wenzelm@32257
   495
fun neg_clausify_tac ctxt =
wenzelm@32262
   496
  neg_skolemize_tac ctxt THEN'
wenzelm@32257
   497
  SUBGOAL (fn (prop, i) =>
wenzelm@32257
   498
    let val ts = Logic.strip_assums_hyp prop in
wenzelm@32257
   499
      EVERY'
wenzelm@32283
   500
       [Subgoal.FOCUS
wenzelm@32257
   501
         (fn {prems, ...} =>
wenzelm@32257
   502
           (Method.insert_tac
blanchet@36398
   503
             (map forall_intr_vars (maps neg_clausify prems)) i)) ctxt,
wenzelm@32257
   504
        REPEAT_DETERM_N (length ts) o etac thin_rl] i
paulson@21999
   505
     end);
paulson@21999
   506
wenzelm@27184
   507
wenzelm@27184
   508
(** setup **)
wenzelm@27184
   509
wenzelm@27184
   510
val setup =
wenzelm@27184
   511
  perhaps saturate_skolem_cache #>
wenzelm@27184
   512
  Theory.at_end clause_cache_endtheory;
paulson@18510
   513
wenzelm@20461
   514
end;