src/HOL/Tools/Sledgehammer/sledgehammer_fact_preprocessor.ML
author blanchet
Tue Jun 22 14:28:22 2010 +0200 (2010-06-22 ago)
changeset 37498 b426cbdb5a23
parent 37496 9ae78e12e126
child 37500 7587b6e63454
permissions -rw-r--r--
removed Sledgehammer's support for the DFG syntax;
this removes 350 buggy lines from Sledgehammer. SPASS 3.5 and above support the TPTP syntax.
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
blanchet@37171
    10
  val chained_prefix: string
wenzelm@32955
    11
  val trace: bool Unsynchronized.ref
wenzelm@32955
    12
  val trace_msg: (unit -> string) -> unit
blanchet@37410
    13
  val skolem_theory_name: string
blanchet@35865
    14
  val skolem_prefix: string
blanchet@36492
    15
  val skolem_infix: string
blanchet@37399
    16
  val is_skolem_const_name: string -> bool
wenzelm@27179
    17
  val cnf_axiom: theory -> thm -> thm list
wenzelm@27184
    18
  val multi_base_blacklist: string list
blanchet@37348
    19
  val is_theorem_bad_for_atps: thm -> bool
wenzelm@35568
    20
  val type_has_topsort: typ -> bool
blanchet@37348
    21
  val cnf_rules_pairs:
blanchet@37348
    22
    theory -> (string * thm) list -> (thm * (string * int)) list
blanchet@37496
    23
  val saturate_skolem_cache: theory -> theory option
blanchet@37498
    24
  val auto_saturate_skolem_cache: bool Unsynchronized.ref
blanchet@37348
    25
    (* for emergency use where the Skolem cache causes problems *)
blanchet@36398
    26
  val neg_clausify: thm -> thm list
blanchet@36398
    27
  val neg_conjecture_clauses:
blanchet@36398
    28
    Proof.context -> thm -> int -> thm list list * (string * typ) list
blanchet@36394
    29
  val neg_clausify_tac: Proof.context -> int -> tactic
wenzelm@24669
    30
  val setup: theory -> theory
wenzelm@21505
    31
end;
mengj@19196
    32
blanchet@35826
    33
structure Sledgehammer_Fact_Preprocessor : SLEDGEHAMMER_FACT_PREPROCESSOR =
paulson@15997
    34
struct
paulson@15347
    35
blanchet@35865
    36
open Sledgehammer_FOL_Clause
blanchet@35865
    37
blanchet@37171
    38
(* Used to label theorems chained into the goal. *)
blanchet@37171
    39
val chained_prefix = "Sledgehammer.chained_"
blanchet@37171
    40
wenzelm@32955
    41
val trace = Unsynchronized.ref false;
blanchet@35865
    42
fun trace_msg msg = if !trace then tracing (msg ()) else ();
blanchet@35865
    43
blanchet@37410
    44
val skolem_theory_name = "Sledgehammer.Sko"
blanchet@35865
    45
val skolem_prefix = "sko_"
blanchet@36492
    46
val skolem_infix = "$"
wenzelm@32955
    47
wenzelm@33832
    48
fun freeze_thm th = #1 (Drule.legacy_freeze_thaw th);
paulson@20863
    49
wenzelm@35568
    50
val type_has_topsort = Term.exists_subtype
wenzelm@35568
    51
  (fn TFree (_, []) => true
wenzelm@35568
    52
    | TVar (_, []) => true
wenzelm@35568
    53
    | _ => false);
wenzelm@27184
    54
wenzelm@28544
    55
paulson@15997
    56
(**** Transformation of Elimination Rules into First-Order Formulas****)
paulson@15347
    57
wenzelm@29064
    58
val cfalse = cterm_of @{theory HOL} HOLogic.false_const;
wenzelm@29064
    59
val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const);
wenzelm@20461
    60
paulson@21430
    61
(*Converts an elim-rule into an equivalent theorem that does not have the
paulson@21430
    62
  predicate variable.  Leaves other theorems unchanged.  We simply instantiate the
paulson@21430
    63
  conclusion variable to False.*)
paulson@16009
    64
fun transform_elim th =
paulson@21430
    65
  case concl_of th of    (*conclusion variable*)
blanchet@35963
    66
       @{const Trueprop} $ (v as Var (_, @{typ bool})) =>
wenzelm@29064
    67
           Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th
blanchet@35963
    68
    | v as Var(_, @{typ prop}) =>
wenzelm@29064
    69
           Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th
paulson@21430
    70
    | _ => th;
paulson@15997
    71
paulson@24742
    72
(*To enforce single-threading*)
paulson@24742
    73
exception Clausify_failure of theory;
wenzelm@20461
    74
wenzelm@28544
    75
paulson@16009
    76
(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
paulson@16009
    77
blanchet@36492
    78
(*Keep the full complexity of the original name*)
blanchet@36492
    79
fun flatten_name s = space_implode "_X" (Long_Name.explode s);
blanchet@36492
    80
blanchet@37399
    81
fun skolem_name thm_name j var_name =
blanchet@37399
    82
  skolem_prefix ^ thm_name ^ "_" ^ Int.toString j ^
blanchet@36492
    83
  skolem_infix ^ (if var_name = "" then "g" else flatten_name var_name)
blanchet@36492
    84
blanchet@37399
    85
(* Hack: Could return false positives (e.g., a user happens to declare a
blanchet@37399
    86
   constant called "SomeTheory.sko_means_shoe_in_$wedish". *)
blanchet@37399
    87
val is_skolem_const_name =
blanchet@37399
    88
  Long_Name.base_name
blanchet@37399
    89
  #> String.isPrefix skolem_prefix andf String.isSubstring skolem_infix
blanchet@37399
    90
paulson@24742
    91
fun rhs_extra_types lhsT rhs =
paulson@24742
    92
  let val lhs_vars = Term.add_tfreesT lhsT []
paulson@24742
    93
      fun add_new_TFrees (TFree v) =
wenzelm@24821
    94
            if member (op =) lhs_vars v then I else insert (op =) (TFree v)
wenzelm@24821
    95
        | add_new_TFrees _ = I
paulson@24742
    96
      val rhs_consts = fold_aterms (fn Const c => insert (op =) c | _ => I) rhs []
paulson@24742
    97
  in fold (#2 #> Term.fold_atyps add_new_TFrees) rhs_consts [] end;
paulson@24742
    98
blanchet@37399
    99
fun skolem_type_and_args bound_T body =
blanchet@37399
   100
  let
blanchet@37399
   101
    val args1 = OldTerm.term_frees body
blanchet@37399
   102
    val Ts1 = map type_of args1
blanchet@37399
   103
    val Ts2 = rhs_extra_types (Ts1 ---> bound_T) body
blanchet@37399
   104
    val args2 = map (fn T => Free (gensym "vsk", T)) Ts2
blanchet@37399
   105
  in (Ts2 ---> Ts1 ---> bound_T, args2 @ args1) end
blanchet@37399
   106
blanchet@37348
   107
(* Traverse a theorem, declaring Skolem function definitions. String "s" is the
blanchet@37348
   108
   suggested prefix for the Skolem constants. *)
blanchet@37349
   109
fun declare_skolem_funs s th thy =
wenzelm@27174
   110
  let
blanchet@37399
   111
    val skolem_count = Unsynchronized.ref 0    (* FIXME ??? *)
blanchet@37399
   112
    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (s', T, p)))
blanchet@37399
   113
                (axs, thy) =
blanchet@37399
   114
        (*Existential: declare a Skolem function, then insert into body and continue*)
blanchet@37399
   115
        let
blanchet@37399
   116
          val id = skolem_name s (Unsynchronized.inc skolem_count) s'
blanchet@37399
   117
          val (cT, args) = skolem_type_and_args T body
blanchet@37399
   118
          val rhs = list_abs_free (map dest_Free args,
blanchet@37410
   119
                                   HOLogic.choice_const T $ body)
blanchet@37399
   120
                  (*Forms a lambda-abstraction over the formal parameters*)
blanchet@37399
   121
          val (c, thy) =
blanchet@37399
   122
            Sign.declare_const ((Binding.conceal (Binding.name id), cT), NoSyn) thy
blanchet@37399
   123
          val cdef = id ^ "_def"
blanchet@37399
   124
          val ((_, ax), thy) =
blanchet@37399
   125
            Thm.add_def true false (Binding.name cdef, Logic.mk_equals (c, rhs)) thy
blanchet@37399
   126
          val ax' = Drule.export_without_context ax
blanchet@37399
   127
        in dec_sko (subst_bound (list_comb (c, args), p)) (ax' :: axs, thy) end
blanchet@35963
   128
      | dec_sko (Const (@{const_name All}, _) $ (Abs (a, T, p))) thx =
blanchet@37399
   129
        (*Universal quant: insert a free variable into body and continue*)
blanchet@37399
   130
        let val fname = Name.variant (OldTerm.add_term_names (p, [])) a
blanchet@37399
   131
        in dec_sko (subst_bound (Free (fname, T), p)) thx end
blanchet@35963
   132
      | dec_sko (@{const "op &"} $ p $ q) thx = dec_sko q (dec_sko p thx)
blanchet@35963
   133
      | dec_sko (@{const "op |"} $ p $ q) thx = dec_sko q (dec_sko p thx)
blanchet@35963
   134
      | dec_sko (@{const Trueprop} $ p) thx = dec_sko p thx
blanchet@37498
   135
      | dec_sko _ thx = thx
blanchet@37349
   136
  in dec_sko (prop_of th) ([], thy) end
paulson@18141
   137
blanchet@37410
   138
fun mk_skolem_id t =
blanchet@37436
   139
  let val T = fastype_of t in
blanchet@37496
   140
    Const (@{const_name skolem_id}, T --> T) $ t
blanchet@37436
   141
  end
blanchet@37410
   142
paulson@18141
   143
(*Traverse a theorem, accumulating Skolem function definitions.*)
blanchet@37399
   144
fun assume_skolem_funs inline s th =
blanchet@37399
   145
  let
blanchet@37399
   146
    val skolem_count = Unsynchronized.ref 0   (* FIXME ??? *)
blanchet@37399
   147
    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (s', T, p))) defs =
blanchet@37399
   148
        (*Existential: declare a Skolem function, then insert into body and continue*)
blanchet@37399
   149
        let
blanchet@37399
   150
          val skos = map (#1 o Logic.dest_equals) defs  (*existing sko fns*)
blanchet@37399
   151
          val args = subtract (op =) skos (OldTerm.term_frees body) (*the formal parameters*)
blanchet@37399
   152
          val Ts = map type_of args
blanchet@37399
   153
          val cT = Ts ---> T (* FIXME: use "skolem_type_and_args" *)
blanchet@37399
   154
          val id = skolem_name s (Unsynchronized.inc skolem_count) s'
blanchet@37399
   155
          val c = Free (id, cT)
blanchet@37410
   156
          val rhs = list_abs_free (map dest_Free args,
blanchet@37410
   157
                                   HOLogic.choice_const T $ body)
blanchet@37410
   158
                    |> inline ? mk_skolem_id
blanchet@37399
   159
                (*Forms a lambda-abstraction over the formal parameters*)
blanchet@37399
   160
          val def = Logic.mk_equals (c, rhs)
blanchet@37399
   161
          val comb = list_comb (if inline then rhs else c, args)
blanchet@37399
   162
        in dec_sko (subst_bound (comb, p)) (def :: defs) end
blanchet@37399
   163
      | dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) defs =
blanchet@37399
   164
        (*Universal quant: insert a free variable into body and continue*)
blanchet@37399
   165
        let val fname = Name.variant (OldTerm.add_term_names (p,[])) a
blanchet@37399
   166
        in dec_sko (subst_bound (Free(fname,T), p)) defs end
blanchet@37399
   167
      | dec_sko (@{const "op &"} $ p $ q) defs = dec_sko q (dec_sko p defs)
blanchet@37399
   168
      | dec_sko (@{const "op |"} $ p $ q) defs = dec_sko q (dec_sko p defs)
blanchet@37399
   169
      | dec_sko (@{const Trueprop} $ p) defs = dec_sko p defs
blanchet@37498
   170
      | dec_sko _ defs = defs
paulson@20419
   171
  in  dec_sko (prop_of th) []  end;
paulson@20419
   172
paulson@20419
   173
paulson@24827
   174
(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
paulson@20419
   175
paulson@20419
   176
(*Returns the vars of a theorem*)
paulson@20419
   177
fun vars_of_thm th =
wenzelm@22691
   178
  map (Thm.cterm_of (theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th []);
paulson@20419
   179
paulson@20419
   180
(*Make a version of fun_cong with a given variable name*)
paulson@20419
   181
local
paulson@20419
   182
    val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*)
paulson@20419
   183
    val cx = hd (vars_of_thm fun_cong');
paulson@20419
   184
    val ty = typ_of (ctyp_of_term cx);
paulson@20445
   185
    val thy = theory_of_thm fun_cong;
paulson@20419
   186
    fun mkvar a = cterm_of thy (Var((a,0),ty));
paulson@20419
   187
in
paulson@20419
   188
fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong'
paulson@20419
   189
end;
paulson@20419
   190
paulson@20863
   191
(*Removes the lambdas from an equation of the form t = (%x. u).  A non-negative n,
paulson@20863
   192
  serves as an upper bound on how many to remove.*)
paulson@20863
   193
fun strip_lambdas 0 th = th
wenzelm@24669
   194
  | strip_lambdas n th =
paulson@20863
   195
      case prop_of th of
blanchet@35963
   196
          _ $ (Const (@{const_name "op ="}, _) $ _ $ Abs (x, _, _)) =>
wenzelm@24669
   197
              strip_lambdas (n-1) (freeze_thm (th RS xfun_cong x))
wenzelm@24669
   198
        | _ => th;
paulson@20419
   199
blanchet@37416
   200
fun is_quasi_lambda_free (Const (@{const_name skolem_id}, _) $ _) = true
blanchet@37416
   201
  | is_quasi_lambda_free (t1 $ t2) =
blanchet@37416
   202
    is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2
blanchet@37416
   203
  | is_quasi_lambda_free (Abs _) = false
blanchet@37416
   204
  | is_quasi_lambda_free _ = true
wenzelm@20461
   205
wenzelm@32010
   206
val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B}));
wenzelm@32010
   207
val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
wenzelm@32010
   208
val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
paulson@20863
   209
paulson@24827
   210
(*FIXME: requires more use of cterm constructors*)
paulson@24827
   211
fun abstract ct =
wenzelm@28544
   212
  let
wenzelm@28544
   213
      val thy = theory_of_cterm ct
paulson@25256
   214
      val Abs(x,_,body) = term_of ct
blanchet@35963
   215
      val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct)
paulson@24827
   216
      val cxT = ctyp_of thy xT and cbodyT = ctyp_of thy bodyT
wenzelm@27184
   217
      fun makeK() = instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] @{thm abs_K}
paulson@24827
   218
  in
paulson@24827
   219
      case body of
paulson@24827
   220
          Const _ => makeK()
paulson@24827
   221
        | Free _ => makeK()
paulson@24827
   222
        | Var _ => makeK()  (*though Var isn't expected*)
wenzelm@27184
   223
        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
paulson@24827
   224
        | rator$rand =>
wenzelm@27184
   225
            if loose_bvar1 (rator,0) then (*C or S*)
wenzelm@27179
   226
               if loose_bvar1 (rand,0) then (*S*)
wenzelm@27179
   227
                 let val crator = cterm_of thy (Abs(x,xT,rator))
wenzelm@27179
   228
                     val crand = cterm_of thy (Abs(x,xT,rand))
wenzelm@27184
   229
                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
wenzelm@27184
   230
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
wenzelm@27179
   231
                 in
wenzelm@27179
   232
                   Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
wenzelm@27179
   233
                 end
wenzelm@27179
   234
               else (*C*)
wenzelm@27179
   235
                 let val crator = cterm_of thy (Abs(x,xT,rator))
wenzelm@27184
   236
                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
wenzelm@27184
   237
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
wenzelm@27179
   238
                 in
wenzelm@27179
   239
                   Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
wenzelm@27179
   240
                 end
wenzelm@27184
   241
            else if loose_bvar1 (rand,0) then (*B or eta*)
wenzelm@36945
   242
               if rand = Bound 0 then Thm.eta_conversion ct
wenzelm@27179
   243
               else (*B*)
wenzelm@27179
   244
                 let val crand = cterm_of thy (Abs(x,xT,rand))
wenzelm@27179
   245
                     val crator = cterm_of thy rator
wenzelm@27184
   246
                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
wenzelm@27184
   247
                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
blanchet@37349
   248
                 in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end
wenzelm@27179
   249
            else makeK()
blanchet@37349
   250
        | _ => raise Fail "abstract: Bad term"
paulson@24827
   251
  end;
paulson@20863
   252
blanchet@37349
   253
(* Traverse a theorem, remplacing lambda-abstractions with combinators. *)
blanchet@37349
   254
fun do_introduce_combinators ct =
blanchet@37416
   255
  if is_quasi_lambda_free (term_of ct) then
blanchet@37349
   256
    Thm.reflexive ct
blanchet@37349
   257
  else case term_of ct of
blanchet@37349
   258
    Abs _ =>
blanchet@37349
   259
    let
blanchet@37349
   260
      val (cv, cta) = Thm.dest_abs NONE ct
blanchet@37349
   261
      val (v, _) = dest_Free (term_of cv)
blanchet@37349
   262
      val u_th = do_introduce_combinators cta
blanchet@37349
   263
      val cu = Thm.rhs_of u_th
blanchet@37349
   264
      val comb_eq = abstract (Thm.cabs cv cu)
blanchet@37349
   265
    in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end
blanchet@37349
   266
  | _ $ _ =>
blanchet@37349
   267
    let val (ct1, ct2) = Thm.dest_comb ct in
blanchet@37349
   268
        Thm.combination (do_introduce_combinators ct1)
blanchet@37349
   269
                        (do_introduce_combinators ct2)
blanchet@37349
   270
    end
blanchet@37349
   271
blanchet@37349
   272
fun introduce_combinators th =
blanchet@37416
   273
  if is_quasi_lambda_free (prop_of th) then
blanchet@37349
   274
    th
paulson@24827
   275
  else
blanchet@37349
   276
    let
blanchet@37349
   277
      val th = Drule.eta_contraction_rule th
blanchet@37349
   278
      val eqth = do_introduce_combinators (cprop_of th)
blanchet@37349
   279
    in Thm.equal_elim eqth th end
blanchet@37349
   280
    handle THM (msg, _, _) =>
blanchet@37349
   281
           (warning ("Error in the combinator translation of " ^
blanchet@37349
   282
                     Display.string_of_thm_without_context th ^
blanchet@37349
   283
                     "\nException message: " ^ msg ^ ".");
blanchet@37349
   284
            (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@37349
   285
            TrueI)
paulson@16009
   286
paulson@16009
   287
(*cterms are used throughout for efficiency*)
wenzelm@29064
   288
val cTrueprop = Thm.cterm_of @{theory HOL} HOLogic.Trueprop;
paulson@16009
   289
paulson@16009
   290
(*cterm version of mk_cTrueprop*)
paulson@16009
   291
fun c_mkTrueprop A = Thm.capply cTrueprop A;
paulson@16009
   292
paulson@16009
   293
(*Given an abstraction over n variables, replace the bound variables by free
paulson@16009
   294
  ones. Return the body, along with the list of free variables.*)
wenzelm@20461
   295
fun c_variant_abs_multi (ct0, vars) =
paulson@16009
   296
      let val (cv,ct) = Thm.dest_abs NONE ct0
paulson@16009
   297
      in  c_variant_abs_multi (ct, cv::vars)  end
paulson@16009
   298
      handle CTERM _ => (ct0, rev vars);
paulson@16009
   299
wenzelm@20461
   300
(*Given the definition of a Skolem function, return a theorem to replace
wenzelm@20461
   301
  an existential formula by a use of that function.
paulson@18141
   302
   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
blanchet@37399
   303
fun skolem_theorem_of_def inline def =
blanchet@37399
   304
  let
blanchet@37410
   305
      val (c, rhs) = Thm.dest_equals (cprop_of (freeze_thm def))
blanchet@37410
   306
      val rhs' = rhs |> inline ? (snd o Thm.dest_comb)
blanchet@37410
   307
      val (ch, frees) = c_variant_abs_multi (rhs', [])
blanchet@37410
   308
      val (chilbert, cabs) = ch |> Thm.dest_comb
wenzelm@26627
   309
      val thy = Thm.theory_of_cterm chilbert
wenzelm@26627
   310
      val t = Thm.term_of chilbert
blanchet@37399
   311
      val T =
blanchet@37399
   312
        case t of
blanchet@37410
   313
          Const (@{const_name Eps}, Type (@{type_name fun}, [_, T])) => T
blanchet@37410
   314
        | _ => raise TERM ("skolem_theorem_of_def: expected \"Eps\"", [t])
wenzelm@22596
   315
      val cex = Thm.cterm_of thy (HOLogic.exists_const T)
paulson@16009
   316
      val ex_tm = c_mkTrueprop (Thm.capply cex cabs)
blanchet@37399
   317
      and conc =
blanchet@37399
   318
        Drule.list_comb (if inline then rhs else c, frees)
blanchet@37399
   319
        |> Drule.beta_conv cabs |> c_mkTrueprop
blanchet@37399
   320
      fun tacf [prem] =
blanchet@37410
   321
        (if inline then rewrite_goals_tac @{thms skolem_id_def_raw}
blanchet@37410
   322
         else rewrite_goals_tac [def])
blanchet@37410
   323
        THEN rtac ((prem |> inline ? rewrite_rule @{thms skolem_id_def_raw})
blanchet@37410
   324
                   RS @{thm someI_ex}) 1
wenzelm@23352
   325
  in  Goal.prove_internal [ex_tm] conc tacf
paulson@18141
   326
       |> forall_intr_list frees
wenzelm@26653
   327
       |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
wenzelm@35845
   328
       |> Thm.varifyT_global
paulson@18141
   329
  end;
paulson@16009
   330
paulson@24742
   331
paulson@20863
   332
(*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)
paulson@24937
   333
fun to_nnf th ctxt0 =
wenzelm@27179
   334
  let val th1 = th |> transform_elim |> zero_var_indexes
wenzelm@32262
   335
      val ((_, [th2]), ctxt) = Variable.import true [th1] ctxt0
wenzelm@32262
   336
      val th3 = th2
wenzelm@35625
   337
        |> Conv.fconv_rule Object_Logic.atomize
wenzelm@32262
   338
        |> Meson.make_nnf ctxt |> strip_lambdas ~1
paulson@24937
   339
  in  (th3, ctxt)  end;
paulson@16009
   340
paulson@18141
   341
(*Generate Skolem functions for a theorem supplied in nnf*)
blanchet@37399
   342
fun skolem_theorems_of_assume inline s th =
blanchet@37399
   343
  map (skolem_theorem_of_def inline o Thm.assume o cterm_of (theory_of_thm th))
blanchet@37399
   344
      (assume_skolem_funs inline s th)
paulson@18141
   345
paulson@25007
   346
blanchet@37349
   347
(*** Blacklisting (more in "Sledgehammer_Fact_Filter") ***)
paulson@25007
   348
blanchet@37348
   349
val max_lambda_nesting = 3
wenzelm@27184
   350
blanchet@37348
   351
fun term_has_too_many_lambdas max (t1 $ t2) =
blanchet@37348
   352
    exists (term_has_too_many_lambdas max) [t1, t2]
blanchet@37348
   353
  | term_has_too_many_lambdas max (Abs (_, _, t)) =
blanchet@37348
   354
    max = 0 orelse term_has_too_many_lambdas (max - 1) t
blanchet@37348
   355
  | term_has_too_many_lambdas _ _ = false
paulson@25007
   356
blanchet@37348
   357
fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
paulson@25007
   358
blanchet@37348
   359
(* Don't count nested lambdas at the level of formulas, since they are
blanchet@37348
   360
   quantifiers. *)
blanchet@37348
   361
fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =
blanchet@37348
   362
    formula_has_too_many_lambdas (T :: Ts) t
blanchet@37348
   363
  | formula_has_too_many_lambdas Ts t =
blanchet@37348
   364
    if is_formula_type (fastype_of1 (Ts, t)) then
blanchet@37348
   365
      exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))
blanchet@37348
   366
    else
blanchet@37348
   367
      term_has_too_many_lambdas max_lambda_nesting t
paulson@25007
   368
blanchet@37348
   369
(* The max apply depth of any "metis" call in "Metis_Examples" (on 31-10-2007)
blanchet@37348
   370
   was 11. *)
blanchet@37348
   371
val max_apply_depth = 15
wenzelm@27184
   372
blanchet@37348
   373
fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
blanchet@37348
   374
  | apply_depth (Abs (_, _, t)) = apply_depth t
blanchet@37348
   375
  | apply_depth _ = 0
paulson@25256
   376
blanchet@37348
   377
fun is_formula_too_complex t =
blanchet@37348
   378
  apply_depth t > max_apply_depth orelse Meson.too_many_clauses NONE t orelse
blanchet@37348
   379
  formula_has_too_many_lambdas [] t
wenzelm@27184
   380
paulson@25243
   381
fun is_strange_thm th =
paulson@25243
   382
  case head_of (concl_of th) of
blanchet@35963
   383
      Const (a, _) => (a <> @{const_name Trueprop} andalso
blanchet@35963
   384
                       a <> @{const_name "=="})
paulson@25243
   385
    | _ => false;
paulson@25243
   386
blanchet@37348
   387
fun is_theorem_bad_for_atps thm =
blanchet@37348
   388
  let val t = prop_of thm in
blanchet@37348
   389
    is_formula_too_complex t orelse exists_type type_has_topsort t orelse
blanchet@37348
   390
    is_strange_thm thm
blanchet@37348
   391
  end
paulson@25243
   392
blanchet@35963
   393
(* FIXME: put other record thms here, or declare as "no_atp" *)
paulson@25007
   394
val multi_base_blacklist =
blanchet@35963
   395
  ["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",
blanchet@35963
   396
   "split_asm", "cases", "ext_cases"];
paulson@25007
   397
paulson@22731
   398
fun fake_name th =
wenzelm@27865
   399
  if Thm.has_name_hint th then flatten_name (Thm.get_name_hint th)
paulson@22731
   400
  else gensym "unknown_thm_";
paulson@22731
   401
wenzelm@27184
   402
(*Skolemize a named theorem, with Skolem functions as additional premises.*)
blanchet@37399
   403
fun skolemize_theorem s th =
blanchet@37345
   404
  if member (op =) multi_base_blacklist (Long_Name.base_name s) orelse
blanchet@37348
   405
     is_theorem_bad_for_atps th then
blanchet@37345
   406
    []
wenzelm@27184
   407
  else
wenzelm@27184
   408
    let
wenzelm@36603
   409
      val ctxt0 = Variable.global_thm_context th
blanchet@37349
   410
      val (nnfth, ctxt) = to_nnf th ctxt0
blanchet@37399
   411
      val inline = exists_type (exists_subtype (can dest_TFree)) (prop_of nnfth)
blanchet@37399
   412
      val defs = skolem_theorems_of_assume inline s nnfth
blanchet@37349
   413
      val (cnfs, ctxt) = Meson.make_cnf defs nnfth ctxt
blanchet@37349
   414
    in
blanchet@37349
   415
      cnfs |> map introduce_combinators
blanchet@37349
   416
           |> Variable.export ctxt ctxt0
blanchet@37349
   417
           |> Meson.finish_cnf
blanchet@37349
   418
    end
blanchet@37349
   419
    handle THM _ => []
wenzelm@27184
   420
paulson@24742
   421
(*The cache prevents repeated clausification of a theorem, and also repeated declaration of
paulson@24742
   422
  Skolem functions.*)
wenzelm@33522
   423
structure ThmCache = Theory_Data
wenzelm@22846
   424
(
wenzelm@28544
   425
  type T = thm list Thmtab.table * unit Symtab.table;
wenzelm@28544
   426
  val empty = (Thmtab.empty, Symtab.empty);
wenzelm@26618
   427
  val extend = I;
wenzelm@33522
   428
  fun merge ((cache1, seen1), (cache2, seen2)) : T =
wenzelm@27184
   429
    (Thmtab.merge (K true) (cache1, cache2), Symtab.merge (K true) (seen1, seen2));
wenzelm@22846
   430
);
paulson@22516
   431
wenzelm@27184
   432
val lookup_cache = Thmtab.lookup o #1 o ThmCache.get;
wenzelm@27184
   433
val already_seen = Symtab.defined o #2 o ThmCache.get;
wenzelm@20461
   434
wenzelm@27184
   435
val update_cache = ThmCache.map o apfst o Thmtab.update;
wenzelm@27184
   436
fun mark_seen name = ThmCache.map (apsnd (Symtab.update (name, ())));
paulson@25007
   437
blanchet@36228
   438
(* Convert Isabelle theorems into axiom clauses. *)
wenzelm@27179
   439
fun cnf_axiom thy th0 =
wenzelm@27184
   440
  let val th = Thm.transfer thy th0 in
wenzelm@27184
   441
    case lookup_cache thy th of
blanchet@37416
   442
      SOME cls => cls
blanchet@37416
   443
    | NONE => map Thm.close_derivation (skolemize_theorem (fake_name th) th)
paulson@22516
   444
  end;
paulson@15347
   445
paulson@18141
   446
paulson@22471
   447
(**** Translate a set of theorems into CNF ****)
paulson@15347
   448
blanchet@37486
   449
fun pair_name_cls _ (_, []) = []
paulson@19894
   450
  | pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss)
wenzelm@20461
   451
paulson@21290
   452
(*The combination of rev and tail recursion preserves the original order*)
blanchet@37416
   453
fun cnf_rules_pairs thy =
blanchet@37416
   454
  let
blanchet@37416
   455
    fun aux pairs [] = pairs
blanchet@37416
   456
      | aux pairs ((name, th) :: ths) =
blanchet@37416
   457
        let
blanchet@37416
   458
          val new_pairs = pair_name_cls 0 (name, cnf_axiom thy th)
blanchet@37416
   459
                          handle THM _ => [] |
blanchet@37416
   460
                                 CLAUSE _ => []
blanchet@37416
   461
        in aux (new_pairs @ pairs) ths end
blanchet@37416
   462
  in aux [] o rev end
mengj@19353
   463
mengj@19196
   464
blanchet@35865
   465
(**** Convert all facts of the theory into FOL or HOL clauses ****)
paulson@15347
   466
wenzelm@28544
   467
local
wenzelm@28544
   468
wenzelm@28544
   469
fun skolem_def (name, th) thy =
wenzelm@36603
   470
  let val ctxt0 = Variable.global_thm_context th in
blanchet@37348
   471
    case try (to_nnf th) ctxt0 of
wenzelm@28544
   472
      NONE => (NONE, thy)
blanchet@37349
   473
    | SOME (nnfth, ctxt) =>
blanchet@37348
   474
      let val (defs, thy') = declare_skolem_funs (flatten_name name) nnfth thy
blanchet@37349
   475
      in (SOME (th, ctxt0, ctxt, nnfth, defs), thy') end
wenzelm@28544
   476
  end;
paulson@24742
   477
blanchet@37349
   478
fun skolem_cnfs (th, ctxt0, ctxt, nnfth, defs) =
wenzelm@28544
   479
  let
blanchet@37399
   480
    val (cnfs, ctxt) =
blanchet@37399
   481
      Meson.make_cnf (map (skolem_theorem_of_def false) defs) nnfth ctxt
wenzelm@28544
   482
    val cnfs' = cnfs
blanchet@37349
   483
      |> map introduce_combinators
blanchet@37349
   484
      |> Variable.export ctxt ctxt0
wenzelm@28544
   485
      |> Meson.finish_cnf
wenzelm@28544
   486
      |> map Thm.close_derivation;
wenzelm@28544
   487
    in (th, cnfs') end;
wenzelm@28544
   488
wenzelm@28544
   489
in
paulson@24742
   490
wenzelm@27184
   491
fun saturate_skolem_cache thy =
wenzelm@28544
   492
  let
wenzelm@33306
   493
    val facts = PureThy.facts_of thy;
wenzelm@33306
   494
    val new_facts = (facts, []) |-> Facts.fold_static (fn (name, ths) =>
wenzelm@33306
   495
      if Facts.is_concealed facts name orelse already_seen thy name then I
wenzelm@33306
   496
      else cons (name, ths));
wenzelm@28544
   497
    val new_thms = (new_facts, []) |-> fold (fn (name, ths) =>
blanchet@37399
   498
      if member (op =) multi_base_blacklist (Long_Name.base_name name) then
blanchet@37399
   499
        I
blanchet@37399
   500
      else
blanchet@37399
   501
        fold_index (fn (i, th) =>
blanchet@37410
   502
          if is_theorem_bad_for_atps th orelse
blanchet@37410
   503
             is_some (lookup_cache thy th) then
blanchet@37399
   504
            I
blanchet@37399
   505
          else
blanchet@37399
   506
            cons (name ^ "_" ^ string_of_int (i + 1), Thm.transfer thy th)) ths)
wenzelm@28544
   507
  in
blanchet@37399
   508
    if null new_facts then
blanchet@37399
   509
      NONE
wenzelm@28544
   510
    else
wenzelm@28544
   511
      let
wenzelm@28544
   512
        val (defs, thy') = thy
wenzelm@28544
   513
          |> fold (mark_seen o #1) new_facts
wenzelm@28544
   514
          |> fold_map skolem_def (sort_distinct (Thm.thm_ord o pairself snd) new_thms)
wenzelm@28544
   515
          |>> map_filter I;
wenzelm@29368
   516
        val cache_entries = Par_List.map skolem_cnfs defs;
wenzelm@28544
   517
      in SOME (fold update_cache cache_entries thy') end
wenzelm@28544
   518
  end;
wenzelm@27184
   519
wenzelm@28544
   520
end;
paulson@24854
   521
blanchet@37498
   522
val auto_saturate_skolem_cache = Unsynchronized.ref true
paulson@20457
   523
blanchet@37498
   524
fun conditionally_saturate_skolem_cache thy =
blanchet@37498
   525
  if !auto_saturate_skolem_cache then saturate_skolem_cache thy else NONE
wenzelm@27179
   526
blanchet@36398
   527
paulson@21999
   528
(*** Converting a subgoal into negated conjecture clauses. ***)
paulson@21999
   529
wenzelm@32262
   530
fun neg_skolemize_tac ctxt =
blanchet@37332
   531
  EVERY' [rtac ccontr, Object_Logic.atomize_prems_tac, Meson.skolemize_tac ctxt]
blanchet@36398
   532
blanchet@35869
   533
val neg_clausify =
blanchet@37349
   534
  single
blanchet@37349
   535
  #> Meson.make_clauses_unsorted
blanchet@37349
   536
  #> map introduce_combinators
blanchet@37349
   537
  #> Meson.finish_cnf
paulson@21999
   538
wenzelm@32257
   539
fun neg_conjecture_clauses ctxt st0 n =
wenzelm@32257
   540
  let
blanchet@37332
   541
    (* "Option" is thrown if the assumptions contain schematic variables. *)
blanchet@37332
   542
    val st = Seq.hd (neg_skolemize_tac ctxt n st0) handle Option.Option => st0
blanchet@37332
   543
    val ({params, prems, ...}, _) =
blanchet@37332
   544
      Subgoal.focus (Variable.set_body false ctxt) n st
blanchet@37332
   545
  in (map neg_clausify prems, map (dest_Free o term_of o #2) params) end
paulson@21999
   546
wenzelm@24669
   547
(*Conversion of a subgoal to conjecture clauses. Each clause has
paulson@21999
   548
  leading !!-bound universal variables, to express generality. *)
wenzelm@32257
   549
fun neg_clausify_tac ctxt =
wenzelm@32262
   550
  neg_skolemize_tac ctxt THEN'
wenzelm@32257
   551
  SUBGOAL (fn (prop, i) =>
wenzelm@32257
   552
    let val ts = Logic.strip_assums_hyp prop in
wenzelm@32257
   553
      EVERY'
wenzelm@32283
   554
       [Subgoal.FOCUS
wenzelm@32257
   555
         (fn {prems, ...} =>
wenzelm@32257
   556
           (Method.insert_tac
blanchet@36398
   557
             (map forall_intr_vars (maps neg_clausify prems)) i)) ctxt,
wenzelm@32257
   558
        REPEAT_DETERM_N (length ts) o etac thin_rl] i
paulson@21999
   559
     end);
paulson@21999
   560
wenzelm@27184
   561
wenzelm@27184
   562
(** setup **)
wenzelm@27184
   563
wenzelm@27184
   564
val setup =
blanchet@37498
   565
  perhaps conditionally_saturate_skolem_cache
blanchet@37498
   566
  #> Theory.at_end conditionally_saturate_skolem_cache
paulson@18510
   567
wenzelm@20461
   568
end;