src/HOL/Tools/Sledgehammer/sledgehammer_fol_clause.ML
author blanchet
Mon Apr 19 11:54:07 2010 +0200 (2010-04-19 ago)
changeset 36222 0e3e49bd658d
parent 36221 3abbae8a10cd
child 36378 f32c567dbcaa
permissions -rw-r--r--
don't use readable names if proof reconstruction is needed, because it uses the structure of names
blanchet@35826
     1
(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fol_clause.ML
wenzelm@33311
     2
    Author:     Jia Meng, Cambridge University Computer Laboratory
paulson@15347
     3
wenzelm@33311
     4
Storing/printing FOL clauses and arity clauses.  Typed equality is
wenzelm@33311
     5
treated differently.
wenzelm@33311
     6
blanchet@36218
     7
FIXME: combine with sledgehammer_hol_clause!
paulson@15347
     8
*)
paulson@15347
     9
blanchet@35826
    10
signature SLEDGEHAMMER_FOL_CLAUSE =
wenzelm@24310
    11
sig
wenzelm@24310
    12
  val schematic_var_prefix: string
wenzelm@24310
    13
  val fixed_var_prefix: string
wenzelm@24310
    14
  val tvar_prefix: string
wenzelm@24310
    15
  val tfree_prefix: string
wenzelm@24310
    16
  val clause_prefix: string
wenzelm@24310
    17
  val const_prefix: string
wenzelm@24310
    18
  val tconst_prefix: string
wenzelm@24310
    19
  val class_prefix: string
wenzelm@24310
    20
  val union_all: ''a list list -> ''a list
wenzelm@24310
    21
  val const_trans_table: string Symtab.table
wenzelm@24310
    22
  val type_const_trans_table: string Symtab.table
wenzelm@24310
    23
  val ascii_of: string -> string
wenzelm@24310
    24
  val undo_ascii_of: string -> string
wenzelm@24310
    25
  val paren_pack : string list -> string
wenzelm@24310
    26
  val make_schematic_var : string * int -> string
paulson@18868
    27
  val make_fixed_var : string -> string
paulson@18868
    28
  val make_schematic_type_var : string * int -> string
wenzelm@24310
    29
  val make_fixed_type_var : string -> string
immler@30151
    30
  val make_fixed_const : bool -> string -> string
immler@30151
    31
  val make_fixed_type_const : bool -> string -> string
paulson@18868
    32
  val make_type_class : string -> string
blanchet@36169
    33
  type name = string * string
blanchet@36169
    34
  type name_pool = string Symtab.table * string Symtab.table
blanchet@36169
    35
  val empty_name_pool : bool -> name_pool option
blanchet@36169
    36
  val pool_map : ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
blanchet@36169
    37
  val nice_name : name -> name_pool option -> string * name_pool option
wenzelm@24310
    38
  datatype kind = Axiom | Conjecture
wenzelm@24310
    39
  type axiom_name = string
wenzelm@24310
    40
  datatype fol_type =
blanchet@36169
    41
    TyVar of name |
blanchet@36169
    42
    TyFree of name |
blanchet@36169
    43
    TyConstr of name * fol_type list
blanchet@36170
    44
  val string_of_fol_type :
blanchet@36170
    45
    fol_type -> name_pool option -> string * name_pool option
wenzelm@24310
    46
  datatype type_literal = LTVar of string * string | LTFree of string * string
wenzelm@24310
    47
  exception CLAUSE of string * term
paulson@24940
    48
  val add_typs : typ list -> type_literal list
paulson@24940
    49
  val get_tvar_strs: typ list -> string list
wenzelm@24310
    50
  datatype arLit =
wenzelm@24310
    51
      TConsLit of class * string * string list
wenzelm@24310
    52
    | TVarLit of class * string
blanchet@35865
    53
  datatype arity_clause = ArityClause of
paulson@24937
    54
   {axiom_name: axiom_name, conclLit: arLit, premLits: arLit list}
blanchet@35865
    55
  datatype classrel_clause = ClassrelClause of
paulson@24937
    56
   {axiom_name: axiom_name, subclass: class, superclass: class}
blanchet@35865
    57
  val make_classrel_clauses: theory -> class list -> class list -> classrel_clause list
blanchet@35865
    58
  val make_arity_clauses_dfg: bool -> theory -> string list -> class list -> class list * arity_clause list
blanchet@35865
    59
  val make_arity_clauses: theory -> string list -> class list -> class list * arity_clause list
blanchet@36218
    60
  val add_type_sort_preds: typ -> int Symtab.table -> int Symtab.table
blanchet@36218
    61
  val add_classrel_clause_preds :
blanchet@36218
    62
    classrel_clause -> int Symtab.table -> int Symtab.table
wenzelm@24310
    63
  val class_of_arityLit: arLit -> class
blanchet@36218
    64
  val add_arity_clause_preds: arity_clause -> int Symtab.table -> int Symtab.table
blanchet@36218
    65
  val add_fol_type_funcs: fol_type -> int Symtab.table -> int Symtab.table
blanchet@36218
    66
  val add_arity_clause_funcs:
blanchet@36218
    67
    arity_clause -> int Symtab.table -> int Symtab.table
wenzelm@24310
    68
  val init_functab: int Symtab.table
mengj@19719
    69
  val dfg_sign: bool -> string -> string
paulson@24937
    70
  val dfg_of_typeLit: bool -> type_literal -> string
paulson@24937
    71
  val gen_dfg_cls: int * string * kind * string list * string list * string list -> string
wenzelm@24310
    72
  val string_of_preds: (string * Int.int) list -> string
wenzelm@24310
    73
  val string_of_funcs: (string * int) list -> string
wenzelm@24310
    74
  val string_of_symbols: string -> string -> string
mengj@19719
    75
  val string_of_start: string -> string
mengj@19719
    76
  val string_of_descrip : string -> string
wenzelm@24310
    77
  val dfg_tfree_clause : string -> string
blanchet@35865
    78
  val dfg_classrel_clause: classrel_clause -> string
blanchet@35865
    79
  val dfg_arity_clause: arity_clause -> string
wenzelm@24310
    80
  val tptp_sign: bool -> string -> string
paulson@24937
    81
  val tptp_of_typeLit : bool -> type_literal -> string
paulson@24937
    82
  val gen_tptp_cls : int * string * kind * string list * string list -> string
wenzelm@24310
    83
  val tptp_tfree_clause : string -> string
blanchet@35865
    84
  val tptp_arity_clause : arity_clause -> string
blanchet@35865
    85
  val tptp_classrel_clause : classrel_clause -> string
wenzelm@24310
    86
end
paulson@15347
    87
blanchet@35826
    88
structure Sledgehammer_FOL_Clause : SLEDGEHAMMER_FOL_CLAUSE =
paulson@15347
    89
struct
paulson@15347
    90
blanchet@36063
    91
open Sledgehammer_Util
blanchet@36063
    92
paulson@15347
    93
val schematic_var_prefix = "V_";
paulson@15347
    94
val fixed_var_prefix = "v_";
paulson@15347
    95
paulson@17230
    96
val tvar_prefix = "T_";
paulson@17230
    97
val tfree_prefix = "t_";
paulson@15347
    98
wenzelm@24310
    99
val clause_prefix = "cls_";
wenzelm@24310
   100
val arclause_prefix = "clsarity_"
paulson@17525
   101
val clrelclause_prefix = "clsrel_";
paulson@15347
   102
paulson@17230
   103
val const_prefix = "c_";
wenzelm@24310
   104
val tconst_prefix = "tc_";
wenzelm@24310
   105
val class_prefix = "class_";
paulson@15347
   106
blanchet@36218
   107
fun union_all xss = fold (union (op =)) xss []
paulson@17775
   108
blanchet@35865
   109
(* Provide readable names for the more common symbolic functions *)
paulson@15347
   110
val const_trans_table =
blanchet@35865
   111
  Symtab.make [(@{const_name "op ="}, "equal"),
blanchet@35865
   112
               (@{const_name Orderings.less_eq}, "lessequals"),
blanchet@35865
   113
               (@{const_name "op &"}, "and"),
blanchet@35865
   114
               (@{const_name "op |"}, "or"),
blanchet@35865
   115
               (@{const_name "op -->"}, "implies"),
blanchet@35865
   116
               (@{const_name "op :"}, "in"),
blanchet@35865
   117
               (@{const_name fequal}, "fequal"),
blanchet@35865
   118
               (@{const_name COMBI}, "COMBI"),
blanchet@35865
   119
               (@{const_name COMBK}, "COMBK"),
blanchet@35865
   120
               (@{const_name COMBB}, "COMBB"),
blanchet@35865
   121
               (@{const_name COMBC}, "COMBC"),
blanchet@35865
   122
               (@{const_name COMBS}, "COMBS")];
paulson@15347
   123
paulson@17230
   124
val type_const_trans_table =
blanchet@35865
   125
  Symtab.make [("*", "prod"), ("+", "sum"), ("~=>", "map")];
paulson@15347
   126
paulson@15610
   127
(*Escaping of special characters.
paulson@15610
   128
  Alphanumeric characters are left unchanged.
paulson@15610
   129
  The character _ goes to __
paulson@15610
   130
  Characters in the range ASCII space to / go to _A to _P, respectively.
paulson@24183
   131
  Other printing characters go to _nnn where nnn is the decimal ASCII code.*)
paulson@24183
   132
val A_minus_space = Char.ord #"A" - Char.ord #" ";
paulson@15610
   133
paulson@24183
   134
fun stringN_of_int 0 _ = ""
paulson@24183
   135
  | stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ Int.toString (n mod 10);
paulson@15610
   136
paulson@15347
   137
fun ascii_of_c c =
paulson@15610
   138
  if Char.isAlphaNum c then String.str c
paulson@15610
   139
  else if c = #"_" then "__"
wenzelm@24310
   140
  else if #" " <= c andalso c <= #"/"
paulson@15610
   141
       then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))
wenzelm@24310
   142
  else if Char.isPrint c
paulson@24183
   143
       then ("_" ^ stringN_of_int 3 (Char.ord c))  (*fixed width, in case more digits follow*)
paulson@15610
   144
  else ""
paulson@15347
   145
paulson@15610
   146
val ascii_of = String.translate ascii_of_c;
paulson@15610
   147
paulson@24183
   148
(** Remove ASCII armouring from names in proof files **)
paulson@24183
   149
paulson@24183
   150
(*We don't raise error exceptions because this code can run inside the watcher.
paulson@24183
   151
  Also, the errors are "impossible" (hah!)*)
paulson@24183
   152
fun undo_ascii_aux rcs [] = String.implode(rev rcs)
paulson@24183
   153
  | undo_ascii_aux rcs [#"_"] = undo_ascii_aux (#"_"::rcs) []  (*ERROR*)
paulson@24183
   154
      (*Three types of _ escapes: __, _A to _P, _nnn*)
paulson@24183
   155
  | undo_ascii_aux rcs (#"_" :: #"_" :: cs) = undo_ascii_aux (#"_"::rcs) cs
wenzelm@24310
   156
  | undo_ascii_aux rcs (#"_" :: c :: cs) =
paulson@24183
   157
      if #"A" <= c andalso c<= #"P"  (*translation of #" " to #"/"*)
paulson@24183
   158
      then undo_ascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs
wenzelm@24310
   159
      else
paulson@24183
   160
        let val digits = List.take (c::cs, 3) handle Subscript => []
wenzelm@24310
   161
        in
paulson@24183
   162
            case Int.fromString (String.implode digits) of
paulson@24183
   163
                NONE => undo_ascii_aux (c:: #"_"::rcs) cs  (*ERROR*)
paulson@24183
   164
              | SOME n => undo_ascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))
paulson@24183
   165
        end
paulson@24183
   166
  | undo_ascii_aux rcs (c::cs) = undo_ascii_aux (c::rcs) cs;
paulson@24183
   167
paulson@24183
   168
val undo_ascii_of = undo_ascii_aux [] o String.explode;
paulson@15347
   169
paulson@17525
   170
(* convert a list of strings into one single string; surrounded by brackets *)
paulson@18218
   171
fun paren_pack [] = ""   (*empty argument list*)
paulson@18218
   172
  | paren_pack strings = "(" ^ commas strings ^ ")";
paulson@17525
   173
paulson@21509
   174
(*TSTP format uses (...) rather than the old [...]*)
paulson@21509
   175
fun tptp_pack strings = "(" ^ space_implode " | " strings ^ ")";
paulson@17525
   176
paulson@17525
   177
paulson@16925
   178
(*Remove the initial ' character from a type variable, if it is present*)
paulson@16925
   179
fun trim_type_var s =
paulson@16925
   180
  if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
paulson@16925
   181
  else error ("trim_type: Malformed type variable encountered: " ^ s);
paulson@16925
   182
paulson@16903
   183
fun ascii_of_indexname (v,0) = ascii_of v
paulson@17525
   184
  | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;
paulson@15347
   185
paulson@17230
   186
fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v);
paulson@15347
   187
fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);
paulson@15347
   188
wenzelm@24310
   189
fun make_schematic_type_var (x,i) =
paulson@16925
   190
      tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));
paulson@16925
   191
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));
paulson@15347
   192
blanchet@36062
   193
(* HACK because SPASS 3.0 truncates identifiers to 63 characters. (This is
blanchet@36062
   194
   solved in 3.7 and perhaps in earlier versions too.) *)
blanchet@36062
   195
(* 32-bit hash, so we expect no collisions. *)
blanchet@36062
   196
fun controlled_length dfg s =
blanchet@36063
   197
  if dfg andalso size s > 60 then Word.toString (hashw_string (s, 0w0)) else s;
paulson@23075
   198
immler@30151
   199
fun lookup_const dfg c =
wenzelm@17412
   200
    case Symtab.lookup const_trans_table c of
paulson@17230
   201
        SOME c' => c'
immler@30151
   202
      | NONE => controlled_length dfg (ascii_of c);
paulson@17230
   203
immler@30151
   204
fun lookup_type_const dfg c =
wenzelm@17412
   205
    case Symtab.lookup type_const_trans_table c of
paulson@17230
   206
        SOME c' => c'
immler@30151
   207
      | NONE => controlled_length dfg (ascii_of c);
paulson@18411
   208
blanchet@36062
   209
(* "op =" MUST BE "equal" because it's built into ATPs. *)
blanchet@36062
   210
fun make_fixed_const _ (@{const_name "op ="}) = "equal"
blanchet@36062
   211
  | make_fixed_const dfg c = const_prefix ^ lookup_const dfg c;
paulson@18411
   212
immler@30151
   213
fun make_fixed_type_const dfg c = tconst_prefix ^ lookup_type_const dfg c;
quigley@17150
   214
wenzelm@17261
   215
fun make_type_class clas = class_prefix ^ ascii_of clas;
quigley@17150
   216
quigley@17150
   217
blanchet@36169
   218
(**** name pool ****)
blanchet@36169
   219
 
blanchet@36169
   220
type name = string * string
blanchet@36169
   221
type name_pool = string Symtab.table * string Symtab.table
blanchet@36169
   222
blanchet@36222
   223
fun empty_name_pool readable_names =
blanchet@36222
   224
  if readable_names then SOME (`I Symtab.empty) else NONE
blanchet@36169
   225
blanchet@36169
   226
fun pool_map f xs =
blanchet@36170
   227
  fold_rev (fn x => fn (ys, pool) => f x pool |>> (fn y => y :: ys)) xs
blanchet@36170
   228
  o pair []
blanchet@36169
   229
blanchet@36169
   230
fun add_nice_name full_name nice_prefix j the_pool =
blanchet@36169
   231
  let
blanchet@36169
   232
    val nice_name = nice_prefix ^ (if j = 0 then "" else "_" ^ Int.toString j)
blanchet@36169
   233
  in
blanchet@36169
   234
    case Symtab.lookup (snd the_pool) nice_name of
blanchet@36169
   235
      SOME full_name' =>
blanchet@36169
   236
      if full_name = full_name' then (nice_name, the_pool)
blanchet@36169
   237
      else add_nice_name full_name nice_prefix (j + 1) the_pool
blanchet@36169
   238
    | NONE =>
blanchet@36169
   239
      (nice_name, (Symtab.update_new (full_name, nice_name) (fst the_pool),
blanchet@36169
   240
                   Symtab.update_new (nice_name, full_name) (snd the_pool)))
blanchet@36169
   241
  end
blanchet@36169
   242
blanchet@36169
   243
fun translate_first_char f s =
blanchet@36169
   244
  String.str (f (String.sub (s, 0))) ^ String.extract (s, 1, NONE)
blanchet@36169
   245
blanchet@36222
   246
fun readable_name full_name s =
blanchet@36169
   247
  let
blanchet@36169
   248
    val s = s |> Long_Name.base_name
blanchet@36169
   249
              |> fold remove_all ["\<^sub>", "\<^bsub>", "\<^esub>", "\<^isub>"]
blanchet@36169
   250
    val s' = s |> explode |> rev |> dropwhile (curry (op =) "'")
blanchet@36169
   251
    val s' =
blanchet@36169
   252
      (s' |> rev
blanchet@36169
   253
          |> implode
blanchet@36169
   254
          |> String.translate
blanchet@36221
   255
                 (fn c => if Char.isAlphaNum c orelse c = #"_" then String.str c
blanchet@36221
   256
                          else ""))
blanchet@36169
   257
      ^ replicate_string (String.size s - length s') "_"
blanchet@36169
   258
    val s' =
blanchet@36169
   259
      if s' = "" orelse not (Char.isAlpha (String.sub (s', 0))) then "X" ^ s'
blanchet@36169
   260
      else s'
blanchet@36169
   261
    val s' = if s' = "op" then full_name else s'
blanchet@36169
   262
  in
blanchet@36169
   263
    case (Char.isLower (String.sub (full_name, 0)),
blanchet@36169
   264
          Char.isLower (String.sub (s', 0))) of
blanchet@36169
   265
      (true, false) => translate_first_char Char.toLower s'
blanchet@36169
   266
    | (false, true) => translate_first_char Char.toUpper s'
blanchet@36169
   267
    | _ => s'
blanchet@36169
   268
  end
blanchet@36169
   269
blanchet@36169
   270
fun nice_name (full_name, _) NONE = (full_name, NONE)
blanchet@36169
   271
  | nice_name (full_name, desired_name) (SOME the_pool) =
blanchet@36169
   272
    case Symtab.lookup (fst the_pool) full_name of
blanchet@36169
   273
      SOME nice_name => (nice_name, SOME the_pool)
blanchet@36222
   274
    | NONE => add_nice_name full_name (readable_name full_name desired_name) 0
blanchet@36222
   275
                            the_pool
blanchet@36169
   276
              |> apsnd SOME
blanchet@36169
   277
blanchet@36169
   278
(**** Definitions and functions for FOL clauses, for conversion to TPTP or DFG
blanchet@36169
   279
      format ****)
paulson@15347
   280
paulson@21509
   281
datatype kind = Axiom | Conjecture;
paulson@23385
   282
paulson@15347
   283
type axiom_name = string;
paulson@15347
   284
paulson@15347
   285
(**** Isabelle FOL clauses ****)
paulson@15347
   286
blanchet@36168
   287
datatype fol_type =
blanchet@36169
   288
  TyVar of name |
blanchet@36169
   289
  TyFree of name |
blanchet@36169
   290
  TyConstr of name * fol_type list
mengj@18402
   291
blanchet@36170
   292
fun string_of_fol_type (TyVar sp) pool = nice_name sp pool
blanchet@36170
   293
  | string_of_fol_type (TyFree sp) pool = nice_name sp pool
blanchet@36170
   294
  | string_of_fol_type (TyConstr (sp, tys)) pool =
blanchet@36170
   295
    let
blanchet@36170
   296
      val (s, pool) = nice_name sp pool
blanchet@36170
   297
      val (ss, pool) = pool_map string_of_fol_type tys pool
blanchet@36170
   298
    in (s ^ paren_pack ss, pool) end
wenzelm@24310
   299
paulson@18798
   300
(*First string is the type class; the second is a TVar or TFfree*)
paulson@18798
   301
datatype type_literal = LTVar of string * string | LTFree of string * string;
paulson@15347
   302
paulson@17404
   303
exception CLAUSE of string * term;
paulson@15347
   304
wenzelm@24310
   305
(*Make literals for sorted type variables*)
paulson@24940
   306
fun sorts_on_typs_aux (_, [])   = []
paulson@24940
   307
  | sorts_on_typs_aux ((x,i),  s::ss) =
paulson@24940
   308
      let val sorts = sorts_on_typs_aux ((x,i), ss)
paulson@22643
   309
      in
paulson@22643
   310
          if s = "HOL.type" then sorts
paulson@24940
   311
          else if i = ~1 then LTFree(make_type_class s, make_fixed_type_var x) :: sorts
paulson@24940
   312
          else LTVar(make_type_class s, make_schematic_type_var (x,i)) :: sorts
paulson@22643
   313
      end;
quigley@17150
   314
paulson@24940
   315
fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s)
paulson@24940
   316
  | sorts_on_typs (TVar (v,s))  = sorts_on_typs_aux (v,s);
paulson@24940
   317
paulson@18798
   318
fun pred_of_sort (LTVar (s,ty)) = (s,1)
paulson@22643
   319
  | pred_of_sort (LTFree (s,ty)) = (s,1)
quigley@17150
   320
paulson@24937
   321
(*Given a list of sorted type variables, return a list of type literals.*)
blanchet@36218
   322
fun add_typs Ts = fold (union (op =)) (map sorts_on_typs Ts) []
mengj@20015
   323
paulson@29676
   324
(*The correct treatment of TFrees like 'a in lemmas (axiom clauses) is not clear.
paulson@29676
   325
  * Ignoring them leads to unsound proofs, since we do nothing to ensure that 'a
paulson@29676
   326
    in a lemma has the same sort as 'a in the conjecture.
paulson@29676
   327
  * Deleting such clauses will lead to problems with locales in other use of local results
paulson@29676
   328
    where 'a is fixed. Probably we should delete clauses unless the sorts agree.
paulson@29676
   329
  * Currently we include a class constraint in the clause, exactly as with TVars.
paulson@29676
   330
*)
paulson@29676
   331
mengj@20015
   332
(** make axiom and conjecture clauses. **)
mengj@20015
   333
mengj@20015
   334
fun get_tvar_strs [] = []
paulson@24940
   335
  | get_tvar_strs ((TVar (indx,s))::Ts) =
paulson@24940
   336
      insert (op =) (make_schematic_type_var indx) (get_tvar_strs Ts)
paulson@24940
   337
  | get_tvar_strs((TFree _)::Ts) = get_tvar_strs Ts
mengj@20015
   338
wenzelm@24310
   339
mengj@19354
   340
paulson@15347
   341
(**** Isabelle arities ****)
paulson@15347
   342
wenzelm@24310
   343
datatype arLit = TConsLit of class * string * string list
paulson@22643
   344
               | TVarLit of class * string;
wenzelm@24310
   345
blanchet@35865
   346
datatype arity_clause =
wenzelm@24310
   347
         ArityClause of {axiom_name: axiom_name,
wenzelm@24310
   348
                         conclLit: arLit,
wenzelm@24310
   349
                         premLits: arLit list};
paulson@15347
   350
paulson@15347
   351
paulson@18798
   352
fun gen_TVars 0 = []
paulson@18798
   353
  | gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n-1);
paulson@15347
   354
paulson@18411
   355
fun pack_sort(_,[])  = []
paulson@18411
   356
  | pack_sort(tvar, "HOL.type"::srt) = pack_sort(tvar, srt)   (*IGNORE sort "type"*)
paulson@22643
   357
  | pack_sort(tvar, cls::srt) =  (cls, tvar) :: pack_sort(tvar, srt);
wenzelm@24310
   358
paulson@18411
   359
(*Arity of type constructor tcon :: (arg1,...,argN)res*)
immler@30151
   360
fun make_axiom_arity_clause dfg (tcons, axiom_name, (cls,args)) =
paulson@21560
   361
   let val tvars = gen_TVars (length args)
paulson@17845
   362
       val tvars_srts = ListPair.zip (tvars,args)
paulson@17845
   363
   in
paulson@24937
   364
      ArityClause {axiom_name = axiom_name, 
immler@30151
   365
                   conclLit = TConsLit (cls, make_fixed_type_const dfg tcons, tvars),
paulson@22643
   366
                   premLits = map TVarLit (union_all(map pack_sort tvars_srts))}
paulson@17845
   367
   end;
paulson@15347
   368
paulson@15347
   369
paulson@15347
   370
(**** Isabelle class relations ****)
paulson@15347
   371
blanchet@35865
   372
datatype classrel_clause =
wenzelm@24310
   373
         ClassrelClause of {axiom_name: axiom_name,
wenzelm@24310
   374
                            subclass: class,
wenzelm@24310
   375
                            superclass: class};
wenzelm@24310
   376
paulson@21290
   377
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
paulson@21432
   378
fun class_pairs thy [] supers = []
paulson@21432
   379
  | class_pairs thy subs supers =
blanchet@36218
   380
      let
blanchet@36218
   381
        val class_less = Sorts.class_less (Sign.classes_of thy)
blanchet@36218
   382
        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
blanchet@36218
   383
        fun add_supers sub = fold (add_super sub) supers
blanchet@36218
   384
      in fold add_supers subs [] end
paulson@15347
   385
blanchet@35865
   386
fun make_classrel_clause (sub,super) =
paulson@21290
   387
  ClassrelClause {axiom_name = clrelclause_prefix ^ ascii_of sub ^ "_" ^ ascii_of super,
wenzelm@24310
   388
                  subclass = make_type_class sub,
paulson@21290
   389
                  superclass = make_type_class super};
paulson@15347
   390
paulson@21290
   391
fun make_classrel_clauses thy subs supers =
blanchet@35865
   392
  map make_classrel_clause (class_pairs thy subs supers);
paulson@18868
   393
paulson@18868
   394
paulson@18868
   395
(** Isabelle arities **)
paulson@17845
   396
immler@30151
   397
fun arity_clause dfg _ _ (tcons, []) = []
immler@30151
   398
  | arity_clause dfg seen n (tcons, ("HOL.type",_)::ars) =  (*ignore*)
immler@30151
   399
      arity_clause dfg seen n (tcons,ars)
immler@30151
   400
  | arity_clause dfg seen n (tcons, (ar as (class,_)) :: ars) =
paulson@21373
   401
      if class mem_string seen then (*multiple arities for the same tycon, class pair*)
immler@30151
   402
          make_axiom_arity_clause dfg (tcons, lookup_type_const dfg tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::
immler@30151
   403
          arity_clause dfg seen (n+1) (tcons,ars)
paulson@21373
   404
      else
immler@30151
   405
          make_axiom_arity_clause dfg (tcons, lookup_type_const dfg tcons ^ "_" ^ class, ar) ::
immler@30151
   406
          arity_clause dfg (class::seen) n (tcons,ars)
paulson@17845
   407
immler@30151
   408
fun multi_arity_clause dfg [] = []
blanchet@36218
   409
  | multi_arity_clause dfg ((tcons, ars) :: tc_arlists) =
blanchet@36218
   410
      arity_clause dfg [] 1 (tcons, ars) @ multi_arity_clause dfg tc_arlists
paulson@17845
   411
paulson@22643
   412
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
paulson@22643
   413
  provided its arguments have the corresponding sorts.*)
paulson@21373
   414
fun type_class_pairs thy tycons classes =
paulson@21373
   415
  let val alg = Sign.classes_of thy
blanchet@36218
   416
      fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
blanchet@36218
   417
      fun add_class tycon class =
blanchet@36218
   418
        cons (class, domain_sorts tycon class)
blanchet@36218
   419
        handle Sorts.CLASS_ERROR _ => I
blanchet@36218
   420
      fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
paulson@21373
   421
  in  map try_classes tycons  end;
paulson@21373
   422
paulson@22643
   423
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
paulson@22643
   424
fun iter_type_class_pairs thy tycons [] = ([], [])
paulson@22643
   425
  | iter_type_class_pairs thy tycons classes =
paulson@22643
   426
      let val cpairs = type_class_pairs thy tycons classes
haftmann@33040
   427
          val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
haftmann@33040
   428
            |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
wenzelm@24310
   429
          val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
haftmann@33042
   430
      in (union (op =) classes' classes, union (op =) cpairs' cpairs) end;
wenzelm@24310
   431
immler@30151
   432
fun make_arity_clauses_dfg dfg thy tycons classes =
wenzelm@24310
   433
  let val (classes', cpairs) = iter_type_class_pairs thy tycons classes
immler@30151
   434
  in  (classes', multi_arity_clause dfg cpairs)  end;
immler@30151
   435
val make_arity_clauses = make_arity_clauses_dfg false;
paulson@17845
   436
paulson@18868
   437
(**** Find occurrences of predicates in clauses ****)
paulson@18868
   438
wenzelm@24310
   439
(*FIXME: multiple-arity checking doesn't work, as update_new is the wrong
paulson@18868
   440
  function (it flags repeated declarations of a function, even with the same arity)*)
paulson@18868
   441
blanchet@36218
   442
fun update_many keypairs = fold Symtab.update keypairs
paulson@18868
   443
blanchet@36218
   444
val add_type_sort_preds = update_many o map pred_of_sort o sorts_on_typs
paulson@17845
   445
blanchet@36218
   446
fun add_classrel_clause_preds (ClassrelClause {subclass, superclass, ...}) =
blanchet@36218
   447
  Symtab.update (subclass, 1) #> Symtab.update (superclass, 1)
paulson@17845
   448
paulson@22643
   449
fun class_of_arityLit (TConsLit (tclass, _, _)) = tclass
paulson@22643
   450
  | class_of_arityLit (TVarLit (tclass, _)) = tclass;
paulson@21373
   451
blanchet@36218
   452
fun add_arity_clause_preds (ArityClause {conclLit, premLits, ...}) =
blanchet@36218
   453
  let
blanchet@36218
   454
    val classes = map (make_type_class o class_of_arityLit)
blanchet@36218
   455
                      (conclLit :: premLits)
blanchet@36218
   456
  in fold (Symtab.update o rpair 1) classes end;
paulson@18868
   457
paulson@18868
   458
(*** Find occurrences of functions in clauses ***)
paulson@18868
   459
blanchet@36218
   460
fun add_fol_type_funcs (TyVar _) = I
blanchet@36218
   461
  | add_fol_type_funcs (TyFree (s, _)) = Symtab.update (s, 0)
blanchet@36218
   462
  | add_fol_type_funcs (TyConstr ((s, _), tys)) =
blanchet@36218
   463
    Symtab.update (s, length tys) #> fold add_fol_type_funcs tys
paulson@18868
   464
paulson@20038
   465
(*TFrees are recorded as constants*)
paulson@24940
   466
fun add_type_sort_funcs (TVar _, funcs) = funcs
paulson@24940
   467
  | add_type_sort_funcs (TFree (a, _), funcs) =
paulson@20038
   468
      Symtab.update (make_fixed_type_var a, 0) funcs
paulson@20038
   469
blanchet@36218
   470
fun add_arity_clause_funcs (ArityClause {conclLit,...}) funcs =
paulson@22643
   471
  let val TConsLit (_, tcons, tvars) = conclLit
paulson@18868
   472
  in  Symtab.update (tcons, length tvars) funcs  end;
paulson@17845
   473
paulson@23075
   474
(*This type can be overlooked because it is built-in...*)
paulson@23075
   475
val init_functab = Symtab.update ("tc_itself", 1) Symtab.empty;
paulson@23075
   476
paulson@18868
   477
paulson@18868
   478
(**** String-oriented operations ****)
paulson@15347
   479
wenzelm@24310
   480
fun string_of_clausename (cls_id,ax_name) =
paulson@17525
   481
    clause_prefix ^ ascii_of ax_name ^ "_" ^ Int.toString cls_id;
paulson@17317
   482
wenzelm@24310
   483
fun string_of_type_clsname (cls_id,ax_name,idx) =
paulson@17525
   484
    string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
paulson@18863
   485
wenzelm@24310
   486
paulson@18868
   487
(**** Producing DFG files ****)
quigley@17150
   488
paulson@18863
   489
(*Attach sign in DFG syntax: false means negate.*)
paulson@18863
   490
fun dfg_sign true s = s
wenzelm@24310
   491
  | dfg_sign false s = "not(" ^ s ^ ")"
paulson@18863
   492
paulson@24937
   493
fun dfg_of_typeLit pos (LTVar (s,ty))  = dfg_sign pos (s ^ "(" ^ ty ^ ")")
paulson@24937
   494
  | dfg_of_typeLit pos (LTFree (s,ty)) = dfg_sign pos (s ^ "(" ^ ty ^ ")");
wenzelm@24310
   495
paulson@18868
   496
(*Enclose the clause body by quantifiers, if necessary*)
wenzelm@24310
   497
fun dfg_forall [] body = body
paulson@18868
   498
  | dfg_forall vars body = "forall([" ^ commas vars ^ "],\n" ^ body ^ ")"
quigley@17150
   499
paulson@24937
   500
fun gen_dfg_cls (cls_id, ax_name, Axiom, lits, tylits, vars) =
paulson@24937
   501
      "clause( %(axiom)\n" ^
paulson@24937
   502
      dfg_forall vars ("or(" ^ commas (tylits@lits) ^ ")") ^ ",\n" ^
paulson@24937
   503
      string_of_clausename (cls_id,ax_name) ^  ").\n\n"
paulson@24937
   504
  | gen_dfg_cls (cls_id, ax_name, Conjecture, lits, _, vars) =
paulson@24937
   505
      "clause( %(negated_conjecture)\n" ^
paulson@24937
   506
      dfg_forall vars ("or(" ^ commas lits ^ ")") ^ ",\n" ^
paulson@24937
   507
      string_of_clausename (cls_id,ax_name) ^  ").\n\n";
quigley@17150
   508
paulson@18798
   509
fun string_of_arity (name, num) =  "(" ^ name ^ "," ^ Int.toString num ^ ")"
quigley@17150
   510
paulson@18856
   511
fun string_of_preds [] = ""
paulson@18856
   512
  | string_of_preds preds = "predicates[" ^ commas(map string_of_arity preds) ^ "].\n";
quigley@17150
   513
paulson@18856
   514
fun string_of_funcs [] = ""
paulson@18856
   515
  | string_of_funcs funcs = "functions[" ^ commas(map string_of_arity funcs) ^ "].\n" ;
quigley@17150
   516
wenzelm@24310
   517
fun string_of_symbols predstr funcstr =
paulson@17234
   518
  "list_of_symbols.\n" ^ predstr  ^ funcstr  ^ "end_of_list.\n\n";
quigley@17150
   519
paulson@18798
   520
fun string_of_start name = "begin_problem(" ^ name ^ ").\n\n";
quigley@17150
   521
wenzelm@24310
   522
fun string_of_descrip name =
wenzelm@24310
   523
  "list_of_descriptions.\nname({*" ^ name ^
paulson@18868
   524
  "*}).\nauthor({*Isabelle*}).\nstatus(unknown).\ndescription({*auto-generated*}).\nend_of_list.\n\n"
quigley@17150
   525
paulson@18863
   526
fun dfg_tfree_clause tfree_lit =
paulson@21509
   527
  "clause( %(negated_conjecture)\n" ^ "or( " ^ tfree_lit ^ "),\n" ^ "tfree_tcs" ^ ").\n\n"
paulson@18863
   528
paulson@22643
   529
fun dfg_of_arLit (TConsLit (c,t,args)) =
paulson@22643
   530
      dfg_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")
paulson@22643
   531
  | dfg_of_arLit (TVarLit (c,str)) =
paulson@22643
   532
      dfg_sign false (make_type_class c ^ "(" ^ str ^ ")")
wenzelm@24310
   533
paulson@20038
   534
fun dfg_classrelLits sub sup =  "not(" ^ sub ^ "(T)), " ^ sup ^ "(T)";
paulson@17525
   535
blanchet@35865
   536
fun dfg_classrel_clause (ClassrelClause {axiom_name,subclass,superclass,...}) =
paulson@18868
   537
  "clause(forall([T],\nor( " ^ dfg_classrelLits subclass superclass ^ ")),\n" ^
paulson@18868
   538
  axiom_name ^ ").\n\n";
wenzelm@24310
   539
paulson@21560
   540
fun string_of_ar axiom_name = arclause_prefix ^ ascii_of axiom_name;
paulson@21560
   541
paulson@24937
   542
fun dfg_arity_clause (ArityClause{axiom_name,conclLit,premLits,...}) =
paulson@22643
   543
  let val TConsLit (_,_,tvars) = conclLit
paulson@18868
   544
      val lits = map dfg_of_arLit (conclLit :: premLits)
paulson@18863
   545
  in
paulson@24937
   546
      "clause( %(axiom)\n" ^
paulson@18868
   547
      dfg_forall tvars ("or( " ^ commas lits ^ ")") ^ ",\n" ^
paulson@21560
   548
      string_of_ar axiom_name ^ ").\n\n"
paulson@18863
   549
  end;
paulson@18863
   550
quigley@17150
   551
paulson@18869
   552
(**** Produce TPTP files ****)
paulson@18868
   553
paulson@21509
   554
fun tptp_sign true s = s
paulson@21509
   555
  | tptp_sign false s = "~ " ^ s
paulson@18868
   556
blanchet@36167
   557
fun tptp_of_typeLit pos (LTVar (s, ty))  = tptp_sign pos (s ^ "(" ^ ty ^ ")")
blanchet@36167
   558
  | tptp_of_typeLit pos (LTFree (s, ty)) = tptp_sign pos (s ^ "(" ^ ty ^ ")")
blanchet@36167
   559
blanchet@36167
   560
fun tptp_cnf name kind formula =
blanchet@36167
   561
  "cnf(" ^ name ^ ", " ^ kind ^ ",\n    " ^ formula ^ ").\n"
wenzelm@24310
   562
blanchet@36167
   563
fun gen_tptp_cls (cls_id, ax_name, Axiom, lits, tylits) =
blanchet@36167
   564
      tptp_cnf (string_of_clausename (cls_id, ax_name)) "axiom"
blanchet@36167
   565
               (tptp_pack (tylits @ lits))
blanchet@36167
   566
  | gen_tptp_cls (cls_id, ax_name, Conjecture, lits, _) =
blanchet@36167
   567
      tptp_cnf (string_of_clausename (cls_id, ax_name)) "negated_conjecture"
blanchet@36167
   568
               (tptp_pack lits)
paulson@15347
   569
paulson@18863
   570
fun tptp_tfree_clause tfree_lit =
blanchet@36167
   571
    tptp_cnf "tfree_tcs" "negated_conjecture" (tptp_pack [tfree_lit])
wenzelm@24310
   572
paulson@22643
   573
fun tptp_of_arLit (TConsLit (c,t,args)) =
paulson@22643
   574
      tptp_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")
paulson@22643
   575
  | tptp_of_arLit (TVarLit (c,str)) =
paulson@22643
   576
      tptp_sign false (make_type_class c ^ "(" ^ str ^ ")")
wenzelm@24310
   577
paulson@24937
   578
fun tptp_arity_clause (ArityClause{axiom_name,conclLit,premLits,...}) =
blanchet@36167
   579
  tptp_cnf (string_of_ar axiom_name) "axiom"
blanchet@36167
   580
           (tptp_pack (map tptp_of_arLit (conclLit :: premLits)))
paulson@15347
   581
wenzelm@24310
   582
fun tptp_classrelLits sub sup =
paulson@21509
   583
  let val tvar = "(T)"
paulson@21509
   584
  in  tptp_pack [tptp_sign false (sub^tvar), tptp_sign true (sup^tvar)]  end;
paulson@15347
   585
blanchet@35865
   586
fun tptp_classrel_clause (ClassrelClause {axiom_name,subclass,superclass,...}) =
blanchet@36167
   587
  tptp_cnf axiom_name "axiom" (tptp_classrelLits subclass superclass)
quigley@17150
   588
paulson@15347
   589
end;