src/HOL/Tools/res_atp.ML
author paulson
Fri Nov 24 13:24:30 2006 +0100 (2006-11-24)
changeset 21509 6c5755ad9cae
parent 21506 b2a673894ce5
child 21563 b4718f2c15f0
permissions -rw-r--r--
ATP linkup now generates "new TPTP" rather than "old TPTP"
     1 (*  Author: Jia Meng, Cambridge University Computer Laboratory, NICTA
     2     ID: $Id$
     3     Copyright 2004 University of Cambridge
     4 
     5 ATPs with TPTP format input.
     6 *)
     7 
     8 (*Currently unused, during debugging*)
     9 signature RES_ATP =
    10 sig
    11   val prover: string ref
    12   val custom_spass: string list ref
    13   val destdir: string ref
    14   val helper_path: string -> string -> string
    15   val problem_name: string ref
    16   val time_limit: int ref
    17   val set_prover: string -> unit
    18    
    19   datatype mode = Auto | Fol | Hol
    20   val linkup_logic_mode : mode ref
    21   val write_subgoal_file: bool -> mode -> Proof.context -> thm list -> thm list -> int -> string
    22   val vampire_time: int ref
    23   val eprover_time: int ref
    24   val spass_time: int ref
    25   val run_vampire: int -> unit
    26   val run_eprover: int -> unit
    27   val run_spass: int -> unit
    28   val vampireLimit: unit -> int
    29   val eproverLimit: unit -> int
    30   val spassLimit: unit -> int
    31   val atp_method: (Proof.context -> thm list -> int -> tactic) ->
    32     Method.src -> Proof.context -> Proof.method
    33   val cond_rm_tmp: string -> unit
    34   val fol_keep_types: bool ref
    35   val hol_full_types: unit -> unit
    36   val hol_partial_types: unit -> unit
    37   val hol_const_types_only: unit -> unit
    38   val hol_no_types: unit -> unit
    39   val hol_typ_level: unit -> ResHolClause.type_level
    40   val include_all: bool ref
    41   val run_relevance_filter: bool ref
    42   val run_blacklist_filter: bool ref
    43   val blacklist: string list ref
    44   val add_all : unit -> unit
    45   val add_claset : unit -> unit
    46   val add_simpset : unit -> unit
    47   val add_clasimp : unit -> unit
    48   val add_atpset : unit -> unit
    49   val rm_all : unit -> unit
    50   val rm_claset : unit -> unit
    51   val rm_simpset : unit -> unit
    52   val rm_atpset : unit -> unit
    53   val rm_clasimp : unit -> unit
    54   val is_fol_thms : thm list -> bool
    55 end;
    56 
    57 structure ResAtp =
    58 struct
    59 
    60 fun timestamp s = Output.debug ("At " ^ Time.toString (Time.now()) ^ ": " ^ s);
    61 
    62 (********************************************************************)
    63 (* some settings for both background automatic ATP calling procedure*)
    64 (* and also explicit ATP invocation methods                         *)
    65 (********************************************************************)
    66 
    67 (*** background linkup ***)
    68 val call_atp = ref false; 
    69 val hook_count = ref 0;
    70 val time_limit = ref 60;
    71 val prover = ref "";   
    72 
    73 fun set_prover atp = 
    74   case String.map Char.toLower atp of
    75       "e" => 
    76           (ReduceAxiomsN.max_new := 100;
    77            ReduceAxiomsN.theory_const := false;
    78            prover := "E")
    79     | "spass" => 
    80           (ReduceAxiomsN.max_new := 40;
    81            ReduceAxiomsN.theory_const := true;
    82            prover := "spass")
    83     | "vampire" => 
    84           (ReduceAxiomsN.max_new := 60;
    85            ReduceAxiomsN.theory_const := false;
    86            prover := "vampire")
    87     | _ => error ("No such prover: " ^ atp);
    88 
    89 val _ = set_prover "E"; (* use E as the default prover *)
    90 
    91 val custom_spass =   (*specialized options for SPASS*)
    92       ref ["-Auto=0","-FullRed=0","-IORe","-IOFc","-RTaut","-RFSub","-RBSub"];
    93 val destdir = ref "";   (*Empty means write files to /tmp*)
    94 val problem_name = ref "prob";
    95 
    96 (*Return the path to a "helper" like SPASS or tptp2X, first checking that
    97   it exists.  FIXME: modify to use Path primitives and move to some central place.*)  
    98 fun helper_path evar base =
    99   case getenv evar of
   100       "" => error  ("Isabelle environment variable " ^ evar ^ " not defined")
   101     | home => 
   102         let val path = home ^ "/" ^ base
   103         in  if File.exists (File.unpack_platform_path path) then path 
   104 	    else error ("Could not find the file " ^ path)
   105 	end;  
   106 
   107 fun probfile_nosuffix _ = 
   108   if !destdir = "" then File.platform_path (File.tmp_path (Path.basic (!problem_name)))
   109   else if File.exists (File.unpack_platform_path (!destdir))
   110   then !destdir ^ "/" ^ !problem_name
   111   else error ("No such directory: " ^ !destdir);
   112 
   113 fun prob_pathname n = probfile_nosuffix n ^ "_" ^ Int.toString n;
   114 
   115 
   116 (*** ATP methods ***)
   117 val vampire_time = ref 60;
   118 val eprover_time = ref 60;
   119 val spass_time = ref 60;
   120 
   121 fun run_vampire time =  
   122     if (time >0) then vampire_time:= time
   123     else vampire_time:=60;
   124 
   125 fun run_eprover time = 
   126     if (time > 0) then eprover_time:= time
   127     else eprover_time:=60;
   128 
   129 fun run_spass time = 
   130     if (time > 0) then spass_time:=time
   131     else spass_time:=60;
   132 
   133 
   134 fun vampireLimit () = !vampire_time;
   135 fun eproverLimit () = !eprover_time;
   136 fun spassLimit () = !spass_time;
   137 
   138 val fol_keep_types = ResClause.keep_types;
   139 val hol_full_types = ResHolClause.full_types;
   140 val hol_partial_types = ResHolClause.partial_types;
   141 val hol_const_types_only = ResHolClause.const_types_only;
   142 val hol_no_types = ResHolClause.no_types;
   143 fun hol_typ_level () = ResHolClause.find_typ_level ();
   144 fun is_typed_hol () = 
   145     let val tp_level = hol_typ_level()
   146     in
   147 	not (tp_level = ResHolClause.T_NONE)
   148     end;
   149 
   150 fun atp_input_file () =
   151     let val file = !problem_name 
   152     in
   153 	if !destdir = "" then File.platform_path (File.tmp_path (Path.basic file))
   154 	else if File.exists (File.unpack_platform_path (!destdir))
   155 	then !destdir ^ "/" ^ file
   156 	else error ("No such directory: " ^ !destdir)
   157     end;
   158 
   159 val include_all = ref true;
   160 val include_simpset = ref false;
   161 val include_claset = ref false; 
   162 val include_atpset = ref true;
   163 
   164 (*Tests show that follow_defs gives VERY poor results with "include_all"*)
   165 fun add_all() = (include_all:=true; ReduceAxiomsN.follow_defs := false);
   166 fun rm_all() = include_all:=false;
   167 
   168 fun add_simpset() = include_simpset:=true;
   169 fun rm_simpset() = include_simpset:=false;
   170 
   171 fun add_claset() = include_claset:=true;
   172 fun rm_claset() = include_claset:=false;
   173 
   174 fun add_clasimp() = (include_simpset:=true;include_claset:=true);
   175 fun rm_clasimp() = (include_simpset:=false;include_claset:=false);
   176 
   177 fun add_atpset() = include_atpset:=true;
   178 fun rm_atpset() = include_atpset:=false;
   179 
   180 
   181 (**** relevance filter ****)
   182 val run_relevance_filter = ReduceAxiomsN.run_relevance_filter;
   183 val run_blacklist_filter = ref true;
   184 
   185 (******************************************************************)
   186 (* detect whether a given problem (clauses) is FOL/HOL/HOLC/HOLCS *)
   187 (******************************************************************)
   188 
   189 datatype logic = FOL | HOL | HOLC | HOLCS;
   190 
   191 fun string_of_logic FOL = "FOL"
   192   | string_of_logic HOL = "HOL"
   193   | string_of_logic HOLC = "HOLC"
   194   | string_of_logic HOLCS = "HOLCS";
   195 
   196 fun is_fol_logic FOL = true
   197   | is_fol_logic  _ = false
   198 
   199 (*HOLCS will not occur here*)
   200 fun upgrade_lg HOLC _ = HOLC
   201   | upgrade_lg HOL HOLC = HOLC
   202   | upgrade_lg HOL _ = HOL
   203   | upgrade_lg FOL lg = lg; 
   204 
   205 (* check types *)
   206 fun has_bool_hfn (Type("bool",_)) = true
   207   | has_bool_hfn (Type("fun",_)) = true
   208   | has_bool_hfn (Type(_, Ts)) = exists has_bool_hfn Ts
   209   | has_bool_hfn _ = false;
   210 
   211 fun is_hol_fn tp =
   212     let val (targs,tr) = strip_type tp
   213     in
   214 	exists (has_bool_hfn) (tr::targs)
   215     end;
   216 
   217 fun is_hol_pred tp =
   218     let val (targs,tr) = strip_type tp
   219     in
   220 	exists (has_bool_hfn) targs
   221     end;
   222 
   223 exception FN_LG of term;
   224 
   225 fun fn_lg (t as Const(f,tp)) (lg,seen) = 
   226     if is_hol_fn tp then (upgrade_lg HOL lg, insert (op =) t seen) else (lg, insert (op =) t seen) 
   227   | fn_lg (t as Free(f,tp)) (lg,seen) = 
   228     if is_hol_fn tp then (upgrade_lg HOL lg, insert (op =) t seen) else (lg, insert (op =) t seen) 
   229   | fn_lg (t as Var(f,tp)) (lg,seen) =
   230     if is_hol_fn tp then (upgrade_lg HOL lg,insert (op =) t seen) else (lg,insert (op =) t seen)
   231   | fn_lg (t as Abs(_,_,_)) (lg,seen) = (upgrade_lg HOLC lg,insert (op =) t seen)
   232   | fn_lg f _ = raise FN_LG(f); 
   233 
   234 
   235 fun term_lg [] (lg,seen) = (lg,seen)
   236   | term_lg (tm::tms) (FOL,seen) =
   237       let val (f,args) = strip_comb tm
   238 	  val (lg',seen') = if f mem seen then (FOL,seen) 
   239 			    else fn_lg f (FOL,seen)
   240       in
   241 	if is_fol_logic lg' then ()
   242         else Output.debug ("Found a HOL term: " ^ Display.raw_string_of_term f);
   243         term_lg (args@tms) (lg',seen')
   244       end
   245   | term_lg _ (lg,seen) = (lg,seen)
   246 
   247 exception PRED_LG of term;
   248 
   249 fun pred_lg (t as Const(P,tp)) (lg,seen)= 
   250       if is_hol_pred tp then (upgrade_lg HOL lg, insert (op =) t seen) 
   251       else (lg,insert (op =) t seen) 
   252   | pred_lg (t as Free(P,tp)) (lg,seen) =
   253       if is_hol_pred tp then (upgrade_lg HOL lg, insert (op =) t seen) 
   254       else (lg,insert (op =) t seen)
   255   | pred_lg (t as Var(_,_)) (lg,seen) = (upgrade_lg HOL lg, insert (op =) t seen)
   256   | pred_lg P _ = raise PRED_LG(P);
   257 
   258 
   259 fun lit_lg (Const("Not",_) $ P) (lg,seen) = lit_lg P (lg,seen)
   260   | lit_lg P (lg,seen) =
   261       let val (pred,args) = strip_comb P
   262 	  val (lg',seen') = if pred mem seen then (lg,seen) 
   263 			    else pred_lg pred (lg,seen)
   264       in
   265 	if is_fol_logic lg' then ()
   266 	else Output.debug ("Found a HOL predicate: " ^ Display.raw_string_of_term pred);
   267 	term_lg args (lg',seen')
   268       end;
   269 
   270 fun lits_lg [] (lg,seen) = (lg,seen)
   271   | lits_lg (lit::lits) (FOL,seen) =
   272       let val (lg,seen') = lit_lg lit (FOL,seen)
   273       in
   274 	if is_fol_logic lg then ()
   275 	else Output.debug ("Found a HOL literal: " ^ Display.raw_string_of_term lit);
   276 	lits_lg lits (lg,seen')
   277       end
   278   | lits_lg lits (lg,seen) = (lg,seen);
   279 
   280 fun dest_disj_aux (Const("Trueprop",_) $ t) disjs = dest_disj_aux t disjs
   281   | dest_disj_aux (Const ("op |", _) $ t $ t') disjs = dest_disj_aux t (dest_disj_aux t' disjs)
   282   | dest_disj_aux t disjs = t::disjs;
   283 
   284 fun dest_disj t = dest_disj_aux t [];
   285 
   286 fun logic_of_clause tm = lits_lg (dest_disj tm);
   287 
   288 fun logic_of_clauses [] (lg,seen) = (lg,seen)
   289   | logic_of_clauses (cls::clss) (FOL,seen) =
   290     let val (lg,seen') = logic_of_clause cls (FOL,seen)
   291 	val _ =
   292           if is_fol_logic lg then ()
   293           else Output.debug ("Found a HOL clause: " ^ Display.raw_string_of_term cls)
   294     in
   295 	logic_of_clauses clss (lg,seen')
   296     end
   297   | logic_of_clauses (cls::clss) (lg,seen) = (lg,seen);
   298 
   299 fun problem_logic_goals_aux [] (lg,seen) = lg
   300   | problem_logic_goals_aux (subgoal::subgoals) (lg,seen) = 
   301     problem_logic_goals_aux subgoals (logic_of_clauses subgoal (lg,seen));
   302     
   303 fun problem_logic_goals subgoals = problem_logic_goals_aux subgoals (FOL,[]);
   304 
   305 fun is_fol_thms ths = ((fst(logic_of_clauses (map prop_of ths) (FOL,[]))) = FOL);
   306 
   307 (***************************************************************)
   308 (* Retrieving and filtering lemmas                             *)
   309 (***************************************************************)
   310 
   311 (*** white list and black list of lemmas ***)
   312 
   313 (*The rule subsetI is frequently omitted by the relevance filter.*)
   314 val whitelist = ref [subsetI]; 
   315   
   316 (*Names of theorems (not theorem lists! See multi_blacklist below) to be banned. 
   317 
   318   These theorems typically produce clauses that are prolific (match too many equality or
   319   membership literals) and relate to seldom-used facts. Some duplicate other rules.
   320   FIXME: this blacklist needs to be maintained using theory data and added to using
   321   an attribute.*)
   322 val blacklist = ref
   323   ["Datatype.prod.size",
   324    "Divides.dvd_0_left_iff",
   325    "Finite_Set.card_0_eq",
   326    "Finite_Set.card_infinite",
   327    "Finite_Set.Max_ge",
   328    "Finite_Set.Max_in",
   329    "Finite_Set.Max_le_iff",
   330    "Finite_Set.Max_less_iff",
   331    "Finite_Set.max.f_below_strict_below.below_f_conv", (*duplicates in Orderings.*)
   332    "Finite_Set.max.f_below_strict_below.strict_below_f_conv", (*duplicates in Orderings.*)
   333    "Finite_Set.Min_ge_iff",
   334    "Finite_Set.Min_gr_iff",
   335    "Finite_Set.Min_in",
   336    "Finite_Set.Min_le",
   337    "Finite_Set.min.f_below_strict_below.below_f_conv",        (*duplicates in Orderings.*)
   338    "Finite_Set.min.f_below_strict_below.strict_below_f_conv", (*duplicates in Orderings.*)
   339    "Fun.vimage_image_eq",   (*involves an existential quantifier*)
   340    "HOL.split_if_asm",     (*splitting theorem*)
   341    "HOL.split_if",         (*splitting theorem*)
   342    "IntDef.abs_split",
   343    "IntDef.Integ.Abs_Integ_inject",
   344    "IntDef.Integ.Abs_Integ_inverse",
   345    "IntDiv.zdvd_0_left",
   346    "List.append_eq_append_conv",
   347    "List.hd_Cons_tl",   (*Says everything is [] or Cons. Probably prolific.*)
   348    "List.in_listsD",
   349    "List.in_listsI",
   350    "List.lists.Cons",
   351    "List.listsE",
   352    "Nat.less_one", (*not directional? obscure*)
   353    "Nat.not_gr0",
   354    "Nat.one_eq_mult_iff", (*duplicate by symmetry*)
   355    "Nat.of_nat_0_eq_iff",
   356    "Nat.of_nat_eq_0_iff",
   357    "Nat.of_nat_le_0_iff",
   358    "NatSimprocs.divide_le_0_iff_number_of",  (*too many clauses*)
   359    "NatSimprocs.divide_less_0_iff_number_of",
   360    "NatSimprocs.equation_minus_iff_1",  (*not directional*)
   361    "NatSimprocs.equation_minus_iff_number_of", (*not directional*)
   362    "NatSimprocs.le_minus_iff_1", (*not directional*)
   363    "NatSimprocs.le_minus_iff_number_of",  (*not directional*)
   364    "NatSimprocs.less_minus_iff_1", (*not directional*)
   365    "NatSimprocs.less_minus_iff_number_of", (*not directional*)
   366    "NatSimprocs.minus_equation_iff_number_of", (*not directional*)
   367    "NatSimprocs.minus_le_iff_1", (*not directional*)
   368    "NatSimprocs.minus_le_iff_number_of", (*not directional*)
   369    "NatSimprocs.minus_less_iff_1", (*not directional*)
   370    "NatSimprocs.mult_le_cancel_left_number_of", (*excessive case analysis*)
   371    "NatSimprocs.mult_le_cancel_right_number_of", (*excessive case analysis*)
   372    "NatSimprocs.mult_less_cancel_left_number_of", (*excessive case analysis*)
   373    "NatSimprocs.mult_less_cancel_right_number_of", (*excessive case analysis*)
   374    "NatSimprocs.zero_le_divide_iff_number_of", (*excessive case analysis*)
   375    "NatSimprocs.zero_less_divide_iff_number_of",
   376    "OrderedGroup.abs_0_eq", (*duplicate by symmetry*)
   377    "OrderedGroup.diff_eq_0_iff_eq", (*prolific?*)
   378    "OrderedGroup.join_0_eq_0",
   379    "OrderedGroup.meet_0_eq_0",
   380    "OrderedGroup.pprt_eq_0",   (*obscure*)
   381    "OrderedGroup.pprt_eq_id",   (*obscure*)
   382    "OrderedGroup.pprt_mono",   (*obscure*)
   383    "Orderings.split_max",      (*splitting theorem*)
   384    "Orderings.split_min",      (*splitting theorem*)
   385    "Power.zero_less_power_abs_iff",
   386    "Product_Type.split_eta_SetCompr",   (*involves an existential quantifier*)
   387    "Product_Type.split_paired_Ball_Sigma",     (*splitting theorem*)
   388    "Product_Type.split_paired_Bex_Sigma",      (*splitting theorem*)
   389    "Product_Type.split_split_asm",             (*splitting theorem*)
   390    "Product_Type.split_split",                 (*splitting theorem*)
   391    "Product_Type.unit_abs_eta_conv",
   392    "Product_Type.unit_induct",
   393    "Relation.diagI",
   394    "Relation.Domain_def",   (*involves an existential quantifier*)
   395    "Relation.Image_def",   (*involves an existential quantifier*)
   396    "Relation.ImageI",
   397    "Ring_and_Field.divide_cancel_left", (*fields are seldom used & often prolific*)
   398    "Ring_and_Field.divide_cancel_right",
   399    "Ring_and_Field.divide_divide_eq_left",
   400    "Ring_and_Field.divide_divide_eq_right",
   401    "Ring_and_Field.divide_eq_0_iff",
   402    "Ring_and_Field.divide_eq_1_iff",
   403    "Ring_and_Field.divide_eq_eq_1",
   404    "Ring_and_Field.divide_le_0_1_iff",
   405    "Ring_and_Field.divide_le_eq_1_neg",  (*obscure and prolific*)
   406    "Ring_and_Field.divide_le_eq_1_pos",  (*obscure and prolific*)
   407    "Ring_and_Field.divide_less_0_1_iff",
   408    "Ring_and_Field.divide_less_eq_1_neg",  (*obscure and prolific*)
   409    "Ring_and_Field.divide_less_eq_1_pos",  (*obscure and prolific*)
   410    "Ring_and_Field.eq_divide_eq_1", (*duplicate by symmetry*)
   411    "Ring_and_Field.field_mult_cancel_left",
   412    "Ring_and_Field.field_mult_cancel_right",
   413    "Ring_and_Field.inverse_le_iff_le_neg",
   414    "Ring_and_Field.inverse_le_iff_le",
   415    "Ring_and_Field.inverse_less_iff_less_neg",
   416    "Ring_and_Field.inverse_less_iff_less",
   417    "Ring_and_Field.le_divide_eq_1_neg", (*obscure and prolific*)
   418    "Ring_and_Field.le_divide_eq_1_pos", (*obscure and prolific*)
   419    "Ring_and_Field.less_divide_eq_1_neg", (*obscure and prolific*)
   420    "Ring_and_Field.less_divide_eq_1_pos", (*obscure and prolific*)
   421    "Ring_and_Field.one_eq_divide_iff",  (*duplicate by symmetry*)
   422    "Set.Collect_bex_eq",   (*involves an existential quantifier*)
   423    "Set.Collect_ex_eq",   (*involves an existential quantifier*)
   424    "Set.Diff_eq_empty_iff", (*redundant with paramodulation*)
   425    "Set.Diff_insert0",
   426    "Set.empty_Union_conv",   (*redundant with paramodulation*)
   427    "Set.full_SetCompr_eq",   (*involves an existential quantifier*)
   428    "Set.image_Collect",      (*involves an existential quantifier*)
   429    "Set.image_def",          (*involves an existential quantifier*)
   430    "Set.Int_UNIV",  (*redundant with paramodulation*)
   431    "Set.Inter_iff", (*We already have InterI, InterE*)
   432    "Set.psubsetE",    (*too prolific and obscure*)
   433    "Set.psubsetI",
   434    "Set.singleton_insert_inj_eq'",
   435    "Set.singleton_insert_inj_eq",
   436    "Set.singletonD",  (*these two duplicate some "insert" lemmas*)
   437    "Set.singletonI",
   438    "Set.Un_empty", (*redundant with paramodulation*)
   439    "Set.UNION_def",   (*involves an existential quantifier*)
   440    "Set.Union_empty_conv", (*redundant with paramodulation*)
   441    "Set.Union_iff",              (*We already have UnionI, UnionE*)
   442    "SetInterval.atLeastAtMost_iff", (*obscure and prolific*)
   443    "SetInterval.atLeastLessThan_iff", (*obscure and prolific*)
   444    "SetInterval.greaterThanAtMost_iff", (*obscure and prolific*)
   445    "SetInterval.greaterThanLessThan_iff", (*obscure and prolific*)
   446    "SetInterval.ivl_subset"];  (*excessive case analysis*)
   447 
   448 
   449 (*These might be prolific but are probably OK, and min and max are basic.
   450    "Orderings.max_less_iff_conj", 
   451    "Orderings.min_less_iff_conj",
   452    "Orderings.min_max.below_inf.below_inf_conv",
   453    "Orderings.min_max.below_sup.above_sup_conv",
   454 Very prolific and somewhat obscure:
   455    "Set.InterD",
   456    "Set.UnionI",
   457 *)
   458 
   459 (*** retrieve lemmas from clasimpset and atpset, may filter them ***)
   460 
   461 (*Hashing to detect duplicate and variant clauses, e.g. from the [iff] attribute*)
   462 
   463 exception HASH_CLAUSE and HASH_STRING;
   464 
   465 (*Catches (for deletion) theorems automatically generated from other theorems*)
   466 fun insert_suffixed_names ht x = 
   467      (Polyhash.insert ht (x^"_iff1", ()); 
   468       Polyhash.insert ht (x^"_iff2", ()); 
   469       Polyhash.insert ht (x^"_dest", ())); 
   470 
   471 (*Reject theorems with names like "List.filter.filter_list_def" or
   472   "Accessible_Part.acc.defs", as these are definitions arising from packages.
   473   FIXME: this will also block definitions within locales*)
   474 fun is_package_def a =
   475    length (NameSpace.unpack a) > 2 andalso 
   476    String.isSuffix "_def" a  orelse  String.isSuffix "_defs" a;
   477 
   478 fun make_banned_test xs = 
   479   let val ht = Polyhash.mkTable (Polyhash.hash_string, op =)
   480                                 (6000, HASH_STRING)
   481       fun banned s = 
   482             isSome (Polyhash.peek ht s) orelse is_package_def s
   483   in  app (fn x => Polyhash.insert ht (x,())) (!blacklist);
   484       app (insert_suffixed_names ht) (!blacklist @ xs); 
   485       banned
   486   end;
   487 
   488 (** a hash function from Term.term to int, and also a hash table **)
   489 val xor_words = List.foldl Word.xorb 0w0;
   490 
   491 fun hashw_term ((Const(c,_)), w) = Polyhash.hashw_string (c,w)
   492   | hashw_term ((Free(a,_)), w) = Polyhash.hashw_string (a,w)
   493   | hashw_term ((Var(_,_)), w) = w
   494   | hashw_term ((Bound i), w) = Polyhash.hashw_int(i,w)
   495   | hashw_term ((Abs(_,_,t)), w) = hashw_term (t, w)
   496   | hashw_term ((P$Q), w) = hashw_term (Q, (hashw_term (P, w)));
   497 
   498 fun hash_literal (Const("Not",_)$P) = Word.notb(hashw_term(P,0w0))
   499   | hash_literal P = hashw_term(P,0w0);
   500 
   501 fun hash_term t = Word.toIntX (xor_words (map hash_literal (dest_disj t)));
   502 
   503 fun equal_thm (thm1,thm2) = Term.aconv(prop_of thm1, prop_of thm2);
   504 
   505 (*Create a hash table for clauses, of the given size*)
   506 fun mk_clause_table n =
   507       Polyhash.mkTable (hash_term o prop_of, equal_thm)
   508                        (n, HASH_CLAUSE);
   509 
   510 (*Use a hash table to eliminate duplicates from xs. Argument is a list of
   511   (thm * (string * int)) tuples. The theorems are hashed into the table. *)
   512 fun make_unique xs = 
   513   let val ht = mk_clause_table 7000
   514   in
   515       Output.debug("make_unique gets " ^ Int.toString (length xs) ^ " clauses");
   516       app (ignore o Polyhash.peekInsert ht) xs;  
   517       Polyhash.listItems ht
   518   end;
   519 
   520 (*Remove existing axiom clauses from the conjecture clauses, as this can dramatically
   521   boost an ATP's performance (for some reason)*)
   522 fun subtract_cls c_clauses ax_clauses = 
   523   let val ht = mk_clause_table 2200
   524       fun known x = isSome (Polyhash.peek ht x)
   525   in
   526       app (ignore o Polyhash.peekInsert ht) ax_clauses;  
   527       filter (not o known) c_clauses 
   528   end;
   529 
   530 (*Filter axiom clauses, but keep supplied clauses and clauses in whitelist. 
   531   Duplicates are removed later.*)
   532 fun get_relevant_clauses thy cls_thms white_cls goals =
   533   white_cls @ (ReduceAxiomsN.relevance_filter thy cls_thms goals);
   534 
   535 fun display_thms [] = ()
   536   | display_thms ((name,thm)::nthms) = 
   537       let val nthm = name ^ ": " ^ (string_of_thm thm)
   538       in Output.debug nthm; display_thms nthms  end;
   539  
   540 fun all_valid_thms ctxt =
   541   PureThy.thms_containing (ProofContext.theory_of ctxt) ([], []) @
   542   filter (ProofContext.valid_thms ctxt)
   543     (FactIndex.find (ProofContext.fact_index_of ctxt) ([], []));
   544 
   545 fun multi_name a (th, (n,pairs)) = 
   546   (n+1, (a ^ "(" ^ Int.toString n ^ ")", th) :: pairs)
   547 
   548 fun add_multi_names_aux ((a, []), pairs) = pairs
   549   | add_multi_names_aux ((a, [th]), pairs) = (a,th)::pairs
   550   | add_multi_names_aux ((a, ths), pairs) = #2 (foldl (multi_name a) (1,pairs) ths);
   551 
   552 val multi_blacklist =
   553   ["Set.ball_simps", "Set.bex_simps",  (*quantifier rewriting: useless*)
   554    "Set.disjoint_insert", "Set.insert_disjoint", "Set.Inter_UNIV_conv"];
   555 
   556 val multi_base_blacklist =
   557   ["defs","select_defs","update_defs","induct","inducts","split","splits","split_asm"];
   558 
   559 (*Ignore blacklisted theorem lists*)
   560 fun add_multi_names ((a, ths), pairs) = 
   561   if a mem_string multi_blacklist orelse (Sign.base_name a) mem_string multi_base_blacklist
   562   then pairs
   563   else add_multi_names_aux ((a, ths), pairs);
   564 
   565 fun is_multi (a, ths) = length ths > 1 orelse String.isSuffix ".axioms" a;
   566 
   567 (*The single theorems go BEFORE the multiple ones*)
   568 fun name_thm_pairs ctxt = 
   569   let val (mults,singles) = List.partition is_multi (all_valid_thms ctxt)
   570   in  foldl add_multi_names (foldl add_multi_names [] mults) singles  end;
   571 
   572 fun check_named ("",th) = (warning ("No name for theorem " ^ string_of_thm th); false)
   573   | check_named (_,th) = true;
   574 
   575 (* get lemmas from claset, simpset, atpset and extra supplied rules *)
   576 fun get_clasimp_atp_lemmas ctxt user_thms = 
   577   let val included_thms =
   578 	if !include_all 
   579 	then (tap (fn ths => Output.debug
   580 	             ("Including all " ^ Int.toString (length ths) ^ " theorems")) 
   581 	          (name_thm_pairs ctxt))
   582 	else 
   583 	let val claset_thms =
   584 		if !include_claset then ResAxioms.claset_rules_of ctxt
   585 		else []
   586 	    val simpset_thms = 
   587 		if !include_simpset then ResAxioms.simpset_rules_of ctxt
   588 		else []
   589 	    val atpset_thms =
   590 		if !include_atpset then ResAxioms.atpset_rules_of ctxt
   591 		else []
   592 	    val _ = if !Output.show_debug_msgs 
   593 		    then (Output.debug "ATP theorems: "; display_thms atpset_thms) 
   594 		    else ()		 
   595 	in  claset_thms @ simpset_thms @ atpset_thms  end
   596       val user_rules = filter check_named 
   597                          (map (ResAxioms.pairname)
   598 			   (if null user_thms then !whitelist else user_thms))
   599   in
   600       (filter check_named included_thms, user_rules)
   601   end;
   602 
   603 (*Remove lemmas that are banned from the backlist. Also remove duplicates. *)
   604 fun blacklist_filter ths = 
   605   if !run_blacklist_filter then 
   606       let val _ = Output.debug("blacklist filter gets " ^ Int.toString (length ths) ^ " theorems")
   607           val banned = make_banned_test (map #1 ths)
   608 	  fun ok (a,_) = not (banned a)
   609 	  val okthms = filter ok ths
   610           val _ = Output.debug("...and returns " ^ Int.toString (length okthms))
   611       in  okthms end
   612   else ths;
   613 
   614 (***************************************************************)
   615 (* Type Classes Present in the Axiom or Conjecture Clauses     *)
   616 (***************************************************************)
   617 
   618 fun setinsert (x,s) = Symtab.update (x,()) s;
   619 
   620 fun add_classes (sorts, cset) = foldl setinsert cset (List.concat sorts);
   621 
   622 (*Remove this trivial type class*)
   623 fun delete_type cset = Symtab.delete_safe "HOL.type" cset;
   624 
   625 fun tvar_classes_of_terms ts =
   626   let val sorts_list = map (map #2 o term_tvars) ts
   627   in  Symtab.keys (delete_type (foldl add_classes Symtab.empty sorts_list))  end;
   628 
   629 fun tfree_classes_of_terms ts =
   630   let val sorts_list = map (map #2 o term_tfrees) ts
   631   in  Symtab.keys (delete_type (foldl add_classes Symtab.empty sorts_list))  end;
   632 
   633 (*fold type constructors*)
   634 fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
   635   | fold_type_consts f T x = x;
   636 
   637 val add_type_consts_in_type = fold_type_consts setinsert;
   638 
   639 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
   640 fun add_type_consts_in_term thy =
   641   let val const_typargs = Sign.const_typargs thy
   642       fun add_tcs (Const cT) x = fold add_type_consts_in_type (const_typargs cT) x
   643         | add_tcs (Abs (_, T, u)) x = add_tcs u x
   644         | add_tcs (t $ u) x = add_tcs t (add_tcs u x)
   645         | add_tcs _ x = x
   646   in  add_tcs  end
   647 
   648 fun type_consts_of_terms thy ts =
   649   Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty);
   650 
   651 
   652 (***************************************************************)
   653 (* ATP invocation methods setup                                *)
   654 (***************************************************************)
   655 
   656 fun cnf_hyps_thms ctxt = 
   657     let val ths = Assumption.prems_of ctxt
   658     in fold (fold (insert Thm.eq_thm) o ResAxioms.skolem_thm) ths [] end;
   659 
   660 (*Translation mode can be auto-detected, or forced to be first-order or higher-order*)
   661 datatype mode = Auto | Fol | Hol;
   662 
   663 val linkup_logic_mode = ref Auto;
   664 
   665 (*Ensures that no higher-order theorems "leak out"*)
   666 fun restrict_to_logic logic cls =
   667   if is_fol_logic logic then filter (Meson.is_fol_term o prop_of o fst) cls 
   668 	                else cls;
   669 
   670 (**** Predicates to detect unwanted clauses (prolific or likely to cause unsoundness) ****)
   671 
   672 (** Too general means, positive equality literal with a variable X as one operand,
   673   when X does not occur properly in the other operand. This rules out clearly
   674   inconsistent clauses such as V=a|V=b, though it by no means guarantees soundness. **)
   675  
   676 fun occurs ix =
   677     let fun occ(Var (jx,_)) = (ix=jx)
   678           | occ(t1$t2)      = occ t1 orelse occ t2
   679           | occ(Abs(_,_,t)) = occ t
   680           | occ _           = false
   681     in occ end;
   682 
   683 fun is_recordtype T = not (null (RecordPackage.dest_recTs T));
   684 
   685 (*Unwanted equalities include
   686   (1) those between a variable that does not properly occur in the second operand,
   687   (2) those between a variable and a record, since these seem to be prolific "cases" thms
   688 *)  
   689 fun too_general_eqterms (Var (ix,T), t) = not (occurs ix t) orelse is_recordtype T
   690   | too_general_eqterms _ = false;
   691 
   692 fun too_general_equality (Const ("op =", _) $ x $ y) =
   693       too_general_eqterms (x,y) orelse too_general_eqterms(y,x)
   694   | too_general_equality _ = false;
   695 
   696 (* tautologous? *)
   697 fun is_taut (Const ("Trueprop", _) $ Const ("True", _)) = true
   698   | is_taut _ = false;
   699 
   700 (*True if the term contains a variable whose (atomic) type is in the given list.*)
   701 fun has_typed_var tycons = 
   702   let fun var_tycon (Var (_, Type(a,_))) = a mem_string tycons
   703         | var_tycon _ = false
   704   in  exists var_tycon o term_vars  end;
   705 
   706 fun unwanted t =
   707     is_taut t orelse has_typed_var ["Product_Type.unit","bool"] t orelse
   708     forall too_general_equality (dest_disj t);
   709 
   710 (*Clauses containing variables of type "unit" or "bool" are unlikely to be useful and
   711   likely to lead to unsound proofs.*)
   712 fun remove_unwanted_clauses cls =
   713   filter (not o unwanted o prop_of o fst) cls;
   714 
   715 fun tptp_writer logic goals filename (axioms,classrels,arities) user_lemmas =
   716     if is_fol_logic logic 
   717     then ResClause.tptp_write_file goals filename (axioms, classrels, arities)
   718     else ResHolClause.tptp_write_file goals filename (axioms, classrels, arities) user_lemmas;
   719 
   720 fun dfg_writer logic goals filename (axioms,classrels,arities) user_lemmas =
   721     if is_fol_logic logic 
   722     then ResClause.dfg_write_file goals filename (axioms, classrels, arities)
   723     else ResHolClause.dfg_write_file goals filename (axioms, classrels, arities) user_lemmas;
   724 
   725 (*Called by the oracle-based methods declared in res_atp_methods.ML*)
   726 fun write_subgoal_file dfg mode ctxt conjectures user_thms n =
   727     let val conj_cls = make_clauses conjectures 
   728                          |> ResAxioms.assume_abstract_list |> Meson.finish_cnf
   729 	val hyp_cls = cnf_hyps_thms ctxt
   730 	val goal_cls = conj_cls@hyp_cls
   731 	val goal_tms = map prop_of goal_cls
   732 	val logic = case mode of 
   733                             Auto => problem_logic_goals [goal_tms]
   734 			  | Fol => FOL
   735 			  | Hol => HOL
   736 	val (included_thms,user_rules) = get_clasimp_atp_lemmas ctxt user_thms
   737 	val cla_simp_atp_clauses = included_thms |> blacklist_filter
   738 	                             |> ResAxioms.cnf_rules_pairs |> make_unique 
   739                                      |> restrict_to_logic logic 
   740                                      |> remove_unwanted_clauses
   741 	val user_cls = ResAxioms.cnf_rules_pairs user_rules
   742 	val thy = ProofContext.theory_of ctxt
   743 	val axclauses = make_unique (get_relevant_clauses thy cla_simp_atp_clauses user_cls goal_tms)
   744 	val keep_types = if is_fol_logic logic then !fol_keep_types else is_typed_hol ()
   745         val subs = tfree_classes_of_terms goal_tms
   746         and axtms = map (prop_of o #1) axclauses
   747         val supers = tvar_classes_of_terms axtms
   748         and tycons = type_consts_of_terms thy (goal_tms@axtms)
   749         (*TFrees in conjecture clauses; TVars in axiom clauses*)
   750         val classrel_clauses = 
   751               if keep_types then ResClause.make_classrel_clauses thy subs supers
   752               else []
   753 	val arity_clauses = if keep_types then ResClause.arity_clause_thy thy tycons supers else []
   754         val writer = if dfg then dfg_writer else tptp_writer 
   755 	and file = atp_input_file()
   756 	and user_lemmas_names = map #1 user_rules
   757     in
   758 	writer logic goal_cls file (axclauses,classrel_clauses,arity_clauses) user_lemmas_names;
   759 	Output.debug ("Writing to " ^ file);
   760 	file
   761     end;
   762 
   763 
   764 (**** remove tmp files ****)
   765 fun cond_rm_tmp file = 
   766     if !Output.show_debug_msgs orelse !destdir <> "" then Output.debug "ATP input kept..." 
   767     else OS.FileSys.remove file;
   768 
   769 
   770 (****** setup ATPs as Isabelle methods ******)
   771 fun atp_meth' tac ths ctxt = 
   772     Method.SIMPLE_METHOD' HEADGOAL
   773     (tac ctxt ths);
   774 
   775 fun atp_meth tac ths ctxt = 
   776     let val thy = ProofContext.theory_of ctxt
   777 	val _ = ResClause.init thy
   778 	val _ = ResHolClause.init thy
   779     in
   780 	atp_meth' tac ths ctxt
   781     end;
   782 
   783 fun atp_method tac = Method.thms_ctxt_args (atp_meth tac);
   784 
   785 (***************************************************************)
   786 (* automatic ATP invocation                                    *)
   787 (***************************************************************)
   788 
   789 (* call prover with settings and problem file for the current subgoal *)
   790 fun watcher_call_provers sign sg_terms (childin, childout, pid) =
   791   let
   792     fun make_atp_list [] n = []
   793       | make_atp_list (sg_term::xs) n =
   794           let
   795             val probfile = prob_pathname n
   796             val time = Int.toString (!time_limit)
   797           in
   798             Output.debug ("problem file in watcher_call_provers is " ^ probfile);
   799             (*options are separated by Watcher.setting_sep, currently #"%"*)
   800             if !prover = "spass"
   801             then
   802               let val spass = helper_path "SPASS_HOME" "SPASS"
   803                   val sopts =
   804    "-Auto%-SOS=1%-PGiven=0%-PProblem=0%-Splits=0%-FullRed=0%-DocProof%-TimeLimit=" ^ time
   805               in 
   806                   ("spass", spass, sopts, probfile) :: make_atp_list xs (n+1)
   807               end
   808             else if !prover = "vampire"
   809 	    then 
   810               let val vampire = helper_path "VAMPIRE_HOME" "vampire"
   811                   val vopts = "--mode casc%-t " ^ time  (*what about -m 100000?*)
   812               in
   813                   ("vampire", vampire, vopts, probfile) :: make_atp_list xs (n+1)
   814               end
   815       	     else if !prover = "E"
   816       	     then
   817 	       let val Eprover = helper_path "E_HOME" "eproof"
   818 	       in
   819 		  ("E", Eprover, 
   820 		     "--tstp-in%-l5%-xAutoDev%-tAutoDev%--silent%--cpu-limit=" ^ time, probfile) ::
   821 		   make_atp_list xs (n+1)
   822 	       end
   823 	     else error ("Invalid prover name: " ^ !prover)
   824           end
   825 
   826     val atp_list = make_atp_list sg_terms 1
   827   in
   828     Watcher.callResProvers(childout,atp_list);
   829     Output.debug "Sent commands to watcher!"
   830   end
   831   
   832 fun trace_array fname =
   833   let val path = File.unpack_platform_path fname
   834   in  Array.app (File.append path o (fn s => s ^ "\n"))  end;
   835 
   836 (*Converting a subgoal into negated conjecture clauses*)
   837 fun neg_clauses th n =
   838   let val tacs = [rtac ccontr, ObjectLogic.atomize_tac, skolemize_tac]
   839       val st = Seq.hd (EVERY' tacs n th)
   840       val negs = Option.valOf (metahyps_thms n st)
   841   in make_clauses negs |> ResAxioms.assume_abstract_list |> Meson.finish_cnf end;
   842 		                       
   843 (*We write out problem files for each subgoal. Argument probfile generates filenames,
   844   and allows the suppression of the suffix "_1" in problem-generation mode.
   845   FIXME: does not cope with &&, and it isn't easy because one could have multiple
   846   subgoals, each involving &&.*)
   847 fun write_problem_files probfile (ctxt,th)  =
   848   let val goals = Thm.prems_of th
   849       val _ = Output.debug ("number of subgoals = " ^ Int.toString (length goals))
   850       val thy = ProofContext.theory_of ctxt
   851       fun get_neg_subgoals [] _ = []
   852         | get_neg_subgoals (gl::gls) n = neg_clauses th n :: get_neg_subgoals gls (n+1)
   853       val goal_cls = get_neg_subgoals goals 1
   854       val logic = case !linkup_logic_mode of
   855 		Auto => problem_logic_goals (map ((map prop_of)) goal_cls)
   856 	      | Fol => FOL
   857 	      | Hol => HOL
   858       val (included_thms,white_thms) = get_clasimp_atp_lemmas ctxt []
   859       val included_cls = included_thms |> blacklist_filter
   860                                        |> ResAxioms.cnf_rules_pairs |> make_unique 
   861                                        |> restrict_to_logic logic
   862                                        |> remove_unwanted_clauses
   863       val _ = Output.debug ("clauses = " ^ Int.toString(length included_cls))
   864       val white_cls = ResAxioms.cnf_rules_pairs white_thms
   865       (*clauses relevant to goal gl*)
   866       val axcls_list = map (fn gl => get_relevant_clauses thy included_cls white_cls [gl])
   867                            goals
   868       val _ = app (fn axcls => Output.debug ("filtered clauses = " ^ Int.toString(length axcls)))
   869                   axcls_list
   870       val keep_types = if is_fol_logic logic then !ResClause.keep_types 
   871                        else is_typed_hol ()
   872       val writer = if !prover = "spass" then dfg_writer else tptp_writer 
   873       fun write_all [] [] _ = []
   874 	| write_all (ccls::ccls_list) (axcls::axcls_list) k =
   875             let val fname = probfile k
   876                 val axcls = make_unique axcls
   877                 val ccls = subtract_cls ccls axcls
   878                 val ccltms = map prop_of ccls
   879                 and axtms = map (prop_of o #1) axcls
   880                 val subs = tfree_classes_of_terms ccltms
   881                 and supers = tvar_classes_of_terms axtms
   882                 and tycons = type_consts_of_terms thy (ccltms@axtms)
   883                 (*TFrees in conjecture clauses; TVars in axiom clauses*)
   884                 val classrel_clauses = 
   885                       if keep_types then ResClause.make_classrel_clauses thy subs supers
   886                       else []
   887                 val _ = Output.debug ("classrel clauses = " ^ Int.toString (length classrel_clauses))
   888                 val arity_clauses = if keep_types then ResClause.arity_clause_thy thy tycons supers
   889                                     else []
   890                 val _ = Output.debug ("arity clauses = " ^ Int.toString (length arity_clauses))
   891                 val clnames = writer logic ccls fname (axcls,classrel_clauses,arity_clauses) []
   892                 val thm_names = Array.fromList clnames
   893                 val _ = if !Output.show_debug_msgs 
   894                         then trace_array (fname ^ "_thm_names") thm_names else ()
   895             in  (thm_names,fname) :: write_all ccls_list axcls_list (k+1)  end
   896       val (thm_names_list, filenames) = ListPair.unzip (write_all goal_cls axcls_list 1)
   897   in
   898       (filenames, thm_names_list)
   899   end;
   900 
   901 val last_watcher_pid = ref (NONE : (TextIO.instream * TextIO.outstream * 
   902                                     Posix.Process.pid * string list) option);
   903 
   904 fun kill_last_watcher () =
   905     (case !last_watcher_pid of 
   906          NONE => ()
   907        | SOME (_, _, pid, files) => 
   908 	  (Output.debug ("Killing old watcher, pid = " ^ string_of_pid pid);
   909 	   Watcher.killWatcher pid;  
   910 	   ignore (map (try cond_rm_tmp) files)))
   911      handle OS.SysErr _ => Output.debug "Attempt to kill watcher failed";
   912 
   913 (*writes out the current clasimpset to a tptp file;
   914   turns off xsymbol at start of function, restoring it at end    *)
   915 fun isar_atp_body (ctxt, th) =
   916   if Thm.no_prems th then ()
   917   else
   918     let
   919       val _ = kill_last_watcher()
   920       val (files,thm_names_list) = write_problem_files prob_pathname (ctxt,th)
   921       val (childin, childout, pid) = Watcher.createWatcher (th, thm_names_list)
   922     in
   923       last_watcher_pid := SOME (childin, childout, pid, files);
   924       Output.debug ("problem files: " ^ space_implode ", " files); 
   925       Output.debug ("pid: " ^ string_of_pid pid);
   926       watcher_call_provers (sign_of_thm th) (Thm.prems_of th) (childin, childout, pid)
   927     end;
   928 
   929 val isar_atp = setmp print_mode [] isar_atp_body;
   930 
   931 (*For ML scripts, and primarily, for debugging*)
   932 fun callatp () = 
   933   let val th = topthm()
   934       val ctxt = ProofContext.init (theory_of_thm th)
   935   in  isar_atp_body (ctxt, th)  end;
   936 
   937 val isar_atp_writeonly = setmp print_mode [] 
   938       (fn (ctxt,th) =>
   939        if Thm.no_prems th then ()
   940        else 
   941          let val probfile = if Thm.nprems_of th = 1 then probfile_nosuffix 
   942           	            else prob_pathname
   943          in ignore (write_problem_files probfile (ctxt,th)) end);
   944 
   945 
   946 (** the Isar toplevel hook **)
   947 
   948 fun invoke_atp_ml (ctxt, goal) =
   949   let val thy = ProofContext.theory_of ctxt;
   950   in
   951     Output.debug ("subgoals in isar_atp:\n" ^ 
   952 		  Pretty.string_of (ProofContext.pretty_term ctxt
   953 		    (Logic.mk_conjunction_list (Thm.prems_of goal))));
   954     Output.debug ("current theory: " ^ Context.theory_name thy);
   955     inc hook_count;
   956     Output.debug ("in hook for time: " ^ Int.toString (!hook_count));
   957     ResClause.init thy;
   958     ResHolClause.init thy;
   959     if !time_limit > 0 then isar_atp (ctxt, goal)
   960     else (warning "Writing problem file only"; isar_atp_writeonly (ctxt, goal))
   961   end;
   962 
   963 val invoke_atp = Toplevel.no_timing o Toplevel.unknown_proof o Toplevel.keep
   964  (fn state =>
   965   let val (ctxt, (_, goal)) = Proof.get_goal (Toplevel.proof_of state)
   966   in  invoke_atp_ml (ctxt, goal)  end);
   967 
   968 val call_atpP =
   969   OuterSyntax.command 
   970     "ProofGeneral.call_atp" 
   971     "call automatic theorem provers" 
   972     OuterKeyword.diag
   973     (Scan.succeed invoke_atp);
   974 
   975 val _ = OuterSyntax.add_parsers [call_atpP];
   976 
   977 end;