src/HOL/Tools/res_clause.ML
author paulson
Tue Nov 22 10:09:11 2005 +0100 (2005-11-22)
changeset 18218 9a7ffce389c3
parent 18199 d236379ea408
child 18275 86cefba6d325
permissions -rw-r--r--
new treatment of polymorphic types, using Sign.const_typargs
     1 (*  Author: Jia Meng, Cambridge University Computer Laboratory
     2 
     3     ID: $Id$
     4     Copyright 2004 University of Cambridge
     5 
     6 ML data structure for storing/printing FOL clauses and arity clauses.
     7 Typed equality is treated differently.
     8 *)
     9 
    10 (* works for writeoutclasimp on typed *)
    11 signature RES_CLAUSE =
    12   sig
    13   val keep_types : bool ref
    14   val special_equal : bool ref
    15   val tagged : bool ref
    16 
    17   exception ARCLAUSE of string
    18   exception CLAUSE of string * term
    19   type arityClause 
    20   type classrelClause
    21   type clause
    22   val init : theory -> unit
    23   val make_axiom_clause : Term.term -> string * int -> clause
    24   val make_conjecture_clauses : term list -> clause list
    25   val get_axiomName : clause ->  string
    26   val isTaut : clause -> bool
    27   val num_of_clauses : clause -> int
    28 
    29   val clause2dfg : clause -> string * string list
    30   val clauses2dfg : clause list -> string -> clause list -> clause list ->
    31 	   (string * int) list -> (string * int) list -> string
    32   val tfree_dfg_clause : string -> string
    33 
    34   val arity_clause_thy: theory -> arityClause list 
    35   val classrel_clauses_thy: theory -> classrelClause list 
    36 
    37   val tptp_arity_clause : arityClause -> string
    38   val tptp_classrelClause : classrelClause -> string
    39   val tptp_clause : clause -> string list
    40   val clause2tptp : clause -> string * string list
    41   val tfree_clause : string -> string
    42   val schematic_var_prefix : string
    43   val fixed_var_prefix : string
    44   val tvar_prefix : string
    45   val tfree_prefix : string
    46   val clause_prefix : string 
    47   val arclause_prefix : string
    48   val const_prefix : string
    49   val tconst_prefix : string 
    50   val class_prefix : string 
    51 
    52   val union_all : ''a list list -> ''a list
    53   val ascii_of : String.string -> String.string
    54   val paren_pack : string list -> string
    55   val bracket_pack : string list -> string
    56   val make_schematic_var : String.string * int -> string
    57   val make_fixed_var : String.string -> string
    58   val make_schematic_type_var : string * int -> string
    59   val make_fixed_type_var : string -> string
    60   val make_fixed_const : String.string -> string		
    61   val make_fixed_type_const : String.string -> string   
    62   val make_type_class : String.string -> string
    63   val isMeta : String.string -> bool
    64   
    65   type typ_var
    66   val mk_typ_var_sort : Term.typ -> typ_var * sort
    67   type type_literal
    68   val add_typs_aux2 : (typ_var * string list) list -> type_literal list * type_literal list
    69   val gen_tptp_cls : int * string * string * string -> string
    70   val gen_tptp_type_cls : int * string * string * string * int -> string
    71   val tptp_of_typeLit : type_literal -> string
    72   end;
    73 
    74 structure ResClause: RES_CLAUSE =
    75 struct
    76 
    77 (* Added for typed equality *)
    78 val special_equal = ref false; (* by default,equality does not carry type information *)
    79 val eq_typ_wrapper = "typeinfo"; (* default string *)
    80 
    81 
    82 val schematic_var_prefix = "V_";
    83 val fixed_var_prefix = "v_";
    84 
    85 val tvar_prefix = "T_";
    86 val tfree_prefix = "t_";
    87 
    88 val clause_prefix = "cls_"; 
    89 val arclause_prefix = "clsarity_" 
    90 val clrelclause_prefix = "clsrel_";
    91 
    92 val const_prefix = "c_";
    93 val tconst_prefix = "tc_"; 
    94 
    95 val class_prefix = "class_"; 
    96 
    97 
    98 fun union_all xss = foldl (op union) [] xss;
    99 
   100  
   101 (*Provide readable names for the more common symbolic functions*)
   102 val const_trans_table =
   103       Symtab.make [("op =", "equal"),
   104 	  	   ("op <=", "lessequals"),
   105 		   ("op <", "less"),
   106 		   ("op &", "and"),
   107 		   ("op |", "or"),
   108 		   ("op +", "plus"),
   109 		   ("op -", "minus"),
   110 		   ("op *", "times"),
   111 		   ("op -->", "implies"),
   112 		   ("{}", "emptyset"),
   113 		   ("op :", "in"),
   114 		   ("op Un", "union"),
   115 		   ("op Int", "inter")];
   116 
   117 val type_const_trans_table =
   118       Symtab.make [("*", "t_prod"),
   119 	  	   ("+", "t_sum"),
   120 		   ("~=>", "t_map")];
   121 
   122 (*Escaping of special characters.
   123   Alphanumeric characters are left unchanged.
   124   The character _ goes to __
   125   Characters in the range ASCII space to / go to _A to _P, respectively.
   126   Other printing characters go to _NNN where NNN is the decimal ASCII code.*)
   127 local
   128 
   129 val A_minus_space = Char.ord #"A" - Char.ord #" ";
   130 
   131 fun ascii_of_c c =
   132   if Char.isAlphaNum c then String.str c
   133   else if c = #"_" then "__"
   134   else if #" " <= c andalso c <= #"/" 
   135        then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))
   136   else if Char.isPrint c then ("_" ^ Int.toString (Char.ord c))
   137   else ""
   138 
   139 in
   140 
   141 val ascii_of = String.translate ascii_of_c;
   142 
   143 end;
   144 
   145 (* convert a list of strings into one single string; surrounded by brackets *)
   146 fun paren_pack [] = ""   (*empty argument list*)
   147   | paren_pack strings = "(" ^ commas strings ^ ")";
   148 
   149 fun bracket_pack strings = "[" ^ commas strings ^ "]";
   150 
   151 
   152 (*Remove the initial ' character from a type variable, if it is present*)
   153 fun trim_type_var s =
   154   if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
   155   else error ("trim_type: Malformed type variable encountered: " ^ s);
   156 
   157 fun ascii_of_indexname (v,0) = ascii_of v
   158   | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;
   159 
   160 fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v);
   161 fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);
   162 
   163 fun make_schematic_type_var (x,i) = 
   164       tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));
   165 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));
   166 
   167 fun make_fixed_const c =
   168     case Symtab.lookup const_trans_table c of
   169         SOME c' => c'
   170       | NONE =>  const_prefix ^ ascii_of c;
   171 
   172 fun make_fixed_type_const c = 
   173     case Symtab.lookup type_const_trans_table c of
   174         SOME c' => c'
   175       | NONE =>  tconst_prefix ^ ascii_of c;
   176 
   177 fun make_type_class clas = class_prefix ^ ascii_of clas;
   178 
   179 
   180 
   181 (***** definitions and functions for FOL clauses, prepared for conversion into TPTP format or SPASS format. *****)
   182 
   183 val keep_types = ref true;
   184 
   185 datatype kind = Axiom | Hypothesis | Conjecture;
   186 fun name_of_kind Axiom = "axiom"
   187   | name_of_kind Hypothesis = "hypothesis"
   188   | name_of_kind Conjecture = "conjecture";
   189 
   190 type clause_id = int;
   191 type axiom_name = string;
   192 
   193 
   194 type polarity = bool;
   195 
   196 type indexname = Term.indexname;
   197 
   198 
   199 (* "tag" is used for vampire specific syntax  *)
   200 type tag = bool; 
   201 
   202 
   203 (**** Isabelle FOL clauses ****)
   204 
   205 val tagged = ref false;
   206 
   207 type pred_name = string;
   208 type sort = Term.sort;
   209 type fol_type = string;
   210 
   211 datatype type_literal = LTVar of string | LTFree of string;
   212 
   213 datatype folTerm = UVar of string * fol_type
   214                  | Fun of string * fol_type list * folTerm list;
   215 datatype predicate = Predicate of pred_name * fol_type list * folTerm list;
   216 
   217 datatype literal = Literal of polarity * predicate * tag;
   218 
   219 datatype typ_var = FOLTVar of indexname | FOLTFree of string;
   220 
   221 fun mk_typ_var_sort (TFree(a,s)) = (FOLTFree a,s)
   222   | mk_typ_var_sort (TVar(v,s)) = (FOLTVar v,s);
   223 
   224 
   225 
   226 (* ML datatype used to repsent one single clause: disjunction of literals. *)
   227 datatype clause = 
   228 	 Clause of {clause_id: clause_id,
   229 		    axiom_name: axiom_name,
   230 		    kind: kind,
   231 		    literals: literal list,
   232 		    types_sorts: (typ_var * sort) list, 
   233                     tvar_type_literals: type_literal list, 
   234                     tfree_type_literals: type_literal list ,
   235                     tvars: string list,
   236                     predicates: (string*int) list,
   237                     functions: (string*int) list};
   238 
   239 
   240 exception CLAUSE of string * term;
   241 
   242 
   243 (*** make clauses ***)
   244 
   245 fun isFalse (Literal (pol,Predicate(a,_,[]),_)) =
   246       (pol andalso a = "c_False") orelse
   247       (not pol andalso a = "c_True")
   248   | isFalse _ = false;
   249 
   250 fun isTrue (Literal (pol,Predicate(a,_,[]),_)) =
   251       (pol andalso a = "c_True") orelse
   252       (not pol andalso a = "c_False")
   253   | isTrue _ = false;
   254   
   255 fun isTaut (Clause {literals,...}) = exists isTrue literals;  
   256 
   257 fun make_clause (clause_id,axiom_name,kind,literals,
   258                  types_sorts,tvar_type_literals,
   259                  tfree_type_literals,tvars, predicates, functions) =
   260   if forall isFalse literals 
   261   then error "Problem too trivial for resolution (empty clause)"
   262   else
   263      Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind, 
   264              literals = literals, types_sorts = types_sorts,
   265              tvar_type_literals = tvar_type_literals,
   266              tfree_type_literals = tfree_type_literals,
   267              tvars = tvars, predicates = predicates, 
   268              functions = functions};
   269 
   270 
   271 (** Some Clause destructor functions **)
   272 
   273 fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
   274 
   275 fun get_axiomName (Clause cls) = #axiom_name cls;
   276 
   277 fun get_clause_id (Clause cls) = #clause_id cls;
   278 
   279 fun funcs_of_cls (Clause cls) = #functions cls;
   280 
   281 fun preds_of_cls (Clause cls) = #predicates cls;
   282 
   283 
   284 (*Declarations of the current theory--to allow suppressing types.*)
   285 val const_typargs = ref (Library.K [] : (string*typ -> typ list));
   286 
   287 fun num_typargs(s,T) = if !keep_types then length (!const_typargs (s,T)) else 0;
   288 
   289 (*Initialize the type suppression mechanism with the current theory before
   290     producing any clauses!*)
   291 fun init thy = (const_typargs := Sign.const_typargs thy);
   292     
   293 
   294 (*Flatten a type to a string while accumulating sort constraints on the TFrees and
   295   TVars it contains.*)    
   296 fun type_of (Type (a, Ts)) = 
   297       let val (folTyps, (ts, funcs)) = types_of Ts 
   298 	  val t = make_fixed_type_const a
   299       in    
   300 	  ((t ^ paren_pack folTyps), (ts, (t, length Ts)::funcs))
   301       end
   302   | type_of (TFree (a,s)) = 
   303       let val t = make_fixed_type_var a
   304       in (t, ([((FOLTFree a),s)], [(t,0)])) end
   305   | type_of (TVar (v, s)) = (make_schematic_type_var v, ([((FOLTVar v),s)], []))
   306 and types_of Ts =
   307       let val foltyps_ts = map type_of Ts 
   308 	  val (folTyps,ts_funcs) = ListPair.unzip foltyps_ts
   309 	  val (ts, funcslist) = ListPair.unzip ts_funcs
   310       in    
   311 	  (folTyps, (union_all ts, union_all funcslist))
   312       end;
   313 
   314 
   315 fun const_types_of (c,T) = types_of (!const_typargs (c,T));
   316 
   317 (* Any variables created via the METAHYPS tactical should be treated as
   318    universal vars, although it is represented as "Free(...)" by Isabelle *)
   319 val isMeta = String.isPrefix "METAHYP1_"
   320 
   321 fun pred_name_type (Const(c,T)) = 
   322       let val (contys,(folTyps,funcs)) = const_types_of (c,T)
   323       in (make_fixed_const c, (contys,folTyps), funcs) end
   324   | pred_name_type (Free(x,T))  = 
   325       if isMeta x then raise CLAUSE("Predicate Not First Order 1", Free(x,T)) 
   326       else (make_fixed_var x, ([],[]), [])
   327   | pred_name_type (v as Var _) = raise CLAUSE("Predicate Not First Order 2", v)
   328   | pred_name_type t        = raise CLAUSE("Predicate input unexpected", t);
   329 
   330 
   331 (* For typed equality *)
   332 (* here "arg_typ" is the type of "="'s argument's type, not the type of the equality *)
   333 (* Find type of equality arg *)
   334 fun eq_arg_type (Type("fun",[T,_])) = 
   335     let val (folT,_) = type_of T;
   336     in  folT  end;
   337 
   338 fun fun_name_type (Const("op =",T)) args =   (*FIXME: Is this special treatment of = needed??*)
   339       let val t = make_fixed_const "op ="
   340       in (t, ([eq_arg_type T], []), [(t,2)]) end
   341   | fun_name_type (Const(c,T)) args = 
   342       let val t = make_fixed_const c
   343 	  val (contys, (folTyps,funcs)) = const_types_of (c,T)
   344 	  val arity = num_typargs(c,T) + length args
   345       in
   346 	  (t, (contys,folTyps), ((t,arity)::funcs))
   347       end
   348  | fun_name_type (Free(x,T)) args  = 
   349       let val t = make_fixed_var x
   350       in  (t, ([],[]), [(t, length args)]) end
   351   | fun_name_type f args = raise CLAUSE("Function Not First Order 1", f);
   352 
   353 
   354 fun term_of (Var(ind_nm,T)) = 
   355       let val (folType,(ts,funcs)) = type_of T
   356       in
   357 	  (UVar(make_schematic_var ind_nm, folType), (ts, funcs))
   358       end
   359   | term_of (Free(x,T)) = 
   360       let val (folType, (ts,funcs)) = type_of T
   361       in
   362 	  if isMeta x then (UVar(make_schematic_var(x,0),folType),
   363 			    (ts, ((make_schematic_var(x,0)),0)::funcs))
   364 	  else
   365 	      (Fun(make_fixed_var x, [folType], []), 
   366 	       (ts, ((make_fixed_var x),0)::funcs))
   367       end
   368   | term_of (Const(c,T)) =  (* impossible to be equality *)
   369       let val (contys, (folTyps,funcs)) = const_types_of (c,T)
   370       in
   371 	  (Fun(make_fixed_const c, contys, []),
   372 	   (folTyps, ((make_fixed_const c),0)::funcs))
   373       end    
   374   | term_of app = 
   375       let val (f,args) = strip_comb app
   376           val _ = case f of Const(_,_) => ()
   377 			  | Free(s,_)  => 
   378 			      if isMeta s 
   379 			      then raise CLAUSE("Function Not First Order 2", f)
   380 			      else ()
   381 			  | _ => raise CLAUSE("Function Not First Order 3", f);
   382 	  val (funName,(contys,ts1),funcs) = fun_name_type f args
   383 	  val (args',(ts2,funcs')) = terms_of args
   384       in
   385 	  (Fun(funName,contys,args'), 
   386 	   (union_all (ts1::ts2), 
   387 	    union_all(funcs::funcs')))
   388       end
   389   | term_of t = raise CLAUSE("Function Not First Order 4", t)
   390 and terms_of ts =  
   391       let val (args, ts_funcs) = ListPair.unzip (map term_of ts)
   392       in
   393 	  (args, ListPair.unzip ts_funcs)
   394       end
   395 
   396 
   397 fun pred_of (Const("op =", typ), args) =
   398       let val arg_typ = eq_arg_type typ 
   399 	  val (args',(ts,funcs)) = terms_of args
   400 	  val equal_name = make_fixed_const "op ="
   401       in
   402 	  (Predicate(equal_name,[arg_typ],args'),
   403 	   union_all ts, 
   404 	   [((make_fixed_var equal_name), 2)], 
   405 	   union_all funcs)
   406       end
   407   | pred_of (pred,args) = 
   408       let val (predName,(predType,ts1), pfuncs) = pred_name_type pred
   409 	  val (args',(ts2,ffuncs)) = terms_of args
   410 	  val ts3 = union_all (ts1::ts2)
   411 	  val ffuncs' = union_all ffuncs
   412 	  val newfuncs = pfuncs union ffuncs'
   413 	  val arity = 
   414 	    case pred of
   415 		Const (c,T) => num_typargs(c,T) + length args
   416 	      | _ => length args
   417       in
   418 	  (Predicate(predName,predType,args'), ts3, 
   419 	   [(predName, arity)], newfuncs)
   420       end;
   421 
   422 
   423 (*Treatment of literals, possibly negated or tagged*)
   424 fun predicate_of ((Const("Not",_) $ P), polarity, tag) =
   425       predicate_of (P, not polarity, tag)
   426   | predicate_of ((Const("HOL.tag",_) $ P), polarity, tag) =
   427       predicate_of (P, polarity, true)
   428   | predicate_of (term,polarity,tag) =
   429         (pred_of (strip_comb term), polarity, tag);
   430 
   431 fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
   432   | literals_of_term1 (args as (lits, ts, preds, funcs)) (Const("op |",_) $ P $ Q) = 
   433       let val (lits', ts', preds', funcs') = literals_of_term1 args P
   434       in
   435 	  literals_of_term1 (lits', ts', preds' union preds, funcs' union funcs) Q
   436       end
   437   | literals_of_term1 (lits, ts, preds, funcs) P =
   438       let val ((pred, ts', preds', funcs'), pol, tag) = predicate_of (P,true,false)
   439 	  val lits' = Literal(pol,pred,tag) :: lits
   440       in
   441 	  (lits', ts union ts', preds' union preds, funcs' union funcs)
   442       end;
   443 
   444 
   445 val literals_of_term = literals_of_term1 ([],[],[],[]);
   446 
   447 
   448 (* FIX: not sure what to do with these funcs *)
   449 
   450 (*Make literals for sorted type variables*) 
   451 fun sorts_on_typs (_, [])   = ([]) 
   452   | sorts_on_typs (v, "HOL.type" :: s) =
   453       sorts_on_typs (v,s)   (*Ignore sort "type"*)
   454   | sorts_on_typs ((FOLTVar indx), (s::ss)) =
   455       LTVar((make_type_class s) ^ 
   456         "(" ^ (make_schematic_type_var indx) ^ ")") :: 
   457       (sorts_on_typs ((FOLTVar indx), ss))
   458   | sorts_on_typs ((FOLTFree x), (s::ss)) =
   459       LTFree((make_type_class s) ^ "(" ^ (make_fixed_type_var x) ^ ")") :: 
   460       (sorts_on_typs ((FOLTFree x), ss));
   461 
   462 
   463 (*UGLY: seems to be parsing the "show sorts" output, removing anything that
   464   starts with a left parenthesis.*)
   465 fun remove_type str = hd (String.fields (fn c => c = #"(") str);
   466 
   467 fun pred_of_sort (LTVar x) = ((remove_type x),1)
   468 |   pred_of_sort (LTFree x) = ((remove_type x),1)
   469 
   470 
   471 
   472 
   473 (*Given a list of sorted type variables, return two separate lists.
   474   The first is for TVars, the second for TFrees.*)
   475 fun add_typs_aux [] preds  = ([],[], preds)
   476   | add_typs_aux ((FOLTVar indx,s)::tss) preds = 
   477       let val vs = sorts_on_typs (FOLTVar indx, s)
   478           val preds' = (map pred_of_sort vs)@preds
   479 	  val (vss,fss, preds'') = add_typs_aux tss preds'
   480       in
   481 	  (vs union vss, fss, preds'')
   482       end
   483   | add_typs_aux ((FOLTFree x,s)::tss) preds  =
   484       let val fs = sorts_on_typs (FOLTFree x, s)
   485           val preds' = (map pred_of_sort fs)@preds
   486 	  val (vss,fss, preds'') = add_typs_aux tss preds'
   487       in
   488 	  (vss, fs union fss, preds'')
   489       end;
   490 
   491 fun add_typs_aux2 [] = ([],[])
   492   | add_typs_aux2 ((FOLTVar indx,s)::tss) =
   493     let val vs = sorts_on_typs (FOLTVar indx,s)
   494 	val (vss,fss) = add_typs_aux2 tss
   495     in
   496 	(vs union vss,fss)
   497     end
   498   | add_typs_aux2 ((FOLTFree x,s)::tss) =
   499     let val fs = sorts_on_typs (FOLTFree x,s)
   500 	val (vss,fss) = add_typs_aux2 tss
   501     in
   502 	(vss,fs union fss)
   503     end;
   504 
   505 
   506 fun add_typs (Clause cls) preds  = add_typs_aux (#types_sorts cls) preds 
   507 
   508 
   509 (** make axiom clauses, hypothesis clauses and conjecture clauses. **)
   510 
   511 fun get_tvar_strs [] = []
   512   | get_tvar_strs ((FOLTVar indx,s)::tss) = 
   513       let val vstr = make_schematic_type_var indx
   514       in
   515 	  vstr ins (get_tvar_strs tss)
   516       end
   517   | get_tvar_strs((FOLTFree x,s)::tss) = distinct (get_tvar_strs tss)
   518 
   519 (* FIX add preds and funcs to add typs aux here *)
   520 
   521 fun make_axiom_clause_thm thm (ax_name,cls_id) =
   522     let val (lits,types_sorts, preds, funcs) = literals_of_term (prop_of thm)
   523 	val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds 
   524         val tvars = get_tvar_strs types_sorts
   525     in 
   526 	make_clause(cls_id,ax_name,Axiom,
   527 	            lits,types_sorts,tvar_lits,tfree_lits,
   528 	            tvars, preds, funcs)
   529     end;
   530 
   531 
   532 (* check if a clause is FOL first*)
   533 fun make_conjecture_clause n t =
   534     let val _ = check_is_fol_term t
   535 	    handle TERM("check_is_fol_term",_) => raise CLAUSE("Goal is not FOL",t)
   536 	val (lits,types_sorts, preds, funcs) = literals_of_term t
   537 	val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds 
   538         val tvars = get_tvar_strs types_sorts
   539     in
   540 	make_clause(n,"conjecture",Conjecture,
   541 	            lits,types_sorts,tvar_lits,tfree_lits,
   542 	            tvars, preds, funcs)
   543     end;
   544     
   545 fun make_conjecture_clauses_aux _ [] = []
   546   | make_conjecture_clauses_aux n (t::ts) =
   547       make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts
   548 
   549 val make_conjecture_clauses = make_conjecture_clauses_aux 0
   550 
   551 
   552 (*before converting an axiom clause to "clause" format, check if it is FOL*)
   553 fun make_axiom_clause term (ax_name,cls_id) =
   554     let val _ = check_is_fol_term term 
   555 	    handle TERM("check_is_fol_term",_) => raise CLAUSE("Axiom is not FOL", term) 
   556 	val (lits,types_sorts, preds,funcs) = literals_of_term term
   557 	val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds
   558         val tvars = get_tvar_strs types_sorts	
   559     in 
   560 	make_clause(cls_id,ax_name,Axiom,
   561 	            lits,types_sorts,tvar_lits,tfree_lits,
   562 	            tvars, preds,funcs)
   563     end;
   564 
   565 
   566 
   567  
   568 (**** Isabelle arities ****)
   569 
   570 exception ARCLAUSE of string;
   571  
   572 
   573 type class = string; 
   574 type tcons = string; 
   575 
   576 
   577 datatype arLit = TConsLit of bool * (class * tcons * string list) | TVarLit of bool * (class * string);
   578  
   579 datatype arityClause =  
   580 	 ArityClause of {clause_id: clause_id,
   581 	  	         axiom_name: axiom_name,
   582 			 kind: kind,
   583 			 conclLit: arLit,
   584 			 premLits: arLit list};
   585 
   586 
   587 fun get_TVars 0 = []
   588   | get_TVars n = ("T_" ^ (Int.toString n)) :: get_TVars (n-1);
   589 
   590 
   591 
   592 fun pack_sort(_,[])  = raise ARCLAUSE("Empty Sort Found") 
   593   | pack_sort(tvar, [cls]) = [(make_type_class cls, tvar)] 
   594   | pack_sort(tvar, cls::srt) =  (make_type_class cls,tvar) :: (pack_sort(tvar, srt));
   595     
   596     
   597 fun make_TVarLit (b,(cls,str)) = TVarLit(b,(cls,str));
   598 fun make_TConsLit (b,(cls,tcons,tvars)) = TConsLit(b,(make_type_class cls,make_fixed_type_const tcons,tvars));
   599 
   600 fun make_axiom_arity_clause (tcons,n,(res,args)) =
   601    let val nargs = length args
   602        val tvars = get_TVars nargs
   603        val tvars_srts = ListPair.zip (tvars,args)
   604        val tvars_srts' = union_all(map pack_sort tvars_srts)
   605        val false_tvars_srts' = map (pair false) tvars_srts'
   606    in
   607       ArityClause {clause_id = n, kind = Axiom, 
   608                    axiom_name = tcons,
   609                    conclLit = make_TConsLit(true,(res,tcons,tvars)), 
   610                    premLits = map make_TVarLit false_tvars_srts'}
   611    end;
   612     
   613 (*The number of clauses generated from cls, including type clauses*)
   614 fun num_of_clauses (Clause cls) =
   615     let val num_tfree_lits = 
   616 	      if !keep_types then length (#tfree_type_literals cls)
   617 	      else 0
   618     in 	1 + num_tfree_lits  end;
   619 
   620 
   621 (**** Isabelle class relations ****)
   622 
   623 
   624 datatype classrelClause = 
   625 	 ClassrelClause of {clause_id: clause_id,
   626 			    subclass: class,
   627 			    superclass: class option};
   628 
   629 
   630 fun make_axiom_classrelClause n subclass superclass =
   631   ClassrelClause {clause_id = n,
   632                   subclass = subclass, superclass = superclass};
   633 
   634 
   635 fun classrelClauses_of_aux n sub [] = []
   636   | classrelClauses_of_aux n sub (sup::sups) =
   637       make_axiom_classrelClause n sub (SOME sup) :: classrelClauses_of_aux (n+1) sub sups;
   638 
   639 
   640 fun classrelClauses_of (sub,sups) = 
   641     case sups of [] => [make_axiom_classrelClause 0 sub NONE]
   642 	       | _ => classrelClauses_of_aux 0 sub sups;
   643 
   644 
   645 (***** Isabelle arities *****)
   646 
   647 
   648 fun arity_clause _ (tcons, []) = []
   649   | arity_clause n (tcons, ar::ars) =
   650       make_axiom_arity_clause (tcons,n,ar) :: 
   651       arity_clause (n+1) (tcons,ars);
   652 
   653 fun multi_arity_clause [] = []
   654   | multi_arity_clause (tcon_ar :: tcons_ars)  =
   655       arity_clause 0 tcon_ar  @  multi_arity_clause tcons_ars 
   656 
   657 fun arity_clause_thy thy =
   658   let val arities = #arities (Type.rep_tsig (Sign.tsig_of thy))
   659   in multi_arity_clause (Symtab.dest arities) end;
   660 
   661 
   662 (* Isabelle classes *)
   663 
   664 type classrelClauses = classrelClause list Symtab.table;
   665 
   666 val classrel_of = #2 o #classes o Type.rep_tsig o Sign.tsig_of;
   667 fun classrel_clauses_classrel (C: Sorts.classes) = map classrelClauses_of (Graph.dest C);
   668 val classrel_clauses_thy = List.concat o classrel_clauses_classrel o classrel_of;
   669 
   670 
   671 
   672 (****!!!! Changed for typed equality !!!!****)
   673 
   674 fun wrap_eq_type typ t = eq_typ_wrapper ^"(" ^ t ^ "," ^ typ ^ ")";
   675 
   676 (*Only need to wrap equality's arguments with "typeinfo" if the output clauses are typed 
   677  and if we specifically ask for types to be included.   *)
   678 fun string_of_equality (typ,terms) =
   679       let val [tstr1,tstr2] = map string_of_term terms
   680       in
   681 	  if !keep_types andalso !special_equal 
   682 	  then "equal(" ^ (wrap_eq_type typ tstr1) ^ "," ^ 
   683 		 	  (wrap_eq_type typ tstr2) ^ ")"
   684 	  else "equal(" ^ tstr1 ^ "," ^ tstr2 ^ ")"
   685       end
   686 and string_of_term (UVar(x,_)) = x
   687   | string_of_term (Fun("equal",[typ],terms)) = string_of_equality(typ,terms)
   688   | string_of_term (Fun (name,typs,[])) = name (*Overloaded consts like 0 don't get types!*)
   689   | string_of_term (Fun (name,typs,terms)) = 
   690       let val terms_as_strings = map string_of_term terms
   691       in  name ^ (paren_pack (terms_as_strings @ typs))  end
   692   | string_of_term _ = error "string_of_term";      
   693 
   694 (* before output the string of the predicate, check if the predicate corresponds to an equality or not. *)
   695 fun string_of_predicate (Predicate("equal",[typ],terms)) = string_of_equality(typ,terms)
   696   | string_of_predicate (Predicate(name,typs,terms)) = 
   697       let val terms_as_strings = map string_of_term terms
   698       in  name ^ (paren_pack (terms_as_strings @ typs))  end
   699   | string_of_predicate _ = error "string_of_predicate";      
   700 
   701 
   702 fun string_of_clausename (cls_id,ax_name) = 
   703     clause_prefix ^ ascii_of ax_name ^ "_" ^ Int.toString cls_id;
   704 
   705 fun string_of_type_clsname (cls_id,ax_name,idx) = 
   706     string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
   707     
   708 
   709 (********************************)
   710 (* Code for producing DFG files *)
   711 (********************************)
   712 
   713 fun dfg_literal (Literal(pol,pred,tag)) =
   714     let val pred_string = string_of_predicate pred
   715     in
   716 	if pol then pred_string else "not(" ^pred_string ^ ")"  
   717     end;
   718 
   719 
   720 (* FIX: what does this mean? *)
   721 (*fun dfg_of_typeLit (LTVar x) = "not(" ^ x ^ ")"
   722   | dfg_of_typeLit (LTFree x) = "(" ^ x ^ ")";*)
   723 
   724 fun dfg_of_typeLit (LTVar x) =  x 
   725   | dfg_of_typeLit (LTFree x) = x ;
   726  
   727 (*Make the string of universal quantifiers for a clause*)
   728 fun forall_open ([],[]) = ""
   729   | forall_open (vars,tvars) = "forall([" ^ (commas (tvars@vars))^ "],\n"
   730 
   731 fun forall_close ([],[]) = ""
   732   | forall_close (vars,tvars) = ")"
   733 
   734 fun gen_dfg_cls (cls_id,ax_name,knd,lits,tvars,vars) = 
   735     "clause( %(" ^ knd ^ ")\n" ^ forall_open(vars,tvars) ^ 
   736     "or(" ^ lits ^ ")" ^ forall_close(vars,tvars) ^ ",\n" ^ 
   737     string_of_clausename (cls_id,ax_name) ^  ").";
   738 
   739 fun gen_dfg_type_cls (cls_id,ax_name,knd,tfree_lit,idx,tvars,vars) = 
   740     "clause( %(" ^ knd ^ ")\n" ^ forall_open(vars,tvars) ^ 
   741     "or( " ^ tfree_lit ^ ")" ^ forall_close(vars,tvars) ^ ",\n" ^ 
   742     string_of_type_clsname (cls_id,ax_name,idx) ^  ").";
   743 
   744 fun dfg_clause_aux (Clause cls) = 
   745   let val lits = map dfg_literal (#literals cls)
   746       val tvar_lits_strs = 
   747 	  if !keep_types then map dfg_of_typeLit (#tvar_type_literals cls) 
   748 	  else []
   749       val tfree_lits =
   750           if !keep_types then map dfg_of_typeLit (#tfree_type_literals cls)
   751           else []
   752   in
   753       (tvar_lits_strs @ lits, tfree_lits)
   754   end; 
   755 
   756 
   757 fun dfg_folterms (Literal(pol,pred,tag)) = 
   758   let val Predicate (predname, _, folterms) = pred
   759   in  folterms  end
   760 
   761  
   762 fun get_uvars (UVar(a,typ)) = [a] 
   763 |   get_uvars (Fun (_,typ,tlist)) = union_all(map get_uvars tlist)
   764 
   765 
   766 fun is_uvar (UVar _) = true
   767 |   is_uvar (Fun _) = false;
   768 
   769 fun uvar_name (UVar(a,_)) = a
   770 |   uvar_name (Fun (a,_,_)) = raise CLAUSE("Not a variable", Const(a,dummyT));
   771 
   772 fun dfg_vars (Clause cls) =
   773     let val lits = #literals cls
   774         val folterms = List.concat (map dfg_folterms lits)
   775     in 
   776         union_all(map get_uvars folterms)
   777     end
   778 
   779 
   780 fun dfg_tvars (Clause cls) =(#tvars cls)
   781 
   782 
   783 	
   784 (* make this return funcs and preds too? *)
   785 fun string_of_predname (Predicate("equal",_,terms)) = "EQUALITY"
   786   | string_of_predname (Predicate(name,_,terms)) = name
   787     
   788 	
   789 
   790 fun concat_with sep []  = ""
   791   | concat_with sep [x] = "(" ^ x ^ ")"
   792   | concat_with sep (x::xs) = "(" ^ x ^ ")" ^  sep ^ (concat_with sep xs);
   793 
   794 fun dfg_pred (Literal(pol,pred,tag)) ax_name = 
   795     (string_of_predname pred) ^ " " ^ ax_name
   796 
   797 fun dfg_clause cls =
   798     let val (lits,tfree_lits) = dfg_clause_aux cls 
   799              (*"lits" includes the typing assumptions (TVars)*)
   800         val vars = dfg_vars cls
   801         val tvars = dfg_tvars cls
   802 	val knd = string_of_kind cls
   803 	val lits_str = commas lits
   804 	val cls_id = get_clause_id cls
   805 	val axname = get_axiomName cls
   806 	val cls_str = gen_dfg_cls(cls_id,axname,knd,lits_str,tvars, vars) 			
   807         fun typ_clss k [] = []
   808           | typ_clss k (tfree :: tfrees) = 
   809               (gen_dfg_type_cls(cls_id,axname,knd,tfree,k, tvars,vars)) :: 
   810               (typ_clss (k+1) tfrees)
   811     in 
   812 	cls_str :: (typ_clss 0 tfree_lits)
   813     end;
   814 
   815 fun string_of_arity (name, num) =  name ^ "," ^ (Int.toString num) 
   816 
   817 fun string_of_preds preds = 
   818   "predicates[" ^ (concat_with ", " (map string_of_arity preds)) ^ "].\n";
   819 
   820 fun string_of_funcs funcs =
   821   "functions[" ^ (concat_with ", " (map string_of_arity funcs)) ^ "].\n" ;
   822 
   823 
   824 fun string_of_symbols predstr funcstr = 
   825   "list_of_symbols.\n" ^ predstr  ^ funcstr  ^ "end_of_list.\n\n";
   826 
   827 
   828 fun string_of_axioms axstr = 
   829   "list_of_clauses(axioms,cnf).\n" ^ axstr ^ "end_of_list.\n\n";
   830 
   831 
   832 fun string_of_conjectures conjstr = 
   833   "list_of_clauses(conjectures,cnf).\n" ^ conjstr ^ "end_of_list.\n\n";
   834 
   835 fun string_of_descrip () = 
   836   "list_of_descriptions.\nname({*[ File     : ],[ Names    :]*}).\nauthor({*[ Source   :]*}).\nstatus(unknown).\ndescription({*[ Refs     :]*}).\nend_of_list.\n\n"
   837 
   838 
   839 fun string_of_start name = "%------------------------------------------------------------------------------\nbegin_problem(" ^ name ^ ").\n\n";
   840 
   841 
   842 fun string_of_end () = "end_problem.\n%------------------------------------------------------------------------------";
   843 
   844 
   845 fun clause2dfg cls =
   846     let val (lits,tfree_lits) = dfg_clause_aux cls 
   847             (*"lits" includes the typing assumptions (TVars)*)
   848 	val cls_id = get_clause_id cls
   849 	val ax_name = get_axiomName cls
   850         val vars = dfg_vars cls
   851         val tvars = dfg_tvars cls
   852         val funcs = funcs_of_cls cls
   853         val preds = preds_of_cls cls
   854 	val knd = string_of_kind cls
   855 	val lits_str = commas lits
   856 	val cls_str = gen_dfg_cls(cls_id,ax_name,knd,lits_str,tvars,vars) 
   857     in
   858 	(cls_str,tfree_lits) 
   859     end;
   860 
   861 
   862 
   863 fun tfree_dfg_clause tfree_lit =
   864   "clause( %(conjecture)\n" ^ "or( " ^ tfree_lit ^ "),\n" ^ "tfree_tcs" ^ ")."
   865 
   866 
   867 fun gen_dfg_file probname axioms conjectures funcs preds = 
   868     let val axstrs_tfrees = (map clause2dfg axioms)
   869 	val (axstrs, atfrees) = ListPair.unzip axstrs_tfrees
   870         val axstr = (space_implode "\n" axstrs) ^ "\n\n"
   871         val conjstrs_tfrees = (map clause2dfg conjectures)
   872 	val (conjstrs, atfrees) = ListPair.unzip conjstrs_tfrees
   873         val tfree_clss = map tfree_dfg_clause (union_all atfrees) 
   874         val conjstr = (space_implode "\n" (tfree_clss@conjstrs)) ^ "\n\n"
   875         val funcstr = string_of_funcs funcs
   876         val predstr = string_of_preds preds
   877     in
   878        (string_of_start probname) ^ (string_of_descrip ()) ^ 
   879        (string_of_symbols funcstr predstr) ^  
   880        (string_of_axioms axstr) ^
   881        (string_of_conjectures conjstr) ^ (string_of_end ())
   882     end;
   883    
   884 fun clauses2dfg [] probname axioms conjectures funcs preds = 
   885       let val funcs' = (union_all(map funcs_of_cls axioms)) @ funcs
   886 	  val preds' = (union_all(map preds_of_cls axioms)) @ preds
   887       in
   888 	 gen_dfg_file probname axioms conjectures funcs' preds' 
   889       end
   890  | clauses2dfg (cls::clss) probname axioms conjectures funcs preds = 
   891      let val (lits,tfree_lits) = dfg_clause_aux cls
   892 	       (*"lits" includes the typing assumptions (TVars)*)
   893 	 val cls_id = get_clause_id cls
   894 	 val ax_name = get_axiomName cls
   895 	 val vars = dfg_vars cls
   896 	 val tvars = dfg_tvars cls
   897 	 val funcs' = (funcs_of_cls cls) union funcs
   898 	 val preds' = (preds_of_cls cls) union preds
   899 	 val knd = string_of_kind cls
   900 	 val lits_str = concat_with ", " lits
   901 	 val axioms' = if knd = "axiom" then (cls::axioms) else axioms
   902 	 val conjectures' = 
   903 	     if knd = "conjecture" then (cls::conjectures) else conjectures
   904      in
   905 	 clauses2dfg clss probname axioms' conjectures' funcs' preds' 
   906      end;
   907 
   908 
   909 fun string_of_arClauseID (ArityClause {clause_id,axiom_name,...}) =
   910     arclause_prefix ^ ascii_of axiom_name ^ "_" ^ Int.toString clause_id;
   911 
   912 fun string_of_arKind (ArityClause arcls) = name_of_kind(#kind arcls);
   913 
   914 (*FIXME!!! currently is TPTP format!*)
   915 fun dfg_of_arLit (TConsLit(b,(c,t,args))) =
   916       let val pol = if b then "++" else "--"
   917 	  val arg_strs = paren_pack args
   918       in 
   919 	  pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"
   920       end
   921   | dfg_of_arLit (TVarLit(b,(c,str))) =
   922       let val pol = if b then "++" else "--"
   923       in
   924 	  pol ^ c ^ "(" ^ str ^ ")"
   925       end;
   926     
   927 
   928 fun dfg_of_conclLit (ArityClause arcls) = dfg_of_arLit (#conclLit arcls);
   929      
   930 
   931 fun dfg_of_premLits (ArityClause arcls) = map dfg_of_arLit (#premLits arcls);
   932 		
   933 
   934 
   935 (*FIXME: would this have variables in a forall? *)
   936 
   937 fun dfg_arity_clause arcls = 
   938   let val arcls_id = string_of_arClauseID arcls
   939       val concl_lit = dfg_of_conclLit arcls
   940       val prems_lits = dfg_of_premLits arcls
   941       val knd = string_of_arKind arcls
   942       val all_lits = concl_lit :: prems_lits
   943   in
   944       "clause( %(" ^ knd ^ ")\n" ^  "or( " ^ (bracket_pack all_lits) ^ ")),\n" ^
   945        arcls_id ^  ")."
   946   end;
   947 
   948 
   949 (********************************)
   950 (* code to produce TPTP files   *)
   951 (********************************)
   952 
   953 fun tptp_literal (Literal(pol,pred,tag)) =
   954     let val pred_string = string_of_predicate pred
   955 	val tagged_pol = 
   956 	      if (tag andalso !tagged) then (if pol then "+++" else "---")
   957 	      else (if pol then "++" else "--")
   958      in
   959 	tagged_pol ^ pred_string
   960     end;
   961 
   962 fun tptp_of_typeLit (LTVar x) = "--" ^ x
   963   | tptp_of_typeLit (LTFree x) = "++" ^ x;
   964  
   965 
   966 fun gen_tptp_cls (cls_id,ax_name,knd,lits) = 
   967     "input_clause(" ^ string_of_clausename (cls_id,ax_name) ^ "," ^ 
   968     knd ^ "," ^ lits ^ ").";
   969 
   970 fun gen_tptp_type_cls (cls_id,ax_name,knd,tfree_lit,idx) = 
   971     "input_clause(" ^ string_of_type_clsname (cls_id,ax_name,idx) ^ "," ^ 
   972     knd ^ ",[" ^ tfree_lit ^ "]).";
   973 
   974 fun tptp_type_lits (Clause cls) = 
   975     let val lits = map tptp_literal (#literals cls)
   976 	val tvar_lits_strs =
   977 	      if !keep_types 
   978 	      then (map tptp_of_typeLit (#tvar_type_literals cls)) 
   979 	      else []
   980 	val tfree_lits = 
   981 	      if !keep_types
   982 	      then (map tptp_of_typeLit (#tfree_type_literals cls)) 
   983 	      else []
   984     in
   985 	(tvar_lits_strs @ lits, tfree_lits)
   986     end; 
   987 
   988 fun tptp_clause cls =
   989     let val (lits,tfree_lits) = tptp_type_lits cls 
   990             (*"lits" includes the typing assumptions (TVars)*)
   991 	val cls_id = get_clause_id cls
   992 	val ax_name = get_axiomName cls
   993 	val knd = string_of_kind cls
   994 	val lits_str = bracket_pack lits
   995 	val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str) 			 
   996 	fun typ_clss k [] = []
   997           | typ_clss k (tfree :: tfrees) = 
   998               gen_tptp_type_cls(cls_id,ax_name,knd,tfree,k) :: 
   999               typ_clss (k+1) tfrees
  1000     in 
  1001 	cls_str :: (typ_clss 0 tfree_lits)
  1002     end;
  1003 
  1004 fun clause2tptp cls =
  1005     let val (lits,tfree_lits) = tptp_type_lits cls 
  1006             (*"lits" includes the typing assumptions (TVars)*)
  1007 	val cls_id = get_clause_id cls
  1008 	val ax_name = get_axiomName cls
  1009 	val knd = string_of_kind cls
  1010 	val lits_str = bracket_pack lits
  1011 	val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str) 
  1012     in
  1013 	(cls_str,tfree_lits) 
  1014     end;
  1015 
  1016 
  1017 fun tfree_clause tfree_lit =
  1018     "input_clause(" ^ "tfree_tcs," ^ "conjecture" ^ ",[" ^ tfree_lit ^ "]).";
  1019 
  1020 
  1021 fun tptp_of_arLit (TConsLit(b,(c,t,args))) =
  1022       let val pol = if b then "++" else "--"
  1023 	  val  arg_strs = paren_pack args
  1024       in 
  1025 	  pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"
  1026       end
  1027   | tptp_of_arLit (TVarLit(b,(c,str))) =
  1028       let val pol = if b then "++" else "--"
  1029       in
  1030 	  pol ^ c ^ "(" ^ str ^ ")"
  1031       end;
  1032     
  1033 
  1034 fun tptp_of_conclLit (ArityClause arcls) = tptp_of_arLit (#conclLit arcls);
  1035      
  1036 fun tptp_of_premLits (ArityClause arcls) = map tptp_of_arLit (#premLits arcls);
  1037 		
  1038 fun tptp_arity_clause arcls = 
  1039     let val arcls_id = string_of_arClauseID arcls
  1040 	val concl_lit = tptp_of_conclLit arcls
  1041 	val prems_lits = tptp_of_premLits arcls
  1042 	val knd = string_of_arKind arcls
  1043 	val all_lits = concl_lit :: prems_lits
  1044     in
  1045 	"input_clause(" ^ arcls_id ^ "," ^ knd ^ "," ^ 
  1046 	(bracket_pack all_lits) ^ ")."
  1047     end;
  1048 
  1049 fun tptp_classrelLits sub sup = 
  1050     let val tvar = "(T)"
  1051     in 
  1052 	case sup of NONE => "[++" ^ sub ^ tvar ^ "]"
  1053 		  | (SOME supcls) =>  "[--" ^ sub ^ tvar ^ ",++" ^ supcls ^ tvar ^ "]"
  1054     end;
  1055 
  1056 
  1057 fun tptp_classrelClause (ClassrelClause {clause_id,subclass,superclass,...}) =
  1058     let val relcls_id = clrelclause_prefix ^ ascii_of subclass ^ "_" ^ 
  1059                         Int.toString clause_id
  1060 	val lits = tptp_classrelLits (make_type_class subclass) 
  1061 	                (Option.map make_type_class superclass)
  1062     in
  1063 	"input_clause(" ^ relcls_id ^ ",axiom," ^ lits ^ ")."
  1064     end; 
  1065 
  1066 end;