src/HOL/Tools/ATP/recon_transfer_proof.ML
author paulson
Thu Oct 06 10:14:22 2005 +0200 (2005-10-06)
changeset 17772 818cec5f82a4
parent 17746 af59c748371d
child 17775 2679ba74411f
permissions -rw-r--r--
major simplification: removal of the goalstring argument
     1 (*  ID:         $Id$
     2     Author:     Claire Quigley
     3     Copyright   2004  University of Cambridge
     4 *)
     5 
     6 structure Recon_Transfer =
     7 struct
     8 
     9 open Recon_Parse
    10 
    11 infixr 8 ++; infixr 7 >>; infixr 6 ||;
    12 
    13 val trace_path = Path.basic "transfer_trace";
    14 
    15 fun trace s = if !Output.show_debug_msgs then File.append (File.tmp_path trace_path) s 
    16               else ();
    17 
    18 
    19 (* Versions that include type information *)
    20  
    21 (* FIXME rename to str_of_thm *)
    22 fun string_of_thm thm =
    23   setmp show_sorts true (Pretty.str_of o Display.pretty_thm) thm;
    24 
    25 
    26 (* check separate args in the watcher program for separating strings with a * or ; or something *)
    27 
    28 fun clause_strs_to_string [] str = str
    29 |   clause_strs_to_string (x::xs) str = clause_strs_to_string xs (str^x^"%")
    30 
    31 fun thmvars_to_string [] str = str
    32 |   thmvars_to_string (x::xs) str = thmvars_to_string xs (str^x^"%")
    33 
    34 
    35 fun proofstep_to_string Axiom = "Axiom()"
    36 |   proofstep_to_string  (Binary ((a,b), (c,d)))=
    37       "Binary(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"
    38 |   proofstep_to_string (Factor (a,b,c)) =
    39       "Factor("^(string_of_int a)^","^(string_of_int b)^","^(string_of_int c)^")"
    40 |   proofstep_to_string  (Para ((a,b), (c,d)))= 
    41       "Para(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"
    42 |   proofstep_to_string  (MRR ((a,b), (c,d))) =
    43       "MRR(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"
    44 (*|   proofstep_to_string (Rewrite((a,b),(c,d))) =
    45       "Rewrite(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"*)
    46 
    47 
    48 fun proof_to_string (num,(step,clause_strs, thmvars)) =
    49  (string_of_int num)^(proofstep_to_string step)^
    50  "["^(clause_strs_to_string clause_strs "")^"]["^(thmvars_to_string thmvars "")^"]"
    51  
    52 
    53 fun proofs_to_string [] str = str
    54 |   proofs_to_string (x::xs) str = let val newstr = proof_to_string x 
    55                                    in
    56                                        proofs_to_string xs (str^newstr)
    57                                    end
    58 
    59 
    60 
    61 fun init_proofstep_to_string (num, step, clause_strs) =
    62  (string_of_int num)^" "^(proofstep_to_string step)^" "^
    63  (clause_strs_to_string clause_strs "")^" "
    64 
    65 fun init_proofsteps_to_string [] str = str
    66 |   init_proofsteps_to_string (x::xs) str = let val newstr = init_proofstep_to_string x 
    67                                    in
    68                                        init_proofsteps_to_string xs (str^newstr)
    69                                    end
    70   
    71 
    72 
    73 (*** get a string representing the Isabelle ordered axioms ***)
    74 
    75 fun origAx_to_string (num,(meta,thmvars)) =
    76     let val clause_strs = ReconOrderClauses.get_meta_lits_bracket meta
    77     in
    78        (string_of_int num)^"OrigAxiom()["^
    79        (clause_strs_to_string clause_strs "")^"]["^
    80        (thmvars_to_string thmvars "")^"]"
    81     end
    82 
    83 
    84 fun  origAxs_to_string [] str = str
    85 |   origAxs_to_string (x::xs) str = let val newstr = origAx_to_string x 
    86                                    in
    87                                        origAxs_to_string xs (str^newstr)
    88                                    end
    89 
    90 
    91 (*** get a string representing the Isabelle ordered axioms not used in the spass proof***)
    92 
    93 fun extraAx_to_string (num, (meta,thmvars)) =
    94    let val clause_strs = ReconOrderClauses.get_meta_lits_bracket meta
    95    in
    96       (string_of_int num)^"ExtraAxiom()["^
    97       (clause_strs_to_string clause_strs "")^"]"^
    98       "["^(thmvars_to_string thmvars "")^"]"
    99    end;
   100 
   101 fun extraAxs_to_string [] str = str
   102 |   extraAxs_to_string (x::xs) str =
   103       let val newstr = extraAx_to_string x 
   104       in
   105 	  extraAxs_to_string xs (str^newstr)
   106       end;
   107 
   108 fun is_axiom (_,Axiom,str) = true
   109 |   is_axiom (_,_,_) = false
   110 
   111 fun get_step_nums [] nums = nums
   112 |   get_step_nums (( num:int,Axiom, str)::xs) nums = get_step_nums xs (nums@[num])
   113 
   114 exception Noassoc;
   115 
   116 fun assoc_snd a [] = raise Noassoc
   117   | assoc_snd a ((x, y)::t) = if a = y then x else assoc_snd a t;
   118 
   119 (* change to be something using check_order  instead of a = y --> returns true if ASSERTION not raised in checkorder, false otherwise *)
   120 
   121 (*fun get_assoc_snds [] xs assocs= assocs
   122 |   get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_snd x ys))])
   123 *)
   124 (*FIX - should this have vars in it? *)
   125 fun there_out_of_order xs ys = (ReconOrderClauses.checkorder xs ys [] ([],[],[]); true) 
   126                                handle _ => false
   127 
   128 fun assoc_out_of_order a [] = raise Noassoc
   129 |   assoc_out_of_order a ((b,c)::t) = if there_out_of_order a c then b else assoc_out_of_order a t;
   130 
   131 fun get_assoc_snds [] xs assocs= assocs
   132 |   get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_out_of_order x ys))])
   133 
   134 fun add_if_not_inlist [] xs newlist = newlist
   135 |   add_if_not_inlist (y::ys) xs newlist = if (not (y mem xs)) then 
   136                                       add_if_not_inlist ys xs (y::newlist)
   137                                         else add_if_not_inlist ys xs (newlist)
   138 
   139 (*Flattens a list of list of strings to one string*)
   140 fun onestr ls = String.concat (map String.concat ls);
   141 
   142 fun is_clasimp_ax clasimp_num n = n <= clasimp_num 
   143 
   144 fun subone x = x - 1
   145 
   146 fun numstr [] = ""
   147 |   numstr (x::xs) = (string_of_int x)^"%"^(numstr xs)
   148 
   149 
   150 (* retrieve the axioms that were obtained from the clasimpset *)
   151 
   152 fun get_clasimp_cls (clause_arr: (ResClause.clause * thm) array) step_nums = 
   153     let val clasimp_nums = List.filter (is_clasimp_ax (Array.length clause_arr - 1)) 
   154 	                   (map subone step_nums)
   155     in
   156 	map (fn x =>  Array.sub(clause_arr, x)) clasimp_nums
   157     end
   158 
   159 
   160 (*****************************************************)
   161 (* get names of clasimp axioms used                  *)
   162 (*****************************************************)
   163 
   164  fun get_axiom_names step_nums clause_arr =
   165    let 
   166      (* not sure why this is necessary again, but seems to be *)
   167       val _ = (print_mode := (Library.gen_rems (op =) (! print_mode, ["xsymbols", "symbols"])))
   168   
   169      (***********************************************)
   170      (* here need to add the clauses from clause_arr*)
   171      (***********************************************)
   172   
   173       val clasimp_names_cls = get_clasimp_cls clause_arr step_nums 
   174       val clasimp_names = map (ResClause.get_axiomName o #1) clasimp_names_cls
   175       val _ = (print_mode := (["xsymbols", "symbols"] @ ! print_mode))
   176    in
   177       clasimp_names
   178    end
   179    
   180 
   181 fun get_axiom_names_spass proofstr clause_arr =
   182   let (* parse spass proof into datatype *)
   183       val _ = trace ("\nStarted parsing:\n" ^ proofstr)
   184       val proof_steps = parse (#1(lex proofstr))
   185       val _ = trace "\nParsing finished!"
   186       (* get axioms as correctly numbered clauses w.r.t. the Spass proof *)
   187   in
   188     get_axiom_names (get_step_nums (List.filter is_axiom proof_steps) []) clause_arr
   189   end;
   190     
   191  (*String contains multiple lines.
   192   A list consisting of the first number in each line is returned. *)
   193 fun get_linenums proofstr = 
   194   let val numerics = String.tokens (not o Char.isDigit)
   195       fun firstno [] = NONE
   196         | firstno (x::xs) = Int.fromString x
   197       val lines = String.tokens (fn c => c = #"\n") proofstr
   198   in  List.mapPartial (firstno o numerics) lines  end
   199 
   200 fun get_axiom_names_e proofstr clause_arr  =
   201    get_axiom_names (get_linenums proofstr) clause_arr;
   202     
   203  (*String contains multiple lines. We want those of the form 
   204      "*********** [448, input] ***********".
   205   A list consisting of the first number in each line is returned. *)
   206 fun get_vamp_linenums proofstr = 
   207   let val toks = String.tokens (not o Char.isAlphaNum)
   208       fun inputno [n,"input"] = Int.fromString n
   209         | inputno _ = NONE
   210       val lines = String.tokens (fn c => c = #"\n") proofstr
   211   in  List.mapPartial (inputno o toks) lines  end
   212 
   213 fun get_axiom_names_vamp proofstr clause_arr  =
   214    get_axiom_names (get_vamp_linenums proofstr) clause_arr;
   215     
   216 
   217 (***********************************************)
   218 (* get axioms for reconstruction               *)
   219 (***********************************************)
   220 fun numclstr (vars, []) str = str
   221 |   numclstr ( vars, ((num, thm)::rest)) str =
   222       let val newstr = str^(string_of_int num)^" "^(string_of_thm thm)^" "
   223       in
   224         numclstr  (vars,rest) newstr
   225       end
   226 
   227 fun addvars c (a,b)  = (a,b,c)
   228 
   229 fun get_axioms_used proof_steps thms clause_arr  =
   230   let 
   231      val _=  (print_mode := (Library.gen_rems (op =) (! print_mode, ["xsymbols", "symbols"])))
   232      val axioms = (List.filter is_axiom) proof_steps
   233      val step_nums = get_step_nums axioms []
   234 
   235      val clauses = make_clauses thms    (*FIXME: must this be repeated??*)
   236      
   237      val vars = map thm_vars clauses
   238     
   239      val distvars = distinct (fold append vars [])
   240      val clause_terms = map prop_of clauses  
   241      val clause_frees = List.concat (map term_frees clause_terms)
   242 
   243      val frees = map lit_string_with_nums clause_frees;
   244 
   245      val distfrees = distinct frees
   246 
   247      val metas = map Meson.make_meta_clause clauses
   248      val ax_strs = map #3 axioms
   249 
   250      (* literals of -all- axioms, not just those used by spass *)
   251      val meta_strs = map ReconOrderClauses.get_meta_lits metas
   252     
   253      val metas_and_strs = ListPair.zip (metas,meta_strs)
   254      val _ = trace ("\nAxioms: " ^ onestr ax_strs)
   255      val _ = trace ("\nMeta_strs: " ^ onestr meta_strs)
   256 
   257      (* get list of axioms as thms with their variables *)
   258 
   259      val ax_metas = get_assoc_snds ax_strs metas_and_strs []
   260      val ax_vars = map thm_vars ax_metas
   261      val ax_with_vars = ListPair.zip (ax_metas,ax_vars)
   262 
   263      (* get list of extra axioms as thms with their variables *)
   264      val extra_metas = add_if_not_inlist metas ax_metas []
   265      val extra_vars = map thm_vars extra_metas
   266      val extra_with_vars = if (not (extra_metas = []) ) 
   267 			   then ListPair.zip (extra_metas,extra_vars)
   268 			   else []
   269   in
   270      (distfrees,distvars, extra_with_vars,ax_with_vars, ListPair.zip (step_nums,ax_metas))
   271   end;
   272                                             
   273 
   274 (*********************************************************************)
   275 (* Pass in spass string of proof and string version of isabelle goal *)
   276 (* Get out reconstruction steps as a string to be sent to Isabelle   *)
   277 (*********************************************************************)
   278 
   279 fun rules_to_string [] = "NONE"
   280   | rules_to_string xs = "[" ^ space_implode ", " xs ^ "]"
   281 
   282 
   283 (*The signal handler in watcher.ML must be able to read the output of this.*)
   284 fun prover_lemma_list_aux getax proofstr probfile toParent ppid clause_arr = 
   285  let val _ = trace
   286                ("\nGetting lemma names. proofstr is " ^ proofstr ^
   287                 "\nprobfile is " ^ probfile ^
   288                 "  num of clauses is " ^ string_of_int (Array.length clause_arr))
   289      val axiom_names = getax proofstr clause_arr
   290      val ax_str = rules_to_string axiom_names
   291     in 
   292 	 trace ("\nDone. Lemma list is " ^ ax_str);
   293          TextIO.output (toParent, "Success. Lemmas used in automatic proof: " ^
   294                   ax_str ^ "\n");
   295 	 TextIO.output (toParent, probfile ^ "\n");
   296 	 TextIO.flushOut toParent;
   297 	 Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2)
   298     end
   299     handle exn => (*FIXME: exn handler is too general!*)
   300      (trace ("\nprover_lemma_list_aux: In exception handler: " ^ 
   301              Toplevel.exn_message exn);
   302       TextIO.output (toParent, "Translation failed for the proof: " ^ 
   303                      String.toString proofstr ^ "\n");
   304       TextIO.output (toParent, probfile);
   305       TextIO.flushOut toParent;
   306       Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2));
   307 
   308 val e_lemma_list = prover_lemma_list_aux get_axiom_names_e;
   309 
   310 val vamp_lemma_list = prover_lemma_list_aux get_axiom_names_vamp;
   311 
   312 val spass_lemma_list = prover_lemma_list_aux get_axiom_names_spass;
   313 
   314 
   315 (**** Full proof reconstruction for SPASS (not really working) ****)
   316 
   317 fun spass_reconstruct proofstr probfile toParent ppid thms clause_arr = 
   318   let val _ = trace ("\nspass_reconstruct. Proofstr is "^proofstr)
   319       val tokens = #1(lex proofstr)
   320 
   321   (* parse spass proof into datatype *)
   322   (***********************************)
   323       val proof_steps = parse tokens
   324       val _ = trace "\nParsing finished"
   325     
   326   (************************************)
   327   (* recreate original subgoal as thm *)
   328   (************************************)
   329       (* get axioms as correctly numbered clauses w.r.t. the Spass proof *)
   330       (* need to get prems_of thm, then get right one of the prems, relating to whichever*)
   331       (* subgoal this is, and turn it into meta_clauses *)
   332       (* should prob add array and table here, so that we can get axioms*)
   333       (* produced from the clasimpset rather than the problem *)
   334       val (frees,vars,extra_with_vars ,ax_with_vars,numcls) = get_axioms_used proof_steps  thms clause_arr
   335       
   336       (*val numcls_string = numclstr ( vars, numcls) ""*)
   337       val _ = trace "\ngot axioms"
   338 	
   339   (************************************)
   340   (* translate proof                  *)
   341   (************************************)
   342       val _ = trace ("\nabout to translate proof, steps: "
   343                        ^ (init_proofsteps_to_string proof_steps ""))
   344       val (newthm,proof) = translate_proof numcls  proof_steps vars
   345       val _ = trace ("translated proof, steps: "^(init_proofsteps_to_string proof_steps ""))
   346   (***************************************************)
   347   (* transfer necessary steps as strings to Isabelle *)
   348   (***************************************************)
   349       (* turn the proof into a string *)
   350       val reconProofStr = proofs_to_string proof ""
   351       (* do the bit for the Isabelle ordered axioms at the top *)
   352       val ax_nums = map #1 numcls
   353       val ax_strs = map ReconOrderClauses.get_meta_lits_bracket (map #2 numcls)
   354       val numcls_strs = ListPair.zip (ax_nums,ax_strs)
   355       val num_cls_vars =  map (addvars vars) numcls_strs;
   356       val reconIsaAxStr = origAxs_to_string (ListPair.zip (ax_nums,ax_with_vars)) ""
   357       
   358       val extra_nums = if (not (extra_with_vars = [])) then (1 upto (length extra_with_vars))
   359                        else []
   360       val reconExtraAxStr = extraAxs_to_string ( ListPair.zip (extra_nums,extra_with_vars)) ""
   361       val frees_str = "["^(thmvars_to_string frees "")^"]"
   362       val reconstr = (frees_str^reconExtraAxStr^reconIsaAxStr^reconProofStr)
   363       val _ = trace ("\nReconstruction:\n" ^ reconstr)
   364   in 
   365        TextIO.output (toParent, reconstr^"\n");
   366        TextIO.output (toParent, probfile ^ "\n");
   367        TextIO.flushOut toParent;
   368        Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2);
   369        all_tac
   370   end
   371   handle exn => (*FIXME: exn handler is too general!*)
   372    (trace ("\nspass_reconstruct. In exception handler: " ^ Toplevel.exn_message exn);
   373     TextIO.output (toParent,"Translation failed for SPASS proof:"^
   374          String.toString proofstr ^"\n");
   375     TextIO.output (toParent, probfile ^ "\n");
   376     TextIO.flushOut toParent;
   377     Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2); all_tac)
   378 
   379 (**********************************************************************************)
   380 (* At other end, want to turn back into datatype so can apply reconstruct_proof.  *)
   381 (* This will be done by the signal handler                                        *)
   382 (**********************************************************************************)
   383 
   384 (* Parse in the string version of the proof steps for reconstruction *)
   385 (* Isar format: cl1 [BINARY 0 cl2 0];cl1 [PARAMOD 0 cl2 0]; cl1 [DEMOD 0 cl2];cl1 [FACTOR 1 2];*)
   386 
   387 
   388  val term_numstep =
   389         (number ++ (a (Other ",")) ++ number) >> (fn (a, (_, c)) => (a, c))
   390 
   391 val extraaxiomstep = (a (Word "ExtraAxiom"))++ (a (Other "(")) ++(a (Other ")"))
   392             >> (fn (_) => ExtraAxiom)
   393 
   394 
   395 
   396 val origaxiomstep = (a (Word "OrigAxiom"))++ (a (Other "(")) ++(a (Other ")"))
   397             >> (fn (_) => OrigAxiom)
   398 
   399 
   400  val axiomstep = (a (Word "Axiom"))++ (a (Other "(")) ++(a (Other ")"))
   401             >> (fn (_) => Axiom)
   402      
   403 
   404 
   405       
   406  val binarystep = (a (Word "Binary")) ++ (a (Other "(")) ++ (a (Other "(")) 
   407                    ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
   408                    ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
   409             >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Binary (c,e))
   410       
   411 
   412  val parastep = (a (Word "Para")) ++ (a (Other "(")) ++ (a (Other "(")) 
   413                    ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
   414                    ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
   415             >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Para(c, e))
   416       
   417  val mrrstep = (a (Word "MRR")) ++ (a (Other "(")) ++ (a (Other "(")) 
   418                    ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
   419                    ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
   420             >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => MRR(c, e))
   421       
   422 
   423  val factorstep = (a (Word "Factor")) ++ (a (Other "("))
   424                     ++ number ++ (a (Other ","))
   425                        ++ number ++ (a (Other ","))
   426                        ++ number ++  (a (Other ")"))
   427                    
   428             >> (fn (_, (_, (c, (_, (e,(_,(f,_))))))) =>  Factor (c,e,f))
   429 
   430 
   431 (*val rewritestep = (a (Word "Rewrite"))  ++ (a (Other "(")) ++ (a (Other "(")) 
   432                    ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
   433                    ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
   434             >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Rewrite (c,e))*)
   435 
   436 val obviousstep = (a (Word "Obvious")) ++ (a (Other "(")) 
   437                    ++ term_numstep  ++ (a (Other ")")) 
   438             >> (fn (_, (_, (c,_))) => Obvious (c))
   439 
   440  val methodstep = extraaxiomstep || origaxiomstep || axiomstep ||binarystep || factorstep|| parastep || mrrstep || (*rewritestep ||*) obviousstep
   441 
   442 
   443  val number_list_step =
   444         ( number ++ many ((a (Other ",") ++ number)>> #2))
   445         >> (fn (a,b) => (a::b))
   446         
   447  val numberlist_step = a (Other "[")  ++ a (Other "]")
   448                         >>(fn (_,_) => ([]:int list))
   449                        || a (Other "[") ++ number_list_step ++ a (Other "]")
   450                         >>(fn (_,(a,_)) => a)
   451                     
   452 
   453 
   454 (** change this to allow P (x U) *)
   455  fun arglist_step input = 
   456    ( word ++ many word >> (fn (a, b) => (a^" "^(space_implode " " b)))
   457     ||word >> (fn (a) => (a)))input
   458                 
   459 
   460 fun literal_step input = (word ++ a (Other "(") ++ arglist_step ++  a (Other ")")
   461                                           >>(fn (a, (b, (c,d))) => (a^" ("^(c)^")"))
   462                         || arglist_step >> (fn (a) => (a)))input
   463                            
   464 
   465 
   466 (* fun term_step input = (a (Other "~") ++ arglist_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b))
   467                      ||  arglist_step ++ a (Other "%")>> (fn (a,b) => a ))input
   468 *)
   469 
   470 
   471  fun term_step input = (a (Other "~") ++ literal_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b))
   472                      ||  literal_step ++ a (Other "%")>> (fn (a,b) => a ))input
   473 
   474 
   475          
   476 
   477  val term_list_step =
   478         (  term_step ++ many ( term_step))
   479         >> (fn (a,b) => (a::b))
   480         
   481  
   482 val term_lists_step = a (Other "[")  ++ a (Other "]")
   483                         >>(fn (_,_) => ([]:string list))
   484                        || a (Other "[") ++ term_list_step ++ a (Other "]")
   485                         >>(fn (_,(a,_)) => a)
   486                      
   487 
   488  val linestep = number ++ methodstep ++ term_lists_step ++ term_lists_step
   489                 >> (fn (a, (b, (c,d))) => (a,(b,c,d)))
   490     
   491  val lines_step = many linestep
   492 
   493  val alllines_step = (term_lists_step ++ lines_step ) ++ finished >> #1
   494     
   495  val parse_step = #1 o alllines_step
   496 
   497 
   498  (*
   499 val reconstr ="[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]%(EX x::'a::type. ALL y::'a::type. (P::'a::type => bool) x = P y) -->(EX x::'a::type. P x) = (ALL y::'a::type. P y)"
   500 *)
   501 
   502 (************************************************************)
   503 (* Construct an Isar style proof from a list of proof steps *)
   504 (************************************************************)
   505 (* want to assume all axioms, then do haves for the other clauses*)
   506 (* then show for the last step *)
   507 
   508 (* replace ~ by not here *)
   509 val change_nots = String.translate (fn c => if c = #"~" then "\\<not>" else str c);
   510 
   511 fun clstrs_to_string xs = space_implode "; " (map change_nots xs);
   512 
   513 fun thmvars_to_quantstring [] str = str
   514 |   thmvars_to_quantstring (x::[]) str =str^x^". "
   515 |   thmvars_to_quantstring (x::xs) str = thmvars_to_quantstring xs (str^(x^" "))
   516 
   517 
   518 fun clause_strs_to_isar clstrs [] =
   519       "\"\\<lbrakk>"^(clstrs_to_string clstrs)^"\\<rbrakk> \\<Longrightarrow> False\""
   520 |   clause_strs_to_isar clstrs thmvars =
   521       "\"\\<And>"^(thmvars_to_quantstring thmvars "")^
   522       "\\<lbrakk>"^(clstrs_to_string clstrs)^"\\<rbrakk> \\<Longrightarrow> False\""
   523 
   524 fun frees_to_isar_str clstrs = space_implode " " (map change_nots clstrs)
   525 
   526 
   527 (***********************************************************************)
   528 (* functions for producing assumptions for the Isabelle ordered axioms *)
   529 (***********************************************************************)
   530 (*val str = "[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]";       
   531 num, rule, clausestrs, vars*)
   532 
   533 
   534 (* assume the extra clauses - not used in Spass proof *)
   535 
   536 fun is_extraaxiom_step ( num:int,(ExtraAxiom, str, tstr)) = true
   537 |   is_extraaxiom_step (num, _) = false
   538 
   539 fun get_extraaxioms xs = List.filter (is_extraaxiom_step) ( xs)
   540 
   541 fun assume_isar_extraaxiom [] str  = str
   542 |   assume_isar_extraaxiom ((numb,(step, clstr, thmvars))::xs) str  = assume_isar_extraaxiom xs (str^"and cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstr thmvars)^"\n " )
   543 
   544 
   545 
   546 fun assume_isar_extraaxioms  [] = ""
   547 |assume_isar_extraaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n" 
   548                                          in
   549                                              assume_isar_extraaxiom xs str
   550                                          end
   551 
   552 (* assume the Isabelle ordered clauses *)
   553 
   554 fun is_origaxiom_step ( num:int,(OrigAxiom, str, tstr)) = true
   555 |   is_origaxiom_step (num, _) = false
   556 
   557 fun get_origaxioms xs = List.filter (is_origaxiom_step) ( xs)
   558 
   559 fun assume_isar_origaxiom [] str  = str
   560 |   assume_isar_origaxiom ((numb,(step, clstr, thmvars))::xs) str  = assume_isar_origaxiom xs (str^"and cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstr thmvars)^"\n " )
   561 
   562 
   563 
   564 fun assume_isar_origaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n" 
   565                                          in
   566                                              assume_isar_origaxiom xs str
   567                                          end
   568 
   569 
   570 
   571 fun is_axiom_step ( num:int,(Axiom, str, tstr)) = true
   572 |   is_axiom_step (num, _) = false
   573 
   574 fun get_axioms xs = List.filter  (is_axiom_step) ( xs)
   575 
   576 fun have_isar_axiomline (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n"
   577 
   578 fun  by_isar_axiomline (numb,(step, clstrs, thmstrs))="by (rule cl"^ (string_of_int numb)^"') \n"
   579 
   580 
   581 fun isar_axiomline (numb, (step, clstrs, thmstrs))  = (have_isar_axiomline (numb,(step,clstrs, thmstrs )))^( by_isar_axiomline(numb,(step,clstrs, thmstrs )) )
   582 
   583 
   584 fun isar_axiomlines [] str = str
   585 |   isar_axiomlines (x::xs) str = isar_axiomlines xs (str^(isar_axiomline x))
   586 
   587 
   588 fun have_isar_line (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n"
   589 (*FIX: ask Larry to add and mrr attribute *)
   590 
   591 fun by_isar_line ((Binary ((a,b), (c,d)))) = 
   592     "by(rule cl"^
   593 		(string_of_int a)^" [binary "^(string_of_int b)^" cl"^
   594 		(string_of_int c)^" "^(string_of_int d)^"])\n"
   595 |by_isar_line ((MRR ((a,b), (c,d)))) = 
   596     "by(rule cl"^
   597 		(string_of_int a)^" [binary "^(string_of_int b)^" cl"^
   598 		(string_of_int c)^" "^(string_of_int d)^"])\n"
   599 |   by_isar_line ( (Para ((a,b), (c,d)))) =
   600     "by (rule cl"^
   601 		(string_of_int a)^" [paramod "^(string_of_int b)^" cl"^
   602 		(string_of_int c)^" "^(string_of_int d)^"])\n"
   603 |   by_isar_line ((Factor ((a,b,c)))) = 
   604     "by (rule cl"^(string_of_int a)^" [factor "^(string_of_int b)^" "^
   605 		(string_of_int c)^" ])\n"
   606 (*|   by_isar_line ( (Rewrite ((a,b),(c,d)))) =
   607     "by (rule cl"^(string_of_int a)^" [demod "^(string_of_int b)^" "^
   608 		(string_of_int c)^" "^(string_of_int d)^" ])\n"*)
   609 |   by_isar_line ( (Obvious ((a,b)))) =
   610     "by (rule cl"^(string_of_int a)^" [obvious "^(string_of_int b)^" ])\n"
   611 
   612 fun isar_line (numb, (step, clstrs, thmstrs))  = (have_isar_line (numb,(step,clstrs, thmstrs )))^( by_isar_line step)
   613 
   614 
   615 fun isar_lines [] str = str
   616 |   isar_lines (x::xs) str = isar_lines xs (str^(isar_line x))
   617 
   618 fun last_isar_line (numb,( step, clstrs,thmstrs)) = "show \"False\"\n"^(by_isar_line step)
   619 
   620 
   621 fun to_isar_proof (frees, xs) =
   622     let val extraaxioms = get_extraaxioms xs
   623 	val extraax_num = length extraaxioms
   624 	val origaxioms_and_steps = Library.drop (extraax_num, xs)  
   625 	
   626 	val origaxioms = get_origaxioms origaxioms_and_steps
   627 	val origax_num = length origaxioms
   628 	val axioms_and_steps = Library.drop (origax_num + extraax_num, xs)  
   629 	val axioms = get_axioms axioms_and_steps
   630 	
   631 	val steps = Library.drop (origax_num, axioms_and_steps)
   632 	val firststeps = ReconOrderClauses.butlast steps
   633 	val laststep = List.last steps
   634 	
   635 	val isar_proof = 
   636 		("show \"[your goal]\"\n")^
   637 		("proof (rule ccontr,skolemize, make_clauses) \n")^
   638 		("fix "^(frees_to_isar_str frees)^"\n")^
   639 		(assume_isar_extraaxioms extraaxioms)^
   640 		(assume_isar_origaxioms origaxioms)^
   641 		(isar_axiomlines axioms "")^
   642 		(isar_lines firststeps "")^
   643 		(last_isar_line laststep)^
   644 		("qed")
   645 	val _ = trace ("\nto_isar_proof returns " ^ isar_proof)
   646     in
   647 	isar_proof
   648     end;
   649 
   650 (* get fix vars from axioms - all Frees *)
   651 (* check each clause for meta-vars and /\ over them at each step*)
   652 
   653 (*******************************************************)
   654 (* This assumes the thm list  "numcls" is still there  *)
   655 (* In reality, should probably label it with an        *)
   656 (* ID number identifying the subgoal.  This could      *)
   657 (* be passed over to the watcher, e.g.  numcls25       *)
   658 (*******************************************************)
   659 
   660 fun apply_res_thm str  = 
   661   let val tokens = #1 (lex str);
   662       val _ = trace ("\napply_res_thm. str is: "^str^"\n")	
   663       val (frees,recon_steps) = parse_step tokens 
   664   in 
   665       to_isar_proof (frees, recon_steps)
   666   end 
   667 
   668 end;