File recon_transfer_proof.ML (Isabelle2005: October 2005)

# File recon_transfer_proof.ML

    (*  ID:         $Id: recon_transfer_proof.ML,v 1.37 2005/09/29 10:45:16 paulson Exp $
        Author:     Claire Quigley
        Copyright   2004  University of Cambridge
    *)

    structure Recon_Transfer =
    struct

    open Recon_Parse

    infixr 8 ++; infixr 7 >>; infixr 6 ||;

    val trace_path = Path.basic "transfer_trace";

    fun trace s = if !Output.show_debug_msgs then File.append (File.tmp_path trace_path) s
                  else ();

    (* Versions that include type information *)

    (* FIXME rename to str_of_thm *)
    fun string_of_thm thm =
      setmp show_sorts true (Pretty.str_of o Display.pretty_thm) thm;

    (* check separate args in the watcher program for separating strings with a * or ; or something *)

    fun clause_strs_to_string [] str = str
    |   clause_strs_to_string (x::xs) str = clause_strs_to_string xs (str^x^"%")

    fun thmvars_to_string [] str = str
    |   thmvars_to_string (x::xs) str = thmvars_to_string xs (str^x^"%")

    fun proofstep_to_string Axiom = "Axiom()"
    |   proofstep_to_string  (Binary ((a,b), (c,d)))=
          "Binary(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"
    |   proofstep_to_string (Factor (a,b,c)) =
          "Factor("^(string_of_int a)^","^(string_of_int b)^","^(string_of_int c)^")"
    |   proofstep_to_string  (Para ((a,b), (c,d)))=
          "Para(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"
    |   proofstep_to_string  (MRR ((a,b), (c,d))) =
          "MRR(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"
    (*|   proofstep_to_string (Rewrite((a,b),(c,d))) =
          "Rewrite(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"*)

    fun proof_to_string (num,(step,clause_strs, thmvars)) =
     (string_of_int num)^(proofstep_to_string step)^
     "["^(clause_strs_to_string clause_strs "")^"]["^(thmvars_to_string thmvars "")^"]"

    fun proofs_to_string [] str = str
    |   proofs_to_string (x::xs) str = let val newstr = proof_to_string x
                                       in
                                           proofs_to_string xs (str^newstr)
                                       end

    fun init_proofstep_to_string (num, step, clause_strs) =
     (string_of_int num)^" "^(proofstep_to_string step)^" "^
     (clause_strs_to_string clause_strs "")^" "

    fun init_proofsteps_to_string [] str = str
    |   init_proofsteps_to_string (x::xs) str = let val newstr = init_proofstep_to_string x
                                       in
                                           init_proofsteps_to_string xs (str^newstr)
                                       end

    (*** get a string representing the Isabelle ordered axioms ***)

    fun origAx_to_string (num,(meta,thmvars)) =
        let val clause_strs = ReconOrderClauses.get_meta_lits_bracket meta
        in
           (string_of_int num)^"OrigAxiom()["^
           (clause_strs_to_string clause_strs "")^"]["^
           (thmvars_to_string thmvars "")^"]"
        end

    fun  origAxs_to_string [] str = str
    |   origAxs_to_string (x::xs) str = let val newstr = origAx_to_string x
                                       in
                                           origAxs_to_string xs (str^newstr)
                                       end

    (*** get a string representing the Isabelle ordered axioms not used in the spass proof***)

    fun extraAx_to_string (num, (meta,thmvars)) =
       let val clause_strs = ReconOrderClauses.get_meta_lits_bracket meta
       in
          (string_of_int num)^"ExtraAxiom()["^
          (clause_strs_to_string clause_strs "")^"]"^
          "["^(thmvars_to_string thmvars "")^"]"
       end;

    fun extraAxs_to_string [] str = str
    |   extraAxs_to_string (x::xs) str =
          let val newstr = extraAx_to_string x
          in
    	  extraAxs_to_string xs (str^newstr)
          end;

    fun is_axiom (_,Axiom,str) = true
    |   is_axiom (_,_,_) = false

    fun get_step_nums [] nums = nums
    |   get_step_nums (( num:int,Axiom, str)::xs) nums = get_step_nums xs (nums@[num])

    exception Noassoc;

    fun assoc_snd a [] = raise Noassoc
      | assoc_snd a ((x, y)::t) = if a = y then x else assoc_snd a t;

    (* change to be something using check_order  instead of a = y --> returns true if ASSERTION not raised in checkorder, false otherwise *)

    (*fun get_assoc_snds [] xs assocs= assocs
    |   get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_snd x ys))])
    *)
    (*FIX - should this have vars in it? *)
    fun there_out_of_order xs ys = (ReconOrderClauses.checkorder xs ys [] ([],[],[]); true)
                                   handle _ => false

    fun assoc_out_of_order a [] = raise Noassoc
    |   assoc_out_of_order a ((b,c)::t) = if there_out_of_order a c then b else assoc_out_of_order a t;

    fun get_assoc_snds [] xs assocs= assocs
    |   get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_out_of_order x ys))])

    fun add_if_not_inlist [] xs newlist = newlist
    |   add_if_not_inlist (y::ys) xs newlist = if (not (y mem xs)) then
                                          add_if_not_inlist ys xs (y::newlist)
                                            else add_if_not_inlist ys xs (newlist)

    (*Flattens a list of list of strings to one string*)
    fun onestr ls = String.concat (map String.concat ls);

    fun is_clasimp_ax clasimp_num n = n <= clasimp_num

    fun subone x = x - 1

    fun numstr [] = ""
    |   numstr (x::xs) = (string_of_int x)^"%"^(numstr xs)

    (* retrieve the axioms that were obtained from the clasimpset *)

    fun get_clasimp_cls (clause_arr: (ResClause.clause * thm) array) step_nums =
        let val clasimp_nums = List.filter (is_clasimp_ax (Array.length clause_arr - 1))
    	                   (map subone step_nums)
        in
    	map (fn x =>  Array.sub(clause_arr, x)) clasimp_nums
        end

    (*****************************************************)
    (* get names of clasimp axioms used                  *)
    (*****************************************************)

     fun get_axiom_names step_nums clause_arr =
       let
         (* not sure why this is necessary again, but seems to be *)
          val _ = (print_mode := (Library.gen_rems (op =) (! print_mode, ["xsymbols", "symbols"])))

         (***********************************************)
         (* here need to add the clauses from clause_arr*)
         (***********************************************)

          val clasimp_names_cls = get_clasimp_cls clause_arr step_nums
          val clasimp_names = map (ResClause.get_axiomName o #1) clasimp_names_cls
          val _ = (print_mode := (["xsymbols", "symbols"] @ ! print_mode))
       in
          clasimp_names
       end

    fun get_axiom_names_spass proofstr clause_arr =
      let (* parse spass proof into datatype *)
          val _ = trace ("\nStarted parsing:\n" ^ proofstr)
          val proof_steps = parse (#1(lex proofstr))
          val _ = trace "\nParsing finished!"
          (* get axioms as correctly numbered clauses w.r.t. the Spass proof *)
      in
        get_axiom_names (get_step_nums (List.filter is_axiom proof_steps) []) clause_arr
      end;

     (*String contains multiple lines.
      A list consisting of the first number in each line is returned. *)
    fun get_linenums proofstr =
      let val numerics = String.tokens (not o Char.isDigit)
          fun firstno [] = NONE
            | firstno (x::xs) = Int.fromString x
          val lines = String.tokens (fn c => c = #"\n") proofstr
      in  List.mapPartial (firstno o numerics) lines  end

    fun get_axiom_names_e proofstr clause_arr  =
       get_axiom_names (get_linenums proofstr) clause_arr;

     (*String contains multiple lines. We want those of the form
         "*********** [448, input] ***********".
      A list consisting of the first number in each line is returned. *)
    fun get_vamp_linenums proofstr =
      let val toks = String.tokens (not o Char.isAlphaNum)
          fun inputno [n,"input"] = Int.fromString n
            | inputno _ = NONE
          val lines = String.tokens (fn c => c = #"\n") proofstr
      in  List.mapPartial (inputno o toks) lines  end

    fun get_axiom_names_vamp proofstr clause_arr  =
       get_axiom_names (get_vamp_linenums proofstr) clause_arr;

    (***********************************************)
    (* get axioms for reconstruction               *)
    (***********************************************)
    fun numclstr (vars, []) str = str
    |   numclstr ( vars, ((num, thm)::rest)) str =
          let val newstr = str^(string_of_int num)^" "^(string_of_thm thm)^" "
          in
            numclstr  (vars,rest) newstr
          end

    fun addvars c (a,b)  = (a,b,c)

    fun get_axioms_used proof_steps thms clause_arr  =
      let
         val _=  (print_mode := (Library.gen_rems (op =) (! print_mode, ["xsymbols", "symbols"])))
         val axioms = (List.filter is_axiom) proof_steps
         val step_nums = get_step_nums axioms []

         val clauses = make_clauses thms    (*FIXME: must this be repeated??*)

         val vars = map thm_vars clauses

         val distvars = distinct (fold append vars [])
         val clause_terms = map prop_of clauses
         val clause_frees = List.concat (map term_frees clause_terms)

         val frees = map lit_string_with_nums clause_frees;

         val distfrees = distinct frees

         val metas = map Meson.make_meta_clause clauses
         val ax_strs = map #3 axioms

         (* literals of -all- axioms, not just those used by spass *)
         val meta_strs = map ReconOrderClauses.get_meta_lits metas

         val metas_and_strs = ListPair.zip (metas,meta_strs)
         val _ = trace ("\nAxioms: " ^ onestr ax_strs)
         val _ = trace ("\nMeta_strs: " ^ onestr meta_strs)

         (* get list of axioms as thms with their variables *)

         val ax_metas = get_assoc_snds ax_strs metas_and_strs []
         val ax_vars = map thm_vars ax_metas
         val ax_with_vars = ListPair.zip (ax_metas,ax_vars)

         (* get list of extra axioms as thms with their variables *)
         val extra_metas = add_if_not_inlist metas ax_metas []
         val extra_vars = map thm_vars extra_metas
         val extra_with_vars = if (not (extra_metas = []) )
    			   then ListPair.zip (extra_metas,extra_vars)
    			   else []
      in
         (distfrees,distvars, extra_with_vars,ax_with_vars, ListPair.zip (step_nums,ax_metas))
      end;

    (*********************************************************************)
    (* Pass in spass string of proof and string version of isabelle goal *)
    (* Get out reconstruction steps as a string to be sent to Isabelle   *)
    (*********************************************************************)

    fun rules_to_string [] = "NONE"
      | rules_to_string xs = "[" ^ space_implode ", " xs ^ "]"

    fun subst_for a b = String.translate (fn c => str (if c=a then b else c));

    val remove_linebreaks = subst_for #"\n" #"\t";
    val restore_linebreaks = subst_for #"\t" #"\n";

    fun prover_lemma_list_aux getax proofstr goalstring toParent ppid clause_arr =
     let val _ = trace
                   ("\nGetting lemma names. proofstr is " ^ proofstr ^
                    "\ngoalstr is " ^ goalstring ^
                    "\nnum of clauses is " ^ string_of_int (Array.length clause_arr))
         val axiom_names = getax proofstr clause_arr
         val ax_str = rules_to_string axiom_names
        in
    	 trace ("\nDone. Lemma list is " ^ ax_str);
             TextIO.output (toParent, "Success. Lemmas used in automatic proof: " ^
                      ax_str ^ "\n");
    	 TextIO.output (toParent, "goalstring: "^goalstring^"\n");
    	 TextIO.flushOut toParent;
    	 Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2)
        end
        handle exn => (*FIXME: exn handler is too general!*)
         (trace ("\nprover_lemma_list_aux: In exception handler: " ^
                 Toplevel.exn_message exn);
          TextIO.output (toParent, "Translation failed for the proof: " ^
                         remove_linebreaks proofstr ^ "\n");
          TextIO.output (toParent, remove_linebreaks goalstring ^ "\n");
          TextIO.flushOut toParent;
          Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2));

    val e_lemma_list = prover_lemma_list_aux get_axiom_names_e;

    val vamp_lemma_list = prover_lemma_list_aux get_axiom_names_vamp;

    val spass_lemma_list = prover_lemma_list_aux get_axiom_names_spass;

    (**** Full proof reconstruction for SPASS (not really working) ****)

    fun spass_reconstruct proofstr goalstring toParent ppid thms clause_arr =
      let val _ = trace ("\nspass_reconstruct. Proofstr is "^proofstr)
          val tokens = #1(lex proofstr)

      (* parse spass proof into datatype *)
      (***********************************)
          val proof_steps = parse tokens
          val _ = trace "\nParsing finished"

      (************************************)
      (* recreate original subgoal as thm *)
      (************************************)
          (* get axioms as correctly numbered clauses w.r.t. the Spass proof *)
          (* need to get prems_of thm, then get right one of the prems, relating to whichever*)
          (* subgoal this is, and turn it into meta_clauses *)
          (* should prob add array and table here, so that we can get axioms*)
          (* produced from the clasimpset rather than the problem *)
          val (frees,vars,extra_with_vars ,ax_with_vars,numcls) = get_axioms_used proof_steps  thms clause_arr

          (*val numcls_string = numclstr ( vars, numcls) ""*)
          val _ = trace "\ngot axioms"

      (************************************)
      (* translate proof                  *)
      (************************************)
          val _ = trace ("\nabout to translate proof, steps: "
                           ^ (init_proofsteps_to_string proof_steps ""))
          val (newthm,proof) = translate_proof numcls  proof_steps vars
          val _ = trace ("translated proof, steps: "^(init_proofsteps_to_string proof_steps ""))
      (***************************************************)
      (* transfer necessary steps as strings to Isabelle *)
      (***************************************************)
          (* turn the proof into a string *)
          val reconProofStr = proofs_to_string proof ""
          (* do the bit for the Isabelle ordered axioms at the top *)
          val ax_nums = map #1 numcls
          val ax_strs = map ReconOrderClauses.get_meta_lits_bracket (map #2 numcls)
          val numcls_strs = ListPair.zip (ax_nums,ax_strs)
          val num_cls_vars =  map (addvars vars) numcls_strs;
          val reconIsaAxStr = origAxs_to_string (ListPair.zip (ax_nums,ax_with_vars)) ""

          val extra_nums = if (not (extra_with_vars = [])) then (1 upto (length extra_with_vars))
                           else []
          val reconExtraAxStr = extraAxs_to_string ( ListPair.zip (extra_nums,extra_with_vars)) ""
          val frees_str = "["^(thmvars_to_string frees "")^"]"
          val reconstr = (frees_str^reconExtraAxStr^reconIsaAxStr^reconProofStr)
          val _ = trace ("\nReconstruction:\n" ^ reconstr)
      in
           TextIO.output (toParent, reconstr^"\n");
           TextIO.output (toParent, goalstring^"\n");
           TextIO.flushOut toParent;
           Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2);
           all_tac
      end
      handle exn => (*FIXME: exn handler is too general!*)
       (trace ("\nspass_reconstruct. In exception handler: " ^ Toplevel.exn_message exn);
        TextIO.output (toParent,"Translation failed for the proof:"^
             (remove_linebreaks proofstr) ^"\n");
        TextIO.output (toParent, goalstring^"\n");
        TextIO.flushOut toParent;
        Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2); all_tac)

    (**********************************************************************************)
    (* At other end, want to turn back into datatype so can apply reconstruct_proof.  *)
    (* This will be done by the signal handler                                        *)
    (**********************************************************************************)

    (* Parse in the string version of the proof steps for reconstruction *)
    (* Isar format: cl1 [BINARY 0 cl2 0];cl1 [PARAMOD 0 cl2 0]; cl1 [DEMOD 0 cl2];cl1 [FACTOR 1 2];*)

     val term_numstep =
            (number ++ (a (Other ",")) ++ number) >> (fn (a, (_, c)) => (a, c))

    val extraaxiomstep = (a (Word "ExtraAxiom"))++ (a (Other "(")) ++(a (Other ")"))
                >> (fn (_) => ExtraAxiom)

    val origaxiomstep = (a (Word "OrigAxiom"))++ (a (Other "(")) ++(a (Other ")"))
                >> (fn (_) => OrigAxiom)

     val axiomstep = (a (Word "Axiom"))++ (a (Other "(")) ++(a (Other ")"))
                >> (fn (_) => Axiom)

     val binarystep = (a (Word "Binary")) ++ (a (Other "(")) ++ (a (Other "("))
                       ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
                       ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
                >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Binary (c,e))

     val parastep = (a (Word "Para")) ++ (a (Other "(")) ++ (a (Other "("))
                       ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
                       ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
                >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Para(c, e))

     val mrrstep = (a (Word "MRR")) ++ (a (Other "(")) ++ (a (Other "("))
                       ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
                       ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
                >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => MRR(c, e))

     val factorstep = (a (Word "Factor")) ++ (a (Other "("))
                        ++ number ++ (a (Other ","))
                           ++ number ++ (a (Other ","))
                           ++ number ++  (a (Other ")"))

                >> (fn (_, (_, (c, (_, (e,(_,(f,_))))))) =>  Factor (c,e,f))

    (*val rewritestep = (a (Word "Rewrite"))  ++ (a (Other "(")) ++ (a (Other "("))
                       ++ term_numstep  ++ (a (Other ")")) ++ (a (Other ","))
                       ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")"))
                >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Rewrite (c,e))*)

    val obviousstep = (a (Word "Obvious")) ++ (a (Other "("))
                       ++ term_numstep  ++ (a (Other ")"))
                >> (fn (_, (_, (c,_))) => Obvious (c))

     val methodstep = extraaxiomstep || origaxiomstep || axiomstep ||binarystep || factorstep|| parastep || mrrstep || (*rewritestep ||*) obviousstep

     val number_list_step =
            ( number ++ many ((a (Other ",") ++ number)>> #2))
            >> (fn (a,b) => (a::b))

     val numberlist_step = a (Other "[")  ++ a (Other "]")
                            >>(fn (_,_) => ([]:int list))
                           || a (Other "[") ++ number_list_step ++ a (Other "]")
                            >>(fn (_,(a,_)) => a)

    (** change this to allow P (x U) *)
     fun arglist_step input =
       ( word ++ many word >> (fn (a, b) => (a^" "^(space_implode " " b)))
        ||word >> (fn (a) => (a)))input

    fun literal_step input = (word ++ a (Other "(") ++ arglist_step ++  a (Other ")")
                                              >>(fn (a, (b, (c,d))) => (a^" ("^(c)^")"))
                            || arglist_step >> (fn (a) => (a)))input

    (* fun term_step input = (a (Other "~") ++ arglist_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b))
                         ||  arglist_step ++ a (Other "%")>> (fn (a,b) => a ))input
    *)

     fun term_step input = (a (Other "~") ++ literal_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b))
                         ||  literal_step ++ a (Other "%")>> (fn (a,b) => a ))input

     val term_list_step =
            (  term_step ++ many ( term_step))
            >> (fn (a,b) => (a::b))

    val term_lists_step = a (Other "[")  ++ a (Other "]")
                            >>(fn (_,_) => ([]:string list))
                           || a (Other "[") ++ term_list_step ++ a (Other "]")
                            >>(fn (_,(a,_)) => a)

    fun anytoken_step input  = (word>> (fn (a) => a)  ) input
                           handle NOPARSE_WORD => (number>> (fn (a) => string_of_int a)  ) input
                          handle NOPARSE_NUMBER => (other_char >> (fn(a) => a)) input

    fun goalstring_step input= (anytoken_step ++ many (anytoken_step )
                      >> (fn (a,b) =>  (a^" "^(implode b)))) input

     val linestep = number ++ methodstep ++ term_lists_step ++ term_lists_step
                    >> (fn (a, (b, (c,d))) => (a,(b,c,d)))

     val lines_step = many linestep

     val alllines_step = (term_lists_step ++ lines_step ) ++ finished >> #1

     val parse_step = #1 o alllines_step

     (*
    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)"
    *)

    (************************************************************)
    (* Construct an Isar style proof from a list of proof steps *)
    (************************************************************)
    (* want to assume all axioms, then do haves for the other clauses*)
    (* then show for the last step *)

    (* replace ~ by not here *)
    val change_nots = String.translate (fn c => if c = #"~" then "¬" else str c);

    fun clstrs_to_string xs = space_implode "; " (map change_nots xs);

    fun thmvars_to_quantstring [] str = str
    |   thmvars_to_quantstring (x::[]) str =str^x^". "
    |   thmvars_to_quantstring (x::xs) str = thmvars_to_quantstring xs (str^(x^" "))

    fun clause_strs_to_isar clstrs [] =
          "\"[|"^(clstrs_to_string clstrs)^"|] ==> False\""
    |   clause_strs_to_isar clstrs thmvars =
          "\"!!"^(thmvars_to_quantstring thmvars "")^
          "[|"^(clstrs_to_string clstrs)^"|] ==> False\""

    fun frees_to_isar_str clstrs = space_implode " " (map change_nots clstrs)

    (***********************************************************************)
    (* functions for producing assumptions for the Isabelle ordered axioms *)
    (***********************************************************************)
    (*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))[][]";
    num, rule, clausestrs, vars*)

    (* assume the extra clauses - not used in Spass proof *)

    fun is_extraaxiom_step ( num:int,(ExtraAxiom, str, tstr)) = true
    |   is_extraaxiom_step (num, _) = false

    fun get_extraaxioms xs = List.filter (is_extraaxiom_step) ( xs)

    fun assume_isar_extraaxiom [] str  = str
    |   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 " )

    fun assume_isar_extraaxioms  [] = ""
    |assume_isar_extraaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n"
                                             in
                                                 assume_isar_extraaxiom xs str
                                             end

    (* assume the Isabelle ordered clauses *)

    fun is_origaxiom_step ( num:int,(OrigAxiom, str, tstr)) = true
    |   is_origaxiom_step (num, _) = false

    fun get_origaxioms xs = List.filter (is_origaxiom_step) ( xs)

    fun assume_isar_origaxiom [] str  = str
    |   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 " )

    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"
                                             in
                                                 assume_isar_origaxiom xs str
                                             end

    fun is_axiom_step ( num:int,(Axiom, str, tstr)) = true
    |   is_axiom_step (num, _) = false

    fun get_axioms xs = List.filter  (is_axiom_step) ( xs)

    fun have_isar_axiomline (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n"

    fun  by_isar_axiomline (numb,(step, clstrs, thmstrs))="by (rule cl"^ (string_of_int numb)^"') \n"

    fun isar_axiomline (numb, (step, clstrs, thmstrs))  = (have_isar_axiomline (numb,(step,clstrs, thmstrs )))^( by_isar_axiomline(numb,(step,clstrs, thmstrs )) )

    fun isar_axiomlines [] str = str
    |   isar_axiomlines (x::xs) str = isar_axiomlines xs (str^(isar_axiomline x))

    fun have_isar_line (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n"
    (*FIX: ask Larry to add and mrr attribute *)

    fun by_isar_line ((Binary ((a,b), (c,d)))) =
        "by(rule cl"^
    		(string_of_int a)^" [binary "^(string_of_int b)^" cl"^
    		(string_of_int c)^" "^(string_of_int d)^"])\n"
    |by_isar_line ((MRR ((a,b), (c,d)))) =
        "by(rule cl"^
    		(string_of_int a)^" [binary "^(string_of_int b)^" cl"^
    		(string_of_int c)^" "^(string_of_int d)^"])\n"
    |   by_isar_line ( (Para ((a,b), (c,d)))) =
        "by (rule cl"^
    		(string_of_int a)^" [paramod "^(string_of_int b)^" cl"^
    		(string_of_int c)^" "^(string_of_int d)^"])\n"
    |   by_isar_line ((Factor ((a,b,c)))) =
        "by (rule cl"^(string_of_int a)^" [factor "^(string_of_int b)^" "^
    		(string_of_int c)^" ])\n"
    (*|   by_isar_line ( (Rewrite ((a,b),(c,d)))) =
        "by (rule cl"^(string_of_int a)^" [demod "^(string_of_int b)^" "^
    		(string_of_int c)^" "^(string_of_int d)^" ])\n"*)
    |   by_isar_line ( (Obvious ((a,b)))) =
        "by (rule cl"^(string_of_int a)^" [obvious "^(string_of_int b)^" ])\n"

    fun isar_line (numb, (step, clstrs, thmstrs))  = (have_isar_line (numb,(step,clstrs, thmstrs )))^( by_isar_line step)

    fun isar_lines [] str = str
    |   isar_lines (x::xs) str = isar_lines xs (str^(isar_line x))

    fun last_isar_line (numb,( step, clstrs,thmstrs)) = "show \"False\"\n"^(by_isar_line step)

    fun to_isar_proof (frees, xs, goalstring) =
        let val extraaxioms = get_extraaxioms xs
    	val extraax_num = length extraaxioms
    	val origaxioms_and_steps = Library.drop (extraax_num, xs)

    	val origaxioms = get_origaxioms origaxioms_and_steps
    	val origax_num = length origaxioms
    	val axioms_and_steps = Library.drop (origax_num + extraax_num, xs)
    	val axioms = get_axioms axioms_and_steps

    	val steps = Library.drop (origax_num, axioms_and_steps)
    	val firststeps = ReconOrderClauses.butlast steps
    	val laststep = List.last steps
    	val goalstring = implode(ReconOrderClauses.butlast(explode goalstring))

    	val isar_proof =
    		("show \""^goalstring^"\"\n")^
    		("proof (rule ccontr,skolemize, make_clauses) \n")^
    		("fix "^(frees_to_isar_str frees)^"\n")^
    		(assume_isar_extraaxioms extraaxioms)^
    		(assume_isar_origaxioms origaxioms)^
    		(isar_axiomlines axioms "")^
    		(isar_lines firststeps "")^
    		(last_isar_line laststep)^
    		("qed")
    	val _ = trace ("\nto_isar_proof returns " ^ isar_proof)
        in
    	isar_proof
        end;

    (* get fix vars from axioms - all Frees *)
    (* check each clause for meta-vars and /\ over them at each step*)

    (*******************************************************)
    (* This assumes the thm list  "numcls" is still there  *)
    (* In reality, should probably label it with an        *)
    (* ID number identifying the subgoal.  This could      *)
    (* be passed over to the watcher, e.g.  numcls25       *)
    (*******************************************************)

    fun apply_res_thm str goalstring  =
      let val tokens = #1 (lex str);
          val _ = trace ("\napply_res_thm. str is: "^str^" goalstr is: "^goalstring^"\n")
          val (frees,recon_steps) = parse_step tokens
      in
          to_isar_proof (frees, recon_steps, goalstring)
      end

    end;