(* Title:  solve an example by interpreting a method's script

    Author: Walther Neuper 1999

    (c) copyright due to lincense terms.

 *)

 signature SOLVE_PHASE =

 sig

   datatype auto = CompleteCalc | CompleteCalcHead | CompleteModel | CompleteSubpbl 

   | CompleteToSubpbl | Step of int

   val autoord : auto -> int

   type tac'_

   val mk_tac'_ : Tactic.input -> string * Tactic.input

   val specsteps : string list

   val all_solve : auto -> Ctree.pos' list -> Ctree.state ->

     string * Ctree.pos' list * (Ctree.ctree * (int list * Ctree.pos_))

   val complete_solve :

      auto -> Ctree.pos' list -> Ctree.state -> string * Ctree.pos' list * Ctree.state

   val solve : string * Tactic.T -> Ctree.state -> string * Chead.calcstate'

   val inform : Chead.calcstate' -> string -> string * Chead.calcstate'

   val detailrls : Ctree.ctree -> Ctree.pos' -> string * Ctree.ctree * Ctree.pos'

 (* ---- for tests only: shifted from below to remove the Warning "unused" at fun.def. --------- *)

   val get_form : tac'_ -> Ctree.pos' -> Ctree.ctree -> Generate.mout

 (*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\* )

   (*NONE*)

 ( *\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)

 (*----- unused code, kept as hints to design ideas ---------------------------------------------*)

   (* NONE *)

 end

 (**)

 structure Solve(**): SOLVE_PHASE(**) =

 struct

 (**)

 open Ctree;

 type mstID = string;

 type tac'_ = mstID * Tactic.input; (*DG <-> ME*)

 fun mk_tac'_   m = case m of (* scr not cleaned -- will disappear eventually *)

   Tactic.Init_Proof (ppc, spec)    => ("Init_Proof", Tactic.Init_Proof (ppc, spec )) 

 | Tactic.Model_Problem             => ("Model_Problem", Tactic.Model_Problem)

 | Tactic.Refine_Tacitly pblID      => ("Refine_Tacitly", Tactic.Refine_Tacitly pblID)

 | Tactic.Refine_Problem pblID      => ("Refine_Problem", Tactic.Refine_Problem pblID)

 | Tactic.Add_Given cterm'          => ("Add_Given", Tactic.Add_Given cterm') 

 | Tactic.Del_Given cterm'          => ("Del_Given", Tactic.Del_Given cterm') 

 | Tactic.Add_Find cterm'           => ("Add_Find", Tactic.Add_Find cterm') 

 | Tactic.Del_Find cterm'           => ("Del_Find", Tactic.Del_Find cterm') 

 | Tactic.Add_Relation cterm'       => ("Add_Relation", Tactic.Add_Relation cterm') 

 | Tactic.Del_Relation cterm'       => ("Del_Relation", Tactic.Del_Relation cterm') 

 | Tactic.Specify_Theory domID	    => ("Specify_Theory", Tactic.Specify_Theory domID) 

 | Tactic.Specify_Problem pblID     => ("Specify_Problem", Tactic.Specify_Problem pblID)

 | Tactic.Specify_Method metID	    => ("Specify_Method", Tactic.Specify_Method metID) 

 | Tactic.Apply_Method metID	    => ("Apply_Method", Tactic.Apply_Method metID) 

 | Tactic.Check_Postcond pblID	    => ("Check_Postcond", Tactic.Check_Postcond pblID)

 | Tactic.Free_Solve                => ("Free_Solve", Tactic.Free_Solve)

 | Tactic.Rewrite_Inst (subs, thm') => ("Rewrite_Inst", Tactic.Rewrite_Inst (subs, thm')) 

 | Tactic.Rewrite thm'		    => ("Rewrite", Tactic.Rewrite thm') 

 | Tactic.Rewrite_Asm thm'	    => ("Rewrite_Asm", Tactic.Rewrite_Asm thm') 

 | Tactic.Rewrite_Set_Inst (subs, rls')

                => ("Rewrite_Set_Inst", Tactic.Rewrite_Set_Inst (subs, rls')) 

 | Tactic.Rewrite_Set rls'          => ("Rewrite_Set", Tactic.Rewrite_Set rls') 

 | Tactic.End_Ruleset		    => ("End_Ruleset", Tactic.End_Ruleset)

 | Tactic.End_Detail                => ("End_Detail", Tactic.End_Detail)

 | Tactic.Detail_Set rls'           => ("Detail_Set", Tactic.Detail_Set rls')

 | Tactic.Detail_Set_Inst (s, rls') => ("Detail_Set_Inst", Tactic.Detail_Set_Inst (s, rls'))

 | Tactic.Calculate op_             => ("Calculate", Tactic.Calculate op_)

 | Tactic.Substitute sube           => ("Substitute", Tactic.Substitute sube) 

 | Tactic.Apply_Assumption cts'	    => ("Apply_Assumption", Tactic.Apply_Assumption cts')

 | Tactic.Take cterm'               => ("Take", Tactic.Take cterm') 

 | Tactic.Take_Inst cterm'          => ("Take_Inst", Tactic.Take_Inst cterm') 

 | Tactic.Subproblem (domID, pblID) => ("Subproblem", Tactic.Subproblem (domID, pblID)) 

 (*

 | Tactic.Subproblem_Full(spec,cts')=> ("Subproblem_Full", Tactic.Subproblem_Full(spec,cts')) 

 *)

 | Tactic.End_Subproblem            => ("End_Subproblem", Tactic.End_Subproblem)

 | Tactic.CAScmd cterm'		    => ("CAScmd", Tactic.CAScmd cterm')

 | Tactic.Split_And                 => ("Split_And", Tactic.Split_And) 

 | Tactic.Conclude_And		    => ("Conclude_And", Tactic.Conclude_And) 

 | Tactic.Split_Or                  => ("Split_Or", Tactic.Split_Or) 

 | Tactic.Conclude_Or		    => ("Conclude_Or", Tactic.Conclude_Or) 

 | Tactic.Begin_Trans               => ("Begin_Trans", Tactic.Begin_Trans) 

 | Tactic.End_Trans		    => ("End_Trans", Tactic.End_Trans) 

 | Tactic.Begin_Sequ                => ("Begin_Sequ", Tactic.Begin_Sequ) 

 | Tactic.End_Sequ                  => ("End_Sequ", Tactic.Begin_Sequ) 

 | Tactic.Split_Intersect           => ("Split_Intersect", Tactic.Split_Intersect) 

 | Tactic.End_Intersect		    => ("End_Intersect", Tactic.End_Intersect) 

 | Tactic.Check_elementwise cterm'  => ("Check_elementwise", Tactic.Check_elementwise cterm')

 | Tactic.Or_to_List                => ("Or_to_List", Tactic.Or_to_List) 

 | Tactic.Collect_Trues	            => ("Collect_Results", Tactic.Collect_Trues) 

 | Tactic.Empty_Tac               => ("Empty_Tac", Tactic.Empty_Tac)

 | Tactic.Tac string              => ("Tac", Tactic.Tac string)

 | Tactic.End_Proof'                => ("End_Proof'", Tactic.End_Proof')

 | _ => error "mk_tac'_: uncovered case"; 

 type squ = ctree; (* TODO: safe etc. *)

 val specsteps = ["Init_Proof", "Refine_Tacitly", "Refine_Problem", "Model_Problem",

   "Add_Given", "Del_Given", "Add_Find", "Del_Find", "Add_Relation", "Del_Relation",

   "Specify_Theory", "Specify_Problem", "Specify_Method"];

 (*FIXME.WN050821 compare solve    ...   begin_end_prog:

         WN190811: solve ("Apply_Method",.. used by root-pbl + by locate_input_tactic !!!

 *)

 fun solve ("Apply_Method", m as Tactic.Apply_Method' (mI, _, _, ctxt)) (pt, (pos as (p, _))) =

     let

       val itms = case get_obj I pt p of

         PblObj {meth=itms, ...} => itms

       | _ => error "solve Apply_Method: uncovered case get_obj"

       val thy' = get_obj g_domID pt p;

       val thy = Celem.assoc_thy thy';

       val srls = Lucin.get_simplifier (pt, pos)

       val (is, env, ctxt, sc) = case Lucin.init_pstate srls ctxt itms mI of

         (is as Istate.Pstate {env, ...}, ctxt, sc) =>  (is, env, ctxt, sc)

       | _ => error "solve Apply_Method: uncovered case init_pstate"

       val ini = Lucin.init_form thy sc env;

       val p = lev_dn p;

     in 

       case ini of

 	      SOME t =>

           let val (pos,c,_, pt) = 

 		        Generate.generate1 thy (Tactic.Apply_Method' (mI, SOME t, is, ctxt))

 		        (is, ctxt) (lev_on p, Frm)(*implicit Take*) pt;

 	        in ("ok",([(Tactic.Apply_Method mI, Tactic.Apply_Method' (mI, SOME t, is, ctxt), 

 		        ((lev_on p, Frm), (is, ctxt)))], c, (pt, pos))) 

 	        end	      

 	    | NONE => (*execute first tac in the Program, compare solve m*)

 	        let

             val (m', (is', ctxt'), _) =

               LucinNEW.determine_next_tactic (thy', srls) (pt, (p, Res)) sc (is, ctxt);

 	        in 

             case LucinNEW.locate_input_tactic sc (pt, (p, Res)) is' ctxt' m' of

               LucinNEW.Safe_Step (istate, ctxt, tac) =>

                 let

                   val (p'', _, _,pt') =

                     Generate.generate1 (Celem.assoc_thy "Isac_Knowledge") tac

                     (* DEL.^^^^^ ContextC.insert_assumptions asms' ctxt 2nd, fst in Lucin.associate *)

                       (istate, ctxt) (lev_on p, Pbl) pt;

                 in

          	  	    ("ok", ([(Lucin.tac_2tac tac, tac, (p'', (istate, ctxt)))],

                     [(*ctree NOT cut*)], (pt', p'')))

                 end

 		        | _ => (* NotLocatable, but applicable_in from the beginning *)

 		            let

 		              val (p, ps, _, pt) =

 		                Generate.generate_hard (Celem.assoc_thy "Isac_Knowledge") m (p, Frm) pt;

 		            in 

 		              ("not-found-in-script",([(Lucin.tac_2tac m, m, (pos, (is, ctxt)))], ps, (pt, p))) 

 		            end

 	        end

     end

   | solve ("Free_Solve", Tactic.Free_Solve')  (pt, po as (p, _)) =

     let

       val p' = lev_dn_ (p, Res);

       val pt = update_metID pt (par_pblobj pt p) Celem.e_metID;

     in

       ("ok", ([(Tactic.Empty_Tac, Tactic.Empty_Tac_, (po, (Istate.Uistate, ContextC.e_ctxt)))], [], (pt,p')))

     end

   | solve ("Check_Postcond", Tactic.Check_Postcond' (pI, _)) (pt, (p, p_)) =

     let

       val pp = par_pblobj pt p

       val asm = 

         (case get_obj g_tac pt p of (*assumes Check_elementwise IMMEDIATELY BEFORE Check_Postcond*)

 		       Tactic.Check_elementwise _ => (*collects and instantiates asms*)

 		         (snd o (get_obj g_result pt)) p

 		     | _ => get_assumptions_ pt (p,p_))

 	      handle _ => [] (*WN.27.5.03 asms in subpbls not completely clear*)

       val metID = get_obj g_metID pt pp;

       val {srls = srls, scr = sc, ...} = Specify.get_met metID;

       val (loc, pst, ctxt) = case get_loc pt (p, p_) of

         loc as (Istate.Pstate pst, ctxt) => (loc, pst, ctxt)

       | _ => error "solve Check_Postcond: uncovered case get_loc"

       val thy' = get_obj g_domID pt pp;

       val thy = Celem.assoc_thy thy';

       val (_, _, (scval, _(*scsaf*))) = LucinNEW.determine_next_tactic (thy', srls) (pt, (p, p_)) sc loc;

       (*                 Telem.safe should go on to Check_Postcond'   vvvvv *)

     in 

       if pp = [] 

       then

 	      let 

           val is = Istate.Pstate (pst |> Istate.upd_act scval |> Istate.upd_appy Istate.Skip_)

 	        val tac_ = Tactic.Check_Postcond' (pI, (scval, asm))

 	          (*extend Tactic.Check_Postcond' (pI, (scval, asm), scsaf) ^^^^^ *)

 	        val (pos, ps, _, pt) = Generate.generate1 thy tac_ (is, ctxt) (pp, Res) pt;

 	      in ("ok", ([(Tactic.Check_Postcond pI, tac_, ((pp, Res), (is, ctxt)))], ps, (pt, pos))) end

       else

         let (*resume script of parpbl, transfer value of subpbl-script*)

           val ppp = par_pblobj pt (lev_up p);

 	        val thy' = get_obj g_domID pt ppp;

           val thy = Celem.assoc_thy thy';

           val (pst', ctxt') = case get_loc pt (pp, Frm) of

             (Istate.Pstate pst', ctxt') => (pst', ctxt')

           | _ => error "solve Check_Postcond resume script of parpbl: uncovered case get_loc"

 	        val ctxt'' = ContextC.from_subpbl_to_caller ctxt scval ctxt'

           val ((p, p_), ps, _, pt) = Generate.generate1 thy (Tactic.Check_Postcond' (pI, (scval, asm)))

 		        (Istate.Pstate (pst' |> Istate.upd_act scval |> Istate.upd_appy Istate.Skip_), ctxt'') (pp,Res) pt;

        in ("ok", ([(Tactic.Check_Postcond pI, Tactic.Check_Postcond'(pI, (scval, asm)),

   	      ((pp, Res), (Istate.Pstate (pst' |> Istate.upd_act scval |> Istate.upd_appy Istate.Skip_), ctxt'')))], ps, (pt, (p, p_)))) end

      end

   | solve (_, Tactic.End_Proof'') (pt, (p, p_)) =

     ("end-proof", ([(Tactic.Empty_Tac, Tactic.Empty_Tac_, (([], Res), (Istate.Uistate, ContextC.e_ctxt)))], [], (pt, (p, p_))))

   | solve (_, Tactic.End_Detail' t) (pt, (p, p_)) = (* could be done by generate1 ?!? *)

     let (*Rewrite_Set* done at Detail_Set*: this result is already in ctree*)

       val pr = (lev_up p, Res)

     in

       ("ok", ([(Tactic.End_Detail, Tactic.End_Detail' t , ((p, p_), get_loc pt (p, p_)))], [], (pt, pr)))

     end

     (* ======== general case as fall htrough ======== *)

   | solve (_, m) (pt, po as (p, p_)) =

     if Celem.e_metID = get_obj g_metID pt (par_pblobj pt p) (*29.8.02: could be detail, too !!*)

     then

       let

         val ctxt = get_ctxt pt po

         val ((p,p_),ps,_,pt) = Generate.generate1 (Celem.assoc_thy (get_obj g_domID pt (par_pblobj pt p))) 

 		      m (Istate.e_istate, ctxt) (p, p_) pt;

 	    in ("no-method-specified", (*Free_Solve*)

 	      ([(Tactic.Empty_Tac, Tactic.Empty_Tac_, ((p, p_), (Istate.Uistate, ctxt)))], ps, (pt, (p, p_))))

       end

     else

 	    let 

 	      val thy' = get_obj g_domID pt (par_pblobj pt p);

 	      val (_, is, sc) = Lucin.from_pblobj_or_detail' thy' (p,p_) pt;

 	    in

         case LucinNEW.locate_input_tactic sc (pt, po) (fst is) (snd is) m  of

           LucinNEW.Safe_Step (istate, ctxt, tac) =>

             let

                val p' = 

                  case p_ of Frm => p 

                  | Res => lev_on p

                  | _ => error ("solve: call by " ^ pos'2str (p, p_));

                val (p'', _, _,pt') =

                  Generate.generate1 (Celem.assoc_thy "Isac_Knowledge") tac

                  (* DEL.^^^^^ ContextC.insert_assumptions asms' ctxt 2nd, fst in Lucin.associate *)

                    (istate, ctxt) (p', p_) pt;

             in

        		    ("ok", ([(Lucin.tac_2tac tac, tac, (p'', (istate, ctxt)))],

                 [(*ctree NOT cut*)], (pt', p'')))

             end

 	      | LucinNEW.Unsafe_Step (istate, ctxt, tac) =>

             let

                val p' = 

                  case p_ of Frm => p 

                  | Res => lev_on p

                  | _ => error ("solve: call by " ^ pos'2str (p, p_));

                val (p'', _, _,pt') =

                  Generate.generate1 (Celem.assoc_thy "Isac_Knowledge") tac

                  (* DEL.^^^^^ ContextC.insert_assumptions asms' ctxt 2nd, fst in Lucin.associate *)

                    (istate, ctxt) (p', p_) pt;

             in

        		    ("ok", ([(Lucin.tac_2tac tac, tac, (p'', (istate, ctxt)))],

                 [(*ctree NOT cut*)], (pt', p'')))

             end

 	      | _ => (* NotLocatable *)

 	        let 

 	          val (p,ps, _, pt) = Generate.generate_hard (Celem.assoc_thy "Isac_Knowledge") m (p, p_) pt;

 	        in

 	          ("not-found-in-script", ([(Lucin.tac_2tac m, m, (po, is))], ps, (pt, p)))

           end

 	    end;

 (* tell how may steps of a calculation should be done by "fun autocalc"

    FIXXXME040624: does NOT match interfaces/ITOCalc.java

    TODO.WN0512 redesign togehter with autocalc ?                     *)

 datatype auto = 

   Step of int      (*1 do #int steps (may stop in model/specify)

                        IS VERY INEFFICIENT IN MODEL/SPECIY                    *)

 | CompleteModel    (*2 complete modeling

                        if model complete, finish specifying                   *)

 | CompleteCalcHead (*3 complete model/specify in one go                       *)

 | CompleteToSubpbl (*4 stop at the next begin of a subproblem,

                        if none, complete the actual (sub)problem              *)

 | CompleteSubpbl   (*5 complete the actual (sub)problem (incl.ev.subproblems) *)

 | CompleteCalc;    (*6 complete the calculation as a whole                    *)

 fun autoord (Step _ ) = 1

   | autoord CompleteModel = 2

   | autoord CompleteCalcHead = 3

   | autoord CompleteToSubpbl = 4

   | autoord CompleteSubpbl = 5

   | autoord CompleteCalc = 6;

 fun complete_solve auto c (ptp as (_, p as (_, p_))) =

     if p = ([], Res)

     then ("end-of-calculation", [], ptp)

     else

       if member op = [Pbl,Met] p_

       then

         let

           val ptp = Chead.all_modspec ptp

 	        val (_, c', ptp) = all_solve auto c ptp

 	      in complete_solve auto (c @ c') ptp end

       else

         case LucinNEW.do_solve_step ptp of

 	        ((Tactic.Subproblem _, _, _) :: _, c', ptp') =>

 	          if autoord auto < 5

             then ("ok", c @ c', ptp)

 	          else

               let

                 val ptp = Chead.all_modspec ptp'

 	             val (_, c'', ptp) = all_solve auto (c @ c') ptp

 	           in complete_solve auto (c @ c'@ c'') ptp end

 	      | ((Tactic.Check_Postcond _, _, _) :: _, c', ptp' as (_, p')) =>

 	        if autoord auto < 6 orelse p' = ([], Res)

           then ("ok", c @ c', ptp')

 	        else complete_solve auto (c @ c') ptp'

 	      | ((Tactic.End_Detail, _, _) :: _, c', ptp') => 

 	        if autoord auto < 6

           then ("ok", c @ c', ptp')

 	        else complete_solve auto (c @ c') ptp'

 	      | (_, c', ptp') => complete_solve auto (c @ c') ptp'

 and all_solve auto c (ptp as (pt, pos as (p,_)): ctree * pos') = 

     let

       val (_, _, mI) = get_obj g_spec pt p

       val ctxt = get_ctxt pt pos

       val (_, c', ptp) = LucinNEW.begin_end_prog (Tactic.Apply_Method' (mI, NONE, Istate.e_istate, ctxt)) (Istate.e_istate, ctxt) ptp

     in

       complete_solve auto (c @ c') ptp

     end;

 (* aux.fun for detailrls with Rrls, reverse rewriting *)

 fun rul_terms_2nds _ nds _ [] = nds

   | rul_terms_2nds thy nds t ((rule, res as (t', _)) :: rts) =

     (append_atomic [] (Istate.e_istate, ContextC.e_ctxt) t (Tactic.rule2tac thy [] rule) res Complete EmptyPtree) ::

       (rul_terms_2nds thy nds t' rts);

 (* detail steps done internally by Rewrite_Set* into ctree by use of a script *)

 fun detailrls pt (pos as (p, _)) = 

   let

     val t = get_obj g_form pt p

 	  val tac = get_obj g_tac pt p

 	  val rls = (assoc_rls o Tactic.rls_of) tac

     val ctxt = get_ctxt pt pos

   in

     case rls of

 	    Rule.Rrls {scr = Rule.Rfuns {init_state, ...}, ...} => 

 	    let

         val (_, _, _, rul_terms) = init_state t

 	      val newnds = rul_terms_2nds (Proof_Context.theory_of ctxt) [] t rul_terms

 	      val pt''' = ins_chn newnds pt p 

 	    in ("detailrls", pt''', (p @ [length newnds], Res)) end

 	  | _ =>

 	    let

         val is = Generate.init_istate tac t

 	      (*TODO.WN060602 Pstate (["(t_, Problem (Isac,[equation,univar]))"]

 			    is wrong for simpl, but working ?!? *)

 	      val tac_ = Tactic.Apply_Method' (Celem.e_metID(*WN0402: see generate1 !?!*), SOME t, is, ctxt)

 	      val pos' = ((lev_on o lev_dn) p, Frm)

 	      val thy = Celem.assoc_thy "Isac_Knowledge"

 	      val (_, _, _, pt') = Generate.generate1 thy tac_ (is, ctxt) pos' pt (* implicit Take *)

 	      val (_,_, (pt'', _)) = complete_solve CompleteSubpbl [] (pt', pos')

 	      val newnds = children (get_nd pt'' p)

 	      val pt''' = ins_chn newnds pt p (*complete_solve cuts branches after*)

 	    in ("detailrls", pt''', (p @ [length newnds], Res)) end

   end;

 fun get_form (mI, m) (p,p_) pt = 

   case Applicable.applicable_in (p, p_) pt m of

     Chead.Notappl e => Generate.Error' e

   | Chead.Appl m => 

       if member op = specsteps mI

       then

         let val (_, _, f, _, _, _) = Chead.specify m (p, p_) [] pt

         in f end

       else Generate.EmptyMout;

 fun inform (next_cs as (_, _, (pt, pos as (p, _))): Chead.calcstate') istr =

   let

     val ctxt = get_ctxt pt pos (*see TODO.thy*)

   in

     case TermC.parse (Celem.assoc_thy "Isac_Knowledge") istr of

       NONE => ("syntax error in '" ^ istr ^ "'", Chead.e_calcstate' (*TODO: previous cs'*))

     | SOME f_in =>

       let

     	  val f_in = Thm.term_of f_in

         val pos_pred = lev_back(*'*) pos

     	  val f_pred = Ctree.get_curr_formula (pt, pos_pred);

     	  val f_succ = Ctree.get_curr_formula (pt, pos);

       in

         if f_succ = f_in

         then ("same-formula", next_cs) (* ctree not cut with replaceFormula *)

         else

           case Inform.cas_input f_in of

             SOME (pt, _) => ("ok",([], [], (pt, (p, Ctree.Met))))

 			    | NONE => (*/-------------------------------------- NEW fun locate_input_formula------*)

             let

               val (_, _, metID) = get_obj g_spec pt (par_pblobj pt p)

               val {scr = prog, ...} = Specify.get_met metID

               val istate = get_istate pt pos

               val ctxt = get_ctxt pt pos

             in

               case LucinNEW.locate_input_formula prog (pt, pos) istate ctxt f_in of

                 LucinNEW.Step (cstate, _(*istate*), _(*ctxt*)) =>

                 ("ok" , ([], [], cstate (* already contains istate, ctxt *)))

               | LucinNEW.Not_Derivable calcstate' =>

                 let

             		  val pp = Ctree.par_pblobj pt p

             		  val (errpats, nrls, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of

               		    {errpats, nrls, scr = Rule.Prog prog, ...} => (errpats, nrls, prog)

               		  | _ => error "inform: uncovered case of get_met"

             		  val {env, ...} = Ctree.get_istate pt pos |> Istate.the_pstate

             		in

             		  case Inform.check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) of

             		    SOME errpatID => ("error pattern #" ^ errpatID ^ "#", calcstate')

             		  | NONE => ("no derivation found", calcstate')

                 end

             end

       end

   end

 end