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

    Author: Walther Neuper 1999

    (c) copyright due to lincense terms.

 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

         10        20        30        40        50        60        70        80         90      100

 *)

 fun safe (ScrState (_,_,_,_,s,_)) = s

   | safe (RrlsState _) = Safe;

 type mstID = string;

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

 val e_tac'_ = ("Empty_Tac", Empty_Tac):tac'_;

 fun mk_tac'_   m = case m of

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

 | Model_Problem             => ("Model_Problem", Model_Problem)

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

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

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

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

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

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

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

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

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

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

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

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

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

 | Free_Solve                => ("Free_Solve",Free_Solve)

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

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

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

 | Rewrite_Set_Inst (subs, rls')

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

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

 | End_Ruleset		    => ("End_Ruleset", End_Ruleset)

 | End_Detail                => ("End_Detail", End_Detail)

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

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

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

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

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

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

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

 | Group (con, ints) 	    => ("Group", Group (con, ints)) 

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

 (*

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

 *)

 | End_Subproblem            => ("End_Subproblem",End_Subproblem)

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

 | Split_And                 => ("Split_And", Split_And) 

 | Conclude_And		    => ("Conclude_And", Conclude_And) 

 | Split_Or                  => ("Split_Or", Split_Or) 

 | Conclude_Or		    => ("Conclude_Or", Conclude_Or) 

 | Begin_Trans               => ("Begin_Trans", Begin_Trans) 

 | End_Trans		    => ("End_Trans", End_Trans) 

 | Begin_Sequ                => ("Begin_Sequ", Begin_Sequ) 

 | End_Sequ                  => ("End_Sequ", Begin_Sequ) 

 | Split_Intersect           => ("Split_Intersect", Split_Intersect) 

 | End_Intersect		    => ("End_Intersect", End_Intersect) 

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

 | Or_to_List                => ("Or_to_List", Or_to_List) 

 | Collect_Trues	            => ("Collect_Results", Collect_Trues) 

 | Empty_Tac               => ("Empty_Tac",Empty_Tac)

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

 | User                      => ("User",User)

 | End_Proof'                => ("End_Proof'",End_Proof'); 

 (*Detail*)

 val empty_tac'_ = (mk_tac'_ Empty_Tac):tac'_;

 fun mk_tac ((_,m):tac'_) = m; 

 fun mk_mstID ((mI,_):tac'_) = mI;

 fun tac'_2str ((ID,ms):tac'_) = ID ^ (tac2str ms);

 (* TODO: tac2str, tac'_2str NOT tested *)

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

 (*13.9.02--------------

 type ctr = (loc * pos) list;

 val ops = [("PLUS","Groups.plus_class.plus"),("MINUS","Groups.minus_class.minus"),("TIMES","Groups.times_class.times"),

 	   ("cancel","cancel"),("pow","pow"),("sqrt","sqrt")];

 ML {* 

 @{term "PLUS"};   (*Free ("PLUS", "'a") : term*)

 @{term "plus"};   (*Const ("Groups.plus_class.plus", "'a => 'a => 'a")*)

 @{term "MINUS"};  (*Free ("MINUS", "'a")*)

 @{term "minus"};  (*Const ("Groups.minus_class.minus", "'a => 'a => 'a")*)

 @{term "TIMES"};  (*Free ("TIMES", "'a")*)

 @{term "times"};  (*Const ("Groups.times_class.times", "'a => 'a => 'a")*)

 @{term "CANCEL"}; (*Free ("CANCEL", "'a")*)

 @{term "cancel"}; (*Free ("cancel", "'a")*)

 @{term "POWER"};  (*Free ("POWER", "'a")*)

 @{term "pow"};    (*Free ("pow", "'a")*)

 @{term "SQRT"};   (*Free ("SQRT", "'a")*)

 @{term "sqrt"};   (*Const ("NthRoot.sqrt", "RealDef.real => RealDef.real")*)

 *}

 fun op_intern op_ =

   case assoc (ops, op_) of

     SOME op' => op' | NONE => error ("op_intern: no op= "^op_);

 -----------------------*)

 (* use"ME/solve.sml";

    use"solve.sml";

 val ttt = (term_of o the o (parse thy))"Substitute [(bdv,x)] g";

 val ttt = (term_of o the o (parse thy))"Rewrite thmid True g";

   Const ("Script.Rewrite'_Inst",_) $ sub $ Free (thm',_) $ Const (pa,_) $ f'

    *)

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

 		 "Model_Problem",(*"Match_Problem",*)

 		 "Add_Given","Del_Given","Add_Find","Del_Find",

 		 "Add_Relation","Del_Relation",

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

 "-----------------------------------------------------------------------";

 fun step2taci ((tac_, _, pt, p, _):step) = (*FIXXME.040312: redesign step*)

     (tac_2tac tac_, tac_, (p, get_loc pt p)):taci;

 (*FIXME.WN050821 compare solve ... nxt_solv*)

 (* val ("Apply_Method",Apply_Method' (mI,_))=(mI,m);

    val (("Apply_Method",Apply_Method' (mI,_,_)),pt, pos as (p,_))=(m,pt, pos);

    *)

 fun solve ("Apply_Method", m as Apply_Method' (mI, _, _, _)) (pt:ptree, (pos as (p,_))) =

       let val {srls, ...} = get_met mI;

         val PblObj {meth=itms, ...} = get_obj I pt p;

         val thy' = get_obj g_domID pt p;

         val thy = assoc_thy thy';

         val (is as ScrState (env,_,_,_,_,_), ctxt, sc) = init_scrstate thy itms mI;

         val ini = init_form thy sc env;

         val p = lev_dn p;

       in 

         case ini of

 	        SOME t =>

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

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

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

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

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

 	          end	      

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

 	          let

               val (m', (is', ctxt'), _) = next_tac (thy', srls) (pt, (p, Res)) sc (is, ctxt);

 	            val d = e_rls (*FIXME: get simplifier from domID*);

 	          in 

 	            case locate_gen (thy',srls) m' (pt,(p, Res))(sc,d) (is', ctxt') of 

 		            Steps (is'', ss as (m'',f',pt',p',c')::_) =>

 		              ("ok", (map step2taci ss, c', (pt',p')))

 		          | NotLocatable =>  

 		              let val (p,ps,f,pt) = 

 			              generate_hard (assoc_thy "Isac") m (p,Frm) pt;

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

 	          end

       end

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

       let (*val _=tracing"###solve Free_Solve";*)

         val p' = lev_dn_ (p,Res);

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

       in ("ok", ([(Empty_Tac, Empty_Tac_, (po, (Uistate, e_ctxt)))], [], (pt,p')))

       end

   | solve ("Check_Postcond",Check_Postcond' (pI,_)) (pt,(pos as (p,p_))) =

       let (*val _=tracing"###solve Check_Postcond";*)

         val pp = par_pblobj pt p

         val asm = 

           (case get_obj g_tac pt p of

 		         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,...} = get_met metID;

         val loc as (ScrState (E,l,a,_,_,b), ctxt) = get_loc pt (p,p_); 

         val thy' = get_obj g_domID pt pp;

         val thy = assoc_thy thy';

         val (_,_,(scval,scsaf)) = next_tac (thy',srls) (pt,(p,p_)) sc loc;

       in 

         if pp = [] 

         then

 	        let 

             val is = ScrState (E,l,a,scval,scsaf,b)

 	          val tac_ = Check_Postcond'(pI,(scval, map term2str asm))

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

 	        in ("ok", ([(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 = assoc_thy thy';

 	          val metID = get_obj g_metID pt ppp;

             val sc = (#scr o get_met) metID;

             val (ScrState (E,l,a,_,_,b), ctxt') = get_loc pt (pp(*!/p/*),Frm); 

 	          val ctxt'' = transfer_from_subproblem ctxt ctxt'

             val ((p,p_),ps,f,pt) = 

 	            generate1 thy (Check_Postcond' (pI, (scval, map term2str asm)))

 		            (ScrState (E,l,a,scval,scsaf,b), ctxt'') (pp,Res) pt;

        in ("ok", ([(Check_Postcond pI, Check_Postcond'(pI,(scval, map term2str asm)),

 	         ((pp,Res), (ScrState (E,l,a,scval,scsaf,b), ctxt'')))],ps,(pt,(p,p_))))

 	     end

      end

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

       ("end-proof",

        ([(Empty_Tac,Empty_Tac_,(([],Res),(Uistate, e_ctxt)))],[],(pt,(p,p_))))

 (*-----------vvvvvvvvvvv could be done by generate1 ?!?*)

   | solve (_,End_Detail' t) (pt, (p,p_)) =

       let

         val pr as (p',_) = (lev_up p, Res)

 	      val pp = par_pblobj pt p

 	      val r = (fst o (get_obj g_result pt)) p' 

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

 	      val thy' = get_obj g_domID pt pp

 	      val (srls, is, sc) = from_pblobj' thy' pr pt

 	      val (tac_,is',_) = next_tac (thy',srls) (pt,pr) sc is

       in ("ok", ([(End_Detail, End_Detail' t , 

 	      ((p,p_), get_loc pt (p,p_)))], [], (pt,pr)))

       end

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

       if 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,f,pt) = 

 		        generate1 (assoc_thy (get_obj g_domID pt (par_pblobj pt p))) 

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

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

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

         end

       else

 	      let 

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

 	        val (srls, is, sc) = from_pblobj_or_detail' thy' (p,p_) pt;

 		      val d = e_rls; (*FIXME.WN0108: canon.simplifier for domain is missing: generate from domID?*)

 	      in

           case locate_gen (thy',srls) m  (pt,(p,p_)) (sc,d) is of 

 	          Steps (is', ss as (m',f',pt',p',c')::_) =>

 	            let 

 	              (*27.8.02:next_tac may change to other branches in pt FIXXXXME*)

 	            in ("ok", (map step2taci ss, c', (pt',p'))) end

 	        | NotLocatable =>  

 	            let val (p,ps,f,pt) = 

 		            generate_hard (assoc_thy "Isac") m (p,p_) pt;

 	            in ("not-found-in-script",

 		            ([(tac_2tac m, m, (po,is))], ps, (pt,p)))

               end

 	      end;

 (*FIXME.WN050821 compare fun solve ... fun nxt_solv*)

 (* nxt_solv (Apply_Method'     vvv FIXME: get args in applicable_in *)

 fun nxt_solv (Apply_Method' (mI,_,_,_)) _ (pt:ptree, pos as (p,_)) =

       let

         val {srls,ppc,...} = get_met mI;

         val PblObj{meth=itms,origin=(oris,_,_),probl, ...} = get_obj I pt p;

         val itms = if itms <> [] then itms else complete_metitms oris probl [] ppc

         val thy' = get_obj g_domID pt p;

         val thy = assoc_thy thy';

         val (is as ScrState (env,_,_,_,_,_), ctxt, scr) = init_scrstate thy itms mI;

         val ini = init_form thy scr env;

       in 

         case ini of

           SOME t =>

             let

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

 	            val tac_ = Apply_Method' (mI, SOME t, is, ctxt);

 	            val (pos,c,_,pt) = (*implicit Take*)

 	              generate1 thy tac_ (is, ctxt) pos pt

             in ([(Apply_Method mI, tac_, (pos, (is, ctxt)))], c, (pt, pos)):calcstate' end

         | NONE =>

             let

               val pt = update_env pt (fst pos) (SOME (is, ctxt))

 	            val (tacis, c, ptp) = nxt_solve_ (pt, pos)

             in (tacis @ 

 	              [(Apply_Method mI, Apply_Method' (mI, NONE, e_istate, ctxt), (pos, (is, ctxt)))],

 	             c, ptp)

             end

       end

     (*TODO.WN050913 remove unnecessary code below*)

   | nxt_solv (Check_Postcond' (pI,_)) _ (pt, pos as (p,p_))  =

       let

         val pp = par_pblobj pt p

         val asm =

           (case get_obj g_tac pt p of

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

 		           (snd o (get_obj g_result pt)) p

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

 	        handle _ => [] (*FIXME.WN030527 asms in subpbls not completely clear*)

         val metID = get_obj g_metID pt pp;

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

         val loc as (ScrState (E,l,a,_,_,b), ctxt) = get_loc pt (p,p_); 

         val thy' = get_obj g_domID pt pp;

         val thy = assoc_thy thy';

         val (_,_,(scval,scsaf)) = next_tac (thy',srls) (pt,(p,p_)) sc loc;

       in

         if pp = []

         then 

 	        let

             val is = ScrState (E,l,a,scval,scsaf,b)

 	          val tac_ = Check_Postcond'(pI,(scval, map term2str asm))

 	          val ((p,p_),ps,f,pt) = 

 		          generate1 thy tac_ (is, ctxt) (pp,Res) pt;

 	        in ([(Check_Postcond pI, tac_, ((pp,Res), (is, ctxt)))],ps,(pt, (p,p_))) 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 = assoc_thy thy';

 	          val metID = get_obj g_metID pt ppp;

 	          val {scr,...} = get_met metID;

             val (ScrState (E,l,a,_,_,b), ctxt') = get_loc pt (pp(*!/p/*),Frm)

 	          val ctxt'' = transfer_from_subproblem ctxt ctxt'

             val tac_ = Check_Postcond' (pI, (scval, map term2str asm))

 	          val is = ScrState (E,l,a,scval,scsaf,b)

             val ((p,p_),ps,f,pt) = generate1 thy tac_ (is, ctxt'') (pp, Res) pt;

           in ([(Check_Postcond pI, tac_, ((pp, Res), (is, ctxt'')))], ps, (pt, (p,p_))) end

       end

   | nxt_solv (End_Proof'') _ ptp = ([], [], ptp)

   | nxt_solv tac_ is (pt, pos as (p,p_)) =

       let

         val pos =

           case pos of

 		        (p, Met) => ((lev_on o lev_dn) p, Frm)(*begin script*)

 		      | (p, Res) => (lev_on p,Res) (*somewhere in script*)

 		      | _ => pos

 	      val (pos',c,_,pt) = generate1 (assoc_thy "Isac") tac_ is pos pt;

       in ([(tac_2tac tac_, tac_, (pos,is))], c, (pt, pos')) end

 (* find the next tac from the script, nxt_solv will update the ptree *)

 and nxt_solve_ (ptp as (pt, pos as (p,p_))) =

       if e_metID = get_obj g_metID pt (par_pblobj pt p)

       then ([], [], (pt,(p,p_))):calcstate'

       else 

         let 

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

 	        val (srls, is, sc) = from_pblobj_or_detail' thy' (p,p_) pt;

 	        val (tac_,is,(t,_)) = next_tac (thy',srls) (pt,pos) sc is;

 	        (*TODO here ^^^  return finished/helpless/ok !*)

 	      in case tac_ of

 		         End_Detail' _ => ([(End_Detail, End_Detail' (t,[(*FIXME.040215*)]), 

 				       (pos, is))], [], (pt, pos))

 	         | _ => nxt_solv tac_ is ptp end;

 (*.says how may steps of a calculation should be done by "fun autocalc".*)

 (*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 + start solving*)

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

 | 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;

 (* val (auto, c, (ptp as (_, p))) = (auto, (c@c'), ptp);

    *)

 fun complete_solve auto c (ptp as (_, p): ptree * pos') =

   if p = ([], Res)

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

   else

     case nxt_solve_ ptp of

 	    ((Subproblem _, tac_, (_, is))::_, c', ptp') =>

 	      if autoord auto < 5

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

 	      else

           let

             val ptp = all_modspec ptp';

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

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

     | ((Check_Postcond _, tac_, (_, is))::_, c', ptp' as (_, p')) =>

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

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

 	      else complete_solve auto (c @ c') ptp'

     | ((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,_)): ptree * pos') = 

    let

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

      val ctxt = get_ctxt pt pos

      val (_, c', ptp) = nxt_solv (Apply_Method' (mI, NONE, e_istate, ctxt))

 			 (e_istate, ctxt) ptp;

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

 fun complete_solve auto c (ptp as (_, p as (_,p_)): ptree * pos') =

   if p = ([], Res)

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

   else

     if member op = [Pbl,Met] p_

     then

       let

         val ptp = all_modspec ptp

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

 	    in complete_solve auto (c @ c') ptp end

     else

       case nxt_solve_ ptp of

 	      ((Subproblem _, tac_, (_, is))::_, c', ptp') =>

 	        if autoord auto < 5

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

 	        else

             let

               val ptp = all_modspec ptp'

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

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

 	    | ((Check_Postcond _, tac_, (_, is))::_, c', ptp' as (_, p')) =>

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

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

 	        else complete_solve auto (c @ c') ptp'

 	    | ((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,_)): ptree * pos') = 

   let

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

     val ctxt = get_ctxt pt pos

     val (_, c', ptp) = nxt_solv (Apply_Method' (mI, NONE, e_istate, ctxt))

 			(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 t [] = nds

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

     (append_atomic [] (e_istate, e_ctxt) t (rule2tac [] rule) res Complete EmptyPtree) ::

     (rul_terms_2nds nds t' rts);

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

 fun detailrls pt (pos as (p,p_):pos') = 

   let

     val t = get_obj g_form pt p

 	  val tac = get_obj g_tac pt p

 	  val rls = (assoc_rls o rls_of) tac

     val ctxt = get_ctxt pt pos

   in

     case rls of

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

 	      let

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

 	        val newnds = rul_terms_2nds [] t rul_terms

 	        val pt''' = ins_chn newnds pt p 

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

 	  | _ =>

 	      let

           val is = init_istate tac t

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

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

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

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

 	        val thy = assoc_thy "Isac"

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

 	        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):pos') end

   end;

 (* val(mI,m)=m;val ppp=p;(*!!!*)val(p,p_)=pos;val(_,pt,_)=ppp(*!!!*);

    get_form ((mI,m):tac'_) ((p,p_):pos') ppp;

    *)

 fun get_form ((mI,m):tac'_) ((p,p_):pos') pt = 

   case applicable_in (p,p_) pt m of

     Notappl e => Error' (Error_ e)

   | Appl m => 

       (* val Appl m=applicable_in (p,p_) pt m;

          *)

       if member op = specsteps mI

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

 	     in f end

       else let val (*_,_,f,_,_,_*)_ = solve (mI,m) (pt,(p,p_))

 	   in (*f*) EmptyMout end;