(* Title:  "Interpret/lucas-interpreter.sml"

   Author: Walther Neuper

   (c) due to copyright terms

*)

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

"table of contents -----------------------------------------------------------------------------";

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

"----------- Take as 1st stac in program -------------------------------------------------------";

"----------- re-build: fun locate_input_tactic -------------------------------------------------";

"----------- fun locate_input_tactic Helpless, but applicable ----------------------------------";

"----------- re-build: fun find_next_step, mini ------------------------------------------------";

"----------- re-build: fun locate_input_term ---------------------------------------------------";

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

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

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

"----------- Take as 1st stac in program -------------------------------------------------------";

"----------- Take as 1st stac in program -------------------------------------------------------";

"----------- Take as 1st stac in program -------------------------------------------------------";

"compare --- Apply_Method with initial Take by Step.do_next --- in test/../step-solve ----------";

val p = e_pos'; val c = []; 

val (p,_,f,nxt,_,pt) = 

    CalcTreeTEST 

        [(["functionTerm (x^^^2 + 1)", "integrateBy x", "antiDerivative FF"],

          ("Integrate", ["integrate","function"], ["diff","integration"]))];

val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = ("Tac ", ...) --> Add_Given...*)

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

case nxt of (Apply_Method ["diff", "integration"]) => ()

          | _ => error "integrate.sml -- me method [diff,integration] -- spec";

"----- step 8: returns nxt = Rewrite_Set_Inst ([\"(''bdv'', x)\"],\"integration\")";

"~~~~~ fun me, args:"; val (tac, (p:pos'), _, (pt:ctree)) = (nxt, p, c, pt);

"~~~~~ fun Step.by_tactic, args:"; val (tac, (ptp as (pt, p))) = (tac, (pt,p));

val Appl m = applicable_in p pt tac;

 (*if*) Tactic.for_specify' m; (*false*)

"~~~~~ fun loc_solve_ , args:"; val (m, (pt,pos)) = (m, ptp);

"~~~~~ fun Step_Solve.by_tactic , args:"; val (m as Apply_Method' (mI, _, _, ctxt), (pt, (pos as (p,_))))

  = (m, (pt, pos));

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

      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 = LItool.get_simplifier (pt, pos)

      val (is, env, ctxt, sc) = case LItool.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";

(*+*)pstate2str (the_pstate is) = "([\"\n(f_f, x ^^^ 2 + 1)\",\"\n(v_v, x)\"], [], empty, NONE, \n??.empty, ORundef, false, true)";

      val ini = LItool.implicit_take sc env;

      val p = lev_dn p;

      val NONE = (*case*) ini (*of*);

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

              LI.find_next_step sc (pt, (p, Res)) is ctxt;

(*+*)pstate2str (the_pstate is') = "([\"\n(f_f, x ^^^ 2 + 1)\",\"\n(v_v, x)\"], [R,L,R], empty, NONE, \nIntegral x ^^^ 2 + 1 D x, ORundef, false, false)";

  val Safe_Step (_, _, Take' _) = (*case*)

           locate_input_tactic sc (pt, (p, Res)) is' ctxt' m' (*of*);

"~~~~~ fun locate_input_tactic , args:"; val ((Prog prog), cstate, istate, ctxt, tac)

  = (sc, (pt, (p, Res)), is', ctxt', m');

    (*case*) scan_to_tactic1 (prog, (cstate, ctxt, tac)) istate (*of*);

"~~~~~ fun scan_to_tactic1 , args:"; val ((prog, (cctt as ((_, p), _, _))), (Istate.Pstate (ist as {path, ...})))

  = ((prog, (cstate, ctxt, tac)), istate);

    (*if*) path = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (*then*);

  val Accept_Tac1 (_, _, Take' _) =

       scan_dn1 cctt (ist |> set_path [R] |> set_or ORundef) (Program.body_of prog);

"~~~~~ fun scan_dn1 , args:"; val (xxx, ist, (Const ("HOL.Let", _) $ e $ (Abs (id, T, b))))

  = (cctt, (ist |> set_path [R] |> set_or ORundef), (Program.body_of prog));

(*+*) if UnparseC.term2str e = "Take (Integral f_f D v_v)" then () else error "scan_dn1 Integral changed";

    (*case*)

           scan_dn1 xxx (ist |> path_down [L, R]) e (*of*);

    (*======= end of scanning tacticals, a leaf =======*)

"~~~~~ fun scan_dn1 , args:"; val (((pt, p), ctxt, tac), (ist as {eval, or, ...}), t)

  = (xxx, (ist |> path_down [L, R]), e);

val (Program.Tac stac, a') = check_leaf "locate" ctxt eval (get_subst ist) t;

"----------- re-build: fun locate_input_tactic -------------------------------------------------";

"----------- re-build: fun locate_input_tactic -------------------------------------------------";

"----------- re-build: fun locate_input_tactic -------------------------------------------------";

val fmz = ["equality (x+1=(2::real))", "solveFor x","solutions L"];

val (dI',pI',mI') = ("Test", ["sqroot-test","univariate","equation","test"],

   ["Test","squ-equ-test-subpbl1"]);

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = (_, Apply_Method ["Test", "squ-equ-test-subpbl1"])*);

(*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = ("Rewrite_Set", Rewrite_Set "norm_equation")*)

(*//------------------ begin step into ------------------------------------------------------\\*)

(*[1], Res*)val (p'''''_''',_,f,nxt'''''_''',_,pt'''''_''') = me nxt p [] pt; (*nxt = Rewrite_Set "Test_simplify"*)

"~~~~~ fun me , args:"; val (tac, p, _(*NEW remove*), pt) = (nxt, p, [], pt);

    (** )val (***)xxxx(***) ( *("ok", (_, _, (pt, p))) =( **)  (*case*)

      Step.by_tactic tac (pt,p) (*of*);

"~~~~~ fun by_tactic , args:"; val (tac, (ptp as (pt, p))) = (tac, (pt,p));

      val Applicable.Appl m = (*case*) Applicable.applicable_in p pt tac (*of*);

      (*if*) Tactic.for_specify' m; (*false*)

    (** )val (***)xxxxx_x(***) ( *(msg, cs') =( **)

Step_Solve.by_tactic m ptp;

"~~~~~ fun by_tactic , args:"; val (m, (pt, po as (p, p_))) = (m, ptp);

(*+*)val (pt'''''_', (p'''''_', p_'''''_')) = (pt, (p, p_));

    (*if*) Celem.e_metID = get_obj g_metID pt (par_pblobj pt p); (*else*)

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

	      val (is, sc) = LItool.resume_prog thy' (p,p_) pt;

     locate_input_tactic sc (pt, po) (fst is) (snd is) m;

"~~~~~ fun locate_input_tactic , args:"; val (Prog prog, cstate, istate, ctxt, tac)

    = (sc, (pt, po), (fst is), (snd is), m);

      val srls = get_simplifier cstate;

 (** )val Accept_Tac1 ((is as (_,_,_,_,_,strong_ass), ctxt, ss as((tac', _, ctree, pos', _) :: _))) =( **)

  (*case*) scan_to_tactic1 (prog, (cstate, ctxt, tac)) istate (*of*);

"~~~~~ fun scan_to_tactic1 , args:"; val ((prog, (cctt as ((_, p), _, _))), (Istate.Pstate (ist as {path, ...})))

  = ((prog, (cstate, ctxt, tac)), istate);

    (*if*) path = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (*then*);

    (** )val xxxxx_xx = ( **)

           scan_dn1 cctt (ist |> set_path [R] |> set_or ORundef) (Program.body_of prog);

"~~~~~ fun scan_dn1 , args:"; val (xxx, ist, (Const ("HOL.Let", _) $ e $ (Abs (id, T, b))))

  = (cctt, (ist |> set_path [R] |> set_or ORundef), (Program.body_of prog));

  (*case*) scan_dn1 xxx (ist |> path_down [L, R]) e (*of*);

"~~~~~ fun scan_dn1 , args:"; val ((xxx as (cstate, _, _)), ist, (Const ("Tactical.Chain"(*1*), _) $ e1 $ e2 $ a))

  = (xxx, (ist |> path_down [L, R]), e);

  (*case*) scan_dn1 xxx (ist |> path_down_form ([L, L, R], a)) e1 (*of*);

"~~~~~ fun scan_dn1 , args:"; val (xxx, ist, (Const ("Tactical.Try"(*2*), _) $ e))

  = (xxx, (ist |> path_down_form ([L, L, R], a)), e1);

  (*case*) scan_dn1 xxx (ist |> path_down [R]) e (*of*);

    (*======= end of scanning tacticals, a leaf =======*)

"~~~~~ fun scan_dn1 , args:"; val (((pt, p), ctxt, tac), (ist as {env, eval, or, ...}), t)

  = (xxx, (ist |> path_down [R]), e);

    val (Program.Tac stac, a') =

      (*case*) check_leaf "locate" ctxt eval (get_subst ist) t (*of*);

    val LItool.Associated (m, v', ctxt) =

      (*case*) associate pt ctxt (m, stac) (*of*);

       Accept_Tac1 (ist |> set_subst_true  (a', v'), ctxt, m)  (*return value*);

"~~~~~ from scan_dn1 to scan_to_tactic1 return val:"; val (xxxxx_xx)

  = (Accept_Tac1 (ist |> set_subst_true  (a', v'), ctxt, m));

"~~~~~ from scan_to_tactic1 to fun locate_input_tactic return val:"; val Accept_Tac1 ((ist as {assoc, ...}), ctxt, tac')

  = (Accept_Tac1 (ist |> set_subst_true  (a', v'), ctxt, m));

        (*if*) LibraryC.assoc (*then*);

       Safe_Step (Istate.Pstate ist, ctxt, tac')  (*return value*);

"~~~~~ from locate_input_tactic to fun Step_Solve.by_tactic return:"; val Safe_Step (istate, ctxt, tac)

  = (*xxxxx_xx*)(**)Safe_Step (Istate.Pstate ist, ctxt, tac')(**);

(*+*)val (pt, po as (p, p_)) = (pt'''''_', (p'''''_', p_'''''_')); (* from begin of by_tactic *)

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

                    Generate.generate1 tac (istate, ctxt) (pt, (lev_on p, Pbl));

            (*in*)

         	  	    ("ok", ([(Tactic.input_from_T tac, tac, (p'', (istate, ctxt)))],

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

"~~~~~ from Step_Solve.by_tactic \<longrightarrow> Step.by_tactic return:"; val ((msg, cs' : calcstate'))

  =               ("ok", ([(Tactic.input_from_T tac, tac, (p'', (istate, ctxt)) )],

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

"~~~~~ from Step.by_tactic to me return:"; val (("ok", (_, _, (pt, p)))) = (*** )xxxx( ***) ("ok", cs');

	  val (_, ts) =

	    (case Step.do_next p ((pt, Pos.e_pos'), []) of

		    ("ok", (ts as (_, _, _) :: _, _, _)) => ("", ts)

	    | ("helpless", _) => ("helpless: cannot propose tac", [])

	    | ("no-fmz-spec", _) => error "no-fmz-spec"

	    | ("end-of-calculation", (ts, _, _)) => ("", ts)

	    | _ => error "me: uncovered case")

	      handle ERROR msg => raise ERROR msg

	  val tac = 

      case ts of 

        tacis as (_::_) => let val (tac, _, _) = last_elem tacis in tac end 

		  | _ => if p = ([], Pos.Res) then Tactic.End_Proof' else Tactic.Empty_Tac;

   (p, [] : NEW, TESTg_form (pt, p), (Tactic.tac2IDstr tac, tac), Telem.Sundef, pt);

"~~~~~ from me to TOOPLEVEL return:"; val (p,_,f,nxt,_,pt)

   = (*** )xxx( ***) (p, [] : NEW, TESTg_form (pt, p), (Tactic.tac2IDstr tac, tac), Telem.Sundef, pt);

(*//--------------------- check results from modified me ----------------------------------\\*)

if p = ([2], Res) andalso

  pr_ctree pr_short pt = ".    ----- pblobj -----\n1.   x + 1 = 2\n2.   x + 1 = 2\n"

then

  (case nxt of ("Rewrite_Set", Rewrite_Set "Test_simplify") => ()

   | _ => error "")

else error "check results from modified me CHANGED";

(*\\--------------------- check results from modified me ----------------------------------//*)

"~~~~~ from me to TOPLEVEL return:"; val (p,_,f,nxt,_,pt) = (*** )xxx( ***) (**)(p, 000, f, nxt, 000, pt)(**);

(*\\------------------ end step into --------------------------------------------------------//*)

(*[3], Res*)val (p,_,f,nxt,_,pt) = me nxt'''''_''' p'''''_''' [] pt'''''_'''; (*nxt = Subproblem ("Test", ["LINEAR", "univariate", "equation", "test"])*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Model_Problem*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "equality (-1 + x = 0)"*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "solveFor x"*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Find "solutions x_i"*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Theory "Test"*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Problem ["LINEAR", "univariate", "equation", "test"]*)

(*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Method ["Test", "solve_linear"]*)

(*[3], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Apply_Method ["Test", "solve_linear"]*)

(*[3, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set_Inst (["(''bdv'', x)"], "isolate_bdv")*)

(*[3, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "Test_simplify"*)

(*[3, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["LINEAR", "univariate", "equation", "test"]*)

(*[3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_elementwise "Assumptions"*)

(*[4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["sqroot-test", "univariate", "equation", "test"]*)

(*[], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = End_Proof'*)

(*/--------------------- final test ----------------------------------\\*)

if p = ([], Res) andalso f2str f = "[x = 1]" andalso pr_ctree pr_short pt =

  ".    ----- pblobj -----\n" ^

  "1.   x + 1 = 2\n" ^

  "2.   x + 1 + -1 * 2 = 0\n" ^

  "3.    ----- pblobj -----\n" ^

  "3.1.   -1 + x = 0\n" ^

  "3.2.   x = 0 + -1 * -1\n" ^

  "4.   [x = 1]\n"

then case nxt of End_Proof' => () | _ => error "re-build: fun locate_input_tactic changed 1"

else error "re-build: fun locate_input_tactic changed 2";

"----------- fun locate_input_tactic Helpless, but applicable ----------------------------------";

"----------- fun locate_input_tactic Helpless, but applicable ----------------------------------";

"----------- fun locate_input_tactic Helpless, but applicable ----------------------------------";

(*cp from -- try fun applyTactics ------- *)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;

(*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "ordne_alphabetisch"*)

(*[1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "fasse_zusammen"*)

(*+*)if map Tactic.input_to_string (specific_from_prog pt p) =

   ["Rewrite (\"subtrahiere_x_plus_minus\", \"\<lbrakk>?l is_const; ?m is_const\<rbrakk>\n\<Longrightarrow> ?x + ?m * ?v - ?l * ?v = ?x + (?m - ?l) * ?v\")",

    "Rewrite (\"subtrahiere_x_minus_plus\", \"\<lbrakk>?l is_const; ?m is_const\<rbrakk>\n\<Longrightarrow> ?x - ?m * ?v + ?l * ?v = ?x + (- ?m + ?l) * ?v\")"]

  then () else error "specific_from_prog ([1], Res) CHANGED";

(*[2], Res*)val ("ok", (_, _, ptp as (pt, p))) = Step.by_tactic (hd (specific_from_prog pt p)) (pt, p);

(*+*)if map Tactic.input_to_string (specific_from_prog pt p) =

   ["Rewrite (\"tausche_minus\", \"\<lbrakk>?b ist_monom; ?a kleiner ?b\<rbrakk>\n\<Longrightarrow> ?b - ?a = - ?a + ?b\")", "Rewrite (\"tausche_plus_minus\", \"?b kleiner ?c \<Longrightarrow> ?a + ?c - ?b = ?a - ?b + ?c\")",

    "Rewrite (\"subtrahiere_x_plus_minus\", \"\<lbrakk>?l is_const; ?m is_const\<rbrakk>\n\<Longrightarrow> ?x + ?m * ?v - ?l * ?v = ?x + (?m - ?l) * ?v\")",

    "Rewrite (\"subtrahiere_x_minus_plus\", \"\<lbrakk>?l is_const; ?m is_const\<rbrakk>\n\<Longrightarrow> ?x - ?m * ?v + ?l * ?v = ?x + (- ?m + ?l) * ?v\")", "Calculate MINUS"]

  then () else error "specific_from_prog ([1], Res) CHANGED";

(* = ([3], Res)*)val ("ok", (_, _, ptp as (pt, p))) = Step.by_tactic (hd (specific_from_prog pt p)) (pt, p);

(*//----------------- exception PTREE "get_obj f EmptyPtree" raised --------------------------\\*)

(** )val ("ok", (_, _, ptp as (pt, p))) =( **) Step.by_tactic (hd (specific_from_prog pt p)) (pt, p);

"~~~~~ fun Step.by_tactic , args:"; val (tac, (ptp as (pt, p))) = (hd (specific_from_prog pt p), (pt, p));

      val Applicable.Appl m = (*case*) Applicable.applicable_in p pt tac (*of*);

      (*if*) Tactic.for_specify' m; (*false*)

Step_Solve.by_tactic m (pt, p);

"~~~~~ fun by_tactic , args:"; val (m, (pt, po as (p, p_))) = (m, (pt, p));

    (*if*) Celem.e_metID = get_obj g_metID pt (par_pblobj pt p) (*else*);

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

	      val (is, sc) = LItool.resume_prog thy' (p,p_) pt;

  (*case*) locate_input_tactic sc (pt, po) (fst is) (snd is) m (*of*);

"~~~~~ fun locate_input_tactic , args:"; val ((Rule.Prog prog), (cstate as (pt, (*?*)pos(*?*))), istate, ctxt, tac)

  = (sc, (pt, po), (fst is), (snd is), m);

      val srls = LItool.get_simplifier cstate (*TODO: shift into Istate.T*);

  (*case*) scan_to_tactic1 (prog, (cstate, ctxt, tac)) istate (*of*);

"~~~~~ fun scan_to_tactic1 , args:"; val ((prog, (cctt as ((_, p), _, _))), (Istate.Pstate (ist as {path, ...})))

  = ((prog, (cstate, ctxt, tac)), istate);

    (*if*) path = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (*else*);

           go_scan_up1 (prog, cctt) ist;

"~~~~~ and go_scan_up1 , args:"; val ((yyy as (prog, _)), (ist as {path, ...}))

  = ((prog, cctt), ist);

  (*if*) 1 < length path (*then*);

           scan_up1 yyy (ist |> path_up) (at_location (path_up' path) prog);

"~~~~~ fun scan_up1 , args:"; val (yyy, ist, (Const ("Tactical.Try"(*2*), _) $ _))

  = (yyy, (ist |> path_up), (at_location (path_up' path) prog));

           go_scan_up1 yyy ist;

"~~~~~ and go_scan_up1 , args:"; val ((yyy as (prog, _)), (ist as {path, ...}))

  = (yyy, ist);

  (*if*) 1 < length path (*then*);

           scan_up1 yyy (ist |> path_up) (at_location (path_up' path) prog);

"~~~~~ fun scan_up1 , args:"; val ((yyy as (prog, xxx as (cstate, _, _))), ist,

    (Const ("Tactical.Chain"(*3*), _) $ _ ))

  = (yyy, (ist |> path_up), (at_location (path_up' path) prog));

       val e2 = check_Seq_up ist prog

;

  (*case*) scan_dn1 xxx (ist |> path_up_down [R] |> set_or ORundef) e (*of*);

"~~~~~ fun scan_dn1 , args:"; val (yyy, ist, (Const ("Tactical.Chain"(*2*), _) $ _ $ _))

  = (xxx, (ist |> path_up_down [R] |> set_or ORundef), e2);

  (*case*) scan_dn1 xxx (ist |> path_down [L, R]) e1 (*of*);

"~~~~~ fun scan_dn1 , args:"; val (xxx, ist, (Const ("Tactical.Try"(*2*), _) $ e))

  = (xxx, (ist |> path_down [L, R]), e1);

  (*case*) scan_dn1 xxx (ist |> path_down [R]) e (*of*);

    (*======= end of scanning tacticals, a leaf =======*)

"~~~~~ fun scan_dn1 , args:"; val (((pt, p), ctxt, tac), (ist as {eval, act_arg, or, ...}), t)

  = (xxx, (ist |> path_down [R]), e);

    val (Program.Tac stac, a') = (*case*) check_leaf "locate" ctxt eval (get_subst ist) t (*of*);

      val Not_Associated = (*case*) associate pt ctxt (tac, stac) (*of*);

      val ORundef = (*case*) or (*of*);

  val Notappl "norm_equation not applicable" =    

      (*case*) Applicable.applicable_in p pt (LItool.tac_from_prog pt (Celem.assoc_thy "Isac_Knowledge") stac) (*of*);

   (Term_Val1 act_arg) (* return value *);

val Rewrite' ("PolyMinus", "tless_true", _, _, ("tausche_minus",_ (*"?b ist_monom \<Longrightarrow> ?a kleiner ?b \<Longrightarrow> ?b - ?a = - ?a + ?b"*)),

   t, (res, asm)) = m;

if pstate2str ist =

  "([\"\n(t_t, 5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12)\"], [R,L,R,R,L,R,R], empty, SOME t_t, \n" ^

  "- (8 * g) + (- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f) + 10 * g, ORundef, true, false)"

andalso

  UnparseC.term2str t = "- (8 * g) + (- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f) + 10 * g"

andalso

  UnparseC.term2str res = "- (8 * g) + (- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f) + 10 * g"

andalso

  UnparseC.terms2str asm = "[\"4 kleiner 6\",\"6 ist_monom\"]"

then () else error "locate_input_tactic Helpless, but applicable CHANGED";

"----------- re-build: fun find_next_step, mini ------------------------------------------------";

"----------- re-build: fun find_next_step, mini ------------------------------------------------";

"----------- re-build: fun find_next_step, mini ------------------------------------------------";

val fmz = ["Term (a + a ::real)", "normalform n_n"];

val (dI',pI',mI') = ("Poly",["polynomial","simplification"],["simplification","for_polynomials"]);

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

(*[], Pbl*)val (_, ([(tac, _, _)], _, (pt, p))) = Step.do_next p ((pt, Pos.e_pos'), []);(*Model_Problem*)

(*[], Pbl*)val (_, ([(tac, _, _)], _, (pt, p))) = Step.do_next p ((pt, Pos.e_pos'), []);(*Specify_Theory "Poly"*)

(*[], Pbl*)val (_, ([(tac, _, _)], _, (pt, p))) = Step.do_next p ((pt, Pos.e_pos'), []);(*Specify_Problem ["polynomial", "simplification"]*)

(*[], Met*)val (_, ([(tac, _, _)], _, (pt, p))) = Step.do_next p ((pt, e_pos'), []);(*Specify_Method  ["simplification", "for_polynomials"]*)

(*1], Frm*)val (_, ([(tac, _, _)], _, (pt, p))) = Step.do_next p ((pt, e_pos'), []);(*Apply_Method ["simplification", "for_polynomials"]*)

(*[1], Res*)val (_, ([(tac'''''_', _, _)], _, (pt'''''_', p'''''_'))) =

      Step.do_next p ((pt, e_pos'), []);(*Rewrite_Set "norm_Poly"*)

(*//------------------ go into 1 ------------------------------------------------------------\\*)

"~~~~~ fun do_next , args:"; val ((ip as (_, p_)), (ptp as (pt, p), tacis))

  = (p, ((pt, e_pos'), []));

  val pIopt = Ctree.get_pblID (pt, ip);

    (*if*)  ip = ([], Res) (*else*);

      val _ = (*case*) tacis (*of*);

      val SOME _ = (*case*) pIopt (*of*);

      (*if*) member op = [Pos.Pbl, Pos.Met] p_ (*else*);

val ("ok", ([(Rewrite_Set "norm_Poly", _, _)], _, (_, ([1], Res)))) =

Step_Solve.do_next (pt, ip);

"~~~~~ and do_next , args:"; val (ptp as (pt, pos as (p, p_))) =  (pt, ip);

    (*if*) Celem.e_metID = get_obj g_metID pt (par_pblobj pt p) (*else*);

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

	      val ((ist, ctxt), sc) = LItool.resume_prog thy' (p,p_) pt;

val Next_Step (_, _, Rewrite_Set' ("Poly", _, Rule_Set.Seqence {id = "norm_Poly", ...}, _, _)) =

           LI.find_next_step sc (pt, pos) ist ctxt (*of*);

"~~~~~ fun find_next_step , args:"; val ((Rule.Prog prog), (ptp as(pt, (p, _))), (Pstate ist), ctxt)

  = (sc, (pt, pos), ist, ctxt);

val Accept_Tac (Rewrite_Set' ("Poly", _, Rule_Set.Seqence {id = "norm_Poly", ...}, _, _), _, _) =

  (*case*) scan_to_tactic (prog, (ptp, ctxt)) (Pstate ist) (*of*);

"~~~~~ fun scan_to_tactic , args:"; val ((prog, cc), (Pstate (ist as {path, ...})))

  = ((prog, (ptp, ctxt)), (Pstate ist));

  (*if*) path = [] (*then*);

val Accept_Tac (Rewrite_Set' ("Poly", _, Rule_Set.Seqence {id = "norm_Poly", ...}, _, _), _, _) =

            scan_dn cc (trans_scan_dn ist) (Program.body_of prog);

"~~~~~ fun scan_dn , args:"; val ((cc as (_, ctxt)), (ist as {eval, ...}), t)

  = (cc, (trans_scan_dn ist), (Program.body_of prog));

    (*if*) Tactical.contained_in t (*else*);

      val (Program.Tac prog_tac, form_arg) = (*case*) LItool.check_leaf "next  " ctxt eval (get_subst ist) t (*of*);

val Accept_Tac (Rewrite_Set' ("Poly", _, Rule_Set.Seqence {id = "norm_Poly", ...}, _, _), _, _) =

          check_tac cc ist (prog_tac, form_arg)  (*return from xxx*);

"~~~~~ from fun scan_dn\<longrightarrow>fun scan_to_tactic\<longrightarrow>fun find_next_step, return:"; val (Accept_Tac (tac, ist, ctxt))

  = (check_tac cc ist (prog_tac, form_arg));

    Next_Step (Pstate ist, Tactic.insert_assumptions tac ctxt, tac)  (*return from find_next_step*);

"~~~~~ from fun find_next_step\<longrightarrow>and do_next\<longrightarrow>fun zzz, return:"; val (Next_Step (ist, ctxt, tac))

  = (Next_Step (Pstate ist, Tactic.insert_assumptions tac ctxt, tac));

           LI.by_tactic tac (ist, Tactic.insert_assumptions tac ctxt) ptp  (*return from and do_next*);

"~~~~~ from and do_next\<longrightarrow>fun do_next\<longrightarrow>toplevel, return:"; val  (_, ([(tac''''', _, _)], _, (pt''''', p''''')))

  = (LI.by_tactic tac (ist, Tactic.insert_assumptions tac ctxt) ptp);

(*\\------------------ end of go into 1 -----------------------------------------------------//*)

(*[], Res*)val (_, ([(tac''''', _, _)], _, (pt''''', p'''''))) =

      Step.do_next p'''''_' ((pt'''''_', Pos.e_pos'), []);(* Check_Postcond ["polynomial", "simplification"]*)

(*//------------------ go into 2 ------------------------------------------------------------\\*)

"~~~~~ fun do_next , args:"; val ((ip as (_, p_)), (ptp as (pt, p), tacis))

  = (p''''', ((pt''''', e_pos'), []));

  val pIopt = Ctree.get_pblID (pt, ip);

    (*if*)  ip = ([], Res) (*else*);

      val _ = (*case*) tacis (*of*);

      val SOME _ = (*case*) pIopt (*of*);

      (*if*) member op = [Pos.Pbl, Pos.Met] p_ (*else*);

val ("ok", ([(Check_Postcond ["polynomial", "simplification"], _, _)], _, (_, ([], Res)))) =

Step_Solve.do_next (pt, ip);

"~~~~~ and do_next , args:"; val (ptp as (pt, pos as (p, p_))) =  (pt, ip);

    (*if*) Celem.e_metID = get_obj g_metID pt (par_pblobj pt p) (*else*);

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

	      val ((ist, ctxt), sc) = LItool.resume_prog thy' (p,p_) pt;

  (** )val End_Program (ist, tac) = 

 ( *case*) LI.find_next_step sc (pt, pos) ist ctxt (*of*);

"~~~~~ fun find_next_step , args:"; val ((Rule.Prog prog), (ptp as(pt, (p, _))), (Pstate ist), ctxt)

  = (sc, (pt, pos), ist, ctxt);

(*  val Term_Val (Const ("Groups.times_class.times", _) $ Free ("2", _) $ Free ("a", _))*)

  (** )val Term_Val prog_result =

 ( *case*) scan_to_tactic (prog, (ptp, ctxt)) (Pstate ist) (*of*);

"~~~~~ fun scan_to_tactic , args:"; val ((prog, cc), (Pstate (ist as {path, ...})))

  = ((prog, (ptp, ctxt)), (Pstate ist));

  (*if*) path = [] (*else*);

           go_scan_up (prog, cc) (trans_scan_up ist |> set_found);

"~~~~~ fun go_scan_up , args:"; val ((pcc as (sc, _)), (ist as {path, act_arg, found_accept, ...}))

  = ((prog, cc), (trans_scan_up ist(*|> set_found !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! *)));

    (*if*) path = [R] (*then*);

      (*if*) found_accept = true (*then*);

      Term_Val act_arg (*return from go_scan_up*);

"~~~~~ from fun go_scan_up\<longrightarrow>fun scan_to_tactic, return:"; val (Term_Val prog_result) = (Term_Val act_arg);

    Term_Val prog_result  (*return from scan_to_tactic*);

"~~~~~ from fun scan_to_tactic\<longrightarrow>fun find_next_step, return:"; val (Term_Val prog_result) = (Term_Val prog_result);

    val (true, p', _) = (*case*) parent_node pt p (*of*);

              val (_, pblID, _) = get_obj g_spec pt p';

     End_Program (Pstate ist, Tactic.Check_Postcond' (pblID, prog_result))

     (*return from find_next_step*);

"~~~~~ from fun find_next_step\<longrightarrow>and do_next\<longrightarrow>fun zzz, return:"; val (End_Program (ist, tac))

  = (End_Program (Pstate ist, Tactic.Check_Postcond' (pblID,prog_result)));

      val _ = (*case*) tac (*of*);

val ("ok", ([(Check_Postcond ["polynomial", "simplification"], _, _)], _, (_, ([], Res))))

   = LI.by_tactic tac (ist, ctxt) ptp (*return from and do_next*);

"~~~~~ from and do_next\<longrightarrow>top level, return:"; val (_, ([(tac''''', _, _)], _, (pt''''', p''''')))

  = (LI.by_tactic tac (ist, ctxt) ptp);

(*\\------------------ end of go into 2 -----------------------------------------------------//*)

(*[], Und*)val (msg, ([], _, (pt, p))) = Step.do_next p''''' ((pt''''', Pos.e_pos'), []);(**)

show_pt_tac pt; (*[

([], Frm), Simplify (a + a)

. . . . . . . . . . Apply_Method ["simplification","for_polynomials"],

([1], Frm), a + a

. . . . . . . . . . Rewrite_Set "norm_Poly",

([1], Res), 2 * a

. . . . . . . . . . Check_Postcond ["polynomial","simplification"],

([], Res), 2 * a]*)

(*/--- final test ---------------------------------------------------------------------------\\*)

val (res, asm) = (get_obj g_result pt (fst p));

if UnparseC.term2str res = "2 * a" andalso map UnparseC.term2str asm = []

andalso p = ([], Und) andalso msg = "end-of-calculation"

andalso pr_ctree pr_short pt = ".    ----- pblobj -----\n1.   a + a\n"

then 

  case tac''''' of Check_Postcond ["polynomial", "simplification"] => () 

  | _ => error "re-build: fun find_next_step, mini 1"

else error "re-build: fun find_next_step, mini 2"

"----------- re-build: fun locate_input_term ---------------------------------------------------";

"----------- re-build: fun locate_input_term ---------------------------------------------------";

"----------- re-build: fun locate_input_term ---------------------------------------------------";

(*cp from inform.sml

 ----------- appendFormula: on Res + late deriv ------------------------------------------------*)

val fmz = ["equality (x+1=(2::real))", "solveFor x","solutions L"];

val (dI',pI',mI') = ("Test", ["sqroot-test","univariate","equation","test"],

   ["Test","squ-equ-test-subpbl1"]);

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

val (p,_,f,nxt,_,pt) = me nxt p [] pt;

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["Test", "squ-equ-test-subpbl1"]*);

(*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Rewrite_Set "norm_equation"*)

(*+*)if f2str f = "x + 1 = 2" then () else error "locate_input_term at ([1], Frm) CHANGED";

(*[1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Rewrite_Set "Test_simplify"*)

(*+*)if f2str f = "x + 1 + -1 * 2 = 0" then () else error "locate_input_term at ([1], Frm) CHANGED";

show_pt_tac pt; (*[

([], Frm), solve (x + 1 = 2, x)

. . . . . . . . . . Apply_Method ["Test","squ-equ-test-subpbl1"],

([1], Frm), x + 1 = 2

. . . . . . . . . . Rewrite_Set "norm_equation",

([1], Res), x + 1 + -1 * 2 = 0             ///Check_Postcond..ERROR*)

(*//---------- appendFormula 1 "x = 1" \<longrightarrow> Step_Solve.inform \<longrightarrow> LI.locate_input_term ----------\\*)

"~~~~~ fun appendFormula , args:"; val ((*cI, *) ifo: Rule.cterm') = ((**) "x = 1");

    val cs = (*get_calc cI*) ((pt, p), [(*nxt, nxt_, (pos, (ist, ctxt))*)])

    val pos = (*get_pos cI 1*) p

(*+*)val ptp''''' = (pt, p);

(*+*)if snd ptp''''' = ([1], Res) then () else error "old_cs changed";

(*+*)show_pt_tac pt; (*[

(*+*)([], Frm), solve (x + 1 = 2, x)

(*+*). . . . . . . . . . Apply_Method ["Test","squ-equ-test-subpbl1"],

(*+*)([1], Frm), x + 1 = 2

(*+*). . . . . . . . . . Rewrite_Set "norm_equation",

(*+*)([1], Res), x + 1 + -1 * 2 = 0      ///Check_Postcond*)

  val ("ok", cs' as (_, _, ptp')) =

    (*case*) Step.do_next pos cs (*of*);

val ("ok", (_(*use in DG !!!*), [], ptp''''' as (pt''''', p'''''))) = (*case*)

     Step_Solve.by_term ptp' (encode ifo) (*of*);

"~~~~~ fun Step_Solve.by_term , args:"; val ((pt, pos as (p, _)), istr)

  = (ptp', (encode ifo));

  val SOME f_in =

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

  	  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);

      (*if*) f_succ = f_in (*else*);

  val NONE =

        (*case*) In_Chead.cas_input f_in (*of*);

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

(*old*)     val {scr = prog, ...} = Specify.get_met metID

(*old*)     val istate = get_istate_LI pt pos

(*old*)     val ctxt = get_ctxt pt pos

  val LI.Found_Step (cstate'''''_', _(*istate*), _(*ctxt*)) = (*case*)

        LI.locate_input_term prog (pt, pos) istate ctxt f_in (*of*);

"~~~~~ fun locate_input_term , args:"; val ((Rule.Prog _),  ((pt, pos) : Calc.T), (_ : Istate.T), (_ : Proof.context), tm)

  = (prog, (pt, pos), istate, ctxt, f_in);

( *old*)

(*NEW*) LI.locate_input_term (pt, pos) f_in (*of*);

"~~~~~ fun locate_input_term , args:"; val ((pt, pos), tm) = ((pt, pos), f_in);

   		val pos_pred = Pos.lev_back' pos (*f_pred ---"step pos cs"---> f_succ in appendFormula*)

  val ("ok", (_, _, cstate as (pt', pos'))) =

   		(*case*) compare_step ([], [], (pt, pos_pred)) tm (*of*);

(*old* )

    Found_Step (cstate, get_istate_LI pt' pos', get_ctxt pt' pos')  (*return from locate_input_term*);

( *old*)

(*NEW*)     Found_Step cstate (*return from locate_input_term*);

       (*LI.Found_Step ( *)cstate(*, _(*istate*), _(*ctxt*))( *return from locate_input_term*);

"~~~~~ from fun locate_input_term\<longrightarrow>fun Step_Solve.by_term, return:"; val ("ok", (_(*use in DG !!!*), c, ptp as (_, p)))

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

    ("ok", ((*_ use in DG !!!,*) c, ptp(* as (_*), p))(*)*)(*return from Step_Solve.by_term*);

"~~~~~ from fun Step_Solve.by_term\<longrightarrow>(fun appendFormula)!toplevel, return:"; val ("ok", (_(*use in DG !!!*), [], ptp''''' as (pt''''', p''''')))

  = ("ok", ([], [], ptp));

(*fun me requires nxt...*)

    Step.do_next p''''' (ptp''''', []);

  val ("ok", ([(nxt'''''_' as Check_Postcond ["LINEAR", "univariate", "equation", "test"], _, _)], _,

    (pt'''''_', p'''''_'))) = Step.do_next p''''' (ptp''''', [])

(*\\---------- appendFormula 1 "x = 1" \<longrightarrow> Step_Solve.inform \<longrightarrow> LI.locate_input_term ----------//*)

(*//----- REPLACED BY appendFormula 1 "x = 1" \<longrightarrow> Step_Solve.inform \<longrightarrow> LI.locate_input_term -----\\* )

 (*[2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Subproblem ("Test", ["LINEAR", "univariate", "equation", "test"])*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Model_Problem*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "equality (-1 + x = 0)"*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "solveFor x"*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Find "solutions x_i"*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Theory "Test"*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Problem ["LINEAR", "univariate", "equation", "test"]*)

 (*[3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Method ["Test", "solve_linear"]*)

 (*[3], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Apply_Method ["Test", "solve_linear"]*)

 (*[3, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set_Inst (["(''bdv'', x)"], "isolate_bdv")*)

 (*[3, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "Test_simplify"*)

 (*[3, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["LINEAR", "univariate", "equation", "test"]*)

( *\\----- REPLACED BY appendFormula 1 "x = 1" \<longrightarrow> Step_Solve.inform \<longrightarrow> LI.locate_input_term -----//*)

 (*[3], Res*)val (p,_,f,nxt,_,pt) = me nxt'''''_' p'''''_' [] pt'''''_'; (*nxt = Check_elementwise "Assumptions"*)

 (*[4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["sqroot-test", "univariate", "equation", "test"]*)

 (*[], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = End_Proof'*)

(*/--- final test ---------------------------------------------------------------------------\\*)

if p = ([], Res) andalso f2str f = "[x = 1]" andalso pr_ctree pr_short pt =

   ".    ----- pblobj -----\n" ^

   "1.   x + 1 = 2\n" ^

   "2.   x + 1 + -1 * 2 = 0\n" ^

   "3.    ----- pblobj -----\n" ^

   "3.1.   -1 + x = 0\n" ^

   "3.2.   x = 0 + -1 * -1\n" ^

   "3.2.1.   x = 0 + -1 * -1\n" ^

   "3.2.2.   x = 0 + 1\n" (*ATTENTION: see complete Calc below*)

then case nxt of End_Proof' => () | _ => error "re-build: fun locate_input_term CHANGED 1"

else error "re-build: fun locate_input_term CHANGED 2";

show_pt_tac pt; (*[

([], Frm), solve (x + 1 = 2, x)

. . . . . . . . . . Apply_Method ["Test","squ-equ-test-subpbl1"],

([1], Frm), x + 1 = 2

. . . . . . . . . . Rewrite_Set "norm_equation",

([1], Res), x + 1 + -1 * 2 = 0

. . . . . . . . . . Rewrite_Set "Test_simplify",

([2], Res), -1 + x = 0

. . . . . . . . . . Subproblem (Test, ["LINEAR","univariate","equation","test"]),

([3], Pbl), solve (-1 + x = 0, x)

. . . . . . . . . . Apply_Method ["Test","solve_linear"],

([3,1], Frm), -1 + x = 0

. . . . . . . . . . Rewrite_Set_Inst ([(''bdv'', x)], "isolate_bdv"),

([3,1], Res), x = 0 + -1 * -1

. . . . . . . . . . Derive Test_simplify,

([3,2,1], Frm), x = 0 + -1 * -1

. . . . . . . . . . Rewrite ("#: -1 * -1 = 1", "-1 * -1 = 1"),

([3,2,1], Res), x = 0 + 1

. . . . . . . . . . Rewrite ("radd_0", "0 + ?k = ?k"),

([3,2,2], Res), x = 1

. . . . . . . . . . Tactic.input_to_string not impl. for ?!,

([3,2], Res), x = 1

. . . . . . . . . . Check_Postcond ["LINEAR","univariate","equation","test"],

([3], Res), [x = 1]

. . . . . . . . . . Check_Postcond ["sqroot-test","univariate","equation","test"],

([], Res), [x = 1]]*)