(* Title:  "Minisubpbl/100a-init-rootpbl-Maximum.sml"

    Author: Walther Neuper 1105

    (c) copyright due to lincense terms.

 COMPARE Specify/specify.sml --- specify-phase: low level functions ---

 ATTENTION: the file creates buffer overflow if copied in one piece !

 Note: This test --- steps into me --- more than once, to a somewhat extreme extent;

   in order not to get lost while working in Test_Some etc, 

   re-introduce  ML (*--- step into XXXXX ---*) and Co.

   and use Sidekick for orientation.

   Nesting is indicated by  /---   //--   ///-  at the left margin of the comments.

 *)

 (*/------- these overwrite definitions in section above ---\*)

 open Ctree;

 open Pos;

 open TermC;

 open Istate;

 open Tactic;

 open I_Model;

 open P_Model

 open Rewrite;

 open Step;

 open LItool;

 open LI;

 open Test_Code

 open Specify

 open ME_Misc

 open Pre_Conds;

 (*\------- these overwrite definitions in section above ---/*)

 val (_(*example text*),

   (model as ("Constants [r = (7::real)]" :: "Maximum A" :: "AdditionalValues [u, v]" :: 

      "Extremum (A = 2 * u * v - u \<up> 2)" :: 

      "SideConditions [((u::real) / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]" :: 

      "SideConditions [((u::real) / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]" :: 

      "SideConditions [(u::real) / 2 = r * sin \<alpha>, 2 / v = r * cos \<alpha>]" ::

 (*---------------------------------------------,(v::real) / 2 = r * cos \<alpha>]" --- ERROR in example*)

      "FunctionVariable a" :: "FunctionVariable b" :: "FunctionVariable \<alpha>" :: 

      "Domain {0 <..< r}" :: "Domain {0 <..< r}" :: "Domain {0 <..< \<pi> / 2}" ::

      "ErrorBound (\<epsilon> = (0::real))" :: []), 

    refs as ("Diff_App", 

      ["univariate_calculus", "Optimisation"],

      ["Optimisation", "by_univariate_calculus"])))

   = Store.get (Know_Store.get_expls @{theory}) ["Diff_App-No.123a"] ["Diff_App-No.123a"];

 val c = [];

 val return_init_calc = 

  Test_Code.init_calc @{context} [(model, refs)]; (*val Model_Problem = nxt;*)

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

 "~~~~~ fun init_calc , args:"; val (ctxt, [(model, refs as (thy_id, _, _))]) =

   (@{context}, [(model, refs)]);

     val thy = thy_id |> ThyC.get_theory ctxt

     val ((pt, p), tacis) = Step_Specify.initialise' thy (model, refs)

 	  val tac = case tacis of [] => Tactic.Empty_Tac | _ => (#1 o hd) tacis

 	  val f = 

            TESTg_form ctxt (pt,p);

 "~~~~~ fun TESTg_form , args:"; val (ctxt, ptp) = (ctxt, (pt,p));

     val (form, _, _) =

    ME_Misc.pt_extract ctxt ptp;

 "~~~~~ fun pt_extract , args:"; val (ctxt, (pt, (p, p_ as Pbl(*Frm,Pbl*)))) = (ctxt, ptp);

         val ppobj = Ctree.get_obj I pt p

         val f = if Ctree.is_pblobj ppobj then pt_model ppobj p_ else Ctree.get_obj pt_form pt p;

             (*if*) Ctree.is_pblobj ppobj (*then*);

            pt_model ppobj p_ ;

 "~~~~~ fun pt_model , args:"; val ((Ctree.PblObj {probl, spec, origin = (_, spec', hdl), ctxt, ...}), Pbl_) =

   (ppobj, p_);

       val (_, pI, _) = Ctree.get_somespec' spec spec';

 (*    val where_ = if pI = Problem.id_empty then []*)

                (*if*) pI = Problem.id_empty (*else*);

 	          val {where_rls, where_, model, ...} = Problem.from_store ctxt pI

 	          val (_, where_) = 

  Pre_Conds.check ctxt where_rls where_

               (model, I_Model.OLD_to_TEST probl);

 "~~~~~ fun check , args:"; val (ctxt, where_rls, pres, (model_patt, i_model)) =

   (ctxt, where_rls, where_, (model, I_Model.OLD_to_TEST probl));

       val (env_model, (env_subst, env_eval)) = 

            make_environments model_patt i_model;

 "~~~~~ fun make_environments , args:"; val (_, []) = (model_patt, i_model);

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

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

 (*+*)val PblObj {ctxt, probl, ...} = get_obj I pt [];

 (*+*)Proof_Context.theory_of ctxt (*= {Pure, .., Diff_App}*);

 (*+*)val Free ("r", Type ("Real.real", [])) = Syntax.read_term ctxt "r"

 (*+*)val [] = probl

 val return_me_Model_Problem = 

            me nxt p c pt; val Add_Given "Constants [r = 7]" = #4 return_me_Model_Problem;

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

 "~~~~~ fun me , args:"; val (tac as Model_Problem, (p:Pos.pos'), (_:Test_Code.NEW), (pt:Ctree.ctree)) = (nxt, p, c, pt);

       val ctxt = Ctree.get_ctxt pt p

 val return_by_tactic = case

       Step.by_tactic tac (pt,p) of

 		    ("ok", (_, _, ptp)) => ptp;

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

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

 val Applicable.Yes tac' = (*case*)

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

 (*+*)val Model_Problem' _ = tac';

 "~~~~~ fun check , args:"; val (tac, (ctree, pos)) = (tac, (pt, p));

   (*if*) Tactic.for_specify tac (*then*);

 Specify_Step.check tac (ctree, pos);

 "~~~~~ fun check , args:"; val (Tactic.Model_Problem, (pt, pos as (p, _))) =

   (tac, (ctree, pos));

         val (o_model, pI', ctxt) = case Ctree.get_obj I pt p of

           Ctree.PblObj {origin = (o_model, (_, pI', _), _), ctxt, ...} => (o_model, pI', ctxt)

 	      val {model = model_patt, ...} = Problem.from_store (Ctree.get_ctxt pt pos) pI'

 	      val pbl = I_Model.init_TEST o_model model_patt;

 val return_check =

     Applicable.Yes (Tactic.Model_Problem' (pI', I_Model.TEST_to_OLD pbl, []));

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

 val (pt, p) = return_by_tactic;

 val return_do_next = (*case*)

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

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

 "~~~~~ fun do_next , args:"; val (((ip as (_,p_)):pos'), ((ptp as (pt,p), tacis):Calc.state_pre)) =

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

     val pIopt = get_pblID (pt,ip);

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

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

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

     val ("ok", ([(Add_Given "Constants [r = 7]", _, _)], [], _)) =

       Step.switch_specify_solve p_ (pt, ip);

 "~~~~~ fun switch_specify_solve , args:"; val (state_pos, (pt, input_pos)) = (p_, (pt, ip));

       (*if*) Pos.on_specification ([], state_pos) (*then*);

     val ("ok", ([(Add_Given "Constants [r = 7]", _, _)], [], _)) =

       Step.specify_do_next (pt, input_pos);

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

 "~~~~~ fun specify_do_next , args:"; val (ptp as (pt, (p, p_))) = (pt, input_pos);

 (*  val (_, (p_', tac)) =*)

 val return_find_next_step = (*keep for continuing specify_do_next*)

    Specify.find_next_step ptp;

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

 "~~~~~ fun find_next_step , args:"; val ((pt, pos as (_, p_))) = (ptp);

     val {meth = met, origin = origin as (oris, o_refs as (_, pI', mI'), _), probl = pbl,

       spec = refs, ...} = Calc.specify_data (pt, pos);

     val ctxt = Ctree.get_ctxt pt pos;

       (*if*) Ctree.just_created (pt, pos) andalso origin <> Ctree.e_origin (*else*);

         (*if*) p_ = Pos.Pbl (*then*);

 val return_for_problem as ("dummy", (Pbl, Add_Given "Constants [r = 7]")) =

    Specify.for_problem ctxt oris (o_refs, refs) (pbl, I_Model.OLD_to_TEST met);

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

 "~~~~~ fun for_problem , args:"; val (ctxt, oris, ((dI', pI', mI'), (dI, pI, mI)), (pbl, met))

   = (ctxt, oris, (o_refs, refs), (pbl, met));

     val cdI = if dI = ThyC.id_empty then dI' else dI;

     val cpI = if pI = Problem.id_empty then pI' else pI;

     val cmI = if mI = MethodC.id_empty then mI' else mI;

     val {model = pbt, where_rls, where_, ...} = Problem.from_store ctxt cpI;

     val {model = mpc, ...} = MethodC.from_store ctxt cmI;

     val return_check =

  Pre_Conds.check ctxt where_rls where_ (pbt, I_Model.OLD_to_TEST pbl);

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

 "~~~~~ fun check , args:"; val (ctxt, where_rls, pres, (model_patt, i_model)) =

   (ctxt, where_rls, where_, (pbt, I_Model.OLD_to_TEST pbl));

       val return_make_environments =

            make_environments model_patt i_model;

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

 "~~~~~ fun of_max_variant , args:"; val (model_patt, i_model) =

   (model_patt, i_model);

 (*+*)val "[\n(1, [1, 2, 3], false ,#Given, (Inc_TEST Constants [] [__=__, __=__], Position.T)), \n(2, [1, 2, 3], false ,#Find, (Inc_TEST Maximum __, Position.T)), \n(3, [1, 2, 3], false ,#Find, (Inc_TEST AdditionalValues [] [__, __], Position.T)), \n(4, [1, 2, 3], false ,#Relate, (Inc_TEST Extremum (__=__), Position.T)), \n(5, [1, 2], false ,#Relate, (Inc_TEST SideConditions [] [__=__, __=__], Position.T))]"

  = i_model |> I_Model.to_string_TEST ctxt

     val all_variants =

         map (fn (_, variants, _, _, _) => variants) i_model

         |> flat

         |> distinct op =

     val variants_separated = map (filter_variants' i_model) all_variants

     val sums_corr = map (Model_Def.cnt_corrects) variants_separated

     val sum_variant_s = Model_Def.arrange_args sums_corr (1, all_variants)

 (*+*)val [(0, 1), (0, 2), (0, 3)] = sum_variant_s

     val (_, max_variant) = hd (*..crude decision, up to improvement *)

       (sort (fn ((i, _), (j, _)) => int_ord (i, j)) sum_variant_s)

     val i_model_max =

       filter (fn (_, variants, _ , _ ,_) => member (op =) variants max_variant) i_model

     val equal_descr_pairs = map (get_equal_descr i_model) model_patt |> flat

 (*for building make_env_s -------------------------------------------------------------------\*)

 (*!!!*) val ("#Given", (descr, term), pos) =

   Model_Pattern.split_descriptor ctxt ("#Given", @{term "Constants [r = (7::real)]"}, Position.none)

 (*!!!*) val patt = equal_descr_pairs |> hd |> #1

 (*!!!*)val equal_descr_pairs =

   (patt,

   (1, [1, 2, 3], true, "#Given", (Cor_TEST ((descr, (*!*)TermC.isalist2list(*!*) term)), pos)))

   :: tl equal_descr_pairs

 (*for building make_env_s -------------------------------------------------------------------/*)

     val env_model = make_env_model equal_descr_pairs;

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

 "~~~~~ fun make_env_model , args:"; val (equal_descr_pairs) = (equal_descr_pairs);

 val xxx = (fn ((_, (_, id)), (_, _, _, _, (feedb, _)))

        => (mk_env_model id feedb));

 val ((_, (_, id)), (_, _, _, _, (feedb, _))) = nth 4 equal_descr_pairs;

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

 (*||||| ||------------ contine of_max_variant ------------------------------------------------*)

     val equal_givens = filter (fn ((m_field, _), _) => m_field = "#Given") equal_descr_pairs

     val subst_eval_list = make_envs_preconds equal_givens

 val return_make_envs_preconds =

            make_envs_preconds equal_givens;

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

 "~~~~~ fun make_envs_preconds , args:"; val (equal_givens) = (equal_givens);

 val xxx = (fn ((_, (_, id)), (_, _, _, _, (feedb, _))) => discern_feedback id feedb)

 ;

 xxx: (Model_Pattern.single * I_Model.single_TEST) -> ((term * term) * (term * term)) list;

 val return_discern_feedback =

            discern_feedback id feedb;

 (*nth 1 equal_descr_pairs* )

 "~~~~~ fun discern_feedback , args:"; val (id, (Model_Def.Cor_TEST ((descr, ts), _))) = (id, feedb);

 ( *nth 2 equal_descr_pairs*)

 "~~~~~ fun discern_feedback , args:"; val (id, (Model_Def.Inc_TEST ((descr, ts)))) = (id, feedb);

 (*nth 1 equal_descr_pairs* )

 (*+*)val [((Const ("fixes", typ1), Free ("r", typ2)),

            (Free ("r", typ3), value))] = return_discern_feedback

 (*+*)val true = typ1 = typ2

 (*+*)val true = typ3 = HOLogic.realT

 (*+*)val "7" = UnparseC.term ctxt value

 ( *nth 2 equal_descr_pairs*)

 (*+*)val [] = return_discern_feedback

 val return_discern_typ =

            discern_typ id (descr, ts);

 "~~~~~ fun discern_typ , args:"; val (id, (descr, ts)) = (id, (descr, ts));

 (*nth 1 equal_descr_pairs* )

 (*+*)val [((Const ("fixes", typ1), Free ("r", typ2)),

            (Free ("r", typ3), value))] = return_discern_typ

 (*+*)val true = typ1 = typ2

 (*+*)val true = typ3 = HOLogic.realT

 (*+*)val "7" = UnparseC.term ctxt value

 ( *nth 2 equal_descr_pairs*)

 (*+*)val [] = return_discern_typ;

 (**)

            switch_type id ts;

 "~~~~~ fun switch_type , args:"; val (Const (descr_string, _), ts) = (descr, ts);

 (*nth 1 equal_descr_pairs* )

 val return_switch_type_TEST = Const (descr_string, ts |> hd |> TermC.lhs |> type_of)

 (*+*)val Const ("Input_Descript.Constants", typ) = return_switch_type_TEST

 (*+*)val Type ("Real.real", []) = typ

 ( *nth 2 equal_descr_pairs*)

 (*+*)val return_switch_type_TEST = descr

 (**)

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

 (*||||| ||------------ contine of_max_variant ------------------------------------------------*)

     val subst_eval_list = make_envs_preconds equal_givens

     val (env_subst, env_eval) = split_list subst_eval_list

 val make_environments = (i_model_max, env_model, (env_subst, env_eval)); (*GOON*)

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

       val (i_model_max, env_model, (env_subst, env_eval)) = make_environments

 (*!!!/----- we had a helpful argument for constructing env_model and (env_subst, env_eval)---\*)

       val (i_max_variant, env_model, (env_subst, env_eval)) = (i_model_max, [], ([], []))

 (*!!!\----- we had a helpful argument for constructing env_model and (env_subst, env_eval)---/*) 

 (*||||| |------------- contine check -----------------------------------------------------*)

       val pres_subst = map (TermC.subst_atomic_all env_subst) pres;

       val pres_subst_other = map (TermC.subst_atomic_all env_model) (map #2 pres_subst);

       val full_subst = if env_eval = [] then pres_subst_other

         else map (TermC.subst_atomic_all env_eval) (map #2 pres_subst_other)

       val evals = map (eval ctxt where_rls) full_subst

 val return_ = (i_model_max, env_subst, env_eval)

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

 val (preok, _) = return_check;

 (*|||||--------------- contine.. for_problem -------------------------------------------------*)

 val false =

     (*if*) dI' = ThyC.id_empty andalso dI = ThyC.id_empty (*else*);

 val false =

       (*if*) pI' = Problem.id_empty andalso pI = Problem.id_empty (*else*);

 val NONE =

      (*case*) find_first (fn (_, _, _, _, feedb) => I_Model.is_error feedb) pbl (*of*);

 (** )val SOME (fd, ct') as ("#Given", "Constants [r = 7]") =( **)

 (**)val return_item_to_add as SOME ("#Given", xxx) =(**) (*case*) 

    Specify.item_to_add ctxt oris (I_Model.OLD_to_TEST pbl) (*of*);

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

 (*==================== see test/../i_model.sml --- fun item_to_add ---========================*)

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

 val SOME (fd, ct') = return_item_to_add

 (*+*)val ("#Given", "Constants [r = 7]")  = (fd, ct') (*from NEW item_to_add*)

 (*|||||--------------- continue.. for_problem ------------------------------------------------*)

 val return_for_problem_step as ("dummy", (Pbl, Add_Given "Constants [r = 7]"))

   = ("dummy", (Pos.Pbl, P_Model.mk_additem fd ct'))

 (** )return_for_problem_step = return_for_problem( *..would require equality types*)

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

 val return_find_next_step as ("dummy", (Pbl, Add_Given "Constants [r = 7]"))

   = return_for_problem

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

 (*|||----------------- continue.. specify_do_next --------------------------------------------*)

 val (_, (p_', tac as Add_Given "Constants [r = 7]")) = return_find_next_step

     val ist_ctxt =  Ctree.get_loc pt (p, p_)

 (*+*)val Add_Given "Constants [r = 7]" = tac

 val _ =

     (*case*) tac (*of*);

 val return_by_tactic_input as ("ok", ([(Add_Given "Constants [r = 7]", _, _)], [], _)) =

 Step_Specify.by_tactic_input tac (pt, (p, p_'));

 "~~~~~ fun by_tactic_input , args:"; val ((Tactic.Add_Given ct), ptp) =

   (tac, (pt, (p, p_')));

    Specify.by_Add_ "#Given" ct ptp;

 "~~~~~ fun by_Add_ , args:"; val (m_field, ct ,(pt, pos as (_, p_))) =

   ("#Given", ct, ptp);

     val (met, oris, (_, pI', mI'), pbl, (_, pI, mI), ctxt) = SpecificationC.get_data (pt, pos)

     val (i_model, m_patt) =

        if p_ = Pos.Met then

          (met,

            (if mI = MethodC.id_empty then mI' else mI) |> MethodC.from_store ctxt |> #model)

        else

          (pbl,

            (if pI = Problem.id_empty then pI' else pI) |> Problem.from_store ctxt |> #model);

       (*case*)

    I_Model.check_single ctxt m_field oris i_model m_patt ct (*of*);

 "~~~~~ fun check_single , args:"; val (ctxt, m_field, o_model, i_model, m_patt, (str(*, pos*))) =

   (ctxt, m_field, oris, i_model, m_patt, ct);

         val (t as (descriptor $ _)) = Syntax.read_term ctxt str

 (*+*)val "Constants [r = 7]" = UnparseC.term ctxt t;

         val SOME m_field' =

           (*case*) Model_Pattern.get_field descriptor m_patt (*of*);

            (*if*) m_field <> m_field' (*else*);

 (*+*)val "#Given" = m_field; val "#Given" = m_field'

 val ("", ori', all) =

           (*case*) O_Model.contains ctxt m_field o_model t (*of*);

 (*+*)val (_, _, _, _, vals) = hd o_model;

 (*+*)val "Constants [r = 7]" = UnparseC.term ctxt (@{term Constants} $ (hd vals));

 (*+*)if "[\n(1, [\"1\", \"2\", \"3\"], #Given, Constants, [\"[r = 7]\"]), " ^ 

 (*+*)    "\n(2, [\"1\", \"2\", \"3\"], #Find, Maximum, [\"A\"]), " ^ 

 (*+*)    "\n(3, [\"1\", \"2\", \"3\"], #Find, AdditionalValues, [\"[u]\", \"[v]\"]), " ^ 

 (*+*)    "\n(4, [\"1\", \"2\", \"3\"], #Relate, Extremum, [\"A = 2 * u * v - u \<up> 2\"]), " ^ 

 (*+*)    "\n(5, [\"1\", \"2\"], #Relate, SideConditions, [\"[(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]\"]), " ^ 

 (*+*)    "\n(6, [\"3\"], #Relate, SideConditions, [\"[u / 2 = r * sin \<alpha>]\", \"[2 / v = r * cos \<alpha>]\"]), " ^ 

 (*+*)    "\n(7, [\"1\"], #undef, FunctionVariable, [\"a\"]), " ^ 

 (*+*)    "\n(8, [\"2\"], #undef, FunctionVariable, [\"b\"]), \n(9, [\"3\"], #undef, FunctionVariable, [\"\<alpha>\"]), " ^ 

 (*+*)    "\n(10, [\"1\", \"2\"], #undef, Input_Descript.Domain, [\"{0<..<r}\"]), " ^ 

 (*+*)    "\n(11, [\"3\"], #undef, Input_Descript.Domain, [\"{0<..<\<pi> / 2}\"]), " ^ 

 (*+*)    "\n(12, [\"1\", \"2\", \"3\"], #undef, ErrorBound, [\"\<epsilon> = 0\"])]"

 (*+*)= O_Model.to_string ctxt o_model then () else error "o_model CHANGED";

   (*case*) is_notyet_input ctxt i_model all ori' m_patt (*of*);

 "~~~~~ fun is_notyet_input , args:"; val (ctxt, itms, all, (i, v, f, d, ts), pbt) =

   (ctxt, i_model, all, ori', m_patt);

 val SOME (_, (_, pid)) =

   (*case*) find_first (eq1 d) pbt (*of*);

 (*local*)fun eq3 f d (_, _, _, f', itm_) = f = f' andalso d = (I_Model.descriptor itm_);(*local*)

 val SOME (_, _, _, _, itm_) =

     (*case*) find_first (eq3 f d) itms (*of*);

 val ts' = inter op = (o_model_values itm_) ts;

             (*if*) subset op = (ts, ts') (*else*);

 val return_is_notyet_input = ("", 

            ori_2itm itm_ pid all (i, v, f, d, subtract op = ts' ts));

 "~~~~~ fun ori_2itm , args:"; val (itm_, pid, all, (id, vt, fd, d, ts)) =

   (itm_, pid, all, (i, v, f, d, subtract op = ts' ts));

     val ts' = union op = (o_model_values itm_) ts;

     val pval = [Input_Descript.join'''' (d, ts')]

     val complete = if eq_set op = (ts', all) then true else false

 (*+*)val "Inc Constants [] , pen2str" = itm_ |> I_Model.feedback_to_string ctxt

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

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

 val ("ok", (ts as (_, _, _) :: _, _, (pt, p))) = return_do_next

 (*|------------------- continue with me_Model_Problem ----------------------------------------*)

 val tacis as (_::_) =

         (*case*) ts (*of*);

           val (tac, _, _) = last_elem tacis

 val return_Model_Problem = (p, [] : NEW, TESTg_form ctxt (pt, p), tac, Celem.Sundef, pt);

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

 "~~~~~ fun TESTg_form , args:"; val (ctxt, ptp) = (ctxt, (pt, p));

     val (form, _, _) =

    ME_Misc.pt_extract ctxt ptp;

 "~~~~~ fun pt_extract , args:"; val (ctxt, (pt, (p, p_(*Frm,Pbl*)))) = (ctxt, ptp);

         val ppobj = Ctree.get_obj I pt p

         val f = if Ctree.is_pblobj ppobj then pt_model ppobj p_ else Ctree.get_obj pt_form pt p;

           (*if*) Ctree.is_pblobj ppobj (*then*);

            pt_model ppobj p_;

 "~~~~~ fun pt_model , args:"; val ((Ctree.PblObj {probl, spec, origin = (_, o_spec, hdl), ctxt, ...}), 

   Pbl(*Frm,Pbl*)) = (ppobj, p_);

       val (_, _, met_id) = References.select_input o_spec spec

       val (allcorr, _) = Pre_Conds.check_internal ctxt (I_Model.OLD_to_TEST probl) (Pos.Met, met_id)

 val return_pt_model = Ctree.ModSpec (allcorr, Pos.Pbl, hdl, probl, (*where_*)[(*Problem.from_store in check*)], spec)

 (*|------------------- continue with TESTg_form ----------------------------------------------*)

 val Ctree.ModSpec (spec as (_, p_, _, gfr, where_, _)) =

     (*case*) form (*of*);

     Test_Out.PpcKF (  (Test_Out.Problem [],

  			P_Model.from (Proof_Context.theory_of ctxt) gfr where_));

    P_Model.from (Proof_Context.theory_of ctxt) gfr where_;

 "~~~~~ fun from , args:"; val (thy, itms, where_) = ((Proof_Context.theory_of ctxt), gfr, where_);

     fun coll model [] = model

       | coll model ((_, _, _, field, itm_) :: itms) =

         coll (add_sel_ppc thy field model (item_from_feedback thy itm_)) itms;

  val gfr = coll P_Model.empty itms;

 "~~~~~ fun coll , args:"; val (model, ((aaa, bbb_,ccc_, field, itm_) :: itms))

   = (P_Model.empty, itms);

 (*+*)val 4 = length itms;

 (*+*)val itm = nth 1 itms;

            coll P_Model.empty [itm];

 "~~~~~ fun coll , iterate:"; val (model, ((aaa, bbb_,ccc_, field, itm_) :: []))

   = (P_Model.empty, [itm]);

           (add_sel_ppc thy field model (item_from_feedback thy itm_));

 "~~~~~ fun add_sel_ppc , args:"; val ((_: theory), sel, {Given = gi, Where = wh, Find = fi, With = wi, Relate = re}, x )

   = (thy, field, model, (item_from_feedback thy itm_));

    P_Model.item_from_feedback thy itm_;

 "~~~~~ fun item_from_feedback , args:"; val (thy, (I_Model.Inc ((d, ts), _))) = (thy, itm_);

    P_Model.Incompl (UnparseC.term_in_thy thy (Input_Descript.join (d, ts)));

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

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

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

 (*+++*)val {probl, ...} = Calc.specify_data (pt, pos);

 (*+++*)val "[\n(1 ,[1, 2, 3] ,false ,#Given ,Inc Constants [] , pen2str), \n(2 ,[1, 2, 3] ,false ,#Find ,Inc Maximum , pen2str), \n(3 ,[1, 2, 3] ,false ,#Find ,Inc AdditionalValues [] , pen2str), \n(4 ,[1, 2, 3] ,false ,#Relate ,Inc Extremum , pen2str), \n(5 ,[1, 2] ,false ,#Relate ,Inc SideConditions [] , pen2str)]"

  = probl |> I_Model.to_string ctxt

 (*-------------------- contine me's ----------------------------------------------------------*)

 val return_me_add_find_Constants = me nxt p c pt;

                                       val Add_Find "Maximum A" = #4 return_me_add_find_Constants;

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

 (*==================== done in "Minisubpbl/150a-add-given-Maximum.sml" subsequently =======================*)