(* 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_POS probl);

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

  (ctxt, where_rls, where_, (model, I_Model.OLD_to_POS 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*);

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

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

        | _ => raise ERROR "Specify_Step.check Model_Problem: uncovered case Ctree.get_obj"

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

	      val pbl = I_Model.init_POS ctxt 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_POS 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_POS 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_POS 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_POS Constants [] [__=__, __=__], Position.T)), \n(2, [1, 2, 3], false ,#Find, (Inc_POS Maximum __, Position.T)), \n(3, [1, 2, 3], false ,#Find, (Inc_POS AdditionalValues [] [__, __], Position.T)), \n(4, [1, 2, 3], false ,#Relate, (Inc_POS Extremum (__=__), Position.T)), \n(5, [1, 2], false ,#Relate, (Inc_POS SideConditions [] [__=__, __=__], Position.T))]"

 = i_model |> I_Model.to_string_POS 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_POS ((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_POS) -> ((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_POS ((descr, ts), _))) = (id, feedb);

( *nth 2 equal_descr_pairs*)

"~~~~~ fun discern_feedback , args:"; val (id, (Model_Def.Inc_POS ((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_POS = Const (descr_string, ts |> hd |> TermC.lhs |> type_of)

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

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

( *nth 2 equal_descr_pairs*)

(*+*)val return_switch_type_POS = 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_POS 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.TEST_to_OLD 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 (fn (_, (d', _)) => d = d') pbt

val SOME (_, _, _, _, (feedb, _)) =

    (*case*) find_first (fn (_, _, _, f', (feedb, _)) =>

          f = f' andalso d = (descriptor_POS feedb)) itms

            val ts' = inter op = (feedb_values feedb) ts

val false =

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

val return_is_notyet_input = ("",

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

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

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

    val ts' = union op = (feedb_values feedb) ts;

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

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

(*+*)val "Inc_POS Constants [] [__=__, __=__]" = feedb |> I_Model.feedback_POS_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_POS probl) (Pos.Met, met_id)

val return_pt_model = Ctree.ModSpec (allcorr, Pos.Pbl, hdl, I_Model.OLD_to_POS 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 (I_Model.TEST_to_OLD itms);

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

  = (P_Model.empty, I_Model.TEST_to_OLD  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 =======================*)