(* Title:  "Specify/specify.sml"

   Author: Walther Neuper

   (c) due to copyright terms

*)

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

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

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

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

"----------- maximum-example: Specify.finish_phase ---------------------------------------------";

"----------- revise Specify.do_all -------------------------------------------------------------";

"----------- specify-phase: low level functions ------------------------------------------------";

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

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

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

open Pos;

open Ctree;

open Test_Code;

open Tactic;

open Specify;

open Step;

open O_Model;

open I_Model;

open P_Model;

open Specify_Step;

open Test_Code;

(**** maximum-example: Specify.finish_phase  ############################################# ****)

"----------- maximum-example: Specify.finish_phase ---------------------------------------------";

"----------- maximum-example: Specify.finish_phase ---------------------------------------------";

(*//-------- WAS OUT OF Test UNTIL 200209, ERROR PROBABLY FROM INTRO. OF Isabelle's funpack --\\* )

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

     Test_Code.init_calc @{context} 

     [(["fixedValues [r=Arbfix]", "maximum A",

	"valuesFor [a,b]",

	"relations [A=a*b, (a/2) \<up> 2 + (b/2) \<up> 2 = r \<up> 2]",

	"relations [A=a*b, (a/2) \<up> 2 + (b/2) \<up> 2 = r \<up> 2]",

	"relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",

	"boundVariable a", "boundVariable b", "boundVariable alpha",

	"interval {x::real. 0 <= x & x <= 2*r}",

	"interval {x::real. 0 <= x & x <= 2*r}",

	"interval {x::real. 0 <= x & x <= pi}",

	"errorBound (eps=(0::real))"],

       ("Diff_App",["maximum_of", "function"],["Diff_App", "max_by_calculus"])

       )];

 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;

 (*nxt = nxt = Add_Find "valuesFor [a]" FIXME.12.03 +handle Inc !*)

 val pits = get_obj g_pbl pt (fst p);

 writeln (I_Model.to_string ctxt pits);

(*[

(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),

(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, [])),

(1 ,[1,2,3] ,true,#Given,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),

(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A]))]*) 

 val (pt,p) = Specify.finish_phase (pt,p);

 val pits = get_obj g_pbl pt (fst p);

 if I_Model.to_string ctxt pits = "[\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),\n(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),\n(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(vs_, [[a],[b]])),\n(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) \<up> 2 + (b / 2) \<up> 2 = r \<up> 2] ,(rs_, [[A = a * b],[(a / 2) \<up> 2 + (b / 2) \<up> 2 = r \<up> 2]]))]" 

 then () else error "completetest.sml: new behav. in Specify.finish_phase 3";

 writeln (I_Model.to_string ctxt pits);

(*[

(1 ,[1,2,3] ,true,#Given,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),

(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),

(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(valuesFor, [[a],[b]])),

(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) \<up> 2 + (b / 2)  \<up> 

2 = r \<up> 2] ,(relations, [[A = a * b],[(a / 2) \<up> 2 + (b / 2) \<up> 2 = r \<up> 2]]))]*)

 val mits = get_obj g_met pt (fst p);

 if I_Model.to_string ctxt mits = "[\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),\n(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),\n(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(vs_, [[a],[b]])),\n(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) \<up> 2 + (b / 2) \<up> 2 = r \<up> 2] ,(rs_, [[A = a * b],[(a / 2) \<up> 2 + (b / 2) \<up> 2 = r \<up> 2]])),\n(6 ,[1] ,true ,#undef ,Cor boundVariable a ,(v_, [a])),\n(9 ,[1,2] ,true ,#undef ,Cor interval {x. 0 <= x & x <= 2 * r} ,(itv_, [{x. 0 <= x & x <= 2 * r}])),\n(11 ,[1,2,3] ,true ,#undef ,Cor errorBound (eps = 0) ,(err_, [eps = 0]))]" 

 then () else error "completetest.sml: new behav. in Specify.finish_phase 3";

 writeln (I_Model.to_string ctxt mits);

(*[

(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),

(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),

(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(valuesFor, [[a],[b]])),

(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) \<up> 2 + (b / 2)  \<up> 

2 = r \<up> 2] ,(relations, [[A = a * b],[(a / 2) \<up> 2 + (b / 2) \<up> 2 = r \<up> 2]])),

(6 ,[1] ,true ,#undef ,Cor boundVariable a ,(boundVariable, [a])),

(9 ,[1,2] ,true ,#undef ,Cor interval {x. 0 <= x & x <= 2 * r} ,(interval, [{x.

0 <= x & x <= 2 * r}])),

(11 ,[1,2,3] ,true ,#undef ,Cor errorBound (eps = 0) ,(errorBound, [eps = 0]))]*)

( *\\-------- WAS OUT OF Test UNTIL 200209, ERROR PROBABLY FROM INTRO. OF Isabelle's funpack --//*)

(**** revise Specify.do_all ############################################################## ****);

"----------- revise Specify.do_all -------------------------------------------------------------";

"----------- revise Specify.do_all -------------------------------------------------------------";

(* from Minisubplb/100-init-rootpbl.sml:

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>]" :: 

     "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 Know_Store}) ["Diff_App-No.123a"] ["Diff_App-No.123a"];

*)

val model = ("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>]" :: 

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

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

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

val refs = ("Diff_App", 

     ["univariate_calculus", "Optimisation"],

     ["Optimisation", "by_univariate_calculus"])

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

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

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

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

   Specify.do_all (pt, p);

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

"~~~~~ fun do_all , args:"; val (pt, (*old* )pos as( *old*) (p, _)) = (pt, p);

    val (itms, oris, probl, o_refs, spec, ctxt) = case Ctree.get_obj I pt p of

      Ctree.PblObj {meth = itms, origin = (oris, o_spec, _), probl, spec, ctxt, ...}

        => (itms, oris, probl, o_spec, spec, ctxt)

    | _ => raise ERROR "LI.by_tactic: no PblObj"

    val (_, pbl_id', met_id') = References.select_input o_refs spec

    val (pbl_imod, met_imod) = I_Model.s_make_complete ctxt oris

      (I_Model.OLD_to_TEST probl, I_Model.OLD_to_TEST itms) (pbl_id', met_id')

;

(*-------------------- stop step into do_all -------------------------------------------------*)

(*/------------------- check result of I_Model.complete' ------------------------------------\*)

(*+*)if Model_Pattern.to_string @{context} (#model (MethodC.from_store ctxt met_id')) = "[\"" ^

  "(#Given, (Constants, fixes))\", \"" ^

  "(#Given, (Maximum, maxx))\", \"" ^

  "(#Given, (Extremum, extr))\", \"" ^

  "(#Given, (SideConditions, sideconds))\", \"" ^

  "(#Given, (FunctionVariable, funvar))\", \"" ^

  "(#Given, (Input_Descript.Domain, doma))\", \"" ^

  "(#Given, (ErrorBound, err))\", \"" ^

  "(#Find, (AdditionalValues, vals))\"]"

(*+*)then () else error "mod_pat CHANGED";

(*+*)if I_Model.to_string_TEST @{context} met_imod = "[\n" ^

  "(1, [1, 2, 3], true ,#Given, (Cor_TEST Constants [r = 7] , pen2str, Position.T)), \n" ^

  "(2, [1, 2, 3], true ,#Find, (Cor_TEST Maximum A , pen2str, Position.T)), \n" ^

  "(4, [1, 2, 3], true ,#Relate, (Cor_TEST Extremum (A = 2 * u * v - u \<up> 2) , pen2str, Position.T)), \n" ^

  "(5, [1, 2], true ,#Relate, (Cor_TEST SideConditions [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2] , pen2str, Position.T)), \n" ^

  "(7, [1], true ,#undef, (Cor_TEST FunctionVariable a , pen2str, Position.T)), \n" ^

  "(10, [1, 2], true ,#undef, (Cor_TEST Input_Descript.Domain {0<..<r} , pen2str, Position.T)), \n" ^

  "(12, [1, 2, 3], true ,#undef, (Cor_TEST ErrorBound (\<epsilon> = 0) , pen2str, Position.T)), \n" ^

  "(3, [1, 2, 3], true ,#Find, (Cor_TEST AdditionalValues [u, v] , pen2str, Position.T))]"

(*+*)then () else error "met_imod CHANGED";

(*\------------------- check result of I_Model.complete' ------------------------------------/*)

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

(*-------------------- continuing do_all -----------------------------------------------------*)

    val (pt, _) = Ctree.cupdate_problem pt p

      (o_refs, I_Model.TEST_to_OLD pbl_imod, I_Model.TEST_to_OLD met_imod, ctxt)

;

(**** specify-phase: low level functions ################################################# ****)

"----------- specify-phase: low level functions -----------------------------------------";

"----------- specify-phase: low level functions -----------------------------------------";

open Pos;

open Ctree;

open Test_Code;

open Tactic;

open Specify;

open Step;

open O_Model;

open I_Model;

open P_Model;

open Specify_Step;

val formalise = ["Traegerlaenge L", "Streckenlast q_0", "Biegelinie y",

	    "Randbedingungen [y 0 = (0::real), y L = 0, M_b 0 = 0, M_b L = 0]",

(*

  Now follow items for ALL SubProblems,

  since ROOT MethodC must provide values for "actuals" of ALL SubProblems.

  See Biegelinie.thy subsection \<open>Survey on Methods\<close>.

*)

(*

  Items for MethodC "IntegrierenUndKonstanteBestimmen2"

*)

	    "FunktionsVariable x",

    (*"Biegelinie y",          ..already input for Problem above*)

      "AbleitungBiegelinie dy",

      "Biegemoment M_b",

      "Querkraft Q",

(*

  Item for Problem "LINEAR/system", which by [''no_met''] involves refinement

*)

      "GleichungsVariablen [c, c_2, c_3, c_4]"

];

(*

  Note: the above sequence of items follows the sequence of formal arguments (and of model items)

  of MethodC "IntegrierenUndKonstanteBestimmen2"

*)

val references = ("Biegelinie", ["Biegelinien"], ["IntegrierenUndKonstanteBestimmen2"]);

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

(*[], Pbl*)val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(formalise, references)]; (*nxt = Model_Problem*)

(*/------------------- check result of Test_Code.init_calc @{context} ----------------------------------------\*)

(*+*)val (o_model, ("Biegelinie", ["Biegelinien"], ["IntegrierenUndKonstanteBestimmen2"]), _) =

  get_obj g_origin pt (fst p);

(*+*)if O_Model.to_string @{context} o_model = "[\n" ^

  "(1, [\"1\"], #Given, Traegerlaenge, [\"L\"]), \n" ^

  "(2, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(3, [\"1\"], #Find, Biegelinie, [\"y\"]), \n" ^

  "(4, [\"1\"], #Relate, Randbedingungen, [\"[y 0 = 0]\", \"[y L = 0]\", \"[M_b 0 = 0]\", \"[M_b L = 0]\"]), \n" ^

  "(5, [\"1\"], #undef, FunktionsVariable, [\"x\"]), \n" ^

  "(6, [\"1\"], #undef, AbleitungBiegelinie, [\"dy\"]), \n" ^

  "(7, [\"1\"], #undef, Biegemoment, [\"M_b\"]), \n" ^

  "(8, [\"1\"], #undef, Querkraft, [\"Q\"]), \n" ^

  "(9, [\"1\"], #undef, GleichungsVariablen, [\"[c]\", \"[c_2]\", \"[c_3]\", \"[c_4]\"])]"

then () else error "[IntegrierenUndKonstanteBestimmen2] O_Model CHANGED";

(*\------------------- check result of Test_Code.init_calc @{context} ----------------------------------------/*)

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "Traegerlaenge L" = nxt

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "Streckenlast q_0" = nxt

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Find "Biegelinie y" = nxt

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Relation "Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0]" = nxt

(*/---broken elementwise input to lists---\* )

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Add_Relation "Randbedingungen [y L = 0, M_b 0 = 0, M_b L = 0]"*)

( *\---broken elementwise input to lists---/*)

val return_me_Add_Relation_Randbedingungen = me nxt p c pt; (*\<rightarrow>Specify_Problem ["Biegelinien"]*)

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

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

      val ctxt = Ctree.get_ctxt pt p

      val (pt, p) = 

  	    (*Step.by_tactic is here for testing by me; do_next would suffice in me*)

  	    case Step.by_tactic tac (pt, p) of

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

val ("ok", ([(Specify_Theory "Biegelinie", _, _)], _, _)) =

      (*case*)

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

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

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

  (*if*) Pos.on_calc_end ip (*else*);

      val (_, probl_id, _) = Calc.references (pt, p);

val _ =

      (*case*) tacis (*of*);

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

           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*);

           specify_do_next (pt, input_pos);

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

    val (_, (p_', tac)) = Specify.find_next_step ptp

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

val Specify_Theory "Biegelinie" =

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

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

(*|------------------- contine me_Add_Relation_Randbedingungen -------------------------------*)

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

(*[], Pbl*)val (p,_,f,nxt,_,pt) = return_me_Add_Relation_Randbedingungen;

                                                 val Specify_Theory "Biegelinie" = nxt

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Specify_Problem ["Biegelinien"] = nxt

(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Specify_Method ["IntegrierenUndKonstanteBestimmen2"] = nxt

(*[], Met*)val return_me_Specify_Method_IntegrierenUndKonstanteBestimmen2

                                = me nxt p c pt; (*\<rightarrow>Add_Given "FunktionsVariable x"*)

(*/------------------- step into me_Specify_Method_IntegrierenUndKonstanteBestimmen2--------\*)

(*/------------------- initial check for whole me ------------------------------------------\*)

(*+*)val Specify_Method ["IntegrierenUndKonstanteBestimmen2"] = nxt;

(*+*)val {origin = (o_model, o_refs, _), probl = i_pbl, meth = i_met, spec, ...} =

  Calc.specify_data (pt, p);

(*+*)if o_refs = ("Biegelinie", ["Biegelinien"], ["IntegrierenUndKonstanteBestimmen2"])

(*+*)then () else error "initial o_refs CHANGED";

(*+*)if O_Model.to_string @{context} o_model = "[\n" ^

  "(1, [\"1\"], #Given, Traegerlaenge, [\"L\"]), \n" ^

  "(2, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(3, [\"1\"], #Find, Biegelinie, [\"y\"]), \n" ^

  "(4, [\"1\"], #Relate, Randbedingungen, [\"[y 0 = 0]\", \"[y L = 0]\", \"[M_b 0 = 0]\", \"[M_b L = 0]\"]), \n" ^

  "(5, [\"1\"], #undef, FunktionsVariable, [\"x\"]), \n" ^

  "(6, [\"1\"], #undef, AbleitungBiegelinie, [\"dy\"]), \n" ^

  "(7, [\"1\"], #undef, Biegemoment, [\"M_b\"]), \n" ^

  "(8, [\"1\"], #undef, Querkraft, [\"Q\"]), \n" ^

  "(9, [\"1\"], #undef, GleichungsVariablen, [\"[c]\", \"[c_2]\", \"[c_3]\", \"[c_4]\"])]"

(*+*)then () else error "initial o_model CHANGED";

(*+*)if I_Model.to_string @{context} i_pbl = "[\n" ^

  "(1 ,[1] ,true ,#Given ,Cor Traegerlaenge L , pen2str), \n" ^

  "(2 ,[1] ,true ,#Given ,Cor Streckenlast q_0 , pen2str), \n" ^

  "(3 ,[1] ,true ,#Find ,Cor Biegelinie y , pen2str), \n" ^

  "(4 ,[1] ,true ,#Relate ,Cor Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0] , pen2str)]"

(*+*)then () else error "initial i_pbl CHANGED";

(*+*)if I_Model.to_string @{context} i_met = "[]"

(*+*)then () else error "initial i_met CHANGED";

(*+*)val (_, ["Biegelinien"], _) = spec;

(*\------------------- initial check for whole me ------------------------------------------/*)

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

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

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

      Step.by_tactic tac (pt, p) of ("ok", (_, _, ptp)) => ptp;

(*/------------------- check for entry to Step.by_tactic -----------------------------------\*)

(*+*)val Specify_Method ["IntegrierenUndKonstanteBestimmen2"] = tac;

(*+*)val {origin = (o_model, _, _), ...} = Calc.specify_data (pt, p);

(*+*)if O_Model.to_string @{context} o_model = "[\n" ^

  "(1, [\"1\"], #Given, Traegerlaenge, [\"L\"]), \n" ^

  "(2, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(3, [\"1\"], #Find, Biegelinie, [\"y\"]), \n" ^

  "(4, [\"1\"], #Relate, Randbedingungen, [\"[y 0 = 0]\", \"[y L = 0]\", \"[M_b 0 = 0]\", \"[M_b L = 0]\"]), \n" ^

  "(5, [\"1\"], #undef, FunktionsVariable, [\"x\"]), \n" ^

  "(6, [\"1\"], #undef, AbleitungBiegelinie, [\"dy\"]), \n" ^

  "(7, [\"1\"], #undef, Biegemoment, [\"M_b\"]), \n" ^

  "(8, [\"1\"], #undef, Querkraft, [\"Q\"]), \n" ^

  "(9, [\"1\"], #undef, GleichungsVariablen, [\"[c]\", \"[c_2]\", \"[c_3]\", \"[c_4]\"])]"

(*+*)then () else error "o_model AFTER Specify_Method NOTok CHANGED";

(*\------------------- check for Step.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.Specify_Method mID), (ctree, pos)) = (tac, (ctree, pos));

        val (o_model''''', _, i_model''''') =

           Specify_Step.complete_for mID (ctree, pos);

"~~~~~ fun complete_for , args:"; val (mID, (ctree, pos)) = (mID, (ctree, pos));

    val {origin = (o_model, o_refs, _), spec = refs, probl = i_prob, ctxt,

       ...} = Calc.specify_data (ctree, pos);

    val (dI, _, _) = References.select_input o_refs refs;

    val {model = m_patt, where_, where_rls, ...} = MethodC.from_store ctxt mID

    val {origin = (root_model, _, _), ...} = Calc.specify_data (ctree, ([], Pos.Und))

    val (o_model', ctxt') =

   O_Model.complete_for m_patt root_model (o_model, ctxt);

(*/------------------- check entry to O_Model.complete_for -----------------------------------------\*)

(*+*)Model_Pattern.to_string @{context}  m_patt = "[\"" ^

  "(#Given, (Traegerlaenge, l))\", \"" ^

  "(#Given, (Streckenlast, q))\", \"" ^

  "(#Given, (FunktionsVariable, v))\", \"" ^

  "(#Given, (GleichungsVariablen, vs))\", \"" ^

  "(#Given, (AbleitungBiegelinie, id_abl))\", \"" ^

  "(#Find, (Biegelinie, b))\", \"" ^

  "(#Relate, (Randbedingungen, s))\"]";

(*+*) O_Model.to_string @{context} root_model;

(*\------------------- check entry to O_Model.complete_for -----------------------------------------/*)

"~~~~~ fun complete_for , args:"; val (m_patt, root_model, (o_model, ctxt)) = (m_patt, root_model, (o_model, ctxt));

    val  missing = m_patt |> filter_out

      (fn (_, (descriptor, _)) => (member op = (map #4 o_model) descriptor));

    val add = (root_model

      |> filter

        (fn (_, _, _, descriptor, _) => (member op = (map (fst o snd) missing)) descriptor))

;

    ((o_model @ add)

      |> map (fn (a, b, _, descr, e) => (a, b, the (Model_Pattern.get_field descr m_patt), descr, e))

      |> map (fn (_, b, c, d, e) => (b, c, d, e))      (* for correct enumeration *)

      |> add_enumerate                                        (* for correct enumeration *)

      |> map (fn (a, (b, c, d, e)) => (a, b, c, d, e)), (* for correct enumeration *)

    ctxt |> ContextC.add_constraints (add |> values |> TermC.vars')) (*return from O_Model.complete_for*);

"~~~~~ fun complete_for \<longrightarrow>fun Specify_Step.complete_for , return:"; val (o_model', ctxt') =

    ((o_model @ add)

      |> map (fn (a, b, _, descr, e) => (a, b, the (Model_Pattern.get_field descr m_patt), descr, e))

      |> map (fn (_, b, c, d, e) => (b, c, d, e))      (* for correct enumeration *)

      |> add_enumerate                                        (* for correct enumeration *)

      |> map (fn (a, (b, c, d, e)) => (a, b, c, d, e)), (* for correct enumeration *)

    ctxt |> ContextC.add_constraints (add |> values |> TermC.vars'));

(*/------------------- check of result from O_Model.complete_for -----------------------------------\*)

(*+*) O_Model.to_string @{context} o_model'; "O_Model.complete_for: result o_model CHANGED";

(*\------------------- check of result from O_Model.complete_for -----------------------------------/*)

    val thy = ThyC.get_theory @{context} dI

    val (_, (i_model, _)) = M_Match.match_itms_oris ctxt i_prob (m_patt, where_, where_rls) o_model';

  (o_model', ctxt', i_model) (*return from Specify_Step.complete_for*);

"~~~~~ fun complete_for \<longrightarrow>fun Specify_Step.check , return:"; val (o_model, _, i_model) =

  (o_model', ctxt', i_model);

   Applicable.Yes (Tactic.Specify_Method' (mID, o_model, i_model)) (*return from Specify_Step.check*);

"~~~~~ fun Specify_Step.check \<longrightarrow>fun Step.check \<longrightarrow>fun Step.by_tactic , return:"; val (Applicable.Yes tac') =

  (Applicable.Yes (Tactic.Specify_Method' (mID, o_model, i_model)));

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

  val ("ok", ([], [], (_, _))) =

Step_Specify.by_tactic tac' ptp;

"~~~~~ fun by_tactic , args:"; val ((Tactic.Specify_Method' (mID, _, _)), (pt,pos as (p, _))) =

  (tac', ptp);

(*NEW*) val {origin = (o_model, o_refs, _), spec = refs, probl = i_prob, ctxt,

(*NEW*)    ...} = Calc.specify_data (pt, pos);

(*NEW*) val (dI, _, mID) = References.select_input o_refs refs;

(*NEW*) val {model = m_patt, where_, where_rls, ...} = MethodC.from_store ctxt mID

(*NEW*) val {origin = (root_model, _, _), ...} = Calc.specify_data (pt, ([], Und))

(*NEW*) val (o_model', ctxt') = O_Model.complete_for m_patt root_model (o_model, ctxt)

(*NEW*) val thy = ThyC.get_theory @{context} dI

(*NEW*) val (_, (i_model, _)) = M_Match.match_itms_oris ctxt i_prob (m_patt, where_, where_rls) o_model';

(*NEW*) val (pos, _, _, pt) = Specify_Step.add (Tactic.Specify_Method' (mID, o_model', i_model))

(*NEW*)   (Istate_Def.Uistate, ctxt') (pt, pos)

(*/------------------- check result of Step_Specify.by_tactic ------------------------------\*)

(*+*)val {origin = (o_model, _, _), meth, ...} = Calc.specify_data (pt, pos);

(*+*)O_Model.to_string @{context} o_model;

(*+*)if I_Model.to_string @{context} meth = "[\n" ^

  "(1 ,[1] ,true ,#Given ,Cor Traegerlaenge L , pen2str), \n" ^

  "(2 ,[1] ,true ,#Given ,Cor Streckenlast q_0 , pen2str), \n" ^

  "(3 ,[1] ,true ,#Find ,Cor Biegelinie y , pen2str), \n" ^

  "(4 ,[1] ,true ,#Relate ,Cor Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0] , pen2str), \n" ^

  "(5 ,[1] ,false ,#Given ,Mis FunktionsVariable fun_var), \n" ^

  "(6 ,[1] ,false ,#Given ,Mis AbleitungBiegelinie id_der), \n" ^

  "(7 ,[1] ,false ,#Given ,Mis Biegemoment id_momentum), \n" ^

  "(8 ,[1] ,false ,#Given ,Mis Querkraft id_lat_force), \n" ^

  "(9 ,[1] ,false ,#Given ,Mis GleichungsVariablen vs)]"

(*+*)then () else error "result of Step_Specify.by_tactic o_model CHANGED";

(*\------------------- check result of Step_Specify.by_tactic ------------------------------/*)

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

val (_, ([(Add_Given "FunktionsVariable x", _, _)], _, _)) =

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

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

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

  (p'''''_', ((pt'''''_', Pos.e_pos'), []));

  (*if*) Pos.on_calc_end ip (*else*);

     val (_, probl_id, _) = Calc.references (pt, p);

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

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

val (_, ([(Add_Given "FunktionsVariable x", _, _)], _, _)) =

         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 "FunktionsVariable x", _, _)], [], (pt'''''_'', p'''''_''))) =

      Step.specify_do_next (pt, input_pos);

(*/------------------- check result of specify_do_next -------------------------------------\*)

(*+*)val {origin = (ooo_mod, _, _), meth, ...} =  Calc.specify_data (pt'''''_'', p'''''_'');

(*+*) O_Model.to_string @{context} ooo_mod; "result of Step_Specify.by_tactic o_model CHANGED";

(*+*)if I_Model.to_string @{context} meth = "[\n" ^

  "(1 ,[1] ,true ,#Given ,Cor Traegerlaenge L , pen2str), \n" ^

  "(2 ,[1] ,true ,#Given ,Cor Streckenlast q_0 , pen2str), \n" ^

  "(3 ,[1] ,true ,#Find ,Cor Biegelinie y , pen2str), \n" ^

  "(4 ,[1] ,true ,#Relate ,Cor Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0] , pen2str), \n" ^

  "(5 ,[1] ,true ,#Given ,Cor FunktionsVariable x , pen2str), \n" ^

  "(6 ,[1] ,false ,#Given ,Mis AbleitungBiegelinie id_der), \n" ^

  "(7 ,[1] ,false ,#Given ,Mis Biegemoment id_momentum), \n" ^

  "(8 ,[1] ,false ,#Given ,Mis Querkraft id_lat_force), \n" ^

  "(9 ,[1] ,false ,#Given ,Mis GleichungsVariablen vs)]"

(*+*)then () else error "result of Step_Specify.by_tactic i_model CHANGED";

(*\------------------- check result of specify_do_next -------------------------------------/*)

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

(**)val (_, (p_', Add_Given "FunktionsVariable x")) =(**)

   Specify.find_next_step ptp;

"~~~~~ 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, (p, p_)) andalso origin <> Ctree.e_origin (*else*);

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

val return = for_problem ctxt oris (o_refs, refs) (pbl, met);

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

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

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

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

    val (preok, _) = Pre_Conds.check ctxt where_rls where_ (mpc, I_Model.OLD_to_TEST met);

"~~~~~ from fun find_next_step \<longrightarrow>fun specify_do_next , return:"; val (_, (p_', tac)) = (return);

(*/------------------- check within find_next_step -----------------------------------------\*)

(*+*)Model_Pattern.to_string @{context} (MethodC.from_store ctxt mI' |> #model) = "[\"" ^

  "(#Given, (Traegerlaenge, l))\", \"" ^

  "(#Given, (Streckenlast, q))\", \"" ^

  "(#Given, (FunktionsVariable, v))\", \"" ^   (* <---------- take m_field from here !!!*)

  "(#Given, (GleichungsVariablen, vs))\", \"" ^

  "(#Given, (AbleitungBiegelinie, id_abl))\", \"" ^

  "(#Find, (Biegelinie, b))\", \"" ^

  "(#Relate, (Randbedingungen, s))\"]";

(*\------------------- check within find_next_step -----------------------------------------/*)

    (*case*) item_to_add (ThyC.get_theory @{context} (if dI = ThyC.id_empty then dI' else dI)) oris mpc met (*of*);

"~~~~~ ~ fun item_to_add , args:"; val (thy, oris, _, itms) =

  ((ThyC.get_theory @{context} (if dI = ThyC.id_empty then dI' else dI)), oris, mpc, met);

(*OLD*)fun testr_vt v ori = member op= (#2 (ori : O_Model.single)) v (**)andalso (#3 ori) <> "#undef"(**)

      fun testi_vt v itm = member op= (#2 (itm : I_Model.single)) v

      fun test_id ids r = member op= ids (#1 (r : O_Model.single))

      fun test_subset itm (_, _, _, d, ts) = 

        (I_Model.descriptor (#5 (itm: I_Model.single))) = d andalso subset op = (I_Model.o_model_values (#5 itm), ts)

      fun false_and_not_Sup (_, _, false, _, I_Model.Sup _) = false

        | false_and_not_Sup (_, _, false, _, _) = true

        | false_and_not_Sup _ = false

      val v = if itms = [] then 1 else Pre_Conds.max_variant itms

      val vors = if v = 0 then oris else filter (testr_vt v) oris  (* oris..vat *)

      val vits =

        if v = 0

        then itms                                 (* because of dsc without dat *)

  	    else filter (testi_vt v) itms;                             (* itms..vat *)

      val icl = filter false_and_not_Sup vits;                    (* incomplete *)

(*/------------------- check within item_to_add --------------------------------------------\*)

(*+*)if I_Model.to_string @{context} icl = "[\n" ^                 (*.. values, not formals*)

  "(5 ,[1] ,false ,#Given ,Mis FunktionsVariable fun_var), \n" ^   (*.. values, not formals*)

  "(6 ,[1] ,false ,#Given ,Mis AbleitungBiegelinie id_der), \n" ^  (*.. values, not formals*)

  "(7 ,[1] ,false ,#Given ,Mis Biegemoment id_momentum), \n" ^     (*.. values, not formals*)

  "(8 ,[1] ,false ,#Given ,Mis Querkraft id_lat_force), \n" ^      (*.. values, not formals*)

  "(9 ,[1] ,false ,#Given ,Mis GleichungsVariablen vs)]"

(*+*)then () else error "icl within item_to_add CHANGED";

(*+*) O_Model.to_string @{context} vors; "vors within item_to_add CHANGED";

(*+*)if I_Model.to_string @{context} itms = "[\n" ^

  "(1 ,[1] ,true ,#Given ,Cor Traegerlaenge L , pen2str), \n" ^

  "(2 ,[1] ,true ,#Given ,Cor Streckenlast q_0 , pen2str), \n" ^

  "(3 ,[1] ,true ,#Find ,Cor Biegelinie y , pen2str), \n" ^

  "(4 ,[1] ,true ,#Relate ,Cor Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0] , pen2str), \n" ^

  "(5 ,[1] ,false ,#Given ,Mis FunktionsVariable fun_var), \n" ^

  "(6 ,[1] ,false ,#Given ,Mis AbleitungBiegelinie id_der), \n" ^

  "(7 ,[1] ,false ,#Given ,Mis Biegemoment id_momentum), \n" ^

  "(8 ,[1] ,false ,#Given ,Mis Querkraft id_lat_force), \n" ^

  "(9 ,[1] ,false ,#Given ,Mis GleichungsVariablen vs)]"

(*+*)then () else error "i_model  within item_to_add CHANGED";

(*\------------------- check within item_to_add --------------------------------------------/*)

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

        val SOME ori =(*case*) find_first (test_subset (hd icl)) vors (*of*);

(*+*)val (5, [1], "#Given", Const (\<^const_name>\<open>FunktionsVariable\<close>, _), [Free ("x", _)]) = ori

(*+*)val SOME ("#Given", "FunktionsVariable x") =

        SOME

     (I_Model.get_field_term thy ori (hd icl)) (*return from item_to_add*);

"~~~~~ ~~ fun get_field_term , args:"; val (thy, (_, _, _, d, ts), (_, _, _, fd, itm_)) = (thy, ori, (hd icl));

val rrrrr =

  (fd, ((UnparseC.term_in_thy thy) o Input_Descript.join)

    (d, subtract op = (o_model_values itm_) ts)) (*return from get_field_term*);

"~~~~~ ~~ from fun get_field_term \<longrightarrow>fun item_to_add \<longrightarrow>fun find_next_step , return:"; val (SOME (fd, ct')) =

    (SOME rrrrr);

  ("dummy", (Pos.Met, P_Model.mk_additem fd ct')) (*return from find_next_step*);

(*+*)val Add_Given "FunktionsVariable x" = P_Model.mk_additem fd ct';

"~~~~~ from fun find_next_step \<longrightarrow>fun specify_do_next , return:"; val (_, (p_', tac)) =

  ("dummy", (Pos.Met, P_Model.mk_additem fd ct'));

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

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

      ("dummy",

Step_Specify.by_tactic_input tac (pt, (p, p_'))) (*return from specify_do_next*);

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

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

  val ("ok", ([(Add_Given "FunktionsVariable x", _, _)], _, _)) =

     Specify.by_Add_ "#Given" ct ptp (*return from by_tactic_input*);

"~~~~~ ~ 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);

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

    val (i_model, m_patt) = (met,

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

val Add (5, [1], true, "#Given", Cor ((Const (\<^const_name>\<open>FunktionsVariable\<close>, _), [Free ("x", _)]), (Free ("fun_var", _), [Free ("x", _)]))) =

      (*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) =

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

(*.NEW*)      val SOME (t as (descriptor $ _)) = (*case*) ParseC.term_opt ctxt str (*of*);

(*.NEW*)   val SOME m_field = (*case*) Model_Pattern.get_field descriptor m_patt (*of*);

val ("", (5, [1], "#Given", Const (\<^const_name>\<open>FunktionsVariable\<close>, _), [Free ("x", _)]), [Free ("x", _)]) =

          (*case*)

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

"~~~~~ ~~~ fun contains , args:"; val (ctxt, sel, ori, t) = (ctxt, m_field, o_model, t);

    val ots = ((distinct op =) o flat o (map #5)) ori

    val oids = ((map (fst o dest_Free)) o (distinct op =) o flat o (map TermC.vars)) ots

    val (d, ts) = Input_Descript.split t

    val ids = map (fst o dest_Free) (((distinct op =) o (flat o (map TermC.vars))) ts);

    (*if*) (subtract op = oids ids) <> [] (*else*);

	    (*if*) d = TermC.empty (*else*);

	      (*if*) member op = (map #4 ori) d (*then*);

                associate_input ctxt sel (d, ts) ori;

"~~~~~ ~~~~ fun associate_input , args:"; val (ctxt, m_field, (descript, vals), ((id, vat, m_field', descript', vals') :: oris)) =

  (ctxt, sel, (d, ts), ori);

(*/------------------- check within associate_input ------------------------------------------\*)

(*+*)val Add_Given "FunktionsVariable x" = tac;

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

(*+*)val Const (\<^const_name>\<open>FunktionsVariable\<close>, _) = descript;

(*+*)val [Free ("x", _)] = vals;

(*+*)O_Model.to_string @{context} ori = "[\n" ^

  "(1, [\"1\"], #Given, Traegerlaenge, [\"L\"]), \n" ^

  "(2, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(3, [\"1\"], #Find, Biegelinie, [\"y\"]), \n" ^

  "(4, [\"1\"], #Relate, Randbedingungen, [\"[y 0 = 0]\", \"[y L = 0]\", \"[M_b 0 = 0]\", \"[M_b L = 0]\"]), \n" ^

  "(5, [\"1\"], #undef, FunktionsVariable, [\"x\"]), \n" ^

  "(6, [\"1\"], #undef, GleichungsVariablen, [\"[c]\", \"[c_2]\", \"[c_3]\", \"[c_4]\"]), \n" ^

  "(7, [\"1\"], #undef, AbleitungBiegelinie, [\"dy\"])]";

(*+*)val (id, vat, m_field', descript', vals') = nth 5 ori

(*+*)val (5, [1], "#Given", Const (\<^const_name>\<open>FunktionsVariable\<close>, _), [Free ("x", _)]) =

  (id, vat, m_field', descript', vals')

(*\------------------- check within associate_input ----------------------------------------/*)

(*\------------------- step into me_Specify_Method_IntegrierenUndKonstanteBestimmen2--------*)

(*[], Met*)val (p,_,f,nxt,_,pt) = return_me_Specify_Method_IntegrierenUndKonstanteBestimmen2

                                                 val Add_Given "FunktionsVariable x" =  nxt;

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "AbleitungBiegelinie dy" = nxt

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "Biegemoment M_b" = nxt

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "Querkraft Q" = nxt

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "GleichungsVariablen [c, c_2, c_3, c_4]" = nxt

(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Apply_Method ["IntegrierenUndKonstanteBestimmen2"] = nxt

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

(*/------------------- check entry to me Model_Problem -------------------------------------\*)

(*+*)val ([1], Pbl) = p;

(*+*)val (o_model, ("Biegelinie", ["vonBelastungZu", "Biegelinien"], ["Biegelinien", "ausBelastung"]), _) =

  get_obj g_origin pt (fst p);

(*+*)if O_Model.to_string @{context} o_model = "[\n" ^

  "(1, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(2, [\"1\"], #Given, FunktionsVariable, [\"x\"]), \n" ^

  "(3, [\"1\"], #Find, Funktionen, [\"funs'''\"])]"

(*

.. here the O_Model does NOT know, which MethodC will be chosen,

so "belastung_zu_biegelinie q__q v_v b_b id_abl" is NOT known,

"b_b" and "id_abl" are NOT missing.

*)

then () else error "[Biegelinien, ausBelastung] initial O_Model CHANGED";

(*\------------------- check entry to me Model_Problem -------------------------------------/*)

(*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Add_Given "Streckenlast q_0"*)

(*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Add_Given "FunktionsVariable x"*)

(*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Add_Find "Funktionen funs'''":*)

(*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Specify_Theory "Biegelinie"*)

(*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Specify_Problem ["vonBelastungZu", "Biegelinien"]*)

(*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*\<rightarrow>Specify_Method ["Biegelinien", "ausBelastung"]*)

(*[1], Met*)val return_me_Specify_Method_ausBelastung = me nxt p c pt; (*\<rightarrow>Add_Given "Biegelinie y"*)

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

(*+*)val Specify_Method ["Biegelinien", "ausBelastung"] = nxt;

(*+*)(* by \<up> \<up> \<up> \<up>   "b_b" and "id_abl" must be requested: PUT THEM INTO O_Model*)

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

  val ("ok", ([], [], (_, _))) = (*case*)

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

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

  val Applicable.Yes tac' = (*case*) check tac (pt, p) (*of*);

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

  val ("ok", ([], [], (_, _))) =

Step_Specify.by_tactic tac' ptp;

(*/------------------- initial check for Step_Specify.by_tactic ----------------------------\*)

(*+*)val (o_model, ("Biegelinie", ["vonBelastungZu", "Biegelinien"], ["Biegelinien", "ausBelastung"]), _) =

  get_obj g_origin pt (fst p);

(*+*)if O_Model.to_string @{context} o_model = "[\n" ^                                         

  "(1, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(2, [\"1\"], #Given, FunktionsVariable, [\"x\"]), \n" ^

  "(3, [\"1\"], #Find, Funktionen, [\"funs'''\"])]"

(*

.. here the MethodC has been determined by the user,

so "belastung_zu_biegelinie q__q v_v b_b id_abl" IS KNOWN and,

"b_b" and "id_abl" WOULD BE missing (added by O_Model.).

*)

then () else error "[Biegelinien, ausBelastung] O_Model NOT EXTENDED BY MethodC";

(*\------------------- initial check for Step_Specify.by_tactic ----------------------------/*)

"~~~ fun by_tactic , args:"; val ((Tactic.Specify_Method' (mID, _, _)), (pt, pos as (p, _))) =

  (tac', ptp);

(*.NEW*) val {origin = (o_model, o_refs, _), spec = refs, probl = i_prob, meth = i_meth, ctxt,

(*.NEW*)    ...} =Calc.specify_data (pt, pos);

(*.NEW*) val (dI, _, mID) = References.select_input o_refs refs;

(*.NEW*) val {model = m_patt, where_, where_rls, ...} = MethodC.from_store ctxt mID

(*.NEW*) val {origin = (root_model, _, _), ...} = Calc.specify_data (pt, ([], Und))

(*.NEW*) val (o_model', ctxt') = O_Model.complete_for m_patt root_model (o_model, ctxt);

(*/------------------- check for entry to O_Model.complete_for -----------------------------\*)

(*+*)if mID = ["Biegelinien", "ausBelastung"]

(*+*)then () else error "MethodC [Biegelinien, ausBelastung] CHANGED";

(*+*)if Model_Pattern.to_string @{context} m_patt = "[\"" ^

  "(#Given, (Streckenlast, q__q))\", \"" ^

  "(#Given, (FunktionsVariable, v_v))\", \"" ^

  "(#Given, (Biegelinie, b_b))\", \"" ^

  "(#Given, (AbleitungBiegelinie, id_der))\", \"" ^

  "(#Given, (Biegemoment, id_momentum))\", \"" ^

  "(#Given, (Querkraft, id_lat_force))\", \"" ^

  "(#Find, (Funktionen, fun_s))\"]"

(*+*)then () else error "[Biegelinien, ausBelastung] Model_Pattern CHANGED";

(*+*)if O_Model.to_string @{context} o_model = "[\n" ^

  "(1, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(2, [\"1\"], #Given, FunktionsVariable, [\"x\"]), \n" ^

  "(3, [\"1\"], #Find, Funktionen, [\"funs'''\"])]" 

(*+*)then () else error "[Biegelinien, ausBelastung] O_Model NOT EXTENDED BY MethodC CHANGED";

(*+*) O_Model.to_string @{context} root_model;

(*+*) O_Model.to_string @{context} o_model';

  "[Biegelinien, ausBelastung] O_Model EXTENDED BY MethodC CHANGED";

(*\------------------- check for entry to O_Model.complete_for -----------------------------/*)

  O_Model.complete_for m_patt root_model (o_model, ctxt);

"~~~~ fun complete_for , args:"; val (m_patt, root_model, (o_model, ctxt)) =

  (m_patt, root_model, (o_model, ctxt));

    val  missing = m_patt |> filter_out

      (fn (_, (descriptor, _)) => (member op = (map #4 o_model) descriptor))

;

    val add = root_model

      |> filter

        (fn (_, _, _, descriptor, _) => (member op = (map (fst o snd) missing)) descriptor)

;

    (o_model @ add

(*NEW*)|> map (fn (a, b, _, descr, e) => (a, b, the (Model_Pattern.get_field descr m_patt), descr, e))

(*NEW*)

      |> map (fn (_, b, c, d, e) => (b, c, d, e))     

      |> add_enumerate                                       

      |> map (fn (a, (b, c, d, e)) => (a, b, c, d, e)),

    ctxt |> ContextC.add_constraints (add |> O_Model.values |> TermC.vars')) (*return from O_Model.complete_for*);

"~~~~ from fun O_Model.complete_for \<longrightarrow>Step_Specify.by_tactic , return:"; val (o_model', ctxt') =

  ((o_model @ add)

(*NEW*)|> map (fn (a, b, _, descr, e) => (a, b, the (Model_Pattern.get_field descr m_patt), descr, e))

(*NEW*)

      |> map (fn (_, b, c, d, e) => (b, c, d, e))     

      |> add_enumerate                                       

      |> map (fn (a, (b, c, d, e)) => (a, b, c, d, e)),

    ctxt |> ContextC.add_constraints (add |> O_Model.values |> TermC.vars'));

(*/------------------- check within O_Model.complete_for -------------------------------------------\*)

(*+*) O_Model.to_string @{context} o_model';

  "[Biegelinien, ausBelastung] O_Model EXTENDED BY MethodC CHANGED";

(*\------------------- check within O_Model.complete_for -------------------------------------------/*)

(*.NEW*) val thy = ThyC.get_theory @{context} dI

(*.NEW*) val (_, (i_model, _)) = M_Match.match_itms_oris ctxt i_prob (m_patt, where_, where_rls) o_model';

(*.NEW*) val (pos, _, _, pt) = Specify_Step.add (Tactic.Specify_Method' (mID, o_model', i_model))

(*.NEW*)   (Istate_Def.Uistate, ctxt') (pt, pos)

;

(*+*) I_Model.to_string @{context} i_model; "[Biegelinien, ausBelastung] I_Model CHANGED 1";

(*+*)val {origin = (o_model, o_refs, _), spec = refs, probl = i_prob, meth = i_meth, ctxt, ...} =

(*+*)  Calc.specify_data (pt, pos);

(*+*)pos = ([1], Met);

         ("ok", ([], [], (pt, pos)))  (*return from Step_Specify.by_tactic*);

"~~~ from Step_Specify.by_tactic \<longrightarrow>Step.by_tactic \<longrightarrow>fun me , return:"; val ("ok", (_, _, (pt, p))) =

         ("ok", ([], [], (pt, pos)));

(*  val ("helpless", ([(xxxxx, _, _)], _, _)) =  (*case*)*)

  (*  SHOULD BE    \<up> \<up> \<up> \<up> \<up> \<up> \<up> \<up> \<up> Add_Given "Biegelinie y" | Add_Given "AbleitungBiegelinie dy"*)

val ("ok", ([( Add_Given "Biegelinie y", _, _)], [], _)) =

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

"~~ fun do_next , args:"; val ((ip as (_, p_)), (ptp as (pt, p), tacis)) = (p, ((pt, Pos.e_pos'), []));

(*.NEW*)(*if*) on_calc_end ip (*else*);

(*.NEW*)    val (_, probl_id, _) = Calc.references (pt, p);

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

(*.NEW*)      (*if*) probl_id = Problem.id_empty (*else*);

(*.NEW*)val ("ok", ([(Add_Given "Biegelinie y", _, _)], _, _)) =

         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 "Biegelinie y", _, _)], _, _)) =

          specify_do_next (pt, input_pos);

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

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

   Specify.find_next_step ptp;

"~~~~~ 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

;

(*+*)O_Model.to_string @{context} oris = "[\n" ^

  "(1, [\"1\"], #Given, Streckenlast, [\"q_0\"]), \n" ^

  "(2, [\"1\"], #Given, FunktionsVariable, [\"x\"]), \n" ^

  "(3, [\"1\"], #Find, Funktionen, [\"funs'''\"]), \n" ^

  "(4, [\"1\"], #Find, Biegelinie, [\"y\"]), \n" ^

  "(5, [\"1\"], #Given, AbleitungBiegelinie, [\"dy\"])]";

(*+*)val (true, []) = Pre_Conds.check_internal ctxt (I_Model.OLD_to_TEST pbl) (Pos.Met, mI');

(*+*)I_Model.to_string @{context} met = "[\n" ^

  "(1 ,[1] ,true ,#Given ,Cor Streckenlast q_0 ,(q_q, [q_0])), \n" ^

  "(2 ,[1] ,true ,#Given ,Cor FunktionsVariable x ,(v_v, [x])), \n" ^

  "(3 ,[1] ,true ,#Find ,Cor Funktionen funs''' ,(funs''', [funs'''])), \n" ^

  "(4 ,[1] ,false ,#Given ,Mis Biegelinie b_b), \n" ^

  "(5 ,[1] ,false ,#Given ,Mis AbleitungBiegelinie id_abl)]";

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

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

val return = for_method ctxt oris (o_refs, refs) (pbl, met);

"~~~~~ from fun find_next_step \<longrightarrow>fun specify_do_next , return:"; val (_, (p_', tac)) = (return);

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

    val Add_Given "Biegelinie y" = (*case*) tac (*of*);

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

(*+*)val Add_Given "Biegelinie y" = tac;

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

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

  val (_, ([(Add_Given "Biegelinie y", _, _)], _, (p'''''_'', ([1], Met)))) =

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

(*/------------------- check result of Step_Specify.by_tactic_input ------------------------\*)

(*+*)val {meth, ...} = Calc.specify_data (p'''''_'', ([1], Met));

(*+*)I_Model.to_string @{context} meth = "[\n" ^ (* result does NOT show Add_Given "Biegelinie y" *)

  "(1 ,[1] ,true ,#Given ,Cor Streckenlast q_0 ,(q_q, [q_0])), \n" ^

  "(2 ,[1] ,true ,#Given ,Cor FunktionsVariable x ,(v_v, [x])), \n" ^

  "(3 ,[1] ,true ,#Find ,Cor Funktionen funs''' ,(funs''', [funs'''])), \n" ^

  "(4 ,[1] ,false ,#Given ,Mis Biegelinie b_b), \n" ^

  "(5 ,[1] ,false ,#Given ,Mis AbleitungBiegelinie id_abl)]";

(*\------------------- check result of Step_Specify.by_tactic_input ------------------------/*)

"~~~~ 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);

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

    val (i_model, m_patt) = (met,

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

val Add (4, [1], true, "#Given", Cor ((Const (\<^const_name>\<open>Biegelinie\<close>, _), [Free ("y", _)]), (Free ("b_b", _), [Free ("y", _)]))) =

      (*case*)

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

(*/------------------- check for entry to check_single -------------------------------------\*)

(*+*) O_Model.to_string @{context} oris; "[Biegelinien, ausBelastung] O_Model CHANGED for entry";

(*+*) I_Model.to_string ctxt met; "[Biegelinien, ausBelastung] I_Model CHANGED for entry";

(*\------------------- check for entry to check_single -------------------------------------/*)

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

  (ctxt, sel, oris, met, ((#model o MethodC.from_store ctxt) cmI), ct);

      val SOME t = (*case*) ParseC.term_opt ctxt str (*of*);

(*+*)val Const (\<^const_name>\<open>Biegelinie\<close>, _) $ Free ("y", _) = t;

(*("associate_input: input ('Biegelinie y') not found in oris (typed)", (0, [], "#Given", Const (\<^const_name>\<open>Biegelinie\<close>, "(real \<Rightarrow> real) \<Rightarrow> una"), [Free ("y", "real \<Rightarrow> real")]), [])*)

          (*case*)

   contains ctxt m_field o_model t (*of*);

"~~~~~ ~~ fun contains , args:"; val (ctxt, sel, ori, t) = (ctxt, m_field, o_model, t);

    val ots = ((distinct op =) o flat o (map #5)) ori

    val oids = ((map (fst o dest_Free)) o (distinct op =) o flat o (map TermC.vars)) ots

    val (d, ts) = Input_Descript.split t

    val ids = map (fst o dest_Free) (((distinct op =) o (flat o (map TermC.vars))) ts);

    (*if*) (subtract op = oids ids) <> [] (*else*);

	    (*if*) d = TermC.empty (*else*);

	      (*if*) not (subset op = (map make_typeless ts, map make_typeless ots)) (*else*);

  (*case*) O_Model.associate_input' ctxt sel ts ori (*of*);

"~~~~~ ~~~ fun associate_input' , args:"; val (ctxt, sel, ts, ((id, vat, sel', d, ts') :: oris)) = (ctxt, sel, ts, ori);

(*+/---------------- bypass recursion of associate_input' ----------------\*)

(*+*)O_Model.to_string @{context} oris = "[\n" ^

  "(2, [\"1\"], #Given, FunktionsVariable, [\"x\"]), \n" ^

  "(3, [\"1\"], #Find, Funktionen, [\"funs'''\"]), \n" ^

  "(4, [\"1\"], #Find, Biegelinie, [\"y\"]), \n" ^

  "(5, [\"1\"], #Given, AbleitungBiegelinie, [\"dy\"])]";

(*+*)val (id, vat, sel', d, ts') = nth 3 oris; (* 3rd iteration *)

(*+\---------------- bypass recursion of associate_input' ----------------/*)

    (*if*) sel = sel' andalso (inter op = ts ts') <> [] (*else*);

(*/------------------- check within associate_input' -------------------------------\*)

(*+*)if sel = "#Given" andalso sel' = "#Given"

(*+*)then () else error "associate_input' Model_Pattern CHANGED";

(*BUT: m_field can change from root-Problem to sub-MethodC --------------------vvv*)

(* sub-vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv*)

(*+*)if (Problem.from_store ctxt ["vonBelastungZu", "Biegelinien"] |> #model |> Model_Pattern.to_string @{context}) = "[\"" ^

  "(#Given, (Streckenlast, q_q))\", \"" ^

  "(#Given, (FunktionsVariable, v_v))\", \"" ^

  "(#Find, (Funktionen, funs'''))\"]"

(*+*)then () else error "associate_input' Model_Pattern of Subproblem CHANGED";

(* root-vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv ------------------------------------- \<up>*)

(*+*)if (Problem.from_store ctxt ["Biegelinien"] |> #model |> Model_Pattern.to_string @{context}) = "[\"" ^

  "(#Given, (Traegerlaenge, l_l))\", \"" ^

  "(#Given, (Streckenlast, q_q))\", \"" ^

  "(#Find, (Biegelinie, b_b))\", \"" ^ (*------------------------------------- \<up> *)

  "(#Relate, (Randbedingungen, r_b))\"]"

(*+*)then () else error "associate_input' Model_Pattern root-problem CHANGED";

(* sub-vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv*)

(*+*)if (MethodC.from_store ctxt ["Biegelinien", "ausBelastung"] |> #model |> Model_Pattern.to_string @{context}) = "[\"" ^

  "(#Given, (Streckenlast, q__q))\", \"" ^

  "(#Given, (FunktionsVariable, v_v))\", \"" ^

  "(#Given, (Biegelinie, b_b))\", \"" ^

  "(#Given, (AbleitungBiegelinie, id_der))\", \"" ^

  "(#Given, (Biegemoment, id_momentum))\", \"" ^

  "(#Given, (Querkraft, id_lat_force))\", \"" ^

  "(#Find, (Funktionen, fun_s))\"]"

(*+*)then () else error "associate_input' Model_Pattern CHANGED";

(*+*)if UnparseC.term @{context} d = "Biegelinie" andalso UnparseC.terms @{context} ts = "[y]"

(*+*)  andalso UnparseC.terms @{context} ts' = "[y]"

(*+*)then

(*+*)  (case (inter op = ts ts') of [Free ("y", _(*"real \<Rightarrow> real"*))] => () 

(*+*)  | _ => error "check within associate_input' CHANGED 1")

(*+*)else error "check within associate_input' CHANGED 2";

(*\------------------- check within associate_input' -------------------------------/*)

(*|------------------- contine me_Specify_Method_ausBelastung --------------------------------*)

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

(*[1], Met*)val (p,_,f,nxt,_,pt) = return_me_Specify_Method_ausBelastung;

                                                     val Add_Given "Biegelinie y" = nxt

(*[1], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "AbleitungBiegelinie dy"= nxt

(*[1], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "Biegemoment M_b" = nxt

(*[1], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Add_Given "Querkraft Q" = nxt

(*[1], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Apply_Method ["Biegelinien", "ausBelastung"] = nxt

(*[1, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Rewrite ("sym_neg_equal_iff_equal", _)= nxt

(*[1, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Rewrite ("Belastung_Querkraft", _)= nxt

(*[1, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p c pt; val Subproblem ("Biegelinie", ["named", "integrate", "function"])= nxt

(*[1, 3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; val Model_Problem= nxt

(*[1, 3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; val Add_Given "functionTerm (- q_0)"= nxt

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

;

(*/------------------- check result of Add_Given "functionTerm (- q_0)" --------------------\*)

if p = ([1, 3], Pbl) andalso

  f = Test_Out.PpcKF (Test_Out.Problem [], {Find = [Incompl "antiDerivativeName"],

    Given = [Correct "functionTerm (- q_0)", Incompl "integrateBy"], 

    Relate = [], Where = [], With = []})

then

  (case nxt of Add_Given "integrateBy x" => () | _ => error "specify-phase: low level CHANGED 1")

else error "specify-phase: low level CHANGED 2";

(*\------------------- check result of Add_Given "functionTerm (- q_0)" --------------------/*)