test/Tools/isac/Test_Some.thy
author Walther Neuper <wneuper@ist.tugraz.at>
Sat, 01 Jun 2019 11:09:19 +0200
changeset 59549 e0e3d41ef86c
parent 59542 daae0164a2a3
child 59550 2e7631381921
permissions -rw-r--r--
[-Test_Isac] funpack: repair errors in test, spot remaining errors

Note: check, whether error is due to "switch from Script to partial_function" 4035ec339062
or due to "failed trial to generalise handling of meths which extend the model of a probl" 98298342fb6d
     1 theory Test_Some imports Isac.Build_Thydata
     2 begin 
     3 ML \<open>
     4 (*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\*)
     5                       (* these vvv test, if funs are intermediately opened in structure 
     6                          in case of errors here consider ~~/./xtest-to-coding.sh      *)
     7   open Kernel;
     8   open Math_Engine;            CalcTreeTEST;
     9   open Lucin;                  appy;
    10   open Inform;                 cas_input;
    11   open Rtools;                 trtas2str;
    12   open Chead;                  pt_extract;
    13   open Generate;               (* NONE *)
    14   open Ctree;                  append_problem;
    15   open Specify;                show_ptyps;
    16   open Applicable;             mk_set;
    17   open Solve;                  (* NONE *)
    18   open Selem;                  e_fmz;
    19   open Stool;                  transfer_asms_from_to;
    20   open Tac;                    (* NONE *)
    21   open Model;                  (* NONE *)
    22   open LTool;                  rule2stac;
    23   open Rewrite;                mk_thm;
    24   open Calc;                   get_pair;
    25   open TermC;                  atomt;
    26   open Celem;                  e_pbt;
    27   open Rule;                   string_of_thm;
    28   open Tools;                  eval_lhs;
    29 (*\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)
    30 \<close>
    31 ML_file "Knowledge/biegelinie-3.sml" 
    32 
    33 section \<open>code for copy & paste ===============================================================\<close>
    34 ML \<open>
    35 "~~~~~ fun xxx , args:"; val () = ();
    36 "~~~~~ and xxx , args:"; val () = ();                                                                                     
    37 
    38 "~~~~~ to xxx return val:"; val () = ();
    39 
    40 \<close>
    41 text \<open>
    42   declare [[show_types]] 
    43   declare [[show_sorts]]            
    44   find_theorems "?a <= ?a"
    45   
    46   print_theorems
    47   print_facts
    48   print_statement ""
    49   print_theory
    50   ML_command \<open>Pretty.writeln prt\<close>
    51   declare [[ML_print_depth = 999]]
    52   declare [[ML_exception_trace]]
    53 \<close>
    54 ML \<open>
    55 (*========== inhibit exn WN130909 TODO =========================================================
    56 ============ inhibit exn WN130909 TODO ========================================================*)
    57 (*-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
    58 -.-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-*)
    59 \<close>
    60 
    61 section \<open>===================================================================================\<close>
    62 ML \<open>
    63 "~~~~~ fun xxx , args:"; val () = ();
    64 \<close> ML \<open>
    65 \<close> ML \<open>
    66 \<close> ML \<open>
    67 "~~~~~ fun xxx , args:"; val () = ();
    68 \<close>
    69 
    70 section \<open>================= "Knowledge/partial_fractions.sml" ============================\<close>
    71 ML \<open>
    72 "~~~~~ fun xxx , args:"; val () = ();
    73 \<close> ML \<open>
    74 (* Title:  partial fraction decomposition
    75    Author: Jan Rocnik
    76    (c) due to copyright terms
    77 *)
    78 
    79 "--------------------------------------------------------";
    80 "table of contents --------------------------------------";
    81 "--------------------------------------------------------";
    82 "----------- why helpless here ? ------------------------";
    83 "----------- why not nxt = Model_Problem here ? ---------";
    84 "----------- fun factors_from_solution ------------------";
    85 "----------- Logic.unvarify_global ----------------------";
    86 "----------- eval_drop_questionmarks --------------------";
    87 "----------- = me for met_partial_fraction --------------";
    88 "----------- autoCalculate for met_partial_fraction -----";
    89 "----------- progr.vers.2: check erls for multiply_ansatz";
    90 "----------- progr.vers.2: improve program --------------";
    91 "--------------------------------------------------------";
    92 "--------------------------------------------------------";
    93 "--------------------------------------------------------";
    94 
    95 
    96 "----------- why helpless here ? ------------------------";
    97 "----------- why helpless here ? ------------------------";
    98 "----------- why helpless here ? ------------------------";
    99 \<close> ML \<open>
   100 val fmz = ["filterExpression (X z = 3 / (z - 1/4 + -1/8 * (1/(z::real))))", 
   101   "stepResponse (x[n::real]::bool)"];
   102 val (dI,pI,mI) = ("Isac", ["Inverse", "Z_Transform", "SignalProcessing"], 
   103   ["SignalProcessing","Z_Transform","Inverse"]);
   104 val (p,_,f,nxt,_,pt)  = CalcTreeTEST [(fmz, (dI,pI,mI))]; 
   105 \<close> ML \<open>
   106 val (p,_,f,nxt,_,pt) = me nxt p [] pt; "Add_Given";
   107 val (p,_,f,nxt,_,pt) = me nxt p [] pt; "Add_Find";
   108 val (p,_,f,nxt,_,pt) = me nxt p [] pt; "Specify_Theory";
   109 val (p,_,f,nxt,_,pt) = me nxt p [] pt; "Specify_Problem";
   110 \<close> ML \<open>
   111 (*CURRENT*)(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*Specify_Method ["SignalProcessing", "Z_Transform", "Inverse"])*)
   112 \<close> ML \<open>
   113 val (p,_,f,nxt,_,pt) = me nxt p [] pt; "nxt = Apply_Method";
   114 (*CURRENT*)(*ERROR in creating the environment from formal args. of partial_function "HOL.eq"
   115 and the actual args., ie. items of the guard of "["SignalProcessing","Z_Transform","Inverse"]" by "assoc_by_type":
   116 formal arg "TYPE('a)" doesn't mach an actual arg.
   117 with:
   118 3 formal args: ["TYPE('a)","X_eq","z"]
   119 2 actual args: ["X z = 3 / (z - 1 / 4 + -1 / 8 * (1 / z))","x [n]"]*)
   120 \<close> ML \<open>
   121 val (p,_,f,nxt,_,pt) = me nxt p [] pt; "nxt = Rewrite (ruleZY, Inverse_Z_Transform.ruleZY) --> X z = 3 / (z - 1 / 4 + -1 / 8 * (1 / z))";
   122 val (p''',_,f,nxt''',_,pt''') = me nxt p [] pt; "nxt = Rewrite_Set norm_Rational --> X' z = 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))";
   123 \<close> ML \<open>
   124 "~~~~~ fun me, args:"; val ((_,tac), (p:pos'), _, (pt:ctree)) = (nxt, p, [], pt);
   125 val ("ok", (_, _, ptp)) = locatetac tac (pt,p)
   126 val (pt, p) = ptp;
   127 "~~~~~ fun step, args:"; val (((ip as (_,p_)):pos'), ((ptp as (pt,p), tacis):calcstate)) = 
   128                            (p, ((pt, e_pos'),[]));
   129 val pIopt = get_pblID (pt,ip);
   130 ip = ([],Res); "false";
   131 tacis; " = []";
   132 pIopt; (* = SOME ["Inverse", "Z_Transform", "SignalProcessing"]*)
   133 member op = [Pbl,Met] p_ andalso is_none (get_obj g_env pt (fst p)); "false";
   134 (*nxt_solve_ (pt,ip); "WAS isalist2list applied to NON-list 'no_meth'"
   135    THIS MEANS: replace no_meth by [no_meth] in Script.*)
   136 (*WAS val ("helpless",_) = step p ((pt, e_pos'),[]) *)
   137 (*WAS val (p,_,f,nxt,_,pt) = me nxt p [] pt; "Empty_Tac instead SubProblem";*)
   138 
   139 \<close> ML \<open>
   140 "----------- why not nxt = Model_Problem here ? ---------";
   141 "----------- why not nxt = Model_Problem here ? ---------";
   142 "----------- why not nxt = Model_Problem here ? ---------";
   143 val (p,_,f,nxt,_,pt) = me nxt''' p''' [] pt'''; 
   144 "~~~~~ fun me, args:"; val (((_,tac):tac'_), (p:pos'), _, (pt:ctree)) = (nxt, p, c, pt);
   145 val ("ok", (_, _, ptp)) = locatetac tac (pt,p);
   146 val (pt, p) = ptp;
   147 "~~~~~ fun step, args:"; val (((ip as (_,p_)):pos'), ((ptp as (pt,p), tacis):calcstate)) =
   148                            (p, ((pt, e_pos'),[]));
   149 val pIopt = get_pblID (pt,ip);
   150 ip = ([],Res); " = false";
   151 tacis; " = []";                                         
   152 pIopt (* = SOME ["Inverse", "Z_Transform", "SignalProcessing"]*);
   153 member op = [Pbl,Met] p_ andalso is_none (get_obj g_env pt (fst p)); " = false";
   154 (*                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ leads into
   155 nxt_solve_, which is definitely WRONG (should be nxt_specify_ for FIND_ADD).
   156 This ERROR seems to be introduced together with ctxt, concerns Apply_Method without init_form.
   157 See TODO.txt
   158 *)
   159 
   160 \<close> ML \<open>
   161 "----------- fun factors_from_solution ------------------";
   162 "----------- fun factors_from_solution ------------------";
   163 "----------- fun factors_from_solution ------------------";
   164 val ctxt = Proof_Context.init_global @{theory Isac};
   165 val SOME t = parseNEW ctxt "factors_from_solution [(z::real) = 1 / 2, z = -1 / 4]";
   166 val SOME (_, t') = eval_factors_from_solution "" 0 t thy;
   167 if term2str t' =
   168  "factors_from_solution [z = 1 / 2, z = -1 / 4] = (z - 1 / 2) * (z - -1 / 4)"
   169 then () else error "factors_from_solution broken";
   170 
   171 \<close> ML \<open>
   172 "----------- Logic.unvarify_global ----------------------";
   173 "----------- Logic.unvarify_global ----------------------";
   174 "----------- Logic.unvarify_global ----------------------";
   175 val A_var = parseNEW ctxt "A::real" |> the |> Logic.varify_global
   176 val B_var = parseNEW ctxt "B::real" |> the |> Logic.varify_global
   177 
   178 val denom1 = parseNEW ctxt "(z + -1 * (1 / 2))::real" |> the;
   179 val denom2 = parseNEW ctxt "(z + -1 * (-1 / 4))::real" |> the;
   180 
   181 val test = HOLogic.mk_binop "Groups.plus_class.plus"
   182   (HOLogic.mk_binop "Rings.divide_class.divide" (A_var, denom1),
   183    HOLogic.mk_binop "Rings.divide_class.divide" (B_var, denom2));
   184 
   185 if term2str test = "?A / (z + -1 * (1 / 2)) + ?B / (z + -1 * (-1 / 4))" then ()
   186   else error "HOLogic.mk_binop broken ?";
   187 
   188 (* Logic.unvarify_global test
   189 ---> exception TERM raised (line 539 of "logic.ML"): Illegal fixed variable: "z"
   190 thus we need another fun var2free in termC.sml*)
   191 
   192 \<close> ML \<open>
   193 "----------- = me for met_partial_fraction --------------";
   194 "----------- = me for met_partial_fraction --------------";
   195 "----------- = me for met_partial_fraction --------------";
   196 val fmz =
   197   ["functionTerm (3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z))))",
   198     "solveFor z", "decomposedFunction p_p"];
   199 val (dI',pI',mI') =
   200   ("Partial_Fractions", 
   201     ["partial_fraction", "rational", "simplification"],
   202     ["simplification","of_rationals","to_partial_fraction"]);
   203 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) =
   204               CalcTreeTEST [(fmz, (dI',pI',mI'))]; (*nxt = Model_Problem*)
   205 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "functionTerm (3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z))))")*)
   206 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "solveFor z")*)
   207 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Find "decomposedFunction p_p")*)
   208 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Theory "Partial_Fractions")*)
   209            (*05*)
   210 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Problem ["partial_fraction", "rational", "simplification"])*)
   211 (*[ ], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Method ["simplification", "of_rationals", "to_partial_fraction"])*)
   212 (*[ ], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Apply_Method ["simplification", "of_rationals", "to_partial_fraction"])*)
   213 (*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "norm_Rational")*)
   214 (*[1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Subproblem ("PolyEq", ["abcFormula", "degree_2", "polynomial", "univariate", "equation"]))*)
   215             (*10*)
   216 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Model_Problem)*)
   217 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "equality (-1 + -2 * z + 8 * z ^^^ 2 = 0)")*)
   218 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "solveFor z")*)
   219 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Find "solutions z_i")*)
   220 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Theory "PolyEq")*)
   221 (*[2], Pbl*)(*15*)
   222 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Problem ["abcFormula", "degree_2", "polynomial", "univariate", "equation"])*)
   223 (*[2], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Method ["PolyEq", "solve_d2_polyeq_abc_equation"])*)
   224 (*[2], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Apply_Method ["PolyEq", "solve_d2_polyeq_abc_equation"])*)
   225 (*[2, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set_Inst (["(''bdv'', z)"], "d2_polyeq_abcFormula_simplify"))*)
   226 (*[2, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "polyeq_simplify")*)
   227             (*20*)
   228 (*[2, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Or_to_List)*)
   229 (*[2, 3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_elementwise "Assumptions")*)
   230 (*[2, 4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["abcFormula", "degree_2", "polynomial", "univariate", "equation"])*)
   231 (*[2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Take "3 / ((z - 1 / 2) * (z - -1 / 4))")*)
   232 (*[3], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "ansatz_rls")*)
   233             (*25*)
   234 (*[3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Take "3 / ((z - 1 / 2) * (z - -1 / 4)) = ?A / (z - 1 / 2) + ?B / (z - -1 / 4)")*)
   235 (*[4], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "equival_trans")*)
   236 (*[4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Take "3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)"*)
   237 (*[5], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Substitute ["z = 1 / 2"])*)
   238 (*[5], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*nxt = Rewrite_Set "norm_Rational"*)
   239 (*[6], Res*)val (p''',_,f,nxt''',_,pt''') = me nxt p [] pt;(*nxt = Subproblem ("Isac", ["normalise", "polynomial", "univariate", "equation"]*)
   240             (*30+1*)
   241 (*[7], Pbl*)val (p'''',_,f,nxt'''',_,pt'''') = me nxt''' p''' [] pt'''; (*nxt = Model_Problem*)
   242 (*[7], Pbl*)val (p'v,_,f,nxt'v,_,pt'v) = me nxt'''' p'''' [] pt''''; (*nxt = Add_Given "equality (3 = 3 * AA / 4)")*)
   243 (*[7], Pbl*)val (p'v',_,f,nxt'v',_,pt'v') = me nxt'v p'v [] pt'v; (*nxt = Add_Given "solveFor AA")*)
   244 (*[7], Pbl*)val (p'v'',_,f,nxt'v'',_,pt'v'') = me nxt'v' p'v' [] pt'v'; (*nxt = Add_Find "solutions AA_i")*)
   245 (*[7], Pbl*)val (p,_,f,nxt,_,pt) = me nxt'v'' p'v'' [] pt'v''; (*nxt = Specify_Theory "Isac"*)
   246             (*35*)
   247 (*[7], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Problem ["normalise", "polynomial", "univariate", "equation"])*)
   248 (*[7], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Specify_Method ["PolyEq", "normalise_poly"])*)
   249 (*[7], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Apply_Method ["PolyEq", "normalise_poly"])*)
   250 (*[7, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite ("all_left", "\<not> ?b =!= 0 \<Longrightarrow> (?a = ?b) = (?a - ?b = 0)"))*)
   251 (*[7, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set_Inst (["(''bdv'', AA)"], "make_ratpoly_in")*)
   252                (*40*)
   253 (*[7, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Rewrite_Set "polyeq_simplify"*)
   254 (*[7, 3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Subproblem ("Isac", ["degree_1", "polynomial", "univariate", "equation"])*)
   255 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Model_Problem*)
   256 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "equality (3 + -3 / 4 * AA = 0)"*)
   257 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Add_Given "solveFor AA"*)
   258     (*45*)
   259 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   260 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   261 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   262 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   263 (*[7, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   264     (*50*)
   265 (*[7, 4], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   266 (*[7, 4, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   267 (*[7, 4, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   268 (*[7, 4, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   269 (*[7, 4, 3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   270     (*55*)
   271 (*[7, 4, 4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   272 (*[7, 4, 5], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   273 (*[7, 4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   274 (*[7], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   275 (*[8], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   276     (*60*)
   277 (*[8], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   278 (*[9], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   279 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   280 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   281 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   282     (*65*)
   283 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   284 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   285 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   286 (*[10], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   287 (*[10], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   288     (*70*)
   289 (*[10, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   290 (*[10, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   291 (*[10, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   292 (*[10, 3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   293 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   294     (*75*)
   295 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   296 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   297 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   298 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   299 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   300     (*80*)
   301 (*[10, 4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   302 (*[10, 4], Met*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   303 (*[10, 4, 1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   304 (*[10, 4, 1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   305 (*[10, 4, 2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   306     (*85*)
   307 (*[10, 4, 3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = *)
   308 (*[10, 4, 4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_elementwise "Assumptions"*)
   309 (*[10, 4, 5], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["degree_1", "polynomial", "univariate", "equation"*)
   310 (*[10, 4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["normalise", "polynomial", "univariate", "equation"]*)
   311 
   312 (*[10], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Take "AA / (z - 1 / 2) + BB / (z - -1 / 4)"*)
   313     (*90*)
   314 (*[11], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Substitute ["AA = 4", "BB = -4"]*)
   315 (*[11], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = Check_Postcond ["partial_fraction", "rational", "simplification"]*)
   316 (*[], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt = End_Proof'*) 
   317 
   318 case nxt of
   319   (_, End_Proof') => if f2str f = "4 / (z - 1 / 2) + -4 / (z - -1 / 4)" then () 
   320                      else error "= me .. met_partial_fraction f changed"
   321 | _ => error "= me .. met_partial_fraction nxt changed";
   322 
   323 show_pt_tac pt; (*[
   324 ([], Frm), Problem
   325  (''Partial_Fractions'',
   326   ??.\<^const>String.char.Char ''partial_fraction'' ''rational''
   327    ''simplification'')
   328 . . . . . . . . . . Apply_Method ["simplification","of_rationals","to_partial_fraction"],
   329 ([1], Frm), 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))
   330 . . . . . . . . . . Rewrite_Set "norm_Rational",
   331 ([1], Res), 24 / (-1 + -2 * z + 8 * z ^^^ 2)
   332 . . . . . . . . . . Subproblem (Isac, ["abcFormula","degree_2","polynomial","univariate","equation"]),
   333 ([2], Pbl), solve (-1 + -2 * z + 8 * z ^^^ 2 = 0, z)
   334 . . . . . . . . . . Apply_Method ["PolyEq","solve_d2_polyeq_abc_equation"],
   335 ([2,1], Frm), -1 + -2 * z + 8 * z ^^^ 2 = 0
   336 . . . . . . . . . . Rewrite_Set_Inst ([(''bdv'', z)], "d2_polyeq_abcFormula_simplify"),
   337 ([2,1], Res), z = (- -2 + sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8) \<or>
   338 z = (- -2 - sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8)
   339 . . . . . . . . . . Rewrite_Set "polyeq_simplify",
   340 ([2,2], Res), z = 1 / 2 \<or> z = -1 / 4
   341 . . . . . . . . . . Or_to_List ,
   342 ([2,3], Res), [z = 1 / 2, z = -1 / 4]
   343 . . . . . . . . . . Check_elementwise "Assumptions",
   344 ([2,4], Res), [z = 1 / 2, z = -1 / 4]
   345 . . . . . . . . . . Check_Postcond ["abcFormula","degree_2","polynomial","univariate","equation"],
   346 ([2], Res), [z = 1 / 2, z = -1 / 4]
   347 . . . . . . . . . . Take "3 / ((z - 1 / 2) * (z - -1 / 4))",
   348 ([3], Frm), 3 / ((z - 1 / 2) * (z - -1 / 4))
   349 . . . . . . . . . . Rewrite_Set "ansatz_rls",
   350 ([3], Res), AA / (z - 1 / 2) + BB / (z - -1 / 4)
   351 . . . . . . . . . . Take "3 / ((z - 1 / 2) * (z - -1 / 4)) = AA / (z - 1 / 2) + BB / (z - -1 / 4)",
   352 ([4], Frm), 3 / ((z - 1 / 2) * (z - -1 / 4)) = AA / (z - 1 / 2) + BB / (z - -1 / 4)
   353 . . . . . . . . . . Rewrite_Set "equival_trans",
   354 ([4], Res), 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)
   355 . . . . . . . . . . Substitute ["z = 1 / 2"],
   356 ([5], Res), 3 = AA * (1 / 2 - -1 / 4) + BB * (1 / 2 - 1 / 2)
   357 . . . . . . . . . . Rewrite_Set "norm_Rational",
   358 ([6], Res), 3 = 3 * AA / 4
   359 . . . . . . . . . . Subproblem (Isac, ["normalise","polynomial","univariate","equation"]),
   360 ([7], Pbl), solve (3 = 3 * AA / 4, AA)
   361 . . . . . . . . . . Apply_Method ["PolyEq","normalise_poly"],
   362 ([7,1], Frm), 3 = 3 * AA / 4
   363 . . . . . . . . . . Rewrite ("all_left", "\<not> ?b =!= 0 \<Longrightarrow> (?a = ?b) = (?a - ?b = 0)"),
   364 ([7,1], Res), 3 - 3 * AA / 4 = 0
   365 . . . . . . . . . . Rewrite_Set_Inst ([(''bdv'', AA)], "make_ratpoly_in"),
   366 ([7,2], Res), 3 / 1 + -3 / 4 * AA = 0
   367 . . . . . . . . . . Rewrite_Set "polyeq_simplify",
   368 ([7,3], Res), 3 + -3 / 4 * AA = 0
   369 . . . . . . . . . . Subproblem (Isac, ["degree_1","polynomial","univariate","equation"]),
   370 ([7,4], Pbl), solve (3 + -3 / 4 * AA = 0, AA)
   371 . . . . . . . . . . Apply_Method ["PolyEq","solve_d1_polyeq_equation"],
   372 ([7,4,1], Frm), 3 + -3 / 4 * AA = 0
   373 . . . . . . . . . . Rewrite_Set_Inst ([(''bdv'', AA)], "d1_polyeq_simplify"),
   374 ([7,4,1], Res), AA = -1 * 3 / (-3 / 4)
   375 . . . . . . . . . . Rewrite_Set "polyeq_simplify",
   376 ([7,4,2], Res), AA = -3 / (-3 / 4)
   377 . . . . . . . . . . Rewrite_Set "norm_Rational_parenthesized",
   378 ([7,4,3], Res), AA = 4
   379 . . . . . . . . . . Or_to_List ,
   380 ([7,4,4], Res), [AA = 4]
   381 . . . . . . . . . . Check_elementwise "Assumptions",
   382 ([7,4,5], Res), [AA = 4]
   383 . . . . . . . . . . Check_Postcond ["degree_1","polynomial","univariate","equation"],
   384 ([7,4], Res), [AA = 4]
   385 . . . . . . . . . . Check_Postcond ["normalise","polynomial","univariate","equation"],
   386 ([7], Res), [AA = 4]
   387 . . . . . . . . . . Take "3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)",
   388 ([8], Frm), 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)
   389 . . . . . . . . . . Substitute ["z = -1 / 4"],
   390 ([8], Res), 3 = AA * (-1 / 4 - -1 / 4) + BB * (-1 / 4 - 1 / 2)
   391 . . . . . . . . . . Rewrite_Set "norm_Rational",
   392 ([9], Res), 3 = -3 * BB / 4
   393 . . . . . . . . . . Subproblem (Isac, ["normalise","polynomial","univariate","equation"]),
   394 ([10], Pbl), solve (3 = -3 * BB / 4, BB)
   395 . . . . . . . . . . Apply_Method ["PolyEq","normalise_poly"],
   396 ([10,1], Frm), 3 = -3 * BB / 4
   397 . . . . . . . . . . Rewrite ("all_left", "\<not> ?b =!= 0 \<Longrightarrow> (?a = ?b) = (?a - ?b = 0)"),
   398 ([10,1], Res), 3 - -3 * BB / 4 = 0
   399 . . . . . . . . . . Rewrite_Set_Inst ([(''bdv'', BB)], "make_ratpoly_in"),
   400 ([10,2], Res), 3 / 1 + 3 / 4 * BB = 0
   401 . . . . . . . . . . Rewrite_Set "polyeq_simplify",
   402 ([10,3], Res), 3 + 3 / 4 * BB = 0
   403 . . . . . . . . . . Subproblem (Isac, ["degree_1","polynomial","univariate","equation"]),
   404 ([10,4], Pbl), solve (3 + 3 / 4 * BB = 0, BB)
   405 . . . . . . . . . . Apply_Method ["PolyEq","solve_d1_polyeq_equation"],
   406 ([10,4,1], Frm), 3 + 3 / 4 * BB = 0
   407 . . . . . . . . . . Rewrite_Set_Inst ([(''bdv'', BB)], "d1_polyeq_simplify"),
   408 ([10,4,1], Res), BB = -1 * 3 / (3 / 4)
   409 . . . . . . . . . . Rewrite_Set "polyeq_simplify",
   410 ([10,4,2], Res), BB = -3 / (3 / 4)
   411 . . . . . . . . . . Rewrite_Set "norm_Rational_parenthesized",
   412 ([10,4,3], Res), BB = -4
   413 . . . . . . . . . . Or_to_List ,
   414 ([10,4,4], Res), [BB = -4]
   415 . . . . . . . . . . Check_elementwise "Assumptions",
   416 ([10,4,5], Res), [BB = -4]
   417 . . . . . . . . . . Check_Postcond ["degree_1","polynomial","univariate","equation"],
   418 ([10,4], Res), [BB = -4]
   419 . . . . . . . . . . Check_Postcond ["normalise","polynomial","univariate","equation"],
   420 ([10], Res), [BB = -4]
   421 . . . . . . . . . . Take "AA / (z - 1 / 2) + BB / (z - -1 / 4)",
   422 ([11], Frm), AA / (z - 1 / 2) + BB / (z - -1 / 4)
   423 . . . . . . . . . . Substitute ["AA = 4","BB = -4"],
   424 ([11], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)
   425 . . . . . . . . . . Check_Postcond ["partial_fraction","rational","simplification"],
   426 ([], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)] 
   427 val it = (): unit
   428 *)
   429 
   430 "----------- autoCalculate for met_partial_fraction -----";
   431 "----------- autoCalculate for met_partial_fraction -----";
   432 "----------- autoCalculate for met_partial_fraction -----";
   433 reset_states ();
   434   val fmz =                                             
   435     ["functionTerm (3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z))))", 
   436       "solveFor z", "decomposedFunction p_p"];
   437   val (dI', pI', mI') =
   438     ("Partial_Fractions", 
   439       ["partial_fraction", "rational", "simplification"],
   440       ["simplification","of_rationals","to_partial_fraction"]);
   441 CalcTree [(fmz, (dI' ,pI' ,mI'))];
   442 Iterator 1;
   443 moveActiveRoot 1;
   444 autoCalculate 1 CompleteCalc; 
   445 
   446 val ((pt,p),_) = get_calc 1; val ip = get_pos 1 1;
   447 if p = ip andalso ip = ([], Res) then ()
   448   else error "autoCalculate for met_partial_fraction changed: final pos'";
   449 
   450 val (Form f, tac, asms) = pt_extract (pt, p);
   451 if term2str f = "4 / (z - 1 / 2) + -4 / (z - -1 / 4)" andalso
   452   terms2str' asms =
   453     "[BB = -4,BB is_polyexp,AA is_polyexp,AA = 4," ^
   454     "lhs (-1 + -2 * z + 8 * z ^^^ 2 = 0) has_degree_in z = 2," ^
   455     "lhs (-1 + -2 * z + 8 * z ^^^ 2 = 0) is_poly_in z,z = 1 / 2,z = -1 / 4,z is_polyexp]"
   456 then case tac of NONE => ()
   457   | _ => error "me for met_partial_fraction changed: final result 1"
   458 else error "me for met_partial_fraction changed: final result 2"
   459 
   460 show_pt pt;
   461 (*[
   462 (([], Frm), Problem (Partial_Fractions, [partial_fraction, rational, simplification])),
   463 (([1], Frm), 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))),
   464 (([1], Res), 24 / (-1 + -2 * z + 8 * z ^^^ 2)),
   465 (([2], Pbl), solve (-1 + -2 * z + 8 * z ^^^ 2 = 0, z)),
   466 (([2,1], Frm), -1 + -2 * z + 8 * z ^^^ 2 = 0),
   467 (([2,1], Res), z = (- -2 + sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8) |
   468 z = (- -2 - sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8)),
   469 (([2,2], Res), z = 1 / 2 | z = -1 / 4),
   470 (([2,3], Res), [z = 1 / 2, z = -1 / 4]),
   471 (([2,4], Res), [z = 1 / 2, z = -1 / 4]),
   472 (([2], Res), [z = 1 / 2, z = -1 / 4]),
   473 (([3], Frm), 3 / ((z - 1 / 2) * (z - -1 / 4))),
   474 (([3], Res), ?A / (z - 1 / 2) + ?B / (z - -1 / 4)),
   475 (([4], Frm), 3 / ((z - 1 / 2) * (z - -1 / 4)) = ?A / (z - 1 / 2) + ?B / (z - -1 / 4)),
   476 (([4], Res), 3 = ?A * (z - -1 / 4) + ?B * (z - 1 / 2)),
   477 (([5], Frm), 3 = A * (z - -1 / 4) + B * (z - 1 / 2)),
   478 (([5], Res), 3 = A * (1 / 2 - -1 / 4) + B * (1 / 2 - 1 / 2)),
   479 (([6], Res), 3 = 3 * A / 4),
   480 (([7], Pbl), solve (3 = 3 * A / 4, A)),
   481 (([7,1], Frm), 3 = 3 * A / 4),
   482 (([7,1], Res), 3 - 3 * A / 4 = 0),
   483 (([7,2], Res), 3 / 1 + -3 / 4 * A = 0),
   484 (([7,3], Res), 3 + -3 / 4 * A = 0),
   485 (([7,4], Pbl), solve (3 + -3 / 4 * A = 0, A)),
   486 (([7,4,1], Frm), 3 + -3 / 4 * A = 0),
   487 (([7,4,1], Res), A = -1 * 3 / (-3 / 4)),
   488 (([7,4,2], Res), A = -3 / (-3 / 4)),
   489 (([7,4,3], Res), A = 4),
   490 (([7,4,4], Res), [A = 4]),
   491 (([7,4,5], Res), [A = 4]),
   492 (([7,4], Res), [A = 4]),
   493 (([7], Res), [A = 4]),
   494 (([8], Frm), 3 = A * (z - -1 / 4) + B * (z - 1 / 2)),
   495 (([8], Res), 3 = A * (-1 / 4 - -1 / 4) + B * (-1 / 4 - 1 / 2)),
   496 (([9], Res), 3 = -3 * B / 4),
   497 (([10], Pbl), solve (3 = -3 * B / 4, B)),
   498 (([10,1], Frm), 3 = -3 * B / 4),
   499 (([10,1], Res), 3 - -3 * B / 4 = 0),
   500 (([10,2], Res), 3 / 1 + 3 / 4 * B = 0),
   501 (([10,3], Res), 3 + 3 / 4 * B = 0),
   502 (([10,4], Pbl), solve (3 + 3 / 4 * B = 0, B)),
   503 (([10,4,1], Frm), 3 + 3 / 4 * B = 0),
   504 (([10,4,1], Res), B = -1 * 3 / (3 / 4)),
   505 (([10,4,2], Res), B = -3 / (3 / 4)),
   506 (([10,4,3], Res), B = -4),
   507 (([10,4,4], Res), [B = -4]),
   508 (([10,4,5], Res), [B = -4]),
   509 (([10,4], Res), [B = -4]),
   510 (([10], Res), [B = -4]),
   511 (([11], Frm), A / (z - 1 / 2) + B / (z - -1 / 4)),
   512 (([11], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)),
   513 (([], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4))] *)
   514 
   515 \<close> ML \<open>
   516 "----------- progr.vers.2: check erls for multiply_ansatz";
   517 "----------- progr.vers.2: check erls for multiply_ansatz";
   518 "----------- progr.vers.2: check erls for multiply_ansatz";
   519 (*test for outcommented 3 lines in script: is norm_Rational strong enough?*)
   520 val t = str2term "(3 / ((-1 + -2 * z + 8 * z ^^^ 2) *3/24)) = (3 / ((z - 1 / 2) * (z - -1 / 4)))";
   521 val SOME (t', _) = rewrite_set_ @{theory Isac} true ansatz_rls t;
   522 term2str t' = "3 / ((-1 + -2 * z + 8 * z ^^^ 2) * 3 / 24) =\n?A / (z - 1 / 2) + ?B / (z - -1 / 4)";
   523 
   524 val SOME (t'', _) = rewrite_set_ @{theory Isac} true multiply_ansatz t'; (*true*)
   525 term2str t'' = "(z - 1 / 2) * (z - -1 / 4) * 3 / ((-1 + -2 * z + 8 * z ^^^ 2) * 3 / 24) =\n" ^
   526   "?A * (z - -1 / 4) + ?B * (z - 1 / 2)"; (*true*)
   527 
   528 val SOME (t''', _) = rewrite_set_ @{theory Isac} true norm_Rational t''; 
   529 if term2str t''' = "3 = (AA + -2 * BB + 4 * z * AA + 4 * z * BB) / 4" then () 
   530 else error "ansatz_rls - multiply_ansatz - norm_Rational broken"; 
   531 
   532 (*test for outcommented 3 lines in script: empower erls for x = a*b ==> ...*)
   533 val xxx = append_rls "multiply_ansatz_erls" norm_Rational 
   534   [Calc ("HOL.eq",eval_equal "#equal_")];
   535 
   536 val multiply_ansatz = prep_rls @{theory} (
   537   Rls {id = "multiply_ansatz", preconds = [], rew_ord = ("dummy_ord",dummy_ord), 
   538 	  erls = xxx,
   539 	  srls = Erls, calc = [], errpatts = [],
   540 	  rules = 
   541 	   [Thm ("multiply_2nd_order",num_str @{thm multiply_2nd_order})
   542 	   ], 
   543 	 scr = EmptyScr}:rls);
   544 
   545 rewrite_set_ thy true xxx @{term "a+b = a+(b::real)"}; (*SOME ok*)
   546 rewrite_set_ thy true multiply_ansatz @{term "a+b = a+(b::real)"}; (*why NONE?*)
   547 
   548 "----------- progr.vers.2: improve program --------------";
   549 "----------- progr.vers.2: improve program --------------";
   550 "----------- progr.vers.2: improve program --------------";
   551 (*WN120318 stopped due to much effort with the test above*)
   552      "Script PartFracScript (f_f::real) (zzz::real) =                    " ^(*f_f: 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)), zzz: z*)
   553      " (let f_f = Take f_f;                                       " ^
   554      "   (num_orig::real) = get_numerator f_f;                    " ^(*num_orig: 3*)
   555      "   f_f = (Rewrite_Set norm_Rational False) f_f;             " ^(*f_f: 24 / (-1 + -2 * z + 8 * z ^^^ 2)*)
   556      "   (numer::real) = get_numerator f_f;                       " ^(*numer: 24*)
   557      "   (denom::real) = get_denominator f_f;                     " ^(*denom: -1 + -2 * z + 8 * z ^^^ 2*)
   558      "   (equ::bool) = (denom = (0::real));                       " ^(*equ: -1 + -2 * z + 8 * z ^^^ 2 = 0*)
   559      "   (L_L::bool list) = (SubProblem (PolyEqX,                 " ^
   560      "     [abcFormula, degree_2, polynomial, univariate, equation], " ^
   561      "     [no_met]) [BOOL equ, REAL zzz]);                       " ^(*L_L: [z = 1 / 2, z = -1 / 4]*)
   562      "   (facs::real) = factors_from_solution L_L;                " ^(*facs: (z - 1 / 2) * (z - -1 / 4)*)
   563      "   (eql::real) = Take (num_orig / facs);                    " ^(*eql: 3 / ((z - 1 / 2) * (z - -1 / 4)) *) 
   564      "   (eqr::real) = (Try (Rewrite_Set ansatz_rls False)) eql;  " ^(*eqr: ?A / (z - 1 / 2) + ?B / (z - -1 / 4)*)
   565      "   (eq::bool) = Take (eql = eqr);                           " ^(*eq:  3 / ((z - 1 / 2) * (z - -1 / 4)) = ?A / (z - 1 / 2) + ?B / (z - -1 / 4)*)
   566 (*this has been tested below by rewrite_set_
   567      "   (eeeee::bool) = Take ((num_orig / denom * denom / numer) = (num_orig / facs));" ^(**)
   568      "   (eeeee::bool) = (Rewrite_Set ansatz_rls False) eeeee;" ^(**)
   569      "   eq = (Try (Rewrite_Set multiply_ansatz False)) eeeee;         " ^(*eq: 3 = ?A * (z - -1 / 4) + ?B * (z - 1 / 2)*) 
   570 NEXT try to outcomment the very next line..*)
   571      "   eq = (Try (Rewrite_Set equival_trans False)) eeeee;         " ^(*eq: 3 = ?A * (z - -1 / 4) + ?B * (z - 1 / 2)*) 
   572      "   eq = drop_questionmarks eq;                              " ^(*eq: 3 = A * (z - -1 / 4) + B * (z - 1 / 2)*)
   573      "   (z1::real) = (rhs (NTH 1 L_L));                          " ^(*z1: 1 / 2*)
   574      "   (z2::real) = (rhs (NTH 2 L_L));                          " ^(*z2: -1 / 4*)
   575      "   (eq_a::bool) = Take eq;                                  " ^(*eq_a: 3 = A * (z - -1 / 4) + B * (z - 1 / 2)*)
   576      "   eq_a = (Substitute [zzz = z1]) eq;                       " ^(*eq_a: 3 = A * (1 / 2 - -1 / 4) + B * (1 / 2 - 1 / 2)*)
   577      "   eq_a = (Rewrite_Set norm_Rational False) eq_a;           " ^(*eq_a: 3 = 3 * A / 4*)
   578      "   (sol_a::bool list) =                                     " ^
   579      "     (SubProblem (IsacX, [univariate,equation], [no_met])   " ^
   580      "     [BOOL eq_a, REAL (A::real)]);                          " ^(*sol_a: [A = 4]*)
   581      "   (a::real) = (rhs (NTH 1 sol_a));                         " ^(*a: 4*)
   582      "   (eq_b::bool) = Take eq;                                  " ^(*eq_b: 3 = A * (z - -1 / 4) + B * (z - 1 / 2)*)
   583      "   eq_b = (Substitute [zzz = z2]) eq_b;                     " ^(*eq_b: *)
   584      "   eq_b = (Rewrite_Set norm_Rational False) eq_b;           " ^(*eq_b: *)
   585      "   (sol_b::bool list) =                                     " ^
   586      "     (SubProblem (IsacX, [univariate,equation], [no_met])   " ^
   587      "     [BOOL eq_b, REAL (B::real)]);                          " ^(*sol_b: [B = -4]*)
   588      "   (b::real) = (rhs (NTH 1 sol_b));                         " ^(*b: -4*)
   589      "   eqr = drop_questionmarks eqr;                            " ^(*eqr: A / (z - 1 / 2) + B / (z - -1 / 4)*)
   590      "   (pbz::real) = Take eqr;                                  " ^(*pbz: A / (z - 1 / 2) + B / (z - -1 / 4)*)
   591      "   pbz = ((Substitute [A = a, B = b]) pbz)                  " ^(*pbz: 4 / (z - 1 / 2) + -4 / (z - -1 / 4)*)
   592      " in pbz)"
   593 
   594 \<close> ML \<open>
   595 \<close> ML \<open>
   596 "~~~~~ fun xxx , args:"; val () = ();
   597 \<close>
   598 
   599 section \<open>=============== "Knowledge/biegelinie-3.sml" ===============================\<close>
   600 ML \<open>
   601 "~~~~~ fun xxx , args:"; val () = ();
   602 \<close> ML \<open>
   603 (* "Knowledge/biegelinie-3.sml"
   604    author: Walther Neuper 190515
   605    (c) due to copyright terms
   606 *)
   607 "table of contents -----------------------------------------------";
   608 "-----------------------------------------------------------------";
   609 "----------- see biegelinie-1.sml---------------------------------";
   610 (* problems with generalised handling of meths which extend the model of a probl
   611    since 98298342fb6d: wait for review of whole model-specify phase *)
   612 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. me -----";
   613 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. auto ---";
   614 "-----------------------------------------------------------------";
   615 "-----------------------------------------------------------------";
   616 "-----------------------------------------------------------------";
   617 
   618 \<close> ML \<open>
   619 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. me -----";
   620 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. me -----";
   621 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. me -----";
   622 "----- Bsp 7.70 with me";
   623 val fmz = ["Traegerlaenge L","Streckenlast q_0","Biegelinie y",
   624 	     "Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0]",
   625 	     "FunktionsVariable x", "GleichungsVariablen [c, c_2, c_3, c_4]",
   626        "AbleitungBiegelinie dy"];
   627 val (dI',pI',mI') = ("Biegelinie", ["Biegelinien"],
   628 		     ["IntegrierenUndKonstanteBestimmen2"]);
   629 val p = e_pos'; val c = [];
   630 (*//----------------------------------vvv CalcTreeTEST ----------------------------------------\\*)
   631 (*[], Pbl*)val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; (*nxt = Model_Problem*)
   632 
   633 (*+*)val PblObj {probl, meth, spec = (thy, _ , metID), origin = (oris, _, _), ...} = get_obj I pt (fst p);
   634 (*+*)writeln (oris2str oris); (*[
   635 (1, ["1"], #Given,Traegerlaenge, ["L"]),
   636 (2, ["1"], #Given,Streckenlast, ["q_0"]),
   637 (3, ["1"], #Find,Biegelinie, ["y"]),
   638 (4, ["1"], #Relate,Randbedingungen, ["[y 0 = 0]","[y L = 0]","[M_b 0 = 0]","[M_b L = 0]"]),
   639 (5, ["1"], #undef,FunktionsVariable, ["x"]),
   640 (6, ["1"], #undef,GleichungsVariablen, ["[c]","[c_2]","[c_3]","[c_4]"]),
   641 (7, ["1"], #undef,AbleitungBiegelinie, ["dy"])]*)
   642 (*+*)itms2str_ @{context} probl = "[]";
   643 (*+*)itms2str_ @{context} meth = "[]";
   644 (*\\----------------------------------^^^ CalcTreeTEST ----------------------------------------//*)
   645 
   646 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Given "Traegerlaenge L"*)
   647 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Given "Streckenlast q_0"*)
   648 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Find "Biegelinie y"*)
   649 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Relation "Randbedingungen [y 0 = 0]", ERROR MISSING step: M_b 0 = 0*)
   650 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Relation "Randbedingungen [y L = 0, M_b 0 = 0, M_b L = 0]"*)
   651 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Specify_Theory "Biegelinie"*)
   652 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Specify_Problem ["Biegelinien"]*)
   653 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Specify_Method ["IntegrierenUndKonstanteBestimmen2"]*)
   654 (*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Given "FunktionsVariable x"*)
   655 (*----------- 10 -----------*)
   656 (*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Given "GleichungsVariablen [c, c_2, c_3, c_4]"*)
   657 (*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Given "AbleitungBiegelinie dy*)
   658 (*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Apply_Method ["IntegrierenUndKonstanteBestimmen2"*)
   659 
   660 (*//----------------------------------vvv Apply_Method ["IntegrierenUndKonstanteBestimmen2"----\\*)
   661 (*[1], Pbl*)val (p''''',_,f,nxt''''',_,pt''''') = me nxt p c pt; (*nxt = Model_Problem*)
   662 (*AMBIGUITY in creating the environment from formal args. of partial_function "Biegelinie.Biegelinie2Script"
   663 and the actual args., ie. items of the guard of "["IntegrierenUndKonstanteBestimmen2"]" by "assoc_by_type":
   664 formal arg. "b" type-matches with several...actual args. "["dy","y"]"
   665 selected "dy"
   666 with
   667 formals: ["l","q","v","b","s","vs","id_abl"]
   668 actuals: ["L","q_0","x","[c, c_2, c_3, c_4]","dy","y","[y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0]"]*)
   669 
   670 "~~~~~ fun me , args:"; val ((_, tac), p, _(*NEW remove*), pt) = (nxt, p, c, pt);
   671     val (pt''', p''') =
   672 	    (*locatetac is here for testing by me; step would suffice in me*)
   673 	    case locatetac tac (pt,p) of
   674 		    ("ok", (_, _, ptp)) => ptp
   675 ;
   676 (*+*)p    = ([], Met);
   677 (*+*)p''' = ([1], Pbl);
   678 (*+*)val PblObj {meth, probl, spec = (thy, _ , metID), origin = (oris, _, _), ...} = get_obj I pt''' (fst p''');
   679 (*+*)(*MISSING after locatetac:*)
   680 (*+*)writeln (oris2str oris); (*[
   681 (1, ["1"], #Given,Streckenlast, ["q_0"]),
   682 (2, ["1"], #Given,FunktionsVariable, ["x"]),
   683 (3, ["1"], #Find,Funktionen, ["funs'''"])]
   684 MISSING:
   685                  Biegelinie
   686                  AbleitungBiegelinie
   687 *)
   688 "~~~~~ fun locatetac , args:"; val (tac, (ptp as (pt, p))) = (tac, (pt,p));
   689       val (mI, m) = Solve.mk_tac'_ tac;
   690 val Appl m = (*case*) Applicable.applicable_in p pt m (*of*);
   691 (*if*) member op = Solve.specsteps mI = false; (*else*)
   692 
   693 loc_solve_ (mI,m) ptp;
   694 "~~~~~ fun loc_solve_ , args:"; val (m, (pt, pos)) = ((mI,m), ptp);
   695 
   696 Solve.solve m (pt, pos);
   697 "~~~~~ fun solve , args:"; val (("Apply_Method", m as Tac.Apply_Method' (mI, _, _, _)), (pt, (pos as (p, _)))) =
   698   (m, (pt, pos));
   699 val {srls, ...} = Specify.get_met mI;
   700       val itms = case get_obj I pt p of
   701         PblObj {meth=itms, ...} => itms
   702       | _ => error "solve Apply_Method: uncovered case get_obj"
   703       val thy' = get_obj g_domID pt p;
   704       val thy = Celem.assoc_thy thy';
   705       val (is, env, ctxt, sc) = case Lucin.init_scrstate thy itms mI of
   706         (is as Selem.ScrState (env,_,_,_,_,_), ctxt, sc) =>  (is, env, ctxt, sc)
   707       | _ => error "solve Apply_Method: uncovered case init_scrstate"
   708       val ini = Lucin.init_form thy sc env;
   709       val p = lev_dn p;
   710 val NONE = (*case*) ini (*of*);
   711             val (m', (is', ctxt'), _) = Lucin.next_tac (thy', srls) (pt, (p, Res)) sc (is, ctxt);
   712 	          val d = Rule.e_rls (*FIXME: get simplifier from domID*);
   713 val Steps (_, ss as (_, _, pt', p', c') :: _) =
   714 (*case*) Lucin.locate_gen (thy',srls) m' (pt,(p, Res)) (sc,d) (is', ctxt') (*of*);
   715 
   716 (*+*)val PblObj {meth, probl, spec = (thy, _ , metID), origin = (oris, _, _), ...} = get_obj I pt' (fst p');
   717 (*+*)(*MISSING after locate_gen:*)
   718 (*+*)writeln (oris2str oris); (*[
   719 (1, ["1"], #Given,Streckenlast, ["q_0"]),
   720 (2, ["1"], #Given,FunktionsVariable, ["x"]),
   721 (3, ["1"], #Find,Funktionen, ["funs'''"])]
   722 MISSING:
   723                  Biegelinie
   724                  AbleitungBiegelinie
   725 *)
   726 "~~~~~ fun locate_gen , args:"; val ((thy', srls), m, (pt, p),
   727 	    (scr as Rule.Prog sc, d), (Selem.ScrState (E,l,a,v,S,b), ctxt)) =
   728   ((thy',srls), m', (pt,(p, Res)), (sc,d), (is', ctxt'));
   729 val thy = Celem.assoc_thy thy';
   730 (*if*) l = [] orelse (
   731 		  (*init.in solve..Apply_Method...*)(last_elem o fst) p = 0 andalso snd p = Res) = true;(*then*)
   732 (assy (thy',ctxt,srls,d,Aundef) ((E,[Celem.R],a,v,S,b), [(m,Generate.EmptyMout,pt,p,[])]) (body_of sc));
   733 
   734 "~~~~~ fun assy , args:"; val (ya, ((E,l,a,v,S,b),ss:step list), (Const ("HOL.Let",_) $ e $ (Abs (id,T,body)))) =
   735   ((thy',ctxt,srls,d,Aundef), ((E,[Celem.R],a,v,S,b), [(m,Generate.EmptyMout,pt,p,[])]), (body_of sc));
   736 (*case*) assy ya ((E , l @ [Celem.L, Celem.R], a,v,S,b), ss) e (*of*);
   737 
   738 "~~~~~ fun assy , args:"; val ((thy',ctxt,sr,d,ap), ((E,l,a,v,S,_), (m,_,pt,(p,p_),c)::ss), t) =
   739   (ya, ((E , l @ [Celem.L, Celem.R], a,v,S,b), ss), e);
   740 val (a', LTool.STac stac) = (*case*) handle_leaf "locate" thy' sr E a v t (*of*);
   741 (*+*)writeln (term2str stac); (*SubProblem
   742  (''Biegelinie'', [''vonBelastungZu'', ''Biegelinien''],
   743   [''Biegelinien'', ''ausBelastung''])
   744  [REAL q_0, REAL x, REAL_REAL y, REAL_REAL dy] *)
   745            val p' = 
   746              case p_ of Frm => p 
   747              | Res => lev_on p
   748 		         | _ => error ("assy: call by " ^ pos'2str (p,p_));
   749      val Ass (m,v') = (*case*) assod pt d m stac (*of*);
   750 
   751 "~~~~~ fun assod , args:"; val (pt, _, (Tac.Subproblem' ((domID, pblID, _), _, _, _, _, _)),
   752       (stac as Const ("Script.SubProblem", _) $ (Const ("Product_Type.Pair", _) $ 
   753         dI' $ (Const ("Product_Type.Pair", _) $ pI' $ mI')) $ ags')) =
   754   (pt, d, m, stac);
   755       val dI = HOLogic.dest_string dI';
   756       val thy = Stool.common_subthy (Celem.assoc_thy dI, rootthy pt);
   757 	    val pI = pI' |> HOLogic.dest_list |> map HOLogic.dest_string;
   758 	    val mI = mI' |> HOLogic.dest_list |> map HOLogic.dest_string;
   759 	    val ags = TermC.isalist2list ags';
   760 (*if*) mI = ["no_met"] = false; (*else*)
   761 (*    val (pI, pors, mI) = *)
   762 	      (pI, (Chead.match_ags thy ((#ppc o Specify.get_pbt) pI) ags)
   763 		      handle ERROR "actual args do not match formal args"
   764 		      => (Chead.match_ags_msg pI stac ags(*raise exn*); []), mI);
   765 "~~~~~ fun match_ags , args:"; val (thy, pbt, ags) = (thy, ((#ppc o Specify.get_pbt) pI), ags);
   766 (*+*)pbt;
   767     fun flattup (i, (var, bool, str, itm_)) = (i, var, bool, str, itm_)
   768     val pbt' = filter_out is_copy_named pbt
   769     val cy = filter is_copy_named pbt
   770     val oris' = matc thy pbt' ags []
   771     val cy' = map (cpy_nam pbt' oris') cy
   772     val ors = Specify.add_id (oris' @ cy') (*...appended in order to get into the model-items *)
   773 
   774 (*+*)val c = [];
   775 (*\\----------------------------------^^^ Apply_Method ["IntegrierenUndKonstanteBestimmen2"----//*)
   776 
   777 (*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt''''' p''''' c pt'''''; (*nxt = Add_Given "Streckenlast q_0"*)
   778 (*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Given "FunktionsVariable x"*)
   779 (*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Add_Find "Funktionen funs'''"*)
   780 (*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Specify_Theory "Biegelinie"*)
   781 (*[1], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = Specify_Problem ["vonBelastungZu", "Biegelinien"]*)
   782 (*[1], Pbl*)val (p''''',_,f,nxt''''',_,pt''''') = me nxt p c pt; (*nxt = Specify_Method ["Biegelinien", "ausBelastung"]*)
   783 (*----------- 20 -----------*)
   784 (*//------------------------------------------------vvv Specify_Method ["Biegelinien", "ausBelastung"]-\\*)
   785 (*[1], Pbl*)(*ERROR val (p,_,f,nxt,_,pt) = me nxt''''' p''''' c pt'''''; (*nxt = Apply_Method ["Biegelinien", "ausBelastung"]*)
   786 ERROR itms2args: 'Biegelinie' not in itms*)
   787 
   788 (*SubProblem (_, [''vonBelastungZu'', ''Biegelinien''], _)
   789     [REAL q, REAL v, REAL_REAL b, REAL_REAL id_abl]
   790                      ^^^^^^^^^^^ ..ERROR itms2args: 'Biegelinie' not in itms*)
   791 (*+*)val PblObj {meth, probl, spec = (thy, _ , metID), origin = (oris, _, _), ...} = get_obj I pt''''' (fst p''''');
   792 (*+*)if oris2str oris =
   793 (*+*)  "[\n(1, [\"1\"], #Given,Streckenlast, [\"q_0\"]),\n(2, [\"1\"], #Given,FunktionsVariable, [\"x\"]),\n(3, [\"1\"], #Find,Funktionen, [\"funs'''\"])]"
   794 (*+*)then () else error "([1], Pbl) Specify_Problem ['vonBelastungZu', 'Biegelinien'] changed oris";
   795 writeln (oris2str oris); (*[
   796 (1, ["1"], #Given,Streckenlast, ["q_0"]),
   797 (2, ["1"], #Given,FunktionsVariable, ["x"]),
   798 (3, ["1"], #Find,Funktionen, ["funs'''"])]*)
   799 (*+*)if itms2str_ @{context} probl = "[\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''']))]"
   800 (*+*)then () else error "([1], Pbl) Specify_Problem ['vonBelastungZu', 'Biegelinien'] changed probl";
   801 writeln (itms2str_ @{context} probl); (*[
   802 (1 ,[1] ,true ,#Given ,Cor Streckenlast q_0 ,(q_q, [q_0])),
   803 (2 ,[1] ,true ,#Given ,Cor FunktionsVariable x ,(v_v, [x])),
   804 (3 ,[1] ,true ,#Find ,Cor Funktionen funs''' ,(funs''', [funs''']))]*)
   805 (*+*)if itms2str_ @{context} meth = "[]"
   806 (*+*)then () else error "([1], Pbl) Specify_Problem ['vonBelastungZu', 'Biegelinien'] changed meth";
   807 writeln (itms2str_ @{context} meth); (*[]*)
   808 
   809 "~~~~~ fun me , args:"; val ((_, tac), p, _(*NEW remove*), pt) = (nxt''''', p''''', c, pt''''');
   810 (*  val (pt, p) = *)
   811 	    (*locatetac is here for testing by me; step would suffice in me*)
   812 	    case locatetac tac (pt,p) of
   813 		    ("ok", (_, _, ptp)) => ptp
   814 ;
   815 "~~~~~ fun locatetac , args:"; val (tac, (ptp as (pt, p))) = (tac, (pt,p));
   816       val (mI, m) = Solve.mk_tac'_ tac;
   817 val Chead.Appl m = (*case*) Applicable.applicable_in p pt m (*of*);
   818 (*if*) member op = Solve.specsteps mI = true; (*then*)
   819 
   820 (*val Updated (_, _, (ctree, pos')) =*) loc_specify_ m ptp; (*creates meth-itms*)
   821 "~~~~~ fun loc_specify_ , args:"; val (m, (pt, pos)) = (m, ptp);
   822 (*    val (p, _, f, _, _, pt) =*) Chead.specify m pos [] pt;
   823 
   824 "~~~~~ fun specify , args:"; val ((Tac.Specify_Method' (mID, _, _)), (pos as (p, _)), _, pt) = (m, pos, [], pt);
   825         val (oris, dI', pI', mI', dI, pI, pbl, met, ctxt) = case get_obj I pt p of
   826           PblObj {origin= (oris, (dI', pI', mI'), _), spec= (dI, pI, _), probl = pbl, meth = met, ctxt, ...} =>
   827              (oris, dI', pI', mI', dI, pI, pbl, met, ctxt)
   828         val {ppc, pre, prls,...} = Specify.get_met mID
   829         val thy = Celem.assoc_thy dI
   830         val dI'' = if dI = Rule.e_domID then dI' else dI
   831         val pI'' = if pI = Celem.e_pblID then pI' else pI
   832 ;
   833 (*+*)writeln (oris2str oris); (*[
   834 (1, ["1"], #Given,Streckenlast, ["q_0"]),
   835 (2, ["1"], #Given,FunktionsVariable, ["x"]),
   836 (3, ["1"], #Find,Funktionen, ["funs'''"])]*)
   837 (*+*)writeln (pats2str' ppc);
   838 (*["(#Given, (Streckenlast, q__q))
   839 ","(#Given, (FunktionsVariable, v_v))
   840 ","(#Given, (Biegelinie, id_fun))
   841 ","(#Given, (AbleitungBiegelinie, id_abl))
   842 ","(#Find, (Funktionen, fun_s))"]*)
   843 (*+*)writeln (pats2str' ((#ppc o Specify.get_pbt) pI));
   844 (*["(#Given, (Streckenlast, q_q))
   845 ","(#Given, (FunktionsVariable, v_v))
   846 ","(#Find, (Funktionen, funs'''))"]*)
   847         val oris = Specify.add_field' thy ppc oris
   848         val met = if met = [] then pbl else met
   849         val (_, (itms, pre')) = Specify.match_itms_oris thy met (ppc, pre, prls ) oris
   850 ;
   851 (*+*)writeln (itms2str_ @{context} itms); (*[
   852 (1 ,[1] ,true ,#Given ,Cor Streckenlast q_0 ,(q_q, [q_0])),
   853 (2 ,[1] ,true ,#Given ,Cor FunktionsVariable x ,(v_v, [x])),
   854 (3 ,[1] ,true ,#Find ,Cor Funktionen funs''' ,(funs''', [funs''']))] *)
   855 
   856 (*//----------- hack for funpack: generalise handling of meths which extend problem items -----\\*)
   857 val itms =
   858   if mI' = ["Biegelinien", "ausBelastung"]
   859   then itms @
   860     [(4, [1], true, "#Given", Cor ((Const ("Biegelinie.Biegelinie", Type ("fun", [Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]), Type ("Tools.una", [])])),
   861         [Free ("y", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))]),
   862       (Free ("id_fun", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])])),
   863         [Free ("y", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))] ))),
   864     (5, [1], true, "#Given", Cor ((Const ("Biegelinie.AbleitungBiegelinie", Type ("fun", [Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]), Type ("Tools.una", [])])),
   865         [Free ("dy", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))]),
   866       (Free ("id_abl", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])])),
   867         [Free ("dy", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))] )))]
   868   else itms
   869 (*\\----------- hack for funpack: generalise handling of meths which extend problem items -----//*)
   870 
   871 val itms' = itms @
   872   [(4, [1], true, "#Given", Cor ((@{term "Biegelinie"},
   873       [@{term "y::real \<Rightarrow> real"}]),
   874     (@{term "id_fun::real \<Rightarrow> real"},
   875       [@{term "y::real \<Rightarrow> real"}] ))),
   876   (5, [1], true, "#Given", Cor ((@{term "AbleitungBiegelinie"},
   877       [@{term "dy::real \<Rightarrow> real"}]),
   878     (@{term "id_abl::real \<Rightarrow> real"},
   879       [@{term "dy::real \<Rightarrow> real"}] )))]
   880 val itms'' = itms @
   881   [(4, [1], true, "#Given", Cor ((Const ("Biegelinie.Biegelinie", Type ("fun", [Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]), Type ("Tools.una", [])])),
   882       [Free ("y", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))]),
   883     (Free ("id_fun", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])])),
   884       [Free ("y", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))] ))),
   885   (5, [1], true, "#Given", Cor ((Const ("Biegelinie.AbleitungBiegelinie", Type ("fun", [Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]), Type ("Tools.una", [])])),
   886       [Free ("dy", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))]),
   887     (Free ("id_abl", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])])),
   888       [Free ("dy", Type ("fun", [Type ("Real.real", []), Type ("Real.real", [])]))] )))]
   889 ;
   890 if itms' = itms'' then () else error "itms BUIT BY HAND ARE BROKEN";
   891 (*//-----------------------------------------^^^ Specify_Method ["Biegelinien", "ausBelastung"]-\\*)
   892 
   893 val (p,_,f,nxt,_,pt) = me nxt''''' p''''' c pt''''';
   894 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   895 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   896 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   897 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   898 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   899 (*----------- 30 -----------*)
   900 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   901 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   902 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   903 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   904 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   905 (*----------- 40 -----------*)
   906 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   907 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   908 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   909 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   910 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   911 (*----------- 50 -----------*)
   912 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   913 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   914 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   915 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   916 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   917 (*----------- 60 -----------*)
   918 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   919 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   920 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   921 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   922 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   923 (*----------- 70 -----------*)
   924 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   925 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   926 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   927 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   928 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   929 (*----------- 80 -----------*)
   930 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   931 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   932 \<close> ML \<open>
   933 (**)val (p,_,f,nxt,_,pt) = me nxt p c pt;
   934 \<close> ML \<open>
   935 (*CURRENT*)if p = ([2, 1], Pbl) andalso
   936 (*CURRENT*)  f = PpcKF (Problem [], {Find = [Incompl "equality"], Given = [Incompl "functionEq", Incompl "substitution"], Relate = [], Where = [], With = []})
   937 (*CURRENT*)then
   938 (*CURRENT*)  case nxt of
   939 (*CURRENT*)    ("Add_Given", Add_Given "functionEq (hd [])") => ((*here is an error in partial_function*))
   940 (*CURRENT*)  | _ => error "me biegelinie changed 1"
   941 (*CURRENT*)else error "me biegelinie changed 2";
   942 \<close> ML \<open>
   943 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   944 (*CURRENT*)nxt;(* = ("Tac ", Tac "[error] appl_add: is_known: seek_oridts: input ('substitution (NTH (1 + -4) [])') not found in oris (typed)")*)
   945 \<close> ML \<open>
   946 (*----- due to "switch from Script to partial_function" 4035ec339062 ? 
   947     OR ?due to "failed trial to generalise handling of meths which extend the model of a probl " 98298342fb6d
   948 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   949 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   950 (*----------- 90 -----------*)
   951 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   952 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   953 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   954 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   955 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   956 (*---------- 100 -----------*)
   957 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   958 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   959 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   960 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   961 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   962 (*---------- 110 -----------*)
   963 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   964 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   965 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   966 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   967 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   968 (*---------- 120 -----------*)
   969 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   970 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   971 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   972 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   973 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   974 (*---------- 130 -----------*)
   975 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   976 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   977 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   978 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   979 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   980 
   981 if p = ([3], Pbl)
   982 then
   983   case nxt of
   984     ("Add_Given", Add_Given "solveForVars [c_2, c_3, c_4]") => 
   985     (case f of
   986       PpcKF
   987           (Problem [],
   988            {Find = [Incompl "solution []"], Given =
   989             [Correct
   990               "equalities\n [0 = -1 * c_4 / -1,\n  0 =\n  (-24 * c_4 * EI + -24 * L * c_3 * EI + 12 * L ^^^ 2 * c_2 +\n   4 * L ^^^ 3 * c +\n   -1 * L ^^^ 4 * q_0) /\n  (-24 * EI),\n  0 = c_2, 0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2]",
   991              Incompl "solveForVars [c]"],
   992             Relate = [], Where = [], With = []}) => ()
   993     | _ => error "Bsp.7.70 me changed 1")
   994   | _ => error "Bsp.7.70 me changed 2"
   995 else error "Bsp.7.70 me changed 3";
   996 -----*)
   997 (* NOTE: ^^^^^^^^^^^^^^^^^ no progress already in isabisac15, but not noticed ^^^^^^^^^^^^^^^^^ *)
   998 
   999 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. auto ---";
  1000 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. auto ---";
  1001 "----------- IntegrierenUndKonstanteBestimmen2: Bsp.7.70. auto ---";
  1002 (* the error in this test might be independent from introduction of y, dy
  1003    as arguments in IntegrierenUndKonstanteBestimmen2,
  1004    rather due to so far untested use of "auto" *)
  1005 val fmz = ["Traegerlaenge L","Streckenlast q_0","Biegelinie y",
  1006 	     "Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0]",
  1007 	     "FunktionsVariable x", "GleichungsVariablen [c, c_2, c_3, c_4]",
  1008        "AbleitungBiegelinie dy"];
  1009 val (dI',pI',mI') = ("Biegelinie", ["Biegelinien"],
  1010 		     ["IntegrierenUndKonstanteBestimmen2"]);
  1011 
  1012 reset_states ();
  1013 CalcTree [(fmz, (dI',pI',mI'))];
  1014 Iterator 1;
  1015 moveActiveRoot 1;
  1016 
  1017 (*[], Met*)autoCalculate 1 CompleteCalcHead;
  1018 (*[1], Pbl*)autoCalculate 1 (Step 1); (* into SubProblem *)
  1019 (*[1], Res*)autoCalculate 1 CompleteSubpbl; (**)
  1020 (*[2], Pbl*)autoCalculate 1 (Step 1); (* out of SubProblem *)
  1021 (*[2], Res*)autoCalculate 1 CompleteSubpbl;
  1022 (*[3], Pbl*)autoCalculate 1 (Step 1); (* out of SubProblem *)
  1023 (*[3], Met*)autoCalculate 1 CompleteCalcHead;
  1024 (*[3, 1], Frm*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1025 (*(**)autoCalculate 1 CompleteSubpbl;  error in kernel 4: generate1: not impl.for Empty_Tac_*)
  1026 (*[3, 1], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1027 (*[3, 2], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1028 (*[3, 3], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1029 (*[3, 4], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1030 (*[3, 5], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1031 (*[3, 6], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1032 (*[3, 7], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1033 (*[3, 8], Pbl*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1034 (*[3, 8], Met*)autoCalculate 1 CompleteCalcHead;
  1035 (*[3, 8, 1], Frm*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1036 (*[3, 8, 1], Res*)autoCalculate 1 (Step 1); (* solve SubProblem *)
  1037 (*(**)autoCalculate 1 (Step 1); 
  1038 *** generate1: not impl.for Empty_Tac_ 
  1039 val it = <AUTOCALC><CALCID>1</CALCID><CALCMESSAGE>helpless</CALCMESSAGE></AUTOCALC>: XML.tree *)
  1040 
  1041 val ((pt,_),_) = get_calc 1;
  1042 val ip = get_pos 1 1;
  1043 val (Form f, tac, asms) = pt_extract (pt, ip);
  1044 
  1045 if ip = ([2, 1, 1], Frm) andalso 
  1046 term2str f  = "hd []"
  1047 then 
  1048   case tac of
  1049     SOME Empty_Tac => ()
  1050   | _ => error "ERROR biegel.7.70 changed 1"
  1051 else error "ERROR biegel.7.70 changed 2";
  1052 
  1053 (*----- this state has been reached shortly after 98298342fb6d:
  1054 if ip = ([3, 8, 1], Res) andalso 
  1055 term2str f = "[-1 * c_4 / -1 = 0,\n (6 * c_4 * EI + 6 * L * c_3 * EI + -3 * L ^^^ 2 * c_2 + -1 * L ^^^ 3 * c) /\n (6 * EI) =\n L ^^^ 4 * q_0 / (-24 * EI),\n c_2 = 0, c_2 + L * c = L ^^^ 2 * q_0 / 2]"
  1056 then 
  1057   case tac of
  1058     SOME (Check_Postcond ["normalise", "4x4", "LINEAR", "system"]) => ()
  1059   | _ => error "ERROR biegel.7.70 changed 1"
  1060 else error "ERROR biegel.7.70 changed 2";
  1061 *)
  1062 \<close> ML \<open>
  1063 \<close> ML \<open>
  1064 "~~~~~ fun xxx , args:"; val () = ();
  1065 \<close>
  1066 
  1067 section \<open>===================================================================================\<close>
  1068 ML \<open>
  1069 "~~~~~ fun xxx , args:"; val () = ();
  1070 \<close> ML \<open>
  1071 \<close> ML \<open>
  1072 \<close> ML \<open>
  1073 "~~~~~ fun xxx , args:"; val () = ();
  1074 \<close>
  1075 
  1076 section \<open>code for copy & paste ===============================================================\<close>
  1077 ML \<open>
  1078 "~~~~~ fun xxx , args:"; val () = ();
  1079 "~~~~~ and xxx , args:"; val () = ();
  1080 
  1081 "~~~~~ to xxx  return val:"; val () = ();
  1082 \<close>
  1083 end