test/Tools/isac/Interpret/error-pattern.sml
author wneuper <walther.neuper@jku.at>
Tue, 20 Jul 2021 14:37:56 +0200
changeset 60339 0d22a6bf1fc6
parent 60336 dcb37736d573
child 60340 0ee698b0a703
permissions -rw-r--r--
//reduce the number of TermC.parse*; "//"means: tests broken .

broken tests are outcommented with "reduce the number of TermC.parse*"
     1 (* Title: "Interpret/error-pattern.sml"
     2    Author: Walther Neuper 060225,
     3    (c) due to copyright terms 
     4 
     5 Strange ERROR "Undefined fact: "all_left""
     6 *)
     7 
     8 "-----------------------------------------------------------------";
     9 "table of contents -----------------------------------------------";
    10 "-----------------------------------------------------------------";
    11 "appendForm with miniscript with mini-subpbl:";
    12 "--------- appendFormula: on Res + equ_nrls ----------------------";
    13 "--------- appendFormula: on Frm + equ_nrls ----------------------";
    14 "--------- appendFormula: on Res + NO deriv ----------------------";
    15 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
    16 "replaceForm with miniscript with mini-subpbl:";
    17 "--------- replaceFormula: on Res + = ----------------------------";
    18 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
    19 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
    20 "--------- replaceFormula: cut calculation -----------------------";
    21 "--------- replaceFormula: cut calculation -----------------------";
    22 (* 040307 copied from informtest.sml ... old versions
    23 "--------- maximum-example, UC: Modeling / modifyCalcHead --------";*)
    24 "--------- syntax error ------------------------------------------";
    25 "CAS-command:";
    26 "--------- CAS-command on ([],Pbl) -------------------------------";
    27 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
    28 "--------- locate_input_term [rational,simplification] ----------------------";
    29 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
    30 "--------- Take as 1st tac, start from exp -----------------------";
    31 "--------- implicit_take, start with <NEW> (CAS input) ---------------";
    32 "--------- build fun check_for' ------------------------------";
    33 "--------- build fun check_for' ?bdv -------------------------";
    34 "--------- build fun check_for ------------------------";
    35 "--------- embed fun check_for ------------------------";
    36 "--------- embed fun find_fill_patterns ---------------------------";
    37 "--------- build fun is_exactly_equal, inputFillFormula ----------";
    38 "--------- fun appl_adds -----------------------------------------";
    39 "--------- fun concat_deriv --------------------------------------";
    40 "--------- handle an input formula -------------------------------";
    41 "--------- fun dropwhile' ----------------------------------------";
    42 "-----------------------------------------------------------------";
    43 "-----------------------------------------------------------------";
    44 "-----------------------------------------------------------------";
    45 
    46 
    47 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
    48 "--------- appendFormula: on Res + equ_nrls ----------------------";
    49 "--------- appendFormula: on Res + equ_nrls ----------------------";
    50 "--------- appendFormula: on Res + equ_nrls ----------------------";
    51  val Prog sc = (#scr o MethodC.from_store) ["Test", "squ-equ-test-subpbl1"];
    52  (writeln o UnparseC.term) sc;
    53  val Prog sc = (#scr o MethodC.from_store) ["Test", "solve_linear"];
    54  (writeln o UnparseC.term) sc;
    55 
    56  reset_states ();
    57  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
    58 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
    59 	     ["Test", "squ-equ-test-subpbl1"]))];
    60  Iterator 1; moveActiveRoot 1;
    61  autoCalculate 1 CompleteCalcHead;
    62  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
    63  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
    64 
    65  appendFormula 1 "- 2 * 1 + (1 + x) = 0" (*|> Future.join*); refFormula 1 (get_pos 1 1);
    66  val ((pt,_),_) = get_calc 1;
    67  val str = pr_ctree pr_short pt;
    68 if str =
    69 (".    ----- pblobj -----\n" ^
    70 "1.   x + 1 = 2\n" ^
    71 "2.   x + 1 + - 1 * 2 = 0\n" ^
    72 "2.1.   x + 1 + - 1 * 2 = 0\n" ^
    73 "2.2.   1 + x + - 1 * 2 = 0\n" ^
    74 "2.3.   1 + (x + - 1 * 2) = 0\n" ^
    75 "2.4.   1 + (x + - 2) = 0\n" ^
    76 "2.5.   1 + (x + - 2 * 1) = 0\n" ^
    77 "2.6.   1 + x + - 2 * 1 = 0\n" ) then ()
    78 else error "inform.sml: diff.behav.appendFormula: on Res + equ 1";
    79 
    80  moveDown 1 ([ ],Pbl); refFormula 1 ([1],Frm); (*x + 1 = 2*)
    81  moveDown 1 ([1],Frm); refFormula 1 ([1],Res); (*x + 1 + - 1 * 2 = 0*)
    82 
    83  (*the seven steps of detailed derivation*)
    84  moveDown 1 ([1  ],Res); refFormula 1 ([2,1],Frm); 
    85  moveDown 1 ([2,1],Frm); refFormula 1 ([2,1],Res);
    86  moveDown 1 ([2,1],Res); refFormula 1 ([2,2],Res);
    87  moveDown 1 ([2,2],Res); refFormula 1 ([2,3],Res); 
    88  moveDown 1 ([2,3],Res); refFormula 1 ([2,4],Res);
    89  moveDown 1 ([2,4],Res); refFormula 1 ([2,5],Res);
    90  moveDown 1 ([2,5],Res); refFormula 1 ([2,6],Res);
    91  val ((pt,_),_) = get_calc 1;
    92  if "- 2 * 1 + (1 + x) = 0" = UnparseC.term (fst (get_obj g_result pt [2,6])) then()
    93  else error "inform.sml: diff.behav.appendFormula: on Res + equ 2";
    94 
    95  fetchProposedTactic 1; (*takes Iterator 1 _1_*)
    96 (* <ERROR> error in kernel </ERROR> ALREADY IN 2009-2*)
    97 (*========== inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 =============
    98  val (_,(tac,_,_)::_) = get_calc 1;
    99  if tac = Rewrite_Set "Test_simplify" then ()
   100  else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
   101 ============ inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 ============*)
   102 
   103  autoCalculate 1 CompleteCalc;
   104  val ((pt,_),_) = get_calc 1;
   105  if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
   106  else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
   107  (* autoCalculate 1 CompleteCalc;
   108    val ((pt,p),_) = get_calc 1;
   109    (writeln o istates2str) (get_obj g_loc pt [ ]);  
   110    (writeln o istates2str) (get_obj g_loc pt [1]);  
   111    (writeln o istates2str) (get_obj g_loc pt [2]);  
   112    (writeln o istates2str) (get_obj g_loc pt [3]);  
   113    (writeln o istates2str) (get_obj g_loc pt [3,1]);  
   114    (writeln o istates2str) (get_obj g_loc pt [3,2]);  
   115    (writeln o istates2str) (get_obj g_loc pt [4]);  
   116 
   117    *)
   118 "----------------------------------------------------------";
   119 
   120  val fod = Derive.do_one (@{theory "Isac_Knowledge"}) Atools_erls 
   121 		       ((#rules o Rule_Set.rep) Test_simplify)
   122 		       (sqrt_right false (@{theory "Pure"})) NONE 
   123 		       (TermC.str2term "x + 1 + - 1 * 2 = 0");
   124  (writeln o Derive.trtas2str) fod;
   125 
   126  val ifod = Derive.do_one (@{theory "Isac_Knowledge"}) Atools_erls 
   127 		       ((#rules o Rule_Set.rep) Test_simplify)
   128 		       (sqrt_right false (@{theory "Pure"})) NONE 
   129 		       (TermC.str2term "- 2 * 1 + (1 + x) = 0");
   130  (writeln o Derive.trtas2str) ifod;
   131  fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
   132  val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
   133  val der = fod' @ (map Derive.rev_deriv' rifod');
   134  (writeln o Derive.trtas2str) der;
   135  "----------------------------------------------------------";
   136 DEconstrCalcTree 1;
   137 
   138 "--------- appendFormula: on Frm + equ_nrls ----------------------";
   139 "--------- appendFormula: on Frm + equ_nrls ----------------------";
   140 "--------- appendFormula: on Frm + equ_nrls ----------------------";
   141  reset_states ();
   142  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   143 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   144 	     ["Test", "squ-equ-test-subpbl1"]))];
   145  Iterator 1; moveActiveRoot 1;
   146  autoCalculate 1 CompleteCalcHead;
   147  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
   148  appendFormula 1 "2+ - 1 + x = 2" (*|> Future.join*); refFormula 1 (get_pos 1 1);
   149 
   150  moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (*x + 1 = 2*);
   151 
   152  moveDown 1 ([1  ],Frm); refFormula 1 ([1,1],Frm); 
   153  moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res); 
   154  moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res); 
   155  moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res); 
   156  moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res); 
   157  moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res); 
   158  moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res); 
   159  val ((pt,_),_) = get_calc 1;
   160  if "2 + - 1 + x = 2" = UnparseC.term (fst (get_obj g_result pt [1,6])) then()
   161  else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
   162 
   163  fetchProposedTactic 1; (*takes Iterator 1 _1_*)
   164  val (_,(tac,_,_)::_) = get_calc 1;
   165  case tac of Rewrite_Set "norm_equation" => ()
   166  | _ => error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
   167  autoCalculate 1 CompleteCalc;
   168  val ((pt,_),_) = get_calc 1;
   169  if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
   170  else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
   171 DEconstrCalcTree 1;
   172 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   173 
   174 "--------- appendFormula: on Res + NO deriv ----------------------";
   175 "--------- appendFormula: on Res + NO deriv ----------------------";
   176 "--------- appendFormula: on Res + NO deriv ----------------------";
   177  reset_states ();
   178  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   179 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   180 	     ["Test", "squ-equ-test-subpbl1"]))];
   181  Iterator 1; moveActiveRoot 1;
   182  autoCalculate 1 CompleteCalcHead;
   183  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   184  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
   185 
   186  appendFormula 1 "x = 2" (*|> Future.join*);
   187  val ((pt,p),_) = get_calc 1;
   188  val str = pr_ctree pr_short pt;
   189  writeln str;
   190  if str = ".    ----- pblobj -----\n1.   x + 1 = 2\n" andalso p = ([1], Res)
   191  then ()
   192  else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
   193 
   194  fetchProposedTactic 1;
   195  val (_,(tac,_,_)::_) = get_calc 1;
   196  case tac of Rewrite_Set "Test_simplify" => ()
   197  | _ => error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
   198  autoCalculate 1 CompleteCalc;
   199  val ((pt,_),_) = get_calc 1;
   200  if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
   201  else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
   202 DEconstrCalcTree 1;
   203 
   204 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   205 "--------- appendFormula: on Res + late deriv --------------------";
   206 "--------- appendFormula: on Res + late deriv --------------------";
   207 "--------- appendFormula: on Res + late deriv --------------------";
   208 (*cp with "fun me" to test/../lucas-interpreter.sml:
   209  re-build: fun locate_input_term ---------------------------------------------------"; 
   210 *)
   211  reset_states ();
   212  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   213 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   214 	     ["Test", "squ-equ-test-subpbl1"]))];
   215  Iterator 1; moveActiveRoot 1;
   216  autoCalculate 1 CompleteCalcHead;
   217  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   218  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
   219 
   220  appendFormula 1 "x = 1" (*|> Future.join*);
   221  val ((pt,p),_) = get_calc 1;
   222  val str = pr_ctree pr_short pt;
   223  writeln str;
   224  if str = ".    ----- pblobj -----\n1.   x + 1 = 2\n2.   x + 1 + - 1 * 2 = 0\n3.    ----- pblobj -----\n3.1.   - 1 + x = 0\n3.2.   x = 0 + - 1 * - 1\n3.2.1.   x = 0 + - 1 * - 1\n3.2.2.   x = 0 + 1\n" andalso p = ([3,2], Res)
   225  then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
   226  else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
   227 
   228  fetchProposedTactic 1;
   229  val (_,(tac,_,_)::_) = get_calc 1;
   230  case tac of Check_Postcond ["LINEAR", "univariate", "equation", "test"] => ()
   231  | _ => error "inform.sml: diff.behav.appendFormula: Res + late d 2";
   232  autoCalculate 1 CompleteCalc;
   233  val ((pt,_),_) = get_calc 1;
   234  if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
   235  else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
   236 DEconstrCalcTree 1;
   237 
   238 "--------- appendFormula: on Res + late deriv [x = 3 + - 2]---///--";
   239 "--------- appendFormula: on Res + late deriv [x = 3 + - 2]---///--";
   240 "--------- appendFormula: on Res + late deriv [x = 3 + - 2]---///--";
   241  reset_states ();
   242  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   243 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   244 	     ["Test", "squ-equ-test-subpbl1"]))];
   245  Iterator 1; moveActiveRoot 1;
   246  autoCalculate 1 CompleteCalcHead;
   247  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   248  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
   249  appendFormula 1 "[x = 3 + -2*1]" (*|> Future.join*);
   250  val ((pt,p),_) = get_calc 1;
   251  val str = pr_ctree pr_short pt;
   252  writeln str;
   253  if str=".    ----- pblobj -----\n1.   x + 1 = 2\n2.   x + 1 + - 1 * 2 = 0\n3.    ----- pblobj -----\n3.1.   - 1 + x = 0\n3.2.   x = 0 + - 1 * - 1\n4.   [x = 1]\n4.1.   [x = 1]\n4.2.   [x = - 2 + 3]\n4.3.   [x = 3 + - 2]\n" then ()
   254  else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
   255  autoCalculate 1 CompleteCalc;
   256  val ((pt,p),_) = get_calc 1;
   257  if "[x = 3 + - 2 * 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
   258  (*       ~~~~~~~~~~ simplify as last step in any script ?!*)
   259  else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
   260 DEconstrCalcTree 1;
   261 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   262 
   263 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   264 "--------- replaceFormula: on Res + = ----------------------------";
   265 "--------- replaceFormula: on Res + = ----------------------------";
   266 "--------- replaceFormula: on Res + = ----------------------------";
   267  reset_states ();
   268  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   269 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   270 	     ["Test", "squ-equ-test-subpbl1"]))];
   271  Iterator 1; moveActiveRoot 1;
   272  autoCalculate 1 CompleteCalcHead;
   273  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   274  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
   275  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*- 1 + x*);
   276 
   277  replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
   278  val ((pt,_),_) = get_calc 1;
   279  val str = pr_ctree pr_short pt;
   280 
   281 (* before AK110725 this was
   282 ".    ----- pblobj -----\n
   283 1.   x + 1 = 2\n
   284 2.   x + 1 + - 1 * 2 = 0\n
   285 2.1.   x + 1 + - 1 * 2 = 0\n
   286 2.2.   1 + x + - 1 * 2 = 0\n
   287 2.3.   1 + (x + - 1 * 2) = 0\n
   288 2.4.   1 + (x + -2) = 0\n
   289 2.5.   1 + (x + -2 * 1) = 0\n
   290 2.6.   1 + x + -2 * 1 = 0\n";
   291 *)
   292 if str = 
   293 ".    ----- pblobj -----\n"^
   294 "1.   x + 1 = 2\n"^
   295 "2.   x + 1 + - 1 * 2 = 0\n"^
   296 "2.1.   x + 1 + - 1 * 2 = 0\n"^
   297 "2.2.   1 + x + - 1 * 2 = 0\n"^
   298 "2.3.   1 + (x + - 1 * 2) = 0\n"^
   299 "2.4.   1 + (x + - 2) = 0\n"^
   300 "2.5.   1 + (x + - 2 * 1) = 0\n"^
   301 "2.6.   1 + x + - 2 * 1 = 0\n" then()
   302 else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
   303 
   304  autoCalculate 1 CompleteCalc;
   305  val ((pt,pos as (p,_)),_) = get_calc 1;
   306  if pos = ([],Res) andalso "[x = 1]" = (UnparseC.term o fst) (get_obj g_result pt p) then()
   307  else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
   308 DEconstrCalcTree 1;
   309 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   310 
   311 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   312 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
   313 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
   314 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
   315  reset_states ();
   316  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   317 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   318 	     ["Test", "squ-equ-test-subpbl1"]))];
   319  Iterator 1; moveActiveRoot 1;
   320  autoCalculate 1 CompleteCalcHead;
   321  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   322  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
   323 
   324  replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
   325  val ((pt,_),_) = get_calc 1;
   326  val str = pr_ctree pr_short pt;
   327  writeln str;
   328  if str= ".    ----- pblobj -----\n1.   x + 1 = 2\n1.1.   x + 1 = 2\n1.2.   1 + x = 2\n1.3.   1 + x = - 2 + 4\n1.4.   x + 1 = - 2 + 4\n" then ()
   329  else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
   330  autoCalculate 1 CompleteCalc;
   331  val ((pt,pos as (p,_)),_) = get_calc 1;
   332  if pos = ([],Res) andalso "[x = 1]" = (UnparseC.term o fst)(get_obj g_result pt p) then()
   333  else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
   334 DEconstrCalcTree 1;
   335 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   336 
   337 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
   338 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
   339 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
   340  reset_states ();
   341  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   342 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   343 	     ["Test", "squ-equ-test-subpbl1"]))];
   344  Iterator 1; moveActiveRoot 1;
   345  autoCalculate 1 CompleteCalcHead;
   346  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   347 
   348  replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
   349  val ((pt,_),_) = get_calc 1;
   350  val str = pr_ctree pr_short pt;
   351 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   352     str = ".    ----- pblobj -----\n1.   x + 1 = 2\n";
   353 
   354  if str= ".    ----- pblobj -----\n1.   x + 1 = 2\n1.1.   x + 1 = 2\n1.2.   1 + x = 2\n1.3.   1 + x = - 2 + 4\n1.4.   x + 1 = - 2 + 4\n" then ()
   355  else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
   356  autoCalculate 1 CompleteCalc;
   357  val ((pt,pos as (p,_)),_) = get_calc 1;
   358 (**)pos = ([1], Met)
   359  if pos = ([],Res) andalso "[x = 1]" = (UnparseC.term o fst)(get_obj g_result pt p) then()
   360  else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
   361 DEconstrCalcTree 1;
   362 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   363 
   364 "--------- replaceFormula: cut calculation -----------------------";
   365 "--------- replaceFormula: cut calculation -----------------------";
   366 "--------- replaceFormula: cut calculation -----------------------";
   367  reset_states ();
   368  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   369 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   370 	     ["Test", "squ-equ-test-subpbl1"]))];
   371  Iterator 1; moveActiveRoot 1;
   372  autoCalculate 1 CompleteCalc;
   373  moveActiveRoot 1; moveActiveDown 1;
   374  if get_pos 1 1 = ([1], Frm) then ()
   375  else error "inform.sml: diff.behav. cut calculation 1";
   376 
   377  replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
   378  val ((pt,p),_) = get_calc 1;
   379  val str = pr_ctree pr_short pt;
   380  writeln str;
   381 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   382     p = ([], Res)
   383  if p = ([1], Res) then ()
   384  else error "inform.sml: diff.behav. cut calculation 2";
   385 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   386 
   387 
   388 (* 040307 copied from informtest.sml; ... old version 
   389  "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
   390  "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
   391  "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
   392 
   393  val p = ([],Pbl);
   394  val elems = ["fixedValues [r=Arbfix]", "maximum A", "valuesFor [a,b]",
   395 	      "relations [A=a*b, (a/2) \<up> 2 + (b/2) \<up> 2 = r \<up> 2]",
   396 	      "relations [A=a*b, (a/2) \<up> 2 + (b/2) \<up> 2 = r \<up> 2]",
   397         "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos (alpha::real)]",
   398 	      (* \<up>  these are the elements for the root-problem (in variants)*)
   399               (*vvv these are elements required for subproblems*)
   400 	      "boundVariable a", "boundVariable b", "boundVariable alpha",
   401 	      "interval {x::real. 0 <= x & x <= 2*r}",
   402 	      "interval {x::real. 0 <= x & x <= 2*r}",
   403 	      "interval {x::real. 0 <= x & x <= pi}",
   404 	      "errorBound (eps=(0::real))"]
   405  (*specifying is not interesting for this example*)
   406  val spec = ("DiffApp", ["maximum_of", "function"], 
   407 	     ["DiffApp", "max_by_calculus"]);
   408  (*the empty model with descriptions for user-guidance by Model_Problem*)
   409  val empty_model = [Given ["fixedValues []"],
   410 		    Find ["maximum", "valuesFor"],
   411 		    Relate ["relations []"]];
   412 
   413 
   414  (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
   415  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
   416  (*val nxt = ("Model_Problem", ...*)
   417  val pbl = get_obj g_pbl pt (fst p); (writeln o (I_Model.to_string ctxt)) pbl; 
   418 
   419  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   420  (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
   421  val pbl = get_obj g_pbl pt (fst p); (writeln o (I_Model.to_string ctxt)) pbl; 
   422 (*[
   423 (0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
   424 (0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
   425 (0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
   426 (0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
   427 
   428  (*the empty CalcHead is checked w.r.t the model and re-established as such*)
   429  val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, References.empty);
   430  val pbl = get_obj g_pbl pt (fst p); (writeln o (I_Model.to_string ctxt)) pbl; 
   431  if ocalhd2str ocalhd = "(Pbl, ??.empty, [\n(0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),\n(0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),\n(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),\n(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))], [], \n(\"ThyC.id_empty\", [\"e_pblID\"], [\"e_metID\"]) )" then () else error "informtest.sml: diff.behav. max 1";
   432 
   433  (*there is one input to the model (could be more)*)
   434  val (b,pt,ocalhd) = 
   435      input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
   436 			     Find ["maximum", "valuesFor"],
   437 			     Relate ["relations"]], Pbl, References.empty);
   438  val pbl = get_obj g_pbl pt (fst p); (writeln o (I_Model.to_string ctxt)) pbl; 
   439  if ocalhd2str ocalhd = "(Pbl, ??.empty, [\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),\n(0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),\n(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),\n(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))], [], \n(\"ThyC.id_empty\", [\"e_pblID\"], [\"e_metID\"]) )" then () 
   440  else error "informtest.sml: diff.behav. max 2";
   441 
   442  (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
   443  val (b,pt''''',ocalhd) = 
   444      input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
   445 			     Find ["maximum A", "valuesFor [a,b]"],
   446 			     Relate ["relations [A=a*b, a/2=r*sin alpha, \
   447 				     \b/2=r*cos alpha]"]], Pbl, References.empty);
   448  val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (I_Model.to_string ctxt)) pbl; 
   449  if ocalhd2str ocalhd = ------------ \<up> \<up> \<up> ^ missing !!!*)
   450 
   451  (*this input is complete in variant 1 (variant 3 does not work yet)*)
   452  val (b,pt''''',ocalhd) = 
   453      input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
   454 			     Find ["maximum A", "valuesFor [a,b]"],
   455 			     Relate ["relations [A=a*b, \
   456 				     \(a/2) \<up> 2 + (b/2) \<up> 2 = r \<up> 2]"]], 
   457 		      Pbl, References.empty);
   458  val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (I_Model.to_string ctxt)) pbl; 
   459 
   460  modifycalcheadOK2xml 111 (bool2str b) ocalhd;
   461 *)
   462 DEconstrCalcTree 1;
   463 
   464 "--------- syntax error ------------------------------------------";
   465 "--------- syntax error ------------------------------------------";
   466 "--------- syntax error ------------------------------------------";
   467  reset_states ();
   468  CalcTree [(["equality (x+1=(2::real))", "solveFor x", "solutions L"], 
   469 	    ("Test", ["sqroot-test", "univariate", "equation", "test"],
   470 	     ["Test", "squ-equ-test-subpbl1"]))];
   471  Iterator 1; moveActiveRoot 1;
   472  autoCalculate 1 CompleteCalcHead;
   473  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
   474  autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + - 1 * 2 = 0*);
   475 
   476  appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
   477  val ((pt,_),_) = get_calc 1;
   478  val str = pr_ctree pr_short pt;
   479  writeln str;
   480  if str = ".    ----- pblobj -----\n1.   x + 1 = 2\n" then ()
   481  else error "inform.sml: diff.behav.appendFormula: syntax error";
   482 DEconstrCalcTree 1;
   483 
   484 "--------- CAS-command on ([],Pbl) -------------------------------";
   485 "--------- CAS-command on ([],Pbl) -------------------------------";
   486 "--------- CAS-command on ([],Pbl) -------------------------------";
   487 val (p,_,f,nxt,_,pt) = 
   488     CalcTreeTEST [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
   489 val ifo = "solve (x + 1 = (2::real), x::real)";
   490 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   491 ERROR lev_back': called by ([],_)
   492 
   493 val (_,(_,c,(pt,p))) = Step_Solve.by_term (pt,p) "solve (x + 1 = (2::real), x::real)";
   494 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   495 (*
   496   This trick           \<up> \<up> \<up> micked input of \<up> \<up> \<up> \<up>  \<up> ^^ in the front-end.
   497   The trick worked in changeset fbaff8cf0179, it does not work in 59c5dd27d589 anymore
   498   (TODO hg bisect ?) and raises the ERROR Undefined fact: "xfoldr_Nil".
   499 
   500   Compare tests "CAS-command" in test/../inssort.sml etc.
   501   ---------------------------------------------------------------------------------------------
   502 Test_Tool.show_pt pt;
   503 val nxt = (Apply_Method ["Test", "squ-equ-test-subpbl1"]);
   504 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   505 if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
   506 else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
   507 DEconstrCalcTree 1;
   508 -----------------------------------------------------------------------------------------------*)
   509 
   510 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
   511 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
   512 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
   513 reset_states ();
   514 CalcTree [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
   515 Iterator 1;
   516 moveActiveRoot 1;
   517 replaceFormula 1 "solve(x + 1 = (2::real), x)";
   518 autoCalculate 1 CompleteCalc;
   519 val ((pt,p),_) = get_calc 1;
   520 Test_Tool.show_pt pt;
   521 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\
   522    p = ([], Pbl)
   523 
   524 if p = ([], Res) then ()
   525 else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
   526 DEconstrCalcTree 1;
   527 ----- broken with "reduce the number of TermC.parse*"---------------------------------------//*)
   528 
   529 "--------- inform [rational,simplification] ----------------------";
   530 "--------- inform [rational,simplification] ----------------------";
   531 "--------- inform [rational,simplification] ----------------------";
   532 reset_states ();
   533 CalcTree [(["Term (a * x / (b * x) + c * x / (d * x) + e / f)", "normalform N"],
   534 	("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
   535 Iterator 1; moveActiveRoot 1;
   536 autoCalculate 1 CompleteCalcHead;
   537 
   538 "--- (- 1) give a preview on the calculation without any input";
   539 (*
   540 autoCalculate 1 CompleteCalc;
   541 val ((pt, p), _) = get_calc 1;
   542 Test_Tool.show_pt pt;
   543 [
   544 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   545 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   546 (([1], Res), a / b + c / d + e / f),                             <--- (1) input arbitrary
   547 (([2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   548 (([3], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
   549 (([4], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)), <--- (2) input next
   550 (([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))]  <--- (3) is also final result
   551                                                                           EXAMPLE NOT OPTIMAL
   552 *)
   553 "--- (0) user input as the *first* step does not work, thus impdo at least 1 step";
   554 autoCalculate 1 (Steps 1);
   555 autoCalculate 1 (Steps 1);
   556 val ((pt, p), _) = get_calc 1;
   557 (*Test_Tool.show_pt pt;
   558 [
   559 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   560 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   561 (([1], Res), a / b + c / d + e / f)] 
   562 *)
   563 "--- (1) input an arbitrary next formula";
   564 appendFormula 1 "((a * d) + (c * b)) / (b * d) + e / f" (*|> Future.join*);
   565 val ((pt, p), _) = get_calc 1;
   566 (*Test_Tool.show_pt pt;
   567 [
   568 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   569 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   570 (([1], Res), a / b + c / d + e / f),
   571 (([2,1], Frm), a / b + c / d + e / f),
   572 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   573 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
   574 (([2], Res), (a * d + c * b) / (b * d) + e / f)] 
   575 *)
   576 val ((pt,p),_) = get_calc 1;
   577 
   578 (*TOODOO broken with "reduce the number of TermC.parse*"------------------------------------\\* )
   579    p = ([9], Res)
   580 
   581 if p = ([2], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
   582 else error ("inform.sml: [rational,simplification] 1");
   583 
   584 "--- (2) input the next formula that would be presented by mat-engine";
   585 (* generate a preview:
   586 autoCalculate 1 (Steps 1);
   587 val ((pt, p), _) = get_calc 1;
   588 Test_Tool.show_pt pt;
   589 [
   590 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   591 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   592 (([1], Res), a / b + c / d + e / f),
   593 (([2,1], Frm), a / b + c / d + e / f),
   594 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   595 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
   596 (([2], Res), (a * d + c * b) / (b * d) + e / f),
   597 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]   <--- input this
   598 *)
   599 appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
   600 val ((pt, p), _) = get_calc 1;
   601 (*Test_Tool.show_pt pt;
   602 [
   603 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   604 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   605 (([1], Res), a / b + c / d + e / f),
   606 (([2,1], Frm), a / b + c / d + e / f),
   607 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   608 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
   609 (([2], Res), (a * d + c * b) / (b * d) + e / f),
   610 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))] 
   611 *)
   612 if p = ([3], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
   613 else error ("inform.sml: [rational,simplification] 2");
   614 
   615 "--- (3) input the exact final result";
   616 appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
   617 val ((pt, p), _) = get_calc 1;
   618 (*Test_Tool.show_pt pt;
   619 [
   620 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   621 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   622 (([1], Res), a / b + c / d + e / f),
   623 (([2,1], Frm), a / b + c / d + e / f),
   624 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   625 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
   626 (([2], Res), (a * d + c * b) / (b * d) + e / f),
   627 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   628 (([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   629 (([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
   630 (([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   631 (([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))] 
   632 *)
   633 if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
   634 else error ("inform.sml: [rational,simplification] 3");
   635 
   636 "--- (4) finish the calculation + check the postcondition (in the future)";
   637 autoCalculate 1 CompleteCalc;
   638 val ((pt, p), _) = get_calc 1;
   639 val (t, asm) = get_obj g_result pt [];
   640 if UnparseC.term t = "(a * d * f + b * c * f + b * d * e) / (b * d * f)" andalso
   641 UnparseC.terms asm =(*"[\"b * d * f \<noteq> 0\",\"d \<noteq> 0\",\"b \<noteq> 0\",\"a * x / (b * x) + c * x / (d * x) + e / f is_ratpolyexp\"]"*)
   642                     "[]" (*..found broken in child of 33913fe24685, error covered by  CAS-command *)
   643 then () else error "inform [rational,simplification] changed at end";
   644 (*Test_Tool.show_pt pt;
   645 [
   646 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
   647 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
   648 (([1], Res), a / b + c / d + e / f),
   649 (([2,1], Frm), a / b + c / d + e / f),
   650 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   651 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
   652 (([2], Res), (a * d + c * b) / (b * d) + e / f),
   653 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   654 (([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   655 (([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
   656 (([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   657 (([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
   658 (([5], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
   659 (([6], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)),
   660 (([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))] 
   661 *)
   662 DEconstrCalcTree 1;
   663 ----- broken with "reduce the number of TermC.parse*"------------------------------------//*)
   664 
   665 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
   666 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
   667 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
   668 val t = TermC.str2term "Diff (x \<up> 2 + x + 1, x)";
   669 case t of Const (\<^const_name>\<open>Diff\<close>, _) $ _ => ()
   670 	| _ => raise 
   671 	      error "diff.sml behav.changed for CAS Diff (..., x)";
   672 TermC.atomty t;
   673 "-----------------------------------------------------------------";
   674 (*1>*)reset_states ();
   675 (*2>*)CalcTree [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
   676 (*3>*)Iterator 1;moveActiveRoot 1;
   677 "----- here the Headline has been finished";
   678 (*4>*)moveActiveFormula 1 ([],Pbl);
   679 (*5>*)replaceFormula 1 "Diff (x \<up> 2 + x + 1, x)";
   680 val ((pt,_),_) = get_calc 1;
   681 val PblObj {probl, meth, spec, fmz, loc, ...} = get_obj I pt [];
   682 val (SOME istate, NONE) = loc;
   683 (*default_print_depth 5;*)
   684 writeln"-----------------------------------------------------------";
   685 spec;
   686 writeln (I_Model.to_string ctxt probl);
   687 writeln (I_Model.to_string ctxt meth);
   688 writeln (Istate.string_of (fst istate));
   689 
   690 refFormula 1 ([],Pbl) (*--> correct CalcHead*);
   691  (*081016 NOT necessary (but leave it in Java):*)
   692 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
   693 "----- here the CalcHead has been completed --- ONCE MORE ?????";
   694 
   695 (***difference II***)
   696 val ((pt,p),_) = get_calc 1;
   697 (*val p = ([], Pbl)*)
   698 val PblObj {probl, meth, spec, fmz, loc, ...} = get_obj I pt [];
   699 val (SOME istate, NONE) = loc;
   700 (*default_print_depth 5;*) writeln (Istate.string_of (fst istate));  (*default_print_depth 3;*)
   701 (*Pstate ([],
   702  [], NONE,
   703  ??.empty, Sundef, false)*)
   704 (*default_print_depth 5;*) spec; (*default_print_depth 3;*)
   705 (*("Isac_Knowledge",
   706       ["derivative_of", "function"],
   707       ["diff", "differentiate_on_R"]) : spec*)
   708 writeln (I_Model.to_string ctxt probl);
   709 (*[
   710 (1 ,[1] ,true ,#Given ,Cor functionTerm (x \<up> 2 + x + 1) ,(f_, [x \<up> 2 + x + 1])),
   711 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
   712 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
   713 writeln (I_Model.to_string ctxt meth);
   714 (*[
   715 (1 ,[1] ,true ,#Given ,Cor functionTerm (x \<up> 2 + x + 1) ,(f_, [x \<up> 2 + x + 1])),
   716 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
   717 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
   718 writeln"-----------------------------------------------------------";
   719 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
   720 (*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
   721 autoCalculate 1 CompleteCalc;
   722 val ((pt,p),_) = get_calc 1;
   723 val Form res = (#1 o ME_Misc.pt_extract) (pt, ([],Res));
   724 Test_Tool.show_pt pt;
   725 
   726 if p = ([], Res) andalso UnparseC.term res = "1 + 2 * x" then ()
   727 else error "diff.sml behav.changed for Diff (x \<up> 2 + x + 1, x)";
   728 DEconstrCalcTree 1;
   729 
   730 "--------- Take as 1st tac, start from exp -----------------------";
   731 "--------- Take as 1st tac, start from exp -----------------------";
   732 "--------- Take as 1st tac, start from exp -----------------------";
   733 (*the following input is copied from BridgeLog Java <==> SML,
   734   omitting unnecessary inputs*)
   735 (*1>*)reset_states ();
   736 (*2>*)CalcTree [(["functionTerm (x \<up> 2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac_Knowledge",["derivative_of", "function"],["diff", "differentiate_on_R"]))];
   737 (*3>*)Iterator 1; moveActiveRoot 1;
   738 
   739 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
   740 (***difference II***)
   741 val ((pt,_),_) = get_calc 1;
   742 val PblObj {probl, meth, spec, fmz, loc, ...} = get_obj I pt [];
   743 val (SOME istate, NONE) = loc;
   744 (*default_print_depth 5;*) writeln (Istate.string_of (fst istate));  (*default_print_depth 3;*)
   745 (*Pstate ([],
   746  [], NONE,
   747  ??.empty, Sundef, false)*)
   748 (*default_print_depth 5;*) spec; (*default_print_depth 3;*)
   749 (*("Isac_Knowledge",
   750       ["derivative_of", "function"],
   751       ["diff", "differentiate_on_R"]) : spec*)
   752 writeln (I_Model.to_string ctxt probl);
   753 (*[
   754 (1 ,[1] ,true ,#Given ,Cor functionTerm (x \<up> 2 + x + 1) ,(f_, [x \<up> 2 + x + 1])),
   755 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
   756 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
   757 writeln (I_Model.to_string ctxt meth);
   758 (*[
   759 (1 ,[1] ,true ,#Given ,Cor functionTerm (x \<up> 2 + x + 1) ,(f_, [x \<up> 2 + x + 1])),
   760 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
   761 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
   762 writeln"-----------------------------------------------------------";
   763 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
   764 autoCalculate 1 (Steps 1);
   765 val ((pt,p),_) = get_calc 1;
   766 val Form res = (#1 o ME_Misc.pt_extract) (pt, p);
   767 if UnparseC.term res = "d_d x (x \<up> 2 + x + 1)" then ()
   768 else error "diff.sml Diff (x \<up> 2 + x + 1, x) from exp";
   769 DEconstrCalcTree 1;
   770 
   771 "--------- implicit_take, start with <NEW> (CAS input) ---------------";
   772 "--------- implicit_take, start with <NEW> (CAS input) ---------------";
   773 "--------- implicit_take, start with <NEW> (CAS input) ---------------";
   774 reset_states ();
   775 CalcTree [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
   776 (*[[from sml: > @@@@@begin@@@@@
   777 [[from sml:  1 
   778 [[from sml: <CALCTREE>
   779 [[from sml:    <CALCID> 1 </CALCID>
   780 [[from sml: </CALCTREE>
   781 [[from sml: @@@@@end@@@@@*)
   782 Iterator 1;
   783 (*[[from sml: > @@@@@begin@@@@@
   784 [[from sml:  1 
   785 [[from sml: <ADDUSER>
   786 [[from sml:   <CALCID> 1 </CALCID>
   787 [[from sml:   <USERID> 1 </USERID>
   788 [[from sml: </ADDUSER>
   789 [[from sml: @@@@@end@@@@@*)
   790 moveActiveRoot 1;
   791 (*[[from sml: > @@@@@begin@@@@@
   792 [[from sml:  1 
   793 [[from sml: <CALCITERATOR>
   794 [[from sml:   <CALCID> 1 </CALCID>
   795 [[from sml:   <POSITION>
   796 [[from sml:     <INTLIST>
   797 [[from sml:     </INTLIST>
   798 [[from sml:     <POS> Pbl </POS>
   799 [[from sml:   </POSITION>
   800 [[from sml: </CALCITERATOR>
   801 [[from sml: @@@@@end@@@@@*)
   802 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
   803 (*[[from sml: > @@@@@begin@@@@@                STILL CORRECT
   804 [[from sml:  1 
   805 [[from sml: <GETELEMENTSFROMTO>
   806 [[from sml:   <CALCID> 1 </CALCID>
   807 [[from sml:   <FORMHEADS>
   808 [[from sml:     <CALCFORMULA>
   809 [[from sml:       <POSITION>
   810 [[from sml:         <INTLIST>
   811 [[from sml:         </INTLIST>
   812 [[from sml:         <POS> Pbl </POS>
   813 [[from sml:       </POSITION>
   814 [[from sml:       <FORMULA>
   815 [[from sml:         <MATHML>
   816 [[from sml:           <ISA> ________________________________________________ </ISA>
   817 [[from sml:         </MATHML>
   818 [[from sml: 
   819 [[from sml:       </FORMULA>
   820 [[from sml:     </CALCFORMULA>
   821 [[from sml:   </FORMHEADS>
   822 [[from sml: </GETELEMENTSFROMTO>
   823 [[from sml: @@@@@end@@@@@*)
   824 refFormula 1 ([],Pbl);
   825 (*[[from sml: > @@@@@begin@@@@@                STILL CORRECT
   826 [[from sml:  1 
   827 [[from sml: <REFFORMULA>
   828 [[from sml:   <CALCID> 1 </CALCID>
   829 [[from sml:   <CALCHEAD status = "incorrect">
   830 [[from sml:     <POSITION>
   831 [[from sml:       <INTLIST>
   832 [[from sml:       </INTLIST>
   833 [[from sml:       <POS> Pbl </POS>
   834 [[from sml:     </POSITION>
   835 [[from sml:     <HEAD>
   836 [[from sml:       <MATHML>
   837 [[from sml:         <ISA> Problem (ThyC.id_empty, [e_pblID]) </ISA>
   838 [[from sml:       </MATHML>
   839 [[from sml:     </HEAD>
   840 [[from sml:     <MODEL>
   841 [[from sml:       <GIVEN>  </GIVEN>
   842 [[from sml:       <WHERE>  </WHERE>
   843 [[from sml:       <FIND>  </FIND>
   844 [[from sml:       <RELATE>  </RELATE>
   845 [[from sml:     </MODEL>
   846 [[from sml:     <BELONGSTO> Pbl </BELONGSTO>
   847 [[from sml:     <SPECIFICATION>
   848 [[from sml:       <THEORYID> ThyC.id_empty </THEORYID>
   849 [[from sml:       <PROBLEMID>
   850 [[from sml:         <STRINGLIST>
   851 [[from sml:           <STRING> Problem.id_empty </STRING>
   852 [[from sml:         </STRINGLIST>
   853 [[from sml:       </PROBLEMID>
   854 [[from sml:       <METHODID>
   855 [[from sml:         <STRINGLIST>
   856 [[from sml:           <STRING> e_metID </STRING>
   857 [[from sml:         </STRINGLIST>
   858 [[from sml:       </METHODID>
   859 [[from sml:     </SPECIFICATION>
   860 [[from sml:   </CALCHEAD>
   861 [[from sml: </REFFORMULA>
   862 [[from sml: @@@@@end@@@@@*)
   863 moveActiveFormula 1 ([],Pbl);
   864 (*[[from sml: > @@@@@begin@@@@@
   865 [[from sml:  1 
   866 [[from sml: <CALCITERATOR>
   867 [[from sml:   <CALCID> 1 </CALCID>
   868 [[from sml:   <POSITION>
   869 [[from sml:     <INTLIST>
   870 [[from sml:     </INTLIST>
   871 [[from sml:     <POS> Pbl </POS>
   872 [[from sml:   </POSITION>
   873 [[from sml: </CALCITERATOR>
   874 [[from sml: @@@@@end@@@@@*)
   875 replaceFormula 1 "Simplify (1+2)";
   876 (*[[from sml: > @@@@@begin@@@@@
   877 [[from sml:  1 
   878 [[from sml: <REPLACEFORMULA>
   879 [[from sml:   <CALCID> 1 </CALCID>
   880 [[from sml:   <CALCCHANGED>
   881 [[from sml:     <UNCHANGED>
   882 [[from sml:       <INTLIST>
   883 [[from sml:       </INTLIST>
   884 [[from sml:       <POS> Pbl </POS>
   885 [[from sml:     </UNCHANGED>
   886 [[from sml:     <DELETED>
   887 [[from sml:       <INTLIST>
   888 [[from sml:       </INTLIST>
   889 [[from sml:       <POS> Pbl </POS>
   890 [[from sml:     </DELETED>
   891 [[from sml:     <GENERATED>
   892 [[from sml:       <INTLIST>
   893 [[from sml:       </INTLIST>
   894 [[from sml:       <POS> Met </POS>                           DIFFERENCE: Pbl
   895 [[from sml:     </GENERATED>
   896 [[from sml:   </CALCCHANGED>
   897 [[from sml: </REPLACEFORMULA>
   898 [[from sml: @@@@@end@@@@@*)
   899 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(*              DIFFERENCE: Pbl*);
   900 (*@@@@@begin@@@@@
   901  1
   902 <GETELEMENTSFROMTO>
   903   <CALCID> 1 </CALCID>
   904   <FORMHEADS>
   905     <CALCFORMULA>
   906       <POSITION>
   907         <INTLIST>
   908         </INTLIST>
   909         <POS> Pbl </POS>
   910       </POSITION>
   911       <FORMULA>
   912         <MATHML>
   913           <ISA> Simplify (1 + 2) </ISA>                      WORKS !!!!!
   914         </MATHML>
   915       </FORMULA>
   916     </CALCFORMULA>
   917   </FORMHEADS>
   918 </GETELEMENTSFROMTO>
   919 @@@@@end@@@@@*)
   920 getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
   921 (*[[from sml: > @@@@@begin@@@@@
   922 [[from sml:  1 
   923 [[from sml: <SYSERROR>
   924 [[from sml:   <CALCID> 1 </CALCID>
   925 [[from sml:   <ERROR> error in getFormulaeFromTo </ERROR>
   926 [[from sml: </SYSERROR>
   927 [[from sml: @@@@@end@@@@@*)
   928 (*step into getFormulaeFromTo --- bug corrected...*)
   929 
   930 "--------- build fun check_for' ------------------------------";
   931 "--------- build fun check_for' ------------------------------";
   932 "--------- build fun check_for' ------------------------------";
   933 val subst = [(TermC.str2term "bdv", TermC.str2term "x")]: subst;
   934 val rls = norm_Rational
   935 val pat = TermC.parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
   936 val (res, inf) = (TermC.str2term "(2 + 3)/(3 + 4)", TermC.str2term "2 / 4");
   937 val (res, inf) = (TermC.str2term "(2 + 3)/(3 + 4)", TermC.str2term "1 / 2");
   938 
   939 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern TermC.matches in res*)
   940   rew_sub thy 1 [] e_rew_ord Rule_Set.empty false [] (HOLogic.Trueprop $ pat) res;
   941 if rewritten then NONE else SOME "e_errpatID";
   942 
   943 val norm_res = case rewrite_set_ (Isac()) false rls res' of
   944   NONE => res'
   945 | SOME (norm_res, _) => norm_res
   946 
   947 val norm_inf = case rewrite_set_ (Isac()) false rls inf of
   948   NONE => inf
   949 | SOME (norm_inf, _) => norm_inf;
   950 
   951 res' = inf;
   952 norm_res = norm_inf;
   953 
   954 val pat = TermC.parse_patt @{theory} "(?a + ?b)/?a = ?b";
   955 val (res, inf) = (TermC.str2term "(2 + 3)/2", TermC.str2term "3");
   956 if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
   957 then () else error "error patt example1 changed";
   958 
   959 val pat = TermC.parse_patt @{theory} "(?a + ?b)/(?a + ?c) = ?b / ?c";
   960 val (res, inf) = (TermC.str2term "(2 + 3)/(2 + 4)", TermC.str2term "3 / 4");
   961 if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
   962 then () else error "error patt example2 changed";
   963 
   964 val pat = TermC.parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
   965 val (res, inf) = (TermC.str2term "(2 + 3)/(3 + 4)", TermC.str2term "2 / 4");
   966 if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
   967 then () else error "error patt example3 changed";
   968 
   969 val inf =  TermC.str2term "1 / 2";
   970 if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
   971 then () else error "error patt example3 changed";
   972 
   973 "--------- build fun check_for' ?bdv -------------------------";
   974 "--------- build fun check_for' ?bdv -------------------------";
   975 "--------- build fun check_for' ?bdv -------------------------";
   976 val subst = [(TermC.str2term "bdv", TermC.str2term "x")]: subst;
   977 val t = TermC.str2term "d_d x (x \<up> 2 + sin (x \<up> 4))";
   978 val SOME (t, _) = rewrite_set_inst_ thy false subst norm_diff t;
   979 if UnparseC.term t = "2 * x + cos (x \<up> 4) * 4 * x \<up> 3" then ()
   980 else error "build fun check_for' ?bdv changed 1"; 
   981 
   982 val rls = norm_diff
   983 val pat = TermC.parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)"; 
   984 val (res, inf) = (TermC.str2term "2 * x + d_d x (sin (x \<up> 4))", TermC.str2term "2 * x + cos (4 * x \<up> 3)");
   985 
   986 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern TermC.matches in res*)
   987   rew_sub thy 1 subst e_rew_ord Rule_Set.empty false [] (HOLogic.Trueprop $ pat) res;
   988 if UnparseC.term res' = "2 * x + cos (d_d x (x \<up> 4))" andalso rewritten then ()
   989 else error "build fun check_for' ?bdv changed 2";
   990 
   991 val norm_res = case rewrite_set_inst_ (Isac()) false subst rls  res' of
   992   NONE => res'
   993 | SOME (norm_res, _) => norm_res;
   994 if UnparseC.term norm_res = "2 * x + cos (4 * x \<up> 3)" then ()
   995 else error "build fun check_for' ?bdv changed 3";
   996 
   997 val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of
   998   NONE => inf
   999 | SOME (norm_inf, _) => norm_inf;
  1000 if UnparseC.term norm_inf = "2 * x + cos (4 * x \<up> 3)" then ()
  1001 else error "build fun check_for' ?bdv changed 4";
  1002 
  1003 res' = inf;
  1004 if norm_res = norm_inf then ()
  1005 else error "build fun check_for' ?bdv changed 5";
  1006 
  1007 if Error_Pattern.check_for' (res, inf) (subst: subst) ("errpatID": Error_Pattern.id, pat) rls = SOME "errpatID"
  1008 then () else error "error patt example1 changed";
  1009 
  1010 "--------- build fun check_for ------------------------";
  1011 "--------- build fun check_for ------------------------";
  1012 "--------- build fun check_for ------------------------";
  1013 val (res, inf) =
  1014   (TermC.str2term "d_d x (x \<up> 2) + d_d x (sin (x \<up>  4))",
  1015    TermC.str2term "d_d x (x \<up> 2) + cos (4 * x \<up> 3)");
  1016 val {errpats, nrls = rls, scr = Prog prog, ...} = MethodC.from_store ["diff", "differentiate_on_R"]
  1017 
  1018 val env = [(TermC.str2term "v_v", TermC.str2term "x")];
  1019 val errpats =
  1020   [Error_Pattern.empty, (*generalised for testing*)
  1021    ("chain-rule-diff-both",
  1022      [TermC.parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)",
  1023       TermC.parse_patt @{theory} "d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)",
  1024       TermC.parse_patt @{theory} "d_d ?bdv (?u \<up> ?n) = ?n * ?u \<up> (?n - 1)",
  1025       TermC.parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / ?u",
  1026       TermC.parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u"],
  1027      [@{thm diff_sin_chain}, @{thm diff_cos_chain}, @{thm diff_pow_chain}, 
  1028       @{thm diff_ln_chain}, @{thm  diff_exp_chain}])];
  1029 case Error_Pattern.check_for (res, inf) (prog, env) (errpats, rls) of SOME _ => () 
  1030 | NONE => error "Error_Pattern.check_for broken";
  1031 DEconstrCalcTree 1;
  1032 
  1033 "--------- embed fun check_for ------------------------";
  1034 "--------- embed fun check_for ------------------------";
  1035 "--------- embed fun check_for ------------------------";
  1036 reset_states ();     
  1037 CalcTree
  1038 [(["functionTerm (x \<up> 2 + sin (x \<up> 4))", "differentiateFor x", "derivative f_f'"], 
  1039   ("Isac_Knowledge", ["derivative_of", "function"], ["diff", "differentiate_on_R"]))];
  1040 Iterator 1;
  1041 moveActiveRoot 1;
  1042 autoCalculate 1 CompleteCalcHead;
  1043 autoCalculate 1 (Steps 1);
  1044 autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))*)
  1045 (*autoCalculate 1 (Steps 1);([2], Res), d_d x (x \<up> 2) + cos (x \<up> 4) * d_d x (x \<up> \<up>  4)*)
  1046 
  1047 "~~~~~ fun appendFormula , args:"; val (cI, (ifo:TermC.as_string)) = (1, "d_d x (x \<up> 2) + cos (4 * x \<up> 3)");
  1048 "~~~~~ fun appendFormula' , args:"; val (cI, (ifo: TermC.as_string)) = (cI, ifo);
  1049     val cs = get_calc cI
  1050     val pos = get_pos cI 1;
  1051 (*+*)if pos = ([1], Res) then () else error "inform with (positive) Error_Pattern.check_for broken 1";
  1052     val ("ok", cs' as (_, _, ptp)) = (*case*) Step.do_next pos cs (*of*);
  1053       (*case*) Step_Solve.by_term ptp (encode ifo) (*of*); (*ERROR WAS: "no derivation found"*)
  1054 "~~~~~ fun Step_Solve.by_term , args:"; val (((*next_*)cs as (_, _, (pt, pos as (p, _))): Calc.state_post), istr)
  1055   = (cs', (encode ifo));
  1056     val ctxt = get_ctxt pt pos (*see TODO.thy*)
  1057     val SOME f_in = (*case*) TermC.parseNEW (ThyC.id_to_ctxt "Isac_Knowledge") istr (*of*);
  1058         val pos_pred = lev_back' pos
  1059     	  val f_pred = Ctree.get_curr_formula (pt, pos_pred);
  1060         (*if*) f_pred = f_in; (*else*)
  1061           val NONE = (*case*) CAS_Cmd.input f_in (*of*);
  1062        (*old* )val (_, _, metID) = get_obj g_spec pt (par_pblobj pt p)
  1063        (*old*)val {scr = prog, ...} = MethodC.from_store metID
  1064        (*old*)val istate = get_istate_LI pt pos
  1065        (*old*)val ctxt = get_ctxt pt pos
  1066        ( *old*)
  1067        val LI.Not_Derivable =
  1068              (*case*) LI.locate_input_term (pt, pos) f_in (*of*);
  1069             		  val pp = Ctree.par_pblobj pt p
  1070             		  val (errpats, nrls, prog) = case MethodC.from_store (Ctree.get_obj Ctree.g_metID pt pp) of
  1071               		    {errpats, nrls, scr = Rule.Prog prog, ...} => (errpats, nrls, prog)
  1072               		  | _ => error "inform: uncovered case of MethodC.from_store"
  1073 ;
  1074 (*+*)if Error_Pattern.s_to_string errpats = "[(\"chain-rule-diff-both\",\n[\"d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)\", \"d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)\", \"d_d ?bdv (?u \<up> ?n) = ?n * ?u \<up> (?n - 1)\", \"d_d ?bdv (LogExp.ln ?u) = 1 / ?u\", \"d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u\"],\n[\"d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u\", \"d_d ?bdv (cos ?u) = - sin ?u * d_d ?bdv ?u\", \"d_d ?bdv (?u \<up> ?n) = ?n * ?u \<up> (?n - 1) * d_d ?bdv ?u\", \"d_d ?bdv (LogExp.ln ?u) = d_d ?bdv ?u / ?u\", \"d_d ?bdv (exp ?u) = exp ?u * d_d ?x ?u\"]]"
  1075 (*+*)then () else error "inform with (positive) Error_Pattern.check_for broken 3";
  1076 
  1077             		  val {env, ...} = Ctree.get_istate_LI pt pos |> Istate.the_pstate
  1078 ;
  1079 (*+*)if UnparseC.term f_pred = "d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" andalso
  1080 (*+*)   UnparseC.term f_in = "d_d x (x \<up> 2) + cos (4 * x \<up> 3)"
  1081 (*+*)then () else error "inform with (positive) Error_Pattern.check_for broken 2";
  1082 
  1083              val SOME "chain-rule-diff-both" = (*case*) Error_Pattern.check_for (f_pred, f_in) (prog, env) (errpats, nrls) (*of*);
  1084 
  1085 "--- final check:";
  1086 (*+*)val (_, _, ptp') = cs';
  1087 case Step_Solve.by_term ptp' (encode ifo) of
  1088   ("error pattern #chain-rule-diff-both#", calcstate') => ()
  1089 | _ => error "inform with (positive) Error_Pattern.check_for broken"
  1090 
  1091 
  1092 "--------- embed fun find_fill_patterns ---------------------------";
  1093 "--------- embed fun find_fill_patterns ---------------------------";
  1094 "--------- embed fun find_fill_patterns ---------------------------";
  1095 reset_states ();
  1096 CalcTree
  1097 [(["functionTerm (x \<up> 2 + sin (x \<up> 4))", "differentiateFor x", "derivative f_f'"], 
  1098   ("Isac_Knowledge", ["derivative_of", "function"], ["diff", "differentiate_on_R"]))];
  1099 Iterator 1;
  1100 moveActiveRoot 1;
  1101 autoCalculate 1 CompleteCalcHead;
  1102 autoCalculate 1 (Steps 1);
  1103 autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))*)
  1104 appendFormula 1 "d_d x (x \<up> 2) + cos (4 * x \<up> 3)" (*|> Future.join*);
  1105   (*<CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>*)
  1106   (*or
  1107     <CALCMESSAGE> no derivation found </CALCMESSAGE>*)
  1108 
  1109 "~~~~~ fun findFillpatterns, args:"; val (cI, errpatID) = (1, "chain-rule-diff-both");
  1110   val ((pt, _), _) = get_calc cI
  1111 				val pos = get_pos cI 1;
  1112 "~~~~~ fun find_fill_patterns , args:"; val ((pt, pos as (p, _)), errpatID) = ((pt, pos), errpatID);
  1113     val f_curr = Ctree.get_curr_formula (pt, pos);
  1114     val pp = Ctree.par_pblobj pt p
  1115     val (errpats, prog) = case MethodC.from_store (Ctree.get_obj Ctree.g_metID pt pp) of
  1116       {errpats, scr = Rule.Prog prog, ...} => (errpats, prog)
  1117     | _ => error "find_fill_patterns: uncovered case of MethodC.from_store"
  1118     val {env, ...} = Ctree.get_istate_LI pt pos |> Istate.the_pstate
  1119     val subst = Subst.for_bdv prog env
  1120     val errpatthms = errpats
  1121       |> filter ((curry op = errpatID) o (#1: Error_Pattern.T -> Error_Pattern.id))
  1122       |> map (#3: Error_Pattern.T -> thm list)
  1123       |> flat;
  1124 
  1125 case map (Error_Pattern.fill_from_store subst f_curr errpatID) errpatthms |> flat of
  1126   ("fill-d_d-arg", tm, thm, subs_opt) :: _ => if UnparseC.term tm = 
  1127     "d_d x (x \<up> 2) + d_d x (sin (x \<up> 4)) =\nd_d x (x \<up> 2) + cos (x \<up> 4) * d_d x ?_dummy_1"
  1128     then () else error "find_fill_patterns changed 1a"
  1129 | _ => error "find_fill_patterns changed 1b"
  1130 
  1131 "~~~~~ fun fill_from_store, args:"; val (subst, form, errpatID, thm) =
  1132   (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
  1133         val thmDeriv = Thm.get_name_hint thm
  1134         val (part, thyID) = Thy_Read.thy_containing_thm thmDeriv
  1135         val theID = [part, thyID, "Theorems", ThmC.cut_id thmDeriv]
  1136         val Thy_Write.Hthm {fillpats, ...} = Thy_Read.from_store theID
  1137         val some = map (Error_Pattern.fill_form subst (thm, form) errpatID) fillpats;
  1138 
  1139 case some |> filter is_some |> map the of
  1140   ("fill-d_d-arg", tm, thm, subsopt) :: _ => if UnparseC.term tm = 
  1141     "d_d x (x \<up> 2) + d_d x (sin (x \<up> 4)) =\nd_d x (x \<up> 2) + cos (x \<up> 4) * d_d x ?_dummy_1"
  1142     then () else error "find_fill_patterns changed 2a"
  1143 | _ => error "find_fill_patterns changed 2b"
  1144 
  1145 "~~~~~ fun fill_form, args:";
  1146   val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
  1147   (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
  1148 val (form', _, _, rewritten) =
  1149       rew_sub (Isac()) 1 subst e_rew_ord Rule_Set.empty false [] (HOLogic.Trueprop $ pat) form;
  1150 
  1151 if UnparseC.term form' = "d_d x (x \<up> 2) + cos (x \<up> 4) * d_d x ?_dummy_1" then ()
  1152 else error "find_fill_patterns changed 3";
  1153 
  1154 "~~~~~ to findFillpatterns return val:"; val (fillpats) =
  1155   (map (Error_Pattern.fill_from_store (subs_opt, subst) f_curr errpatID) errpatthms |> flat) (*only from "hd errpatthms"*);
  1156 
  1157 "vvv--- dropped this code WN120730";
  1158 val msg = "fill patterns " ^
  1159   ((map ((apsnd UnparseC.term) o quad2pair) fillpats) |> map pair2str_ |> strs2str_);
  1160 msg =
  1161   "fill patterns #fill-d_d-arg#d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" ^
  1162     " =\nd_d x (x \<up> 2) + cos (x \<up> 4) * d_d x ?_dummy_1" ^
  1163   "#fill-both-args#d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" ^
  1164     " =\nd_d x (x \<up> 2) + cos ?_dummy_2 * d_d x ?_dummy_3" ^
  1165   "#fill-d_d#d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" ^
  1166     " =\nd_d x (x \<up> 2) + cos (x \<up> 4) * ?_dummy_1 x (x \<up> 4)" ^
  1167   "#fill-inner-deriv#d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" ^
  1168     " =\nd_d x (x \<up> 2) + cos (x \<up> 4) * ?_dummy_1" ^
  1169   "#fill-all#d_d x (x \<up> 2) + d_d x (sin (x \<up> 4)) = d_d x (x \<up> 2) + ?_dummy_1#";
  1170 " \<up> --- dropped this code WN120730";
  1171 
  1172 if (map #1 fillpats) =
  1173   ["fill-d_d-arg", "fill-both-args", "fill-d_d", "fill-inner-deriv", "fill-all"]
  1174 then () else error "find_fill_patterns changed 4b";
  1175 DEconstrCalcTree 1;
  1176 
  1177 "--------- build fun is_exactly_equal, inputFillFormula ----------";
  1178 "--------- build fun is_exactly_equal, inputFillFormula ----------";
  1179 "--------- build fun is_exactly_equal, inputFillFormula ----------";
  1180 reset_states ();
  1181 CalcTree
  1182 [(["functionTerm (x \<up> 2 + sin (x \<up> 4))", "differentiateFor x", "derivative f_f'"], 
  1183   ("Isac_Knowledge", ["derivative_of", "function"], ["diff", "differentiate_on_R"]))];
  1184 Iterator 1;
  1185 moveActiveRoot 1;
  1186 autoCalculate 1 CompleteCalcHead;
  1187 autoCalculate 1 (Steps 1);
  1188 autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))*)
  1189 appendFormula 1 "d_d x (x \<up> 2) + cos (4 * x \<up> 3)" (*|> Future.join*); (*<<<<<<<=========================*)
  1190 (* the check for errpat is maximally liberal (whole term modulo "nrls" from "type met"),
  1191   would recognize "cos (4 * x \<up> (4 - 1)) + 2 * x" as well.
  1192   results in <CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>
  1193   instead of <CALCMESSAGE> no derivation found </CALCMESSAGE> *)
  1194   val ((pt,pos), _) = get_calc 1;
  1195   val p = get_pos 1 1;
  1196   val (Form f, _, asms) = ME_Misc.pt_extract (pt, p);
  1197 
  1198   if p = ([1], Res) andalso UnparseC.term f = "d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" then
  1199     case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"], 
  1200       ("diff_sum", thm)) =>
  1201       if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
  1202       else error "embed fun fill_form changed 11"
  1203     | _ => error "embed fun fill_form changed 12"
  1204   else error "embed fun fill_form changed 13";
  1205 
  1206 findFillpatterns 1 "chain-rule-diff-both"; (*<<<<<<<=================================*)
  1207 (*<CALCMESSAGE> fill patterns #fill-d_d-arg#d_d x (x \<up> 2) + d_d x (sin (x \<up>  4)) =
  1208   d_d x (x \<up> 2) + cos (x \<up> 4) * d_d x ?_dummy_1#fill-both-args#...#...#... *)
  1209   val ((pt,pos),_) = get_calc 1;
  1210   val p = get_pos 1 1;
  1211 
  1212   val (Form f, _, asms) = ME_Misc.pt_extract (pt, p);
  1213   if p = ([1], Res) andalso UnparseC.term f = "d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))" then
  1214     case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"], 
  1215       ("diff_sum", thm)) =>
  1216       if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
  1217       else error "embed fun fill_form changed 21"
  1218     | _ => error "embed fun fill_form changed 22"
  1219   else error "embed fun fill_form changed 23";
  1220 
  1221 requestFillformula 1 ("chain-rule-diff-both", "fill-both-args");(*<<<<<<<============*)
  1222   (*<AUTOCALC> ([1], Res) ([2], Res) ([2], Res) </AUTOCALC>*)
  1223   val ((pt,pos),_) = get_calc 1;
  1224   val p = get_pos 1 1;
  1225   val (Form f, _, asms) = ME_Misc.pt_extract (pt, p);
  1226   if p = ([1], Res) andalso existpt [2] pt
  1227     andalso UnparseC.term f = "d_d x (x \<up> 2) + d_d x (sin (x \<up> 4))"
  1228   then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"], 
  1229       ("diff_sum", thm)) =>
  1230       if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
  1231       else error "embed fun fill_form changed 31"
  1232     | _ => error "embed fun fill_form changed 32"
  1233   else error "embed fun fill_form changed 33";
  1234 
  1235 (* input a formula which exactly fills the gaps in a "fillformula"
  1236    presented to the learner immediately before by "requestFillformula (errpatID, fillpatID)":
  1237    errpatID: lhs of the respective thm = lhs of fillformula with fillpatID.
  1238    the respective thm is in the ctree ................
  1239 *)
  1240 "~~~~~ fun inputFillFormula, args:"; val (cI, ifo) =
  1241   (1, "d_d x (x \<up> 2) + cos (x \<up> 4) * d_d x (x \<up> 4)");
  1242     val ((pt, _), _) = get_calc cI
  1243     val pos = get_pos cI 1;
  1244 
  1245 "~~~~~ fun is_exactly_equal, args:"; val ((pt, pos as (p, p_)), istr) = ((pt, pos), ifo);
  1246   val SOME ifo = parseNEW (ThyC.get_theory "Isac_Knowledge" |> ThyC.to_ctxt) istr
  1247   val p' = lev_on p;
  1248   val tac = get_obj g_tac pt p';
  1249 val Rewrite_Inst ([bbb as "(''bdv'', x)"], ("diff_sin_chain", ttt)) = tac;
  1250 if (UnparseC.term o Thm.prop_of) ttt = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
  1251 else error "inputFillFormula changed 10";
  1252   val Applicable.Yes rew = Step.check tac (pt, pos);
  1253   val Rewrite_Inst' (_, _, _, _, _, _, _, (res, _)) = rew;
  1254 
  1255 "~~~~~ to inputFillFormula return val:"; val ("ok", tac) = ("ok", tac);
  1256   val ("ok", (_, c, ptp as (_,p'))) = Step.by_tactic tac (pt, pos);
  1257     upd_calc cI (ptp, []);
  1258     upd_ipos cI 1 p';
  1259     autocalculateOK2xml cI pos (if null c then p' else last_elem c) p';
  1260 
  1261 "~~~~~ final check:";
  1262 val ((pt, _),_) = get_calc 1;
  1263 val p = get_pos 1 1;
  1264 val (Form f, _, asms) = ME_Misc.pt_extract (pt, p);
  1265   if p = ([2], Res) andalso UnparseC.term f = "d_d x (x \<up> 2) + cos (x \<up> 4) * d_d x (x \<up> 4)"
  1266   then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"], 
  1267       ("diff_sin_chain", thm)) =>
  1268       if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
  1269       else error "inputFillFormula changed 111"
  1270     | _ => error "inputFillFormula changed 112"
  1271   else error "inputFillFormula changed 113";
  1272 
  1273 "--------- fun appl_adds -----------------------------------------";
  1274 "--------- fun appl_adds -----------------------------------------";
  1275 "--------- fun appl_adds -----------------------------------------";
  1276 (* val (dI, oris, ppc, pbt, selct::ss) = 
  1277        (dI, pors, probl, ppc, map itms2fstr probl);
  1278    ...vvv
  1279    *)
  1280 (* val (dI, oris, ppc, pbt, (selct::ss))=
  1281        (#1 (References.select ospec spec), oris, []:I_Model.T,
  1282 	((#ppc o Problem.from_store) (#2 (References.select ospec spec))),(imodel2fstr imodel));
  1283    val iii = appl_adds dI oris ppc pbt (selct::ss); 
  1284    tracing(I_Model.to_string thy iii);
  1285 
  1286  val itm = add_single' dI oris ppc pbt selct;
  1287  val ppc = I_Model.add itm ppc;
  1288 
  1289  val _::selct::ss = (selct::ss);
  1290  val itm = add_single' dI oris ppc pbt selct;
  1291  val ppc = I_Model.add itm ppc;
  1292 
  1293  val _::selct::ss = (selct::ss);
  1294  val itm = add_single' dI oris ppc pbt selct;
  1295  val ppc = I_Model.add itm ppc;
  1296  tracing(I_Model.to_string thy ppc);
  1297 
  1298  val _::selct::ss = (selct::ss);
  1299  val itm = add_single' dI oris ppc pbt selct;
  1300  val ppc = I_Model.add itm ppc;
  1301    *)
  1302 "--------- fun concat_deriv --------------------------------------";
  1303 "--------- fun concat_deriv --------------------------------------";
  1304 "--------- fun concat_deriv --------------------------------------";
  1305 (*
  1306  val ({rew_ord, erls, rules,...}, fo, ifo) = 
  1307      (Rule_Set.rep Test_simplify, TermC.str2term "x+1+ - 1*2=0", TermC.str2term "-2*1+(x+1)=0");
  1308  (tracing o Derive.trtas2str) fod';
  1309 > ["
  1310 (x + 1 + - 1 * 2 = 0, Thm ("radd_commute", "?m + ?n = ?n + ?m"), (- 1 * 2 + (x + 1) = 0, []))", "
  1311 (- 1 * 2 + (x + 1) = 0, Thm ("radd_commute", "?m + ?n = ?n + ?m"), (- 1 * 2 + (1 + x) = 0, []))", "
  1312 (- 1 * 2 + (1 + x) = 0, Thm ("radd_left_commute", "?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (- 1 * 2 + x) = 0, []))", "
  1313 (1 + (- 1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))", "- 1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]
  1314 val it = () : unit
  1315  (tracing o Derive.trtas2str) (map Derive.rev_deriv' rifod');
  1316 > ["
  1317 (1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))", "-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))", "
  1318 (1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute", "?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))", "
  1319 (-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute", "?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]
  1320 val it = () : unit
  1321 *)
  1322 "--------- handle an input formula -------------------------------";
  1323 "--------- handle an input formula -------------------------------";
  1324 "--------- handle an input formula -------------------------------";
  1325 (*
  1326 Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:
  1327 Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden, 
  1328 wenn Abteilungen nur auf gleichem Level gesucht werden ?
  1329 WN.040216 
  1330 
  1331 Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml
  1332 
  1333 ------------------------------------------------------------------------------
  1334 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
  1335 ------------------------------------------------------------------------------
  1336 1. "5 * x / (x - 2) - x / (x + 2) = 4"
  1337 ...
  1338 4. "12 * x + 4 * x \<up> 2 = 4 * (-4 + x \<up> 2)",Subproblem["normalise", "poly"..
  1339 ...
  1340 4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..
  1341 ...
  1342 4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"
  1343 ...
  1344 "[x = -4 / 3]"
  1345 ------------------------------------------------------------------------------
  1346 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
  1347 
  1348 (4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
  1349 ------------------------------------------------------------------------------
  1350 
  1351 
  1352 ------------------------------------------------------------------------------
  1353 "Schalk I s.87 Bsp 55b (x/(x \<up> 2 - 6*x+9) - 1/(x \<up> 2 - 3*x) =1/x)";
  1354 ------------------------------------------------------------------------------
  1355 1. "x / (x \<up> 2 - 6 * x + 9) - 1 / (x \<up> 2 - 3 * x) = 1 / x"
  1356 ...
  1357 4. "(3 + (- 1 * x + x \<up> 2)) * x = 1 * (9 * x + (x \<up> 3 + -6 * x \<up> 2))"
  1358                          Subproblem["normalise", "polynomial", "univariate"..
  1359 ...
  1360 4.4. "-6 * x + 5 * x \<up> 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..
  1361 ...
  1362 4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
  1363 4.4.5. "[x = 0, x = 6 / 5]"
  1364 ...
  1365 5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
  1366    "[x = 6 / 5]"
  1367 ------------------------------------------------------------------------------
  1368 (1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]
  1369 
  1370 (4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]
  1371 ------------------------------------------------------------------------------
  1372 
  1373 
  1374 ------------------------------------------------------------------------------
  1375 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1376 ------------------------------------------------------------------------------
  1377 1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"
  1378 ...
  1379 6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"
  1380                              Subproblem["sq", "rootX", "univariate", "equation"]
  1381 ...
  1382 6.6. "144 + 288 * x + 144 * x \<up> 2 = 144 + x \<up> 2 + 288 * x + 143 * x \<up> 2"
  1383                 Subproblem["normalise", "polynomial", "univariate", "equation"]
  1384 ...6.6.3 "0 = 0"    Subproblem["degree_0", "polynomial", "univariate", "equation"]
  1385 ...                                       Or_to_List
  1386 6.6.3.2 "UniversalList"
  1387 ------------------------------------------------------------------------------
  1388 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]
  1389 
  1390 (6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]
  1391 ------------------------------------------------------------------------------
  1392 *)
  1393 (*sh. comments auf 498*)
  1394 "--------- fun dropwhile' ----------------------------------------";
  1395 "--------- fun dropwhile' ----------------------------------------";
  1396 "--------- fun dropwhile' ----------------------------------------";
  1397 (*
  1398  fun equal a b = a=b;
  1399  val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];
  1400  val r_foder = rev foder;  val r_ifoder = rev ifoder;
  1401  dropwhile' equal r_foder r_ifoder;
  1402 > vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list
  1403 
  1404  val foder = [3,4,5]; val ifoder = [11,12,3,4,5];
  1405  val r_foder = rev foder;  val r_ifoder = rev ifoder;
  1406  dropwhile' equal r_foder r_ifoder;
  1407 > val it = ([3], [3, 12, 11]) : int list * int list
  1408 
  1409  val foder = [5]; val ifoder = [11,12,3,4,5];
  1410  val r_foder = rev foder;  val r_ifoder = rev ifoder;
  1411  dropwhile' equal r_foder r_ifoder;
  1412 > val it = ([5], [5, 4, 3, 12, 11]) : int list * int list
  1413 
  1414  val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];
  1415  val r_foder = rev foder;  val r_ifoder = rev ifoder;
  1416  dropwhile' equal r_foder r_ifoder;
  1417 > *** dropwhile': did not start with equal elements*)