test/Tools/isac/Knowledge/integrate.sml
author wneuper <Walther.Neuper@jku.at>
Sat, 04 Feb 2023 17:00:25 +0100
changeset 60675 d841c720d288
parent 60665 fad0cbfb586d
permissions -rw-r--r--
eliminate use of Thy_Info 22: eliminate UnparseC.term, rename "_in_ctxt" -> ""
     1 (* Title:  test/Tools/isac/Knowledge/integrate.sml
     2    Author: Walther Neuper 050826
     3    (c) due to copyright terms
     4 *)
     5 "--------------------------------------------------------";
     6 "table of contents --------------------------------------";
     7 "--------------------------------------------------------";
     8 "----------- parsing ------------------------------------";
     9 "----------- integrate by rewriting ---------------------";
    10 "----------- test add_new_c, TermC.is_f_x ---------------------";
    11 "----------- simplify by ruleset reducing make_ratpoly_in";
    12 "----------- integrate by ruleset -----------------------";
    13 "----------- rewrite 3rd integration in 7.27 ------------";
    14 "----------- check probem type --------------------------";
    15 "----------- me method [diff,integration] ---------------";
    16 "----------- autoCalculate [diff,integration] -----------";
    17 "----------- me method [diff,integration,named] ---------";
    18 "----------- me met [diff,integration,named] Biegelinie.Q";
    19 "----------- method analog to rls 'integration' ---------";
    20 "--------------------------------------------------------";
    21 "--------------------------------------------------------";
    22 "--------------------------------------------------------";
    23 
    24 (*these val/fun provide for exact parsing in Integrate.thy, not Isac.thy;
    25 they are used several times below; TODO remove duplicates*)
    26 val thy = @{theory "Integrate"};
    27 val ctxt = Proof_Context.init_global thy;
    28 
    29 fun str2t str = ParseC.term_opt ctxt str |> the;
    30 fun term2s t = UnparseC.term ctxt t;
    31     
    32 val conditions_in_integration_rules =
    33   Rule_Set.Repeat {id="conditions_in_integration_rules", 
    34     preconds = [], 
    35     rew_ord = ("termlessI",termlessI), 
    36     asm_rls = Rule_Set.Empty, 
    37     prog_rls = Rule_Set.Empty, calc = [], errpatts = [],
    38     rules = [(*for rewriting conditions in Thm's*)
    39 	    Eval ("Prog_Expr.occurs_in", 
    40 		  eval_occurs_in "#occurs_in_"),
    41 	    Thm ("not_true", @{thm not_true}),
    42 	    Thm ("not_false", @{thm not_false})],
    43     program = Empty_Prog};
    44 val subs = [(str2t "bdv::real", str2t "x::real")];
    45 fun rewrit thm str = 
    46     fst (the (rewrite_inst_ ctxt tless_true 
    47 			   conditions_in_integration_rules 
    48 			   true subs thm str));
    49 
    50 
    51 "----------- parsing ------------------------------------";
    52 "----------- parsing ------------------------------------";
    53 "----------- parsing ------------------------------------";
    54 val t = ParseC.parse_test @{context} "Integral x D x";
    55 val t = ParseC.parse_test @{context} "Integral x \<up> 2 D x";
    56 case t of 
    57     Const (\<^const_name>\<open>Integral\<close>, _) $
    58      (Const (\<^const_name>\<open>realpow\<close>, _) $ Free _ $ _) $ Free ("x", _) => ()
    59   | _ => error "integrate.sml: parsing: Integral x \<up> 2 D x";
    60 
    61 val t = ParseC.parse_test @{context} "ff x is_f_x";
    62 case t of Const (\<^const_name>\<open>is_f_x\<close>, _) $ _ => ()
    63 	| _ => error "integrate.sml: parsing: ff x is_f_x";
    64 
    65 
    66 "----------- integrate by rewriting ---------------------";
    67 "----------- integrate by rewriting ---------------------";
    68 "----------- integrate by rewriting ---------------------";
    69 val str = rewrit @{thm "integral_const"} (ParseC.parse_test @{context} "Integral 1 D x");
    70 if term2s str = "1 * x" then () else error "integrate.sml Integral 1 D x";
    71 
    72 val str = rewrit @{thm "integral_const"} (ParseC.parse_test @{context}  "Integral M'/EJ D x");
    73 if term2s str = "M' / EJ * x" then ()
    74 else error "Integral M'/EJ D x   BY integral_const";
    75 
    76 val str = rewrit @{thm "integral_var"} (ParseC.parse_test @{context} "Integral x D x");
    77 if term2s str = "x \<up> 2 / 2" then ()
    78 else error "Integral x D x   BY integral_var";
    79 
    80 val str = rewrit @{thm "integral_add"} (ParseC.parse_test @{context} "Integral x + 1 D x");
    81 if term2s str = "Integral x D x + Integral 1 D x" then ()
    82 else error "Integral x + 1 D x   BY integral_add";
    83 
    84 val str = rewrit @{thm "integral_mult"} (ParseC.parse_test @{context} "Integral M'/EJ * x \<up> 3 D x");
    85 if term2s str = "M' / EJ * Integral x \<up> 3 D x" then ()
    86 else error "Integral M'/EJ * x \<up> 3 D x   BY integral_mult";
    87 
    88 val str = rewrit @{thm "integral_pow"} (ParseC.parse_test @{context} "Integral x \<up> 3 D x");
    89 if term2s str = "x \<up> (3 + 1) / (3 + 1)" then ()
    90 else error "integrate.sml Integral x \<up> 3 D x";
    91 
    92 
    93 "----------- test add_new_c, TermC.is_f_x ---------------------";
    94 "----------- test add_new_c, TermC.is_f_x ---------------------";
    95 "----------- test add_new_c, TermC.is_f_x ---------------------";
    96 val term = ParseC.parse_test @{context} "x \<up> 2 * c + c_2";
    97 val cc = new_c term;
    98 if UnparseC.term @{context} cc = "c_3" then () else error "integrate.sml: new_c ???";
    99 
   100 val SOME (id,t') = eval_add_new_c "" "Integrate.add_new_c" term ctxt;
   101 if UnparseC.term @{context} t' = "x \<up> 2 * c + c_2 = x \<up> 2 * c + c_2 + c_3" then ()
   102 else error "intergrate.sml: diff. eval_add_new_c";
   103 
   104 val cc = ("Integrate.add_new_c", eval_add_new_c "add_new_c_");
   105 val SOME (thmstr, thm) = adhoc_thm1_ @{context} cc term;
   106 
   107 val SOME (t',_) = rewrite_set_ ctxt true add_new_c term;
   108 if UnparseC.term @{context} t' = "x \<up> 2 * c + c_2 + c_3" then ()
   109 else error "intergrate.sml: diff. rewrite_set add_new_c 1";
   110 
   111 val term = ParseC.parse_test @{context} "ff x = x \<up> 2*c + c_2";
   112 val SOME (t',_) = rewrite_set_ ctxt true add_new_c term;
   113 if UnparseC.term @{context} t' = "ff x = x \<up> 2 * c + c_2 + c_3" then ()
   114 else error "intergrate.sml: diff. rewrite_set add_new_c 2";
   115 
   116 
   117 (*WN080222 replace call_new_c with add_new_c----------------------
   118 val term = str2t "new_c (c * x \<up> 2 + c_2)";
   119 val SOME (_,t') = eval_new_c 0 0 term 0;
   120 if term2s t' = "new_c c * x \<up> 2 + c_2 = c_3" then ()
   121 else error "integrate.sml: eval_new_c ???";
   122 
   123 val t = str2t "matches (?u + new_c ?v) (x \<up> 2 / 2)";
   124 val SOME (_,t') = eval_matches "" "Prog_Expr.matches" t thy; term2s t';
   125 if term2s t' = "matches (?u + new_c ?v) (x \<up> 2 / 2) = False" then ()
   126 else error "integrate.sml: matches new_c = False";
   127 
   128 val t = str2t "matches (?u + new_c ?v) (x \<up> 2 / 2 + new_c x \<up> 2 / 2)";
   129 val SOME (_,t') = eval_matches "" "Prog_Expr.matches" t thy; term2s t';
   130 if term2s t'="matches (?u + new_c ?v) (x \<up> 2 / 2 + new_c x \<up> 2 / 2) = True"
   131 then () else error "integrate.sml: matches new_c = True";
   132 
   133 val t = str2t "ff x TermC.is_f_x";
   134 val SOME (_,t') = eval_is_f_x "" "" t thy; term2s t';
   135 if term2s t' = "(ff x TermC.is_f_x) = True" then ()
   136 else error "integrate.sml: eval_is_f_x --> true";
   137 
   138 val t = str2t "q_0/2 * L * x TermC.is_f_x";
   139 val SOME (_,t') = eval_is_f_x "" "" t thy; term2s t';
   140 if term2s t' = "(q_0 / 2 * L * x TermC.is_f_x) = False" then ()
   141 else error "integrate.sml: eval_is_f_x --> false";
   142 
   143 val conditions_in_integration =
   144 Rule_Set.Repeat {id="conditions_in_integration", 
   145      preconds = [], 
   146      rew_ord = ("termlessI",termlessI), 
   147      asm_rls = Rule_Set.Empty, 
   148      prog_rls = Rule_Set.Empty, calc = [], errpatts = [],
   149      rules = [Eval ("Prog_Expr.matches",eval_matches ""),
   150       	Eval ("Integrate.is_f_x", 
   151       	      eval_is_f_x "is_f_x_"),
   152       	Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),
   153       	Thm ("not_false",ThmC.numerals_to_Free @{thm not_false})
   154       	],
   155      program = Empty_Prog};
   156 fun rewrit thm t = 
   157     fst (the (rewrite_inst_ thy tless_true 
   158 			    conditions_in_integration true subs thm t));
   159 val t = rewrit call_for_new_c (str2t "x \<up> 2 / 2"); term2s t;
   160 val t = (rewrit call_for_new_c t)
   161     handle OPTION =>  str2t "no_rewrite";
   162 
   163 val t = rewrit call_for_new_c 
   164 	       (str2t "ff x = q_0/2 *L*x"); term2s t;
   165 val t = (rewrit call_for_new_c 
   166 	       (str2t "ff x = q_0 / 2 * L * x + new_c q_0 / 2 * L * x"))
   167     handle OPTION => (*NOT:  + new_c ..=..!!*)str2t "no_rewrite";
   168 --------------------------------------------------------------------*)
   169 
   170 
   171 "----------- simplify by ruleset reducing make_ratpoly_in";
   172 "----------- simplify by ruleset reducing make_ratpoly_in";
   173 "----------- simplify by ruleset reducing make_ratpoly_in";
   174 val thy = @{theory "Isac_Knowledge"};
   175 val ctxt = Proof_Context.init_global thy;
   176 val subst = [(ParseC.parse_test @{context} "bdv ::real", ParseC.parse_test @{context} "x ::real")]; (*DOESN'T HELP*)
   177 "===== test 1";
   178 val t = ParseC.parse_test @{context} "1/EI * (L * q_0 * x / 2 + - 1 * q_0 * x \<up> 2 / 2)";
   179 
   180 "----- stepwise from the rulesets in simplify_Integral and below-----";
   181 val rls = norm_Rational_noadd_fractions;
   182 case rewrite_set_inst_ ctxt true subs rls t of
   183     SOME _ => error "integrate.sml simplify by ruleset norm_Rational_.#2"
   184   | NONE => ();
   185 
   186 "===== test 2";
   187 val rls = order_add_mult_in;
   188 val SOME (t, []) = rewrite_set_inst_ ctxt true subst rls t;
   189 if UnparseC.term @{context} t = "1 / EI * (L * (q_0 * x) / 2 + - 1 * (q_0 * x \<up> 2) / 2)" then()
   190 else error "integrate.sml simplify by ruleset order_add_mult_in #2";
   191 
   192 "===== test 3";
   193 val rls = discard_parentheses;
   194 val SOME (t, []) = rewrite_set_ ctxt true rls t;
   195 if UnparseC.term @{context} t = "1 / EI * (L * q_0 * x / 2 + - 1 * q_0 * x \<up> 2 / 2)" then ()
   196 else error "integrate.sml simplify by ruleset discard_parenth.. #3";
   197 
   198 "===== test 4";
   199 val subs = [(ParseC.parse_test @{context} "bdv::real", ParseC.parse_test @{context} "x::real")];
   200 val rls = 
   201   (Rule_Set.append_rules "separate_bdv" collect_bdv
   202  	  [Thm ("separate_bdv", @{thm separate_bdv}),
   203  		  (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
   204  		 Thm ("separate_bdv_n", @{thm separate_bdv_n}),
   205       (*"?a * ?bdv \<up> ?n / ?b = ?a / ?b * ?bdv \<up> ?n"*)
   206  		Thm ("separate_1_bdv", @{thm separate_1_bdv}),
   207  		  (*"?bdv / ?b = (1 / ?b) * ?bdv"*)
   208  		Thm ("separate_1_bdv_n", @{thm separate_1_bdv_n})
   209        (*"?bdv \<up> ?n / ?b = 1 / ?b * ?bdv \<up> ?n"*)
   210     ]);
   211 (*show_types := true;  --- do we need type-constraint in thms? *)
   212 @{thm separate_bdv};     (*::?'a does NOT rewrite here WITHOUT type constraint*)
   213 @{thm separate_bdv_n};   (*::real ..because of  \<up> , rewrites*)
   214 @{thm separate_1_bdv};   (*::?'a*)
   215 val xxx = @{thm separate_1_bdv}; (*::?'a*)
   216 @{thm separate_1_bdv_n}; (*::real ..because of  \<up> *)
   217 (*show_types := false; --- do we need type-constraint in thms? YES ?!?!?!*)
   218 
   219 val SOME (t, []) = rewrite_set_inst_ ctxt true subs rls t;
   220 if UnparseC.term @{context} t = "1 / EI * (L * q_0 / 2 * x + - 1 * q_0 / 2 * x \<up> 2)" then ()
   221 else error "integrate.sml simplify by ruleset separate_bdv.. #4";
   222 
   223 "===== test 5";
   224 val t = ParseC.parse_test @{context} "1/EI * (L * q_0 * x / 2 + - 1 * q_0 * x \<up> 2 / 2)";
   225 val rls = simplify_Integral;
   226 val SOME (t,[]) = rewrite_set_inst_ ctxt true subs rls t;
   227 (* given was:   "1 / EI * (L * q_0 * x / 2 + - 1 * q_0 * x \<up> 2 / 2)" *)
   228 if UnparseC.term @{context} t = "1 / EI * (L * q_0 / 2 * x + - 1 * q_0 / 2 * x \<up> 2)" then ()
   229 else error "integrate.sml, simplify_Integral #99";
   230 
   231 "........... 2nd integral ........................................";
   232 "........... 2nd integral ........................................";
   233 "........... 2nd integral ........................................";
   234 val subs = [(ParseC.parse_test @{context} "bdv::real", ParseC.parse_test @{context} "x::real")];
   235 
   236 val thy = @{theory Biegelinie};
   237 val t = ParseC.parse_test @{context} 
   238   "Integral 1 / EI * (L * q_0 / 2 * (x \<up> 2 / 2) + - 1 * q_0 / 2 * (x \<up> 3 / 3)) D x";
   239 
   240 val rls = simplify_Integral;
   241 val SOME (t,[]) = rewrite_set_inst_ ctxt true subs rls t;
   242 if UnparseC.term @{context} t = "Integral 1 / EI * (L * q_0 / 4 * x \<up> 2 + - 1 * q_0 / 6 * x \<up> 3) D x"
   243 then () else raise error "integrate.sml, simplify_Integral #198";
   244 
   245 val rls = integration_rules;
   246 val SOME (t, []) = rewrite_set_ ctxt true rls t;
   247 if UnparseC.term @{context} t = "1 / EI * (L * q_0 / 4 * (x \<up> 3 / 3) + - 1 * q_0 / 6 * (x \<up> 4 / 4))"
   248 then () else error "integrate.sml, simplify_Integral #199";
   249 
   250 
   251 "----------- integrate by ruleset -----------------------";
   252 "----------- integrate by ruleset -----------------------";
   253 "----------- integrate by ruleset -----------------------";
   254 val thy = @{theory "Integrate"};
   255 val rls = integration_rules;
   256 val subs = [(@{term "bdv::real"}, @{term "x::real"})];
   257 (*~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
   258 
   259 val t = ParseC.parse_test ctxt "Integral x D x";
   260 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   261 if UnparseC.term @{context} res = "x \<up> 2 / 2" then () else error "Integral x D x changed";
   262 
   263 val t = ParseC.parse_test ctxt "Integral c * x \<up> 2 + c_2 D x";
   264 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   265 if UnparseC.term @{context} res = "c * (x \<up> 3 / 3) + c_2 * x" then () else error "Integral c * x \<up> 2 + c_2 D x";
   266 
   267 val rls = add_new_c;
   268 val t = ParseC.parse_test ctxt "c * (x \<up> 3 / 3) + c_2 * x";
   269 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   270 if UnparseC.term @{context} res = "c * (x \<up> 3 / 3) + c_2 * x + c_3" then () 
   271 else error "integrate.sml: diff.behav. in add_new_c simpl.";
   272 
   273 val t = ParseC.parse_test ctxt "F x = x \<up> 3 / 3 + x";
   274 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   275 if UnparseC.term @{context} res = "F x = x \<up> 3 / 3 + x + c"(*not "F x + c =..."*) then () 
   276 else error "integrate.sml: diff.behav. in add_new_c equation";
   277 
   278 val rls = simplify_Integral;
   279 (*~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
   280 val t = ParseC.parse_test ctxt "ff x = c * x + - 1 * q_0 * (x \<up> 2 / 2) + c_2";
   281 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   282 if UnparseC.term @{context} res = "ff x = c_2 + c * x + - 1 * q_0 / 2 * x \<up> 2"
   283 then () else error "integrate.sml: diff.behav. in simplify_I #1";
   284 
   285 val rls = integration;
   286 (*~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
   287 val t = ParseC.parse_test ctxt "Integral c * x \<up> 2 + c_2 D x";
   288 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   289 if UnparseC.term @{context} res = "c_3 + c_2 * x + c / 3 * x \<up> 3"
   290 then () else error "integrate.sml: diff.behav. in integration #1";
   291 
   292 val t = ParseC.parse_test ctxt "Integral 3*x \<up> 2 + 2*x + 1 D x";
   293 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   294 if UnparseC.term @{context} res = "c + x + x \<up> 2 + x \<up> 3" then () 
   295 else error "integrate.sml: diff.behav. in integration #2";
   296 
   297 val t = ParseC.parse_test ctxt
   298   "Integral 1 / EI * (L * q_0 / 2 * x + - 1 * q_0 / 2 * x \<up> 2) D x";
   299 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   300 "Integral 1 / EI * (L * q_0 / 2 * x + - 1 * q_0 / 2 * x \<up> 2) D x";
   301 if UnparseC.term @{context} res = "c + 1 / EI * (L * q_0 / 4 * x \<up> 2 + - 1 * q_0 / 6 * x \<up> 3)"
   302 then () else error "integrate.sml: diff.behav. in integration #3";
   303 
   304 val t = ParseC.parse_test ctxt ("Integral " ^ UnparseC.term @{context} res ^ " D x");
   305 val SOME (res, _) = rewrite_set_inst_ ctxt true subs rls t;
   306 if UnparseC.term @{context} res = "c_2 + c * x +\n1 / EI * (L * q_0 / 12 * x \<up> 3 + - 1 * q_0 / 24 * x \<up> 4)"
   307 then () else error "integrate.sml: diff.behav. in integration #4";
   308 
   309 "----------- rewrite 3rd integration in 7.27 ------------";
   310 "----------- rewrite 3rd integration in 7.27 ------------";
   311 "----------- rewrite 3rd integration in 7.27 ------------";
   312 val t = ParseC.parse_test @{context} "Integral 1 / EI * ((L * q_0 * x + - 1 * q_0 * x \<up> 2) / 2) D x";
   313 val SOME(t, _)= rewrite_set_inst_ ctxt true subs simplify_Integral t;
   314 if UnparseC.term @{context} t = 
   315   "Integral 1 / EI * (L * q_0 / 2 * x + - 1 * q_0 / 2 * x \<up> 2) D x"
   316 then () else error "integrate.sml 3rd integration in 7.27, simplify_Integral";
   317 
   318 val SOME(t, _) = rewrite_set_inst_ ctxt true subs integration t;
   319 if UnparseC.term @{context} t = 
   320   "c + 1 / EI * (L * q_0 / 4 * x \<up> 2 + - 1 * q_0 / 6 * x \<up> 3)"
   321 then () else error "integrate.sml 3rd integration in 7.27, integration";
   322 
   323 
   324 "----------- check probem type --------------------------";
   325 "----------- check probem type --------------------------";
   326 "----------- check probem type --------------------------";
   327 val thy = @{theory Integrate};
   328 val model = {Given =["functionTerm f_f", "integrateBy v_v"],
   329 	     Where =[],
   330 	     Find  =["antiDerivative F_F"],
   331 	     With  =[],
   332 	     Relate=[]}:string model;
   333 val chkmodel = ((map (ParseC.parse_test ctxt)) o P_Model.to_list) model;
   334 val t1 = (hd) chkmodel;
   335 val t2 = (hd o tl) chkmodel;
   336 val t3 = (hd o tl o tl) chkmodel;
   337 case t3 of Const (\<^const_name>\<open>antiDerivative\<close>, _) $ _ => ()
   338 	 | _ => error "integrate.sml: Integrate.antiDerivative ???";
   339 
   340 val model = {Given =["functionTerm f_f", "integrateBy v_v"],
   341 	     Where =[],
   342 	     Find  =["antiDerivativeName F_F"],
   343 	     With  =[],
   344 	     Relate=[]}:string model;
   345 val chkmodel = ((map (ParseC.parse_test ctxt)) o P_Model.to_list) model;
   346 val t1 = (hd) chkmodel;
   347 val t2 = (hd o tl) chkmodel;
   348 val t3 = (hd o tl o tl) chkmodel;
   349 case t3 of Const (\<^const_name>\<open>antiDerivativeName\<close>, _) $ _ => ()
   350 	 | _ => error "integrate.sml: Integrate.antiDerivativeName";
   351 
   352 "----- compare 'Find's from problem, script, formalization -------";
   353 val {model,...} = Problem.from_store @{context} ["named", "integrate", "function"];
   354 val ("#Find", (Const (\<^const_name>\<open>antiDerivativeName\<close>, _),
   355 	       F1_ as Free ("F_F", F1_type))) = last_elem model;
   356 val {program = Prog sc,... } = MethodC.from_store ctxt ["diff", "integration", "named"];
   357 val [_,_, F2_] = formal_args sc;
   358 if F1_ = F2_ then () else error "integrate.sml: unequal find's";
   359 
   360 val ((dsc as Const (\<^const_name>\<open>antiDerivativeName\<close>, _)) 
   361 	 $ Free ("ff", F3_type)) = ParseC.parse_test @{context} "antiDerivativeName ff";
   362 if Input_Descript.is_a dsc then () else error "integrate.sml: no description";
   363 if F1_type = F3_type then () 
   364 else error "integrate.sml: unequal types in find's";
   365 
   366 Test_Tool.show_ptyps();
   367 val pbl = Problem.from_store @{context} ["integrate", "function"];
   368 case #cas pbl of SOME (Const (\<^const_name>\<open>Integrate\<close>, _) $ _) => ()
   369 	 | _ => error "integrate.sml: Integrate.Integrate ???";
   370 
   371 
   372 "----------- me method [diff,integration] ---------------";
   373 "----------- me method [diff,integration] ---------------";
   374 "----------- me method [diff,integration] ---------------";
   375 (*exp_CalcInt_No- 1.xml*)
   376 val p = e_pos'; val c = []; 
   377 "----- step 0: returns nxt = Model_Problem ---";
   378 val (p,_,f,nxt,_,pt) = 
   379     Test_Code.init_calc @{context} 
   380         [(["functionTerm (x \<up> 2 + 1)", "integrateBy x", "antiDerivative FF"],
   381           ("Integrate", ["integrate", "function"], ["diff", "integration"]))];
   382 "----- step 1: returns nxt = Add_Given \"functionTerm (x \<up> 2 + 1)\" ---";
   383 val (p,_,f,nxt,_,pt) = me nxt p c pt; (*nxt = ("Tac ", ...) --> Add_Given...*)
   384 "----- step 2: returns nxt = Add_Given \"integrateBy x\" ---";
   385 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   386 "----- step 3: returns nxt = Add_Find \"Integrate.antiDerivative FF\" ---";
   387 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   388 "----- step 4: returns nxt = Specify_Theory \"Integrate\" ---";
   389 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   390 "----- step 5: returns nxt = Specify_Problem [\"integrate\", \"function\"] ---";
   391 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   392 "----- step 6: returns nxt = Specify_Method [\"diff\", \"integration\"] ---";
   393 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   394 "----- step 7: returns nxt = Apply_Method [\"diff\", \"integration\"] ---";
   395 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   396 case nxt of (Apply_Method ["diff", "integration"]) => ()
   397           | _ => error "integrate.sml -- me method [diff,integration] -- spec";
   398 "----- step 8: returns nxt = Rewrite_Set_Inst ([\"(''bdv'', x)\"],\"integration\")";
   399 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   400 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   401 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   402 if f2str f = "c + x + 1 / 3 * x \<up> 3" then ()
   403 else error "integrate.sml -- me method [diff,integration] -- end";
   404 
   405 
   406 "----------- autoCalculate [diff,integration] -----------";
   407 "----------- autoCalculate [diff,integration] -----------";
   408 "----------- autoCalculate [diff,integration] -----------";
   409 States.reset ();
   410 CalcTree @{context}
   411     [(["functionTerm (x \<up> 2 + 1)", "integrateBy x", "antiDerivative FF"], 
   412       ("Integrate", ["integrate", "function"], ["diff", "integration"]))];
   413 Iterator 1;
   414 moveActiveRoot 1;
   415 autoCalculate 1 CompleteCalc;
   416 val ((pt,p),_) = States.get_calc 1; @{make_string} p; Test_Tool.show_pt pt;
   417 val (Form t,_,_) = ME_Misc.pt_extract ctxt (pt, p); 
   418 if UnparseC.term @{context} t = "c + x + 1 / 3 * x \<up> 3" then ()
   419 else error "integrate.sml -- interSteps [diff,integration] -- result";
   420 
   421 
   422 "----------- me method [diff,integration,named] ---------";
   423 "----------- me method [diff,integration,named] ---------";
   424 "----------- me method [diff,integration,named] ---------";
   425 (*exp_CalcInt_No- 2.xml*)
   426 val fmz = ["functionTerm (x \<up> 2 + (1::real))", 
   427 	   "integrateBy x", "antiDerivativeName F"];
   428 val (dI',pI',mI') =
   429   ("Integrate",["named", "integrate", "function"],
   430    ["diff", "integration", "named"]);
   431 val p = e_pos'; val c = []; 
   432 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
   433 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   434 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   435 val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Add_Find *);
   436 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   437 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   438 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   439 val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Apply_Method*);
   440 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   441 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   442 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   443 if f2str f = "F x = c + x + 1 / 3 * x \<up> 3" then() 
   444 else error "integrate.sml: method [diff,integration,named]";
   445 
   446 
   447 "----------- me met [diff,integration,named] Biegelinie.Q";
   448 "----------- me met [diff,integration,named] Biegelinie.Q";
   449 "----------- me met [diff,integration,named] Biegelinie.Q";
   450 (*exp_CalcInt_No-3.xml*)
   451 val fmz = ["functionTerm (- q_0)", 
   452 	   "integrateBy x", "antiDerivativeName Q"];
   453 val (dI',pI',mI') =
   454   ("Biegelinie",["named", "integrate", "function"],
   455    ["diff", "integration", "named"]);
   456 val p = e_pos'; val c = [];
   457 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
   458 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   459 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   460 (*Error Tac Q not in ...*)
   461 val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Add_Find *);
   462 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   463 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   464 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   465 val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Apply_Method*);
   466 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   467 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   468 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   469 if f2str f = "Q x = c + - 1 * q_0 * x" then() 
   470 else error "integrate.sml: method [diff,integration,named] .Q";
   471 
   472