wneuper/isa: test/Tools/isac/Interpret/inform.sml@8e5335c63475 (annotated)

akargl@42176	1	(* Title: tests on inform.sml
akargl@42176	2	Author: Walther Neuper 060225,
neuper@37906	3	(c) due to copyright terms
neuper@37906	4	*)
neuper@37906	5
neuper@37906	6	"-----------------------------------------------------------------";
neuper@37906	7	"table of contents -----------------------------------------------";
neuper@37906	8	"-----------------------------------------------------------------";
neuper@37906	9	"appendForm with miniscript with mini-subpbl:";
neuper@37906	10	"--------- appendFormula: on Res + equ_nrls ----------------------";
neuper@37906	11	"--------- appendFormula: on Frm + equ_nrls ----------------------";
neuper@37906	12	"--------- appendFormula: on Res + NO deriv ----------------------";
neuper@37906	13	"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
neuper@37906	14	"replaceForm with miniscript with mini-subpbl:";
neuper@37906	15	"--------- replaceFormula: on Res + = ----------------------------";
neuper@37906	16	"--------- replaceFormula: on Res + = 1st Nd ---------------------";
neuper@37906	17	"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
neuper@37906	18	"--------- replaceFormula: cut calculation -----------------------";
neuper@37906	19	"--------- replaceFormula: cut calculation -----------------------";
neuper@37906	20	(* 040307 copied from informtest.sml ... old versions
neuper@37906	21	"--------- maximum-example, UC: Modeling / modifyCalcHead --------";*)
neuper@37906	22	"--------- syntax error ------------------------------------------";
neuper@37906	23	"CAS-command:";
neuper@37906	24	"--------- CAS-command on ([],Pbl) -------------------------------";
neuper@37906	25	"--------- CAS-command on ([],Pbl) FE-interface ------------------";
wneuper@59559	26	"--------- locate_input_formula [rational,simplification] ----------------------";
neuper@37906	27	"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
neuper@37906	28	"--------- Take as 1st tac, start from exp -----------------------";
neuper@37906	29	"--------- init_form, start with <NEW> (CAS input) ---------------";
neuper@42423	30	"--------- build fun check_err_patt ------------------------------";
neuper@42426	31	"--------- build fun check_err_patt ?bdv -------------------------";
neuper@42428	32	"--------- build fun check_error_patterns ------------------------";
neuper@42428	33	"--------- embed fun check_error_patterns ------------------------";
neuper@48895	34	"--------- build fun get_fillpats --------------------------------";
neuper@42430	35	"--------- embed fun find_fillpatterns ---------------------------";
neuper@48895	36	"--------- build fun is_exactly_equal, inputFillFormula ----------";
wneuper@59262	37	"--------- fun appl_adds -----------------------------------------";
wneuper@59264	38	"--------- fun concat_deriv --------------------------------------";
wneuper@59264	39	"--------- handle an input formula -------------------------------";
wneuper@59264	40	"--------- fun dropwhile' ----------------------------------------";
neuper@37906	41	"-----------------------------------------------------------------";
neuper@37906	42	"-----------------------------------------------------------------";
neuper@37906	43	"-----------------------------------------------------------------";
neuper@37906	44
neuper@37906	45
neuper@37906	46	"--------- appendFormula: on Res + equ_nrls ----------------------";
neuper@37906	47	"--------- appendFormula: on Res + equ_nrls ----------------------";
neuper@37906	48	"--------- appendFormula: on Res + equ_nrls ----------------------";
neuper@48790	49	val Prog sc = (#scr o get_met) ["Test","squ-equ-test-subpbl1"];
neuper@37906	50	(writeln o term2str) sc;
neuper@48790	51	val Prog sc = (#scr o get_met) ["Test","solve_linear"];
neuper@37906	52	(writeln o term2str) sc;
neuper@37906	53
s1210629013@55445	54	reset_states ();
neuper@41970	55	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	56	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	57	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	58	Iterator 1; moveActiveRoot 1;
wneuper@59248	59	autoCalculate 1 CompleteCalcHead;
walther@59747	60	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	61	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
neuper@37906	62
wneuper@59123	63	appendFormula 1 "-2 * 1 + (1 + x) = 0" (\|> Future.join); refFormula 1 (get_pos 1 1);
neuper@37906	64	val ((pt,_),_) = get_calc 1;
wneuper@59279	65	val str = pr_ctree pr_short pt;
neuper@48895	66	if str =
neuper@48895	67	(". ----- pblobj -----\n" ^
neuper@48895	68	"1. x + 1 = 2\n" ^
neuper@48895	69	"2. x + 1 + -1 * 2 = 0\n" ^
neuper@48895	70	"2.1. x + 1 + -1 * 2 = 0\n" ^
neuper@48895	71	"2.2. 1 + x + -1 * 2 = 0\n" ^
neuper@48895	72	"2.3. 1 + (x + -1 * 2) = 0\n" ^
neuper@48895	73	"2.4. 1 + (x + -2) = 0\n" ^
neuper@48895	74	"2.5. 1 + (x + -2 * 1) = 0\n" ^
neuper@48895	75	"2.6. 1 + x + -2 * 1 = 0\n" ) then ()
neuper@48895	76	else error "inform.sml: diff.behav.appendFormula: on Res + equ 1";
neuper@37906	77
neuper@37906	78	moveDown 1 ([ ],Pbl); refFormula 1 ([1],Frm); (x + 1 = 2)
neuper@37906	79	moveDown 1 ([1],Frm); refFormula 1 ([1],Res); (x + 1 + -1 2 = 0*)
neuper@37906	80
neuper@37906	81	(the seven steps of detailed derivation)
neuper@37906	82	moveDown 1 ([1 ],Res); refFormula 1 ([2,1],Frm);
neuper@37906	83	moveDown 1 ([2,1],Frm); refFormula 1 ([2,1],Res);
neuper@37906	84	moveDown 1 ([2,1],Res); refFormula 1 ([2,2],Res);
neuper@37906	85	moveDown 1 ([2,2],Res); refFormula 1 ([2,3],Res);
neuper@37906	86	moveDown 1 ([2,3],Res); refFormula 1 ([2,4],Res);
neuper@37906	87	moveDown 1 ([2,4],Res); refFormula 1 ([2,5],Res);
neuper@37906	88	moveDown 1 ([2,5],Res); refFormula 1 ([2,6],Res);
neuper@37906	89	val ((pt,_),_) = get_calc 1;
neuper@37906	90	if "-2 * 1 + (1 + x) = 0" = term2str (fst (get_obj g_result pt [2,6])) then()
neuper@38031	91	else error "inform.sml: diff.behav.appendFormula: on Res + equ 2";
neuper@37906	92
neuper@37906	93	fetchProposedTactic 1; (takes Iterator 1 _1_)
neuper@48895	94	(* <ERROR> error in kernel </ERROR> ALREADY IN 2009-2*)
neuper@48895	95	(*========== inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 =============
neuper@37906	96	val (_,(tac,_,_)::_) = get_calc 1;
neuper@37906	97	if tac = Rewrite_Set "Test_simplify" then ()
neuper@38031	98	else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
neuper@48895	99	============ inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 ============*)
akargl@42209	100
wneuper@59248	101	autoCalculate 1 CompleteCalc;
neuper@37906	102	val ((pt,_),_) = get_calc 1;
neuper@37906	103	if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
neuper@38031	104	else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
wneuper@59248	105	(* autoCalculate 1 CompleteCalc;
neuper@37906	106	val ((pt,p),_) = get_calc 1;
neuper@37906	107	(writeln o istates2str) (get_obj g_loc pt [ ]);
neuper@37906	108	(writeln o istates2str) (get_obj g_loc pt [1]);
neuper@37906	109	(writeln o istates2str) (get_obj g_loc pt [2]);
neuper@37906	110	(writeln o istates2str) (get_obj g_loc pt [3]);
neuper@37906	111	(writeln o istates2str) (get_obj g_loc pt [3,1]);
neuper@37906	112	(writeln o istates2str) (get_obj g_loc pt [3,2]);
neuper@37906	113	(writeln o istates2str) (get_obj g_loc pt [4]);
neuper@37906	114
neuper@37906	115	*)
neuper@37906	116	"----------------------------------------------------------";
akargl@42176	117
wneuper@59592	118	val fod = make_deriv (@{theory "Isac_Knowledge"}) Atools_erls
neuper@37906	119	((#rules o rep_rls) Test_simplify)
akargl@42176	120	(sqrt_right false (@{theory "Pure"})) NONE
neuper@37906	121	(str2term "x + 1 + -1 * 2 = 0");
neuper@37906	122	(writeln o trtas2str) fod;
neuper@37906	123
wneuper@59592	124	val ifod = make_deriv (@{theory "Isac_Knowledge"}) Atools_erls
neuper@37906	125	((#rules o rep_rls) Test_simplify)
akargl@42176	126	(sqrt_right false (@{theory "Pure"})) NONE
neuper@37906	127	(str2term "-2 * 1 + (1 + x) = 0");
neuper@37906	128	(writeln o trtas2str) ifod;
akargl@42176	129	fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
neuper@37906	130	val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
neuper@37906	131	val der = fod' @ (map rev_deriv' rifod');
neuper@37906	132	(writeln o trtas2str) der;
neuper@37906	133	"----------------------------------------------------------";
wneuper@59252	134	DEconstrCalcTree 1;
neuper@37906	135
neuper@37906	136	"--------- appendFormula: on Frm + equ_nrls ----------------------";
neuper@37906	137	"--------- appendFormula: on Frm + equ_nrls ----------------------";
neuper@37906	138	"--------- appendFormula: on Frm + equ_nrls ----------------------";
s1210629013@55445	139	reset_states ();
neuper@41970	140	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	141	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	142	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	143	Iterator 1; moveActiveRoot 1;
wneuper@59248	144	autoCalculate 1 CompleteCalcHead;
walther@59747	145	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1) (x + 1 = 2);
wneuper@59123	146	appendFormula 1 "2+ -1 + x = 2" (\|> Future.join); refFormula 1 (get_pos 1 1);
neuper@37906	147
neuper@37906	148	moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (x + 1 = 2);
neuper@37906	149
neuper@37906	150	moveDown 1 ([1 ],Frm); refFormula 1 ([1,1],Frm);
neuper@37906	151	moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res);
neuper@37906	152	moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res);
neuper@37906	153	moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res);
neuper@37906	154	moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res);
neuper@37906	155	moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res);
neuper@37906	156	moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res);
neuper@37906	157	val ((pt,_),_) = get_calc 1;
neuper@37906	158	if "2 + -1 + x = 2" = term2str (fst (get_obj g_result pt [1,6])) then()
neuper@38031	159	else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
neuper@37906	160
neuper@37906	161	fetchProposedTactic 1; (takes Iterator 1 _1_)
neuper@37906	162	val (_,(tac,_,_)::_) = get_calc 1;
wneuper@59253	163	case tac of Rewrite_Set "norm_equation" => ()
wneuper@59253	164	\| _ => error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
wneuper@59248	165	autoCalculate 1 CompleteCalc;
neuper@37906	166	val ((pt,_),_) = get_calc 1;
neuper@37906	167	if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
neuper@38031	168	else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
wneuper@59252	169	DEconstrCalcTree 1;
neuper@37906	170
neuper@37906	171	"--------- appendFormula: on Res + NO deriv ----------------------";
neuper@37906	172	"--------- appendFormula: on Res + NO deriv ----------------------";
neuper@37906	173	"--------- appendFormula: on Res + NO deriv ----------------------";
s1210629013@55445	174	reset_states ();
neuper@41970	175	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	176	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	177	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	178	Iterator 1; moveActiveRoot 1;
wneuper@59248	179	autoCalculate 1 CompleteCalcHead;
walther@59747	180	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	181	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
neuper@37906	182
wneuper@59123	183	appendFormula 1 "x = 2" (\|> Future.join);
neuper@37906	184	val ((pt,p),_) = get_calc 1;
wneuper@59279	185	val str = pr_ctree pr_short pt;
neuper@37906	186	writeln str;
neuper@37906	187	if str = ". ----- pblobj -----\n1. x + 1 = 2\n" andalso p = ([1], Res)
neuper@37906	188	then ()
neuper@38031	189	else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
neuper@37906	190
neuper@37906	191	fetchProposedTactic 1;
neuper@37906	192	val (_,(tac,_,_)::_) = get_calc 1;
wneuper@59253	193	case tac of Rewrite_Set "Test_simplify" => ()
wneuper@59253	194	\| _ => error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
wneuper@59248	195	autoCalculate 1 CompleteCalc;
neuper@37906	196	val ((pt,_),_) = get_calc 1;
neuper@37906	197	if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
neuper@38031	198	else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
wneuper@59252	199	DEconstrCalcTree 1;
neuper@37906	200
neuper@37906	201	"--------- appendFormula: on Res + late deriv --------------------";
neuper@37906	202	"--------- appendFormula: on Res + late deriv --------------------";
neuper@37906	203	"--------- appendFormula: on Res + late deriv --------------------";
s1210629013@55445	204	reset_states ();
neuper@41970	205	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	206	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	207	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	208	Iterator 1; moveActiveRoot 1;
wneuper@59248	209	autoCalculate 1 CompleteCalcHead;
walther@59747	210	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	211	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
neuper@37906	212
wneuper@59123	213	appendFormula 1 "x = 1" (\|> Future.join);
neuper@37906	214	val ((pt,p),_) = get_calc 1;
wneuper@59279	215	val str = pr_ctree pr_short pt;
neuper@37906	216	writeln str;
neuper@37906	217	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)
neuper@37906	218	then () (finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!)
neuper@38031	219	else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
akargl@42176	220
neuper@37906	221	fetchProposedTactic 1;
neuper@37906	222	val (_,(tac,_,_)::_) = get_calc 1;
wneuper@59253	223	case tac of Check_Postcond ["LINEAR", "univariate", "equation", "test"] => ()
wneuper@59253	224	\| _ => error "inform.sml: diff.behav.appendFormula: Res + late d 2";
wneuper@59248	225	autoCalculate 1 CompleteCalc;
neuper@37906	226	val ((pt,_),_) = get_calc 1;
neuper@37906	227	if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
neuper@38031	228	else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
wneuper@59252	229	DEconstrCalcTree 1;
neuper@37906	230
neuper@37906	231	"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
neuper@37906	232	"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
neuper@37906	233	"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
s1210629013@55445	234	reset_states ();
neuper@41970	235	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	236	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	237	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	238	Iterator 1; moveActiveRoot 1;
wneuper@59248	239	autoCalculate 1 CompleteCalcHead;
walther@59747	240	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	241	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
wneuper@59123	242	appendFormula 1 "[x = 3 + -21]" (\|> Future.join*);
neuper@37906	243	val ((pt,p),_) = get_calc 1;
wneuper@59279	244	val str = pr_ctree pr_short pt;
neuper@37906	245	writeln str;
neuper@37906	246	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 ()
neuper@38031	247	else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
wneuper@59248	248	autoCalculate 1 CompleteCalc;
neuper@37906	249	val ((pt,p),_) = get_calc 1;
neuper@37906	250	if "[x = 3 + -2 * 1]" = term2str (fst (get_obj g_result pt [])) then ()
neuper@37906	251	(* ~~~~~~~~~~ simplify as last step in any script ?!*)
neuper@38031	252	else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
wneuper@59252	253	DEconstrCalcTree 1;
neuper@37906	254
neuper@37906	255	"--------- replaceFormula: on Res + = ----------------------------";
neuper@37906	256	"--------- replaceFormula: on Res + = ----------------------------";
neuper@37906	257	"--------- replaceFormula: on Res + = ----------------------------";
s1210629013@55445	258	reset_states ();
neuper@41970	259	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	260	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	261	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	262	Iterator 1; moveActiveRoot 1;
wneuper@59248	263	autoCalculate 1 CompleteCalcHead;
walther@59747	264	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	265	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
walther@59747	266	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(-1 + x);
neuper@37906	267
neuper@37906	268	replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
neuper@37906	269	val ((pt,_),_) = get_calc 1;
wneuper@59279	270	val str = pr_ctree pr_short pt;
akargl@42176	271
neuper@48895	272	(* before AK110725 this was
neuper@48895	273	". ----- pblobj -----\n
neuper@48895	274	1. x + 1 = 2\n
neuper@48895	275	2. x + 1 + -1 * 2 = 0\n
neuper@48895	276	2.1. x + 1 + -1 * 2 = 0\n
neuper@48895	277	2.2. 1 + x + -1 * 2 = 0\n
neuper@48895	278	2.3. 1 + (x + -1 * 2) = 0\n
neuper@48895	279	2.4. 1 + (x + -2) = 0\n
neuper@48895	280	2.5. 1 + (x + -2 * 1) = 0\n
neuper@48895	281	2.6. 1 + x + -2 * 1 = 0\n";
neuper@48895	282	*)
neuper@48895	283	if str =
neuper@48895	284	". ----- pblobj -----\n"^
neuper@48895	285	"1. x + 1 = 2\n"^
neuper@48895	286	"2. x + 1 + -1 * 2 = 0\n"^
neuper@48895	287	"2.1. x + 1 + -1 * 2 = 0\n"^
neuper@48895	288	"2.2. 1 + x + -1 * 2 = 0\n"^
neuper@48895	289	"2.3. 1 + (x + -1 * 2) = 0\n"^
neuper@48895	290	"2.4. 1 + (x + -2) = 0\n"^
neuper@48895	291	"2.5. 1 + (x + -2 * 1) = 0\n"^
neuper@48895	292	"2.6. 1 + x + -2 * 1 = 0\n" then()
neuper@48895	293	else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
akargl@42176	294
wneuper@59248	295	autoCalculate 1 CompleteCalc;
akargl@42176	296	val ((pt,pos as (p,_)),_) = get_calc 1;
akargl@42176	297	if pos = ([],Res) andalso "[x = 1]" = (term2str o fst) (get_obj g_result pt p) then()
neuper@38031	298	else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
wneuper@59252	299	DEconstrCalcTree 1;
neuper@37906	300
neuper@37906	301	"--------- replaceFormula: on Res + = 1st Nd ---------------------";
neuper@37906	302	"--------- replaceFormula: on Res + = 1st Nd ---------------------";
neuper@37906	303	"--------- replaceFormula: on Res + = 1st Nd ---------------------";
s1210629013@55445	304	reset_states ();
neuper@41970	305	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	306	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	307	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	308	Iterator 1; moveActiveRoot 1;
wneuper@59248	309	autoCalculate 1 CompleteCalcHead;
walther@59747	310	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	311	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
neuper@37906	312
neuper@37906	313	replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
neuper@37906	314	val ((pt,_),_) = get_calc 1;
wneuper@59279	315	val str = pr_ctree pr_short pt;
neuper@37906	316	writeln str;
akargl@42176	317	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 ()
neuper@38031	318	else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
wneuper@59248	319	autoCalculate 1 CompleteCalc;
akargl@42176	320	val ((pt,pos as (p,_)),_) = get_calc 1;
akargl@42176	321	if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
neuper@38031	322	else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
wneuper@59252	323	DEconstrCalcTree 1;
neuper@37906	324
neuper@37906	325	"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
neuper@37906	326	"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
neuper@37906	327	"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
s1210629013@55445	328	reset_states ();
neuper@41970	329	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	330	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	331	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	332	Iterator 1; moveActiveRoot 1;
wneuper@59248	333	autoCalculate 1 CompleteCalcHead;
walther@59747	334	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
neuper@37906	335
neuper@37906	336	replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
neuper@37906	337	val ((pt,_),_) = get_calc 1;
wneuper@59279	338	val str = pr_ctree pr_short pt;
neuper@37906	339	writeln str;
akargl@42176	340	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 ()
neuper@38031	341	else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
wneuper@59248	342	autoCalculate 1 CompleteCalc;
akargl@42176	343	val ((pt,pos as (p,_)),_) = get_calc 1;
akargl@42176	344	if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
neuper@38031	345	else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
wneuper@59252	346	DEconstrCalcTree 1;
neuper@37906	347
neuper@37906	348	"--------- replaceFormula: cut calculation -----------------------";
neuper@37906	349	"--------- replaceFormula: cut calculation -----------------------";
neuper@37906	350	"--------- replaceFormula: cut calculation -----------------------";
s1210629013@55445	351	reset_states ();
neuper@41970	352	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	353	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	354	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	355	Iterator 1; moveActiveRoot 1;
wneuper@59248	356	autoCalculate 1 CompleteCalc;
neuper@37906	357	moveActiveRoot 1; moveActiveDown 1;
neuper@37906	358	if get_pos 1 1 = ([1], Frm) then ()
neuper@38031	359	else error "inform.sml: diff.behav. cut calculation 1";
neuper@37906	360
neuper@37906	361	replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
neuper@37906	362	val ((pt,p),_) = get_calc 1;
wneuper@59279	363	val str = pr_ctree pr_short pt;
neuper@37906	364	writeln str;
neuper@37906	365	if p = ([1], Res) then ()
neuper@38031	366	else error "inform.sml: diff.behav. cut calculation 2";
neuper@37906	367
neuper@37906	368
neuper@37906	369	(* 040307 copied from informtest.sml; ... old version
neuper@37906	370	"---------------- maximum-example, UC: Modeling / modifyCalcHead -";
neuper@37906	371	"---------------- maximum-example, UC: Modeling / modifyCalcHead -";
neuper@37906	372	"---------------- maximum-example, UC: Modeling / modifyCalcHead -";
neuper@37906	373
neuper@37906	374	val p = ([],Pbl);
neuper@37906	375	val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
neuper@37906	376	"relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
neuper@37906	377	"relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
wneuper@59582	378	"relations [A=ab, a/2=rsin alpha, b/2=r*cos (alpha::real)]",
neuper@37906	379	(^^^ these are the elements for the root-problem (in variants))
neuper@37906	380	(vvv these are elements required for subproblems)
neuper@37906	381	"boundVariable a","boundVariable b","boundVariable alpha",
neuper@37906	382	"interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906	383	"interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906	384	"interval {x::real. 0 <= x & x <= pi}",
neuper@37906	385	"errorBound (eps=(0::real))"]
neuper@37906	386	(specifying is not interesting for this example)
neuper@38058	387	val spec = ("DiffApp", ["maximum_of","function"],
neuper@37906	388	["DiffApp","max_by_calculus"]);
neuper@37906	389	(the empty model with descriptions for user-guidance by Model_Problem)
neuper@37906	390	val empty_model = [Given ["fixedValues []"],
neuper@37906	391	Find ["maximum", "valuesFor"],
neuper@37906	392	Relate ["relations []"]];
neuper@37906	393
neuper@37906	394
neuper@37906	395	(!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!)
neuper@37906	396	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
neuper@37906	397	(val nxt = ("Model_Problem", ...)
neuper@37924	398	val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
neuper@37906	399
neuper@37906	400	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	401	(nxt = Add_Given "fixedValues [r = Arbfix]")
neuper@37924	402	val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
neuper@37906	403	(*[
neuper@37906	404	(0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
neuper@37906	405	(0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
neuper@37906	406	(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
neuper@37906	407	(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
neuper@37906	408
neuper@37906	409	(the empty CalcHead is checked w.r.t the model and re-established as such)
neuper@37906	410	val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, e_spec);
neuper@37924	411	val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
neuper@38031	412	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(\"e_domID\", [\"e_pblID\"], [\"e_metID\"]) )" then () else error "informtest.sml: diff.behav. max 1";
neuper@37906	413
neuper@37906	414	(there is one input to the model (could be more))
neuper@37906	415	val (b,pt,ocalhd) =
neuper@37906	416	input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
neuper@37906	417	Find ["maximum", "valuesFor"],
neuper@37906	418	Relate ["relations"]], Pbl, e_spec);
neuper@37924	419	val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
neuper@37906	420	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(\"e_domID\", [\"e_pblID\"], [\"e_metID\"]) )" then ()
neuper@38031	421	else error "informtest.sml: diff.behav. max 2";
neuper@37906	422
neuper@37906	423	(*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
neuper@37906	424	val (b,pt''''',ocalhd) =
neuper@37906	425	input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
neuper@37906	426	Find ["maximum A", "valuesFor [a,b]"],
neuper@37906	427	Relate ["relations [A=ab, a/2=rsin alpha, \
neuper@37906	428	\b/2=r*cos alpha]"]], Pbl, e_spec);
neuper@37924	429	val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
neuper@37906	430	if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
neuper@37906	431
neuper@37906	432	(this input is complete in variant 1 (variant 3 does not work yet))
neuper@37906	433	val (b,pt''''',ocalhd) =
neuper@37906	434	input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
neuper@37906	435	Find ["maximum A", "valuesFor [a,b]"],
neuper@37906	436	Relate ["relations [A=a*b, \
neuper@37906	437	\(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
neuper@37906	438	Pbl, e_spec);
neuper@37924	439	val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
neuper@37906	440
neuper@37906	441	modifycalcheadOK2xml 111 (bool2str b) ocalhd;
neuper@37906	442	*)
wneuper@59252	443	DEconstrCalcTree 1;
neuper@37906	444
neuper@37906	445	"--------- syntax error ------------------------------------------";
neuper@37906	446	"--------- syntax error ------------------------------------------";
neuper@37906	447	"--------- syntax error ------------------------------------------";
s1210629013@55445	448	reset_states ();
neuper@41970	449	CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
neuper@41970	450	("Test", ["sqroot-test","univariate","equation","test"],
neuper@37906	451	["Test","squ-equ-test-subpbl1"]))];
neuper@37906	452	Iterator 1; moveActiveRoot 1;
wneuper@59248	453	autoCalculate 1 CompleteCalcHead;
walther@59747	454	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 = 2)
walther@59747	455	autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(x + 1 + -1 2 = 0*);
neuper@37906	456
neuper@37906	457	appendFormula 1 " x - "; (<ERROR> syntax error in ' x - ' </ERROR>)
neuper@37906	458	val ((pt,_),_) = get_calc 1;
wneuper@59279	459	val str = pr_ctree pr_short pt;
neuper@37906	460	writeln str;
neuper@37906	461	if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
neuper@38031	462	else error "inform.sml: diff.behav.appendFormula: syntax error";
wneuper@59252	463	DEconstrCalcTree 1;
neuper@37906	464
neuper@37906	465	"--------- CAS-command on ([],Pbl) -------------------------------";
neuper@37906	466	"--------- CAS-command on ([],Pbl) -------------------------------";
neuper@37906	467	"--------- CAS-command on ([],Pbl) -------------------------------";
neuper@37906	468	val (p,_,f,nxt,_,pt) =
neuper@37906	469	CalcTreeTEST [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
neuper@37906	470	val ifo = "solve(x+1=2,x)";
wneuper@59562	471	val (_,(_,c,(pt,p))) = inform ([],[],(pt,p)) "solve(x+1=2,x)";
neuper@37906	472	show_pt pt;
neuper@37906	473	val nxt = ("Apply_Method",Apply_Method ["Test","squ-equ-test-subpbl1"]);
neuper@37906	474	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	475	if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
neuper@38031	476	else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
wneuper@59252	477	DEconstrCalcTree 1;
neuper@37906	478
neuper@37906	479	"--------- CAS-command on ([],Pbl) FE-interface ------------------";
neuper@37906	480	"--------- CAS-command on ([],Pbl) FE-interface ------------------";
neuper@37906	481	"--------- CAS-command on ([],Pbl) FE-interface ------------------";
s1210629013@55445	482	reset_states ();
neuper@37906	483	CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
neuper@37906	484	Iterator 1;
neuper@37906	485	moveActiveRoot 1;
neuper@37906	486	replaceFormula 1 "solve(x+1=2,x)";
wneuper@59248	487	autoCalculate 1 CompleteCalc;
neuper@37906	488	val ((pt,p),_) = get_calc 1;
neuper@37906	489	show_pt pt;
neuper@37906	490	if p = ([], Res) then ()
neuper@38031	491	else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
wneuper@59252	492	DEconstrCalcTree 1;
neuper@37906	493
wneuper@59562	494	"--------- inform [rational,simplification] ----------------------";
wneuper@59562	495	"--------- inform [rational,simplification] ----------------------";
wneuper@59562	496	"--------- inform [rational,simplification] ----------------------";
s1210629013@55445	497	reset_states ();
neuper@52105	498	CalcTree [(["Term (a * x / (b * x) + c * x / (d * x) + e / f)", "normalform N"],
neuper@52105	499	("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
neuper@37906	500	Iterator 1; moveActiveRoot 1;
wneuper@59248	501	autoCalculate 1 CompleteCalcHead;
neuper@52105	502
neuper@52105	503	"--- (-1) give a preview on the calculation without any input";
neuper@52105	504	(*
wneuper@59248	505	autoCalculate 1 CompleteCalc;
neuper@52105	506	val ((pt, p), _) = get_calc 1;
neuper@52105	507	show_pt pt;
neuper@52105	508	[
neuper@52105	509	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	510	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	511	(([1], Res), a / b + c / d + e / f), <--- (1) input arbitrary
neuper@52105	512	(([2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	513	(([3], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
neuper@52105	514	(([4], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)), <--- (2) input next
neuper@52105	515	(([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))] <--- (3) is also final result
neuper@52105	516	EXAMPLE NOT OPTIMAL
neuper@52105	517	*)
neuper@52105	518	"--- (0) user input as the first step does not work, thus impdo at least 1 step";
walther@59747	519	autoCalculate 1 (Steps 1);
walther@59747	520	autoCalculate 1 (Steps 1);
neuper@52105	521	val ((pt, p), _) = get_calc 1;
neuper@52105	522	(*show_pt pt;
neuper@52105	523	[
neuper@52105	524	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	525	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	526	(([1], Res), a / b + c / d + e / f)]
neuper@52105	527	*)
neuper@52105	528	"--- (1) input an arbitrary next formula";
wneuper@59123	529	appendFormula 1 "((a * d) + (c * b)) / (b * d) + e / f" (\|> Future.join);
neuper@52105	530	val ((pt, p), _) = get_calc 1;
neuper@52105	531	(*show_pt pt;
neuper@52105	532	[
neuper@52105	533	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	534	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	535	(([1], Res), a / b + c / d + e / f),
neuper@52105	536	(([2,1], Frm), a / b + c / d + e / f),
neuper@52105	537	(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	538	(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	539	(([2], Res), (a * d + c * b) / (b * d) + e / f)]
neuper@52105	540	*)
neuper@37906	541	val ((pt,p),_) = get_calc 1;
neuper@52105	542	if p = ([2], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
neuper@38031	543	else error ("inform.sml: [rational,simplification] 1");
neuper@37906	544
neuper@52105	545	"--- (2) input the next formula that would be presented by mat-engine";
neuper@52105	546	(* generate a preview:
walther@59747	547	autoCalculate 1 (Steps 1);
neuper@52105	548	val ((pt, p), _) = get_calc 1;
neuper@52105	549	show_pt pt;
neuper@52105	550	[
neuper@52105	551	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	552	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	553	(([1], Res), a / b + c / d + e / f),
neuper@52105	554	(([2,1], Frm), a / b + c / d + e / f),
neuper@52105	555	(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	556	(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	557	(([2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	558	(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))] <--- input this
neuper@52105	559	*)
wneuper@59123	560	appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (\|> Future.join);
neuper@52105	561	val ((pt, p), _) = get_calc 1;
neuper@52105	562	(*show_pt pt;
neuper@52105	563	[
neuper@52105	564	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	565	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	566	(([1], Res), a / b + c / d + e / f),
neuper@52105	567	(([2,1], Frm), a / b + c / d + e / f),
neuper@52105	568	(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	569	(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	570	(([2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	571	(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
neuper@52105	572	*)
neuper@52105	573	if p = ([3], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
neuper@38031	574	else error ("inform.sml: [rational,simplification] 2");
neuper@37906	575
neuper@52105	576	"--- (3) input the exact final result";
wneuper@59123	577	appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (\|> Future.join);
neuper@52105	578	val ((pt, p), _) = get_calc 1;
neuper@52105	579	(*show_pt pt;
neuper@52105	580	[
neuper@52105	581	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	582	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	583	(([1], Res), a / b + c / d + e / f),
neuper@52105	584	(([2,1], Frm), a / b + c / d + e / f),
neuper@52105	585	(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	586	(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	587	(([2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	588	(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	589	(([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	590	(([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
neuper@52105	591	(([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	592	(([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
neuper@52105	593	*)
neuper@52105	594	if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
neuper@38031	595	else error ("inform.sml: [rational,simplification] 3");
neuper@52105	596
neuper@52105	597	"--- (4) finish the calculation + check the postcondition (in the future)";
wneuper@59248	598	autoCalculate 1 CompleteCalc;
neuper@52105	599	val ((pt, p), _) = get_calc 1;
neuper@52105	600	val (t, asm) = get_obj g_result pt [];
neuper@52105	601	if term2str t = "(a * d * f + b * c * f + b * d * e) / (b * d * f)" andalso
walther@59719	602	terms2str asm = "[\"b * d * f \<noteq> 0\",\"d \<noteq> 0\",\"b \<noteq> 0\",\"a * x / (b * x) + c * x / (d * x) + e / f is_ratpolyexp\"]"
neuper@52105	603	then () else error "inform [rational,simplification] changed at end";
neuper@52105	604	(*show_pt pt;
neuper@52105	605	[
neuper@52105	606	(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
neuper@52105	607	(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
neuper@52105	608	(([1], Res), a / b + c / d + e / f),
neuper@52105	609	(([2,1], Frm), a / b + c / d + e / f),
neuper@52105	610	(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	611	(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	612	(([2], Res), (a * d + c * b) / (b * d) + e / f),
neuper@52105	613	(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	614	(([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	615	(([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
neuper@52105	616	(([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	617	(([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
neuper@52105	618	(([5], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
neuper@52105	619	(([6], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)),
neuper@52105	620	(([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))]
neuper@52105	621	*)
wneuper@59252	622	DEconstrCalcTree 1;
neuper@37906	623
neuper@37906	624	"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
neuper@37906	625	"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
neuper@37906	626	"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
neuper@37906	627	val t = str2term "Diff (x^^^2 + x + 1, x)";
neuper@37906	628	case t of Const ("Diff.Diff", _) $ _ => ()
neuper@37906	629	\| _ => raise
neuper@37906	630	error "diff.sml behav.changed for CAS Diff (..., x)";
neuper@37906	631	atomty t;
neuper@37906	632	"-----------------------------------------------------------------";
s1210629013@55445	633	(1>)reset_states ();
neuper@37906	634	(2>)CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
neuper@37906	635	(3>)Iterator 1;moveActiveRoot 1;
neuper@37906	636	"----- here the Headline has been finished";
neuper@37906	637	(4>)moveActiveFormula 1 ([],Pbl);
neuper@37906	638	(5>)replaceFormula 1 "Diff (x^2 + x + 1, x)";
neuper@37906	639	val ((pt,_),_) = get_calc 1;
neuper@37906	640	val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
neuper@37926	641	val NONE = env;
neuper@37926	642	val (SOME istate, NONE) = loc;
wneuper@59348	643	(default_print_depth 5;)
neuper@37906	644	writeln"-----------------------------------------------------------";
neuper@37906	645	spec;
neuper@37924	646	writeln (itms2str_ ctxt probl);
neuper@37924	647	writeln (itms2str_ ctxt meth);
neuper@48895	648	writeln (istate2str (fst istate));
neuper@37906	649
neuper@37906	650	refFormula 1 ([],Pbl) (--> correct CalcHead);
neuper@37906	651	(081016 NOT necessary (but leave it in Java):)
wneuper@59248	652	(6>)(completeCalcHead)autoCalculate 1 CompleteCalcHead;
neuper@37906	653	"----- here the CalcHead has been completed --- ONCE MORE ?????";
neuper@37906	654
neuper@37906	655	(*difference II*)
neuper@37906	656	val ((pt,p),_) = get_calc 1;
neuper@37906	657	(val p = ([], Pbl))
neuper@37906	658	val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
neuper@37926	659	val NONE = env;
neuper@37926	660	val (SOME istate, NONE) = loc;
wneuper@59348	661	(default_print_depth 5;) writeln (istate2str (fst istate)); (default_print_depth 3;)
wneuper@59583	662	(*Pstate ([],
neuper@37926	663	[], NONE,
neuper@37906	664	??.empty, Sundef, false)*)
wneuper@59348	665	(default_print_depth 5;) spec; (default_print_depth 3;)
wneuper@59592	666	(*("Isac_Knowledge",
neuper@37906	667	["derivative_of", "function"],
neuper@37906	668	["diff", "differentiate_on_R"]) : spec*)
neuper@37924	669	writeln (itms2str_ ctxt probl);
neuper@37906	670	(*[
neuper@37906	671	(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
neuper@37906	672	(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
akargl@42176	673	(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
neuper@37924	674	writeln (itms2str_ ctxt meth);
neuper@37906	675	(*[
neuper@37906	676	(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
neuper@37906	677	(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
akargl@42176	678	(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
neuper@37906	679	writeln"-----------------------------------------------------------";
neuper@37906	680	(7>)fetchProposedTactic 1 (--> Apply_Method);
neuper@37906	681	(WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met))
wneuper@59248	682	autoCalculate 1 CompleteCalc;
neuper@37906	683	val ((pt,p),_) = get_calc 1;
neuper@37906	684	val Form res = (#1 o pt_extract) (pt, ([],Res));
neuper@37906	685	show_pt pt;
neuper@37906	686	if p = ([], Res) andalso term2str res = "1 + 2 * x" then ()
neuper@38031	687	else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
wneuper@59252	688	DEconstrCalcTree 1;
neuper@37906	689
neuper@37906	690	"--------- Take as 1st tac, start from exp -----------------------";
neuper@37906	691	"--------- Take as 1st tac, start from exp -----------------------";
neuper@37906	692	"--------- Take as 1st tac, start from exp -----------------------";
neuper@37906	693	(*the following input is copied from BridgeLog Java <==> SML,
neuper@37906	694	omitting unnecessary inputs*)
s1210629013@55445	695	(1>)reset_states ();
wneuper@59592	696	(2>)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac_Knowledge",["derivative_of","function"],["diff","differentiate_on_R"]))];
neuper@37906	697	(3>)Iterator 1; moveActiveRoot 1;
neuper@37906	698
wneuper@59248	699	(6>)(completeCalcHead)autoCalculate 1 CompleteCalcHead;
neuper@37906	700	(*difference II*)
neuper@37906	701	val ((pt,_),_) = get_calc 1;
neuper@37906	702	val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
neuper@37926	703	val NONE = env;
neuper@37926	704	val (SOME istate, NONE) = loc;
wneuper@59348	705	(default_print_depth 5;) writeln (istate2str (fst istate)); (default_print_depth 3;)
wneuper@59583	706	(*Pstate ([],
neuper@37926	707	[], NONE,
neuper@37906	708	??.empty, Sundef, false)*)
wneuper@59348	709	(default_print_depth 5;) spec; (default_print_depth 3;)
wneuper@59592	710	(*("Isac_Knowledge",
neuper@37906	711	["derivative_of", "function"],
neuper@37906	712	["diff", "differentiate_on_R"]) : spec*)
neuper@37924	713	writeln (itms2str_ ctxt probl);
neuper@37906	714	(*[
neuper@37906	715	(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
neuper@37906	716	(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
akargl@42176	717	(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
neuper@37924	718	writeln (itms2str_ ctxt meth);
neuper@37906	719	(*[
neuper@37906	720	(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
neuper@37906	721	(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
akargl@42176	722	(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
neuper@37906	723	writeln"-----------------------------------------------------------";
neuper@37906	724	(7>)fetchProposedTactic 1 (--> Apply_Method);
walther@59747	725	autoCalculate 1 (Steps 1);
neuper@37906	726	val ((pt,p),_) = get_calc 1;
neuper@37906	727	val Form res = (#1 o pt_extract) (pt, p);
neuper@37906	728	if term2str res = "d_d x (x ^^^ 2 + x + 1)" then ()
neuper@38031	729	else error "diff.sml Diff (x^2 + x + 1, x) from exp";
wneuper@59252	730	DEconstrCalcTree 1;
neuper@37906	731
neuper@37906	732	"--------- init_form, start with <NEW> (CAS input) ---------------";
neuper@37906	733	"--------- init_form, start with <NEW> (CAS input) ---------------";
neuper@37906	734	"--------- init_form, start with <NEW> (CAS input) ---------------";
s1210629013@55445	735	reset_states ();
neuper@37906	736	CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
neuper@37906	737	(*[[from sml: > @@@@@begin@@@@@
neuper@37906	738	[[from sml: 1
neuper@37906	739	[[from sml: <CALCTREE>
neuper@37906	740	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	741	[[from sml: </CALCTREE>
neuper@37906	742	[[from sml: @@@@@end@@@@@*)
neuper@37906	743	Iterator 1;
neuper@37906	744	(*[[from sml: > @@@@@begin@@@@@
neuper@37906	745	[[from sml: 1
neuper@37906	746	[[from sml: <ADDUSER>
neuper@37906	747	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	748	[[from sml: <USERID> 1 </USERID>
neuper@37906	749	[[from sml: </ADDUSER>
neuper@37906	750	[[from sml: @@@@@end@@@@@*)
neuper@37906	751	moveActiveRoot 1;
neuper@37906	752	(*[[from sml: > @@@@@begin@@@@@
neuper@37906	753	[[from sml: 1
neuper@37906	754	[[from sml: <CALCITERATOR>
neuper@37906	755	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	756	[[from sml: <POSITION>
neuper@37906	757	[[from sml: <INTLIST>
neuper@37906	758	[[from sml: </INTLIST>
neuper@37906	759	[[from sml: <POS> Pbl </POS>
neuper@37906	760	[[from sml: </POSITION>
neuper@37906	761	[[from sml: </CALCITERATOR>
neuper@37906	762	[[from sml: @@@@@end@@@@@*)
neuper@37906	763	getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
neuper@37906	764	(*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
neuper@37906	765	[[from sml: 1
neuper@37906	766	[[from sml: <GETELEMENTSFROMTO>
neuper@37906	767	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	768	[[from sml: <FORMHEADS>
neuper@37906	769	[[from sml: <CALCFORMULA>
neuper@37906	770	[[from sml: <POSITION>
neuper@37906	771	[[from sml: <INTLIST>
neuper@37906	772	[[from sml: </INTLIST>
neuper@37906	773	[[from sml: <POS> Pbl </POS>
neuper@37906	774	[[from sml: </POSITION>
neuper@37906	775	[[from sml: <FORMULA>
neuper@37906	776	[[from sml: <MATHML>
neuper@37906	777	[[from sml: <ISA> ________________________________________________ </ISA>
neuper@37906	778	[[from sml: </MATHML>
neuper@37906	779	[[from sml:
neuper@37906	780	[[from sml: </FORMULA>
neuper@37906	781	[[from sml: </CALCFORMULA>
neuper@37906	782	[[from sml: </FORMHEADS>
neuper@37906	783	[[from sml: </GETELEMENTSFROMTO>
neuper@37906	784	[[from sml: @@@@@end@@@@@*)
neuper@37906	785	refFormula 1 ([],Pbl);
neuper@37906	786	(*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
neuper@37906	787	[[from sml: 1
neuper@37906	788	[[from sml: <REFFORMULA>
neuper@37906	789	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	790	[[from sml: <CALCHEAD status = "incorrect">
neuper@37906	791	[[from sml: <POSITION>
neuper@37906	792	[[from sml: <INTLIST>
neuper@37906	793	[[from sml: </INTLIST>
neuper@37906	794	[[from sml: <POS> Pbl </POS>
neuper@37906	795	[[from sml: </POSITION>
neuper@37906	796	[[from sml: <HEAD>
neuper@37906	797	[[from sml: <MATHML>
neuper@37906	798	[[from sml: <ISA> Problem (e_domID, [e_pblID]) </ISA>
neuper@37906	799	[[from sml: </MATHML>
neuper@37906	800	[[from sml: </HEAD>
neuper@37906	801	[[from sml: <MODEL>
neuper@37906	802	[[from sml: <GIVEN> </GIVEN>
neuper@37906	803	[[from sml: <WHERE> </WHERE>
neuper@37906	804	[[from sml: <FIND> </FIND>
neuper@37906	805	[[from sml: <RELATE> </RELATE>
neuper@37906	806	[[from sml: </MODEL>
neuper@37906	807	[[from sml: <BELONGSTO> Pbl </BELONGSTO>
neuper@37906	808	[[from sml: <SPECIFICATION>
neuper@37906	809	[[from sml: <THEORYID> e_domID </THEORYID>
neuper@37906	810	[[from sml: <PROBLEMID>
neuper@37906	811	[[from sml: <STRINGLIST>
neuper@37906	812	[[from sml: <STRING> e_pblID </STRING>
neuper@37906	813	[[from sml: </STRINGLIST>
neuper@37906	814	[[from sml: </PROBLEMID>
neuper@37906	815	[[from sml: <METHODID>
neuper@37906	816	[[from sml: <STRINGLIST>
neuper@37906	817	[[from sml: <STRING> e_metID </STRING>
neuper@37906	818	[[from sml: </STRINGLIST>
neuper@37906	819	[[from sml: </METHODID>
neuper@37906	820	[[from sml: </SPECIFICATION>
neuper@37906	821	[[from sml: </CALCHEAD>
neuper@37906	822	[[from sml: </REFFORMULA>
neuper@37906	823	[[from sml: @@@@@end@@@@@*)
neuper@37906	824	moveActiveFormula 1 ([],Pbl);
neuper@37906	825	(*[[from sml: > @@@@@begin@@@@@
neuper@37906	826	[[from sml: 1
neuper@37906	827	[[from sml: <CALCITERATOR>
neuper@37906	828	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	829	[[from sml: <POSITION>
neuper@37906	830	[[from sml: <INTLIST>
neuper@37906	831	[[from sml: </INTLIST>
neuper@37906	832	[[from sml: <POS> Pbl </POS>
neuper@37906	833	[[from sml: </POSITION>
neuper@37906	834	[[from sml: </CALCITERATOR>
neuper@37906	835	[[from sml: @@@@@end@@@@@*)
neuper@37906	836	replaceFormula 1 "Simplify (1+2)";
neuper@37906	837	(*[[from sml: > @@@@@begin@@@@@
neuper@37906	838	[[from sml: 1
neuper@37906	839	[[from sml: <REPLACEFORMULA>
neuper@37906	840	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	841	[[from sml: <CALCCHANGED>
neuper@37906	842	[[from sml: <UNCHANGED>
neuper@37906	843	[[from sml: <INTLIST>
neuper@37906	844	[[from sml: </INTLIST>
neuper@37906	845	[[from sml: <POS> Pbl </POS>
neuper@37906	846	[[from sml: </UNCHANGED>
neuper@37906	847	[[from sml: <DELETED>
neuper@37906	848	[[from sml: <INTLIST>
neuper@37906	849	[[from sml: </INTLIST>
neuper@37906	850	[[from sml: <POS> Pbl </POS>
neuper@37906	851	[[from sml: </DELETED>
neuper@37906	852	[[from sml: <GENERATED>
neuper@37906	853	[[from sml: <INTLIST>
neuper@37906	854	[[from sml: </INTLIST>
neuper@37906	855	[[from sml: <POS> Met </POS> DIFFERENCE: Pbl
neuper@37906	856	[[from sml: </GENERATED>
neuper@37906	857	[[from sml: </CALCCHANGED>
neuper@37906	858	[[from sml: </REPLACEFORMULA>
neuper@37906	859	[[from sml: @@@@@end@@@@@*)
neuper@37906	860	getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
neuper@37906	861	(*@@@@@begin@@@@@
neuper@37906	862	1
neuper@37906	863	<GETELEMENTSFROMTO>
neuper@37906	864	<CALCID> 1 </CALCID>
neuper@37906	865	<FORMHEADS>
neuper@37906	866	<CALCFORMULA>
neuper@37906	867	<POSITION>
neuper@37906	868	<INTLIST>
neuper@37906	869	</INTLIST>
neuper@37906	870	<POS> Pbl </POS>
neuper@37906	871	</POSITION>
neuper@37906	872	<FORMULA>
neuper@37906	873	<MATHML>
neuper@37906	874	<ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
neuper@37906	875	</MATHML>
neuper@37906	876	</FORMULA>
neuper@37906	877	</CALCFORMULA>
neuper@37906	878	</FORMHEADS>
neuper@37906	879	</GETELEMENTSFROMTO>
neuper@37906	880	@@@@@end@@@@@*)
neuper@37906	881	getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
neuper@37906	882	(*[[from sml: > @@@@@begin@@@@@
neuper@37906	883	[[from sml: 1
neuper@37906	884	[[from sml: <SYSERROR>
neuper@37906	885	[[from sml: <CALCID> 1 </CALCID>
neuper@37906	886	[[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
neuper@37906	887	[[from sml: </SYSERROR>
neuper@37906	888	[[from sml: @@@@@end@@@@@*)
neuper@37906	889	(step into getFormulaeFromTo --- bug corrected...)
neuper@42423	890
neuper@42423	891	"--------- build fun check_err_patt ------------------------------";
neuper@42423	892	"--------- build fun check_err_patt ------------------------------";
neuper@42423	893	"--------- build fun check_err_patt ------------------------------";
neuper@42426	894	val subst = [(str2term "bdv", str2term "x")]: subst;
neuper@42423	895	val rls = norm_Rational
neuper@42423	896	val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
neuper@42423	897	val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
neuper@42423	898	val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "1 / 2");
neuper@42423	899
neuper@42426	900	val (res', _, _, rewritten) = (rewritten: the lhs of the pattern matches in res)
wneuper@59395	901	rew_sub thy 1 [] e_rew_ord e_rls false [] (HOLogic.Trueprop $ pat) res;
neuper@42423	902	if rewritten then NONE else SOME "e_errpatID";
neuper@42423	903
neuper@42423	904	val norm_res = case rewrite_set_ (Isac()) false rls res' of
neuper@42423	905	NONE => res'
neuper@42423	906	\| SOME (norm_res, _) => norm_res
neuper@42423	907
neuper@42423	908	val norm_inf = case rewrite_set_ (Isac()) false rls inf of
neuper@42423	909	NONE => inf
neuper@42423	910	\| SOME (norm_inf, _) => norm_inf;
neuper@42423	911
neuper@42423	912	res' = inf;
neuper@42423	913	norm_res = norm_inf;
neuper@42423	914
neuper@42423	915	val pat = parse_patt @{theory} "(?a + ?b)/?a = ?b";
neuper@42423	916	val (res, inf) = (str2term "(2 + 3)/2", str2term "3");
neuper@42426	917	if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
neuper@42423	918	then () else error "error patt example1 changed";
neuper@42423	919
neuper@42423	920	val pat = parse_patt @{theory} "(?a + ?b)/(?a + ?c) = ?b / ?c";
neuper@42423	921	val (res, inf) = (str2term "(2 + 3)/(2 + 4)", str2term "3 / 4");
neuper@42426	922	if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
neuper@42423	923	then () else error "error patt example2 changed";
neuper@42423	924
neuper@42423	925	val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
neuper@42423	926	val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
neuper@42426	927	if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
neuper@42423	928	then () else error "error patt example3 changed";
neuper@42423	929
neuper@42423	930	val inf = str2term "1 / 2";
neuper@42426	931	if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
neuper@42423	932	then () else error "error patt example3 changed";
neuper@42423	933
neuper@42426	934	"--------- build fun check_err_patt ?bdv -------------------------";
neuper@42426	935	"--------- build fun check_err_patt ?bdv -------------------------";
neuper@42426	936	"--------- build fun check_err_patt ?bdv -------------------------";
neuper@42426	937	val subst = [(str2term "bdv", str2term "x")]: subst;
neuper@42426	938	val t = str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))";
neuper@42426	939	val SOME (t, _) = rewrite_set_inst_ thy false subst norm_diff t;
neuper@42426	940	if term2str t = "2 * x + cos (x ^^^ 4) * 4 * x ^^^ 3" then ()
neuper@42426	941	else error "build fun check_err_patt ?bdv changed 1";
neuper@42423	942
neuper@42426	943	val rls = norm_diff
neuper@42426	944	val pat = parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)";
neuper@42426	945	val (res, inf) = (str2term "2 * x + d_d x (sin (x ^^^ 4))", str2term "2 * x + cos (4 * x ^^^ 3)");
neuper@42426	946
neuper@42426	947	val (res', _, _, rewritten) = (rewritten: the lhs of the pattern matches in res)
wneuper@59395	948	rew_sub thy 1 subst e_rew_ord e_rls false [] (HOLogic.Trueprop $ pat) res;
neuper@42426	949	if term2str res' = "2 * x + cos (d_d x (x ^^^ 4))" andalso rewritten then ()
neuper@42426	950	else error "build fun check_err_patt ?bdv changed 2";
neuper@42426	951
neuper@42426	952	val norm_res = case rewrite_set_inst_ (Isac()) false subst rls res' of
neuper@42426	953	NONE => res'
neuper@42426	954	\| SOME (norm_res, _) => norm_res;
neuper@42426	955	if term2str norm_res = "2 * x + cos (4 * x ^^^ 3)" then ()
neuper@42426	956	else error "build fun check_err_patt ?bdv changed 3";
neuper@42426	957
neuper@42426	958	val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of
neuper@42426	959	NONE => inf
neuper@42426	960	\| SOME (norm_inf, _) => norm_inf;
neuper@42426	961	if term2str norm_inf = "2 * x + cos (4 * x ^^^ 3)" then ()
neuper@42426	962	else error "build fun check_err_patt ?bdv changed 4";
neuper@42426	963
neuper@42426	964	res' = inf;
neuper@42426	965	if norm_res = norm_inf then ()
neuper@42426	966	else error "build fun check_err_patt ?bdv changed 5";
neuper@42426	967
neuper@42426	968	if check_err_patt (res, inf) (subst: subst) ("errpatID": errpatID, pat) rls = SOME "errpatID"
neuper@42426	969	then () else error "error patt example1 changed";
neuper@42426	970
neuper@42428	971	"--------- build fun check_error_patterns ------------------------";
neuper@42428	972	"--------- build fun check_error_patterns ------------------------";
neuper@42428	973	"--------- build fun check_error_patterns ------------------------";
neuper@42428	974	val (res, inf) =
neuper@42428	975	(str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))",
neuper@42428	976	str2term "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)");
neuper@48790	977	val {errpats, nrls = rls, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
neuper@42426	978
neuper@42428	979	val env = [(str2term "v_v", str2term "x")];
neuper@42428	980	val errpats =
neuper@42428	981	[e_errpat, (generalised for testing)
neuper@42428	982	("chain-rule-diff-both",
neuper@42428	983	[parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)",
neuper@42428	984	parse_patt @{theory} "d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)",
neuper@42428	985	parse_patt @{theory} "d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1)",
neuper@42428	986	parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / ?u",
neuper@42428	987	parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u"],
neuper@42428	988	[@{thm diff_sin_chain}, @{thm diff_cos_chain}, @{thm diff_pow_chain},
neuper@42428	989	@{thm diff_ln_chain}, @{thm diff_exp_chain}])]: errpat list;
neuper@42428	990	case check_error_patterns (res, inf) (prog, env) (errpats, rls) of SOME _ => ()
neuper@42428	991	\| NONE => error "check_error_patterns broken";
wneuper@59252	992	DEconstrCalcTree 1;
neuper@42428	993
neuper@42428	994	"--------- embed fun check_error_patterns ------------------------";
neuper@42428	995	"--------- embed fun check_error_patterns ------------------------";
neuper@42428	996	"--------- embed fun check_error_patterns ------------------------";
wneuper@59562	997	reset_states ();
neuper@42428	998	CalcTree
neuper@42428	999	[(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
wneuper@59592	1000	("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
neuper@42428	1001	Iterator 1;
neuper@42428	1002	moveActiveRoot 1;
wneuper@59248	1003	autoCalculate 1 CompleteCalcHead;
walther@59747	1004	autoCalculate 1 (Steps 1);
walther@59747	1005	autoCalculate 1 (Steps 1);(([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)))
walther@59747	1006	(autoCalculate 1 (Steps 1);([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) d_d x (x ^^^ 4)*)
neuper@42428	1007
wneuper@59562	1008	"~~~~~ fun appendFormula , args:"; val (cI, (ifo:cterm')) = (1, "d_d x (x ^ 2) + cos (4 * x ^ 3)");
wneuper@59562	1009	"~~~~~ fun appendFormula' , args:"; val (cI, (ifo: Rule.cterm')) = (cI, ifo);
wneuper@59562	1010	val cs = get_calc cI
wneuper@59562	1011	val pos = get_pos cI 1;
wneuper@59562	1012	(+)if pos = ([1], Res) then () else error "inform with (positive) check_error_patterns broken 1";
wneuper@59562	1013	val ("ok", cs') = (case) step pos cs (of);
wneuper@59562	1014	(case) Solve.inform cs' (encode ifo) (of); (ERROR WAS: "no derivation found")
wneuper@59562	1015	"~~~~~ fun inform , args:"; val (((next_)cs as (_, _, (pt, pos as (p, _))): Chead.calcstate'), istr)
wneuper@59562	1016	= (cs', (encode ifo));
wneuper@59562	1017	val ctxt = get_ctxt pt pos (see TODO.thy)
wneuper@59592	1018	val SOME f_in = (case) TermC.parse (Celem.assoc_thy "Isac_Knowledge") istr (of);
wneuper@59562	1019	val f_in = Thm.term_of f_in
wneuper@59562	1020	val pos_pred = lev_back' pos
wneuper@59562	1021	val f_pred = Ctree.get_curr_formula (pt, pos_pred);
wneuper@59562	1022	(if) f_pred = f_in; (else)
wneuper@59562	1023	val NONE = (case) Inform.cas_input f_in (of);
wneuper@59562	1024	(NEW)val (_, _, metID) = get_obj g_spec pt (par_pblobj pt p)
wneuper@59562	1025	(NEW)val {scr = prog, ...} = Specify.get_met metID
wneuper@59562	1026	(NEW)val istate = get_istate pt pos
wneuper@59562	1027	(NEW)val ctxt = get_ctxt pt pos
wneuper@59562	1028	val LucinNEW.Not_Derivable calcstate' =
wneuper@59562	1029	(case) LucinNEW.locate_input_formula prog (pt, pos) istate ctxt f_in (of);
wneuper@59562	1030	val pp = Ctree.par_pblobj pt p
wneuper@59562	1031	val (errpats, nrls, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of
wneuper@59562	1032	{errpats, nrls, scr = Rule.Prog prog, ...} => (errpats, nrls, prog)
wneuper@59562	1033	\| _ => error "inform: uncovered case of get_met"
wneuper@59562	1034	;
wneuper@59562	1035	(+)if errpats2str 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 ^^^ ?n) = ?n * ?u ^^^ (?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 ^^^ ?n) = ?n * ?u ^^^ (?n - 1) * d_d ?bdv ?u\",\"d_d ?bdv (LogExp.ln ?u) = d_d ?bdv ?u / ?u\",\"d_d ?bdv (E_ ^^^ ?u) = E_ ^^^ ?u * d_d ?x ?u\"]]"
wneuper@59562	1036	(+)then () else error "inform with (positive) check_error_patterns broken 3";
neuper@42428	1037
walther@59685	1038	val {env, ...} = Ctree.get_istate pt pos \|> Istate.the_pstate
wneuper@59562	1039	;
wneuper@59562	1040	(+)if term2str f_pred = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" andalso
wneuper@59562	1041	(+) term2str f_in = "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)"
wneuper@59562	1042	(+)then () else error "inform with (positive) check_error_patterns broken 2";
neuper@42428	1043
wneuper@59562	1044	val SOME "chain-rule-diff-both" = (case) Inform.check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) (of);
neuper@42428	1045
neuper@42428	1046	"--- final check:";
wneuper@59562	1047	case inform cs' (encode ifo) of
neuper@42428	1048	("error pattern #chain-rule-diff-both#", calcstate') => ()
wneuper@59562	1049	\| _ => error "inform with (positive) check_error_patterns broken"
neuper@42428	1050
neuper@48895	1051
neuper@42430	1052	"--------- embed fun find_fillpatterns ---------------------------";
neuper@42430	1053	"--------- embed fun find_fillpatterns ---------------------------";
neuper@42430	1054	"--------- embed fun find_fillpatterns ---------------------------";
s1210629013@55445	1055	reset_states ();
neuper@42430	1056	CalcTree
neuper@42430	1057	[(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
wneuper@59592	1058	("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
neuper@42430	1059	Iterator 1;
neuper@42430	1060	moveActiveRoot 1;
wneuper@59248	1061	autoCalculate 1 CompleteCalcHead;
walther@59747	1062	autoCalculate 1 (Steps 1);
walther@59747	1063	autoCalculate 1 (Steps 1);(([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)))
wneuper@59123	1064	appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (\|> Future.join);
neuper@42430	1065	(<CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>)
neuper@42432	1066	(*or
neuper@42432	1067	<CALCMESSAGE> no derivation found </CALCMESSAGE>*)
neuper@42430	1068
neuper@42433	1069	"~~~~~ fun findFillpatterns, args:"; val (cI, errpatID) = (1, "chain-rule-diff-both");
neuper@42430	1070	val ((pt, _), _) = get_calc cI
neuper@42430	1071	val pos = get_pos cI 1;
walther@59685	1072	"~~~~~ fun find_fillpatterns , args:"; val ((pt, pos as (p, _)), errpatID) = ((pt, pos), errpatID);
walther@59685	1073	val f_curr = Ctree.get_curr_formula (pt, pos);
walther@59685	1074	val pp = Ctree.par_pblobj pt p
walther@59685	1075	val (errpats, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of
walther@59685	1076	{errpats, scr = Rule.Prog prog, ...} => (errpats, prog)
walther@59685	1077	\| _ => error "find_fillpatterns: uncovered case of get_met"
walther@59685	1078	val {env, ...} = Ctree.get_istate pt pos \|> Istate.the_pstate
walther@59685	1079	val subst = Rtools.get_bdv_subst prog env
neuper@42430	1080	val errpatthms = errpats
neuper@42430	1081	\|> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
neuper@42430	1082	\|> map (#3: errpat -> thm list)
neuper@42430	1083	\|> flat;
neuper@42430	1084
neuper@42430	1085	case map (get_fillpats subst f_curr errpatID) errpatthms \|> flat of
neuper@42433	1086	("fill-d_d-arg", tm, thm, subs_opt) :: _ => if term2str tm =
neuper@42432	1087	"d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
neuper@42432	1088	then () else error "find_fillpatterns changed 1a"
neuper@42432	1089	\| _ => error "find_fillpatterns changed 1b"
neuper@42430	1090
neuper@42430	1091	"~~~~~ fun get_fillpats, args:"; val (subst, form, errpatID, thm) =
neuper@42432	1092	(subst, f_curr, errpatID, hd (simulate beginning of "map") errpatthms);
neuper@42430	1093	val thmDeriv = Thm.get_name_hint thm
neuper@42430	1094	val (part, thyID) = thy_containing_thm thmDeriv
neuper@42430	1095	val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]
neuper@42430	1096	val Hthm {fillpats, ...} = get_the theID
neuper@42433	1097	val some = map (get_fillform subst (thm, form) errpatID) fillpats;
neuper@42430	1098
neuper@42430	1099	case some \|> filter is_some \|> map the of
neuper@42433	1100	("fill-d_d-arg", tm, thm, subsopt) :: _ => if term2str tm =
neuper@42432	1101	"d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
neuper@42432	1102	then () else error "find_fillpatterns changed 2a"
neuper@42432	1103	\| _ => error "find_fillpatterns changed 2b"
neuper@42430	1104
neuper@42433	1105	"~~~~~ fun get_fillform, args:";
neuper@42433	1106	val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
neuper@42433	1107	(subst, (thm, form), errpatID, hd (simulate beginning of "map") fillpats);
neuper@42433	1108	val (form', _, _, rewritten) =
wneuper@59395	1109	rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (HOLogic.Trueprop $ pat) form;
neuper@42432	1110
neuper@42432	1111	if term2str form' = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
neuper@42432	1112	else error "find_fillpatterns changed 3";
neuper@42432	1113
neuper@42433	1114	"~~~~~ to findFillpatterns return val:"; val (fillpats) =
neuper@42433	1115	(map (get_fillpats (subs_opt, subst) f_curr errpatID) errpatthms \|> flat) (only from "hd errpatthms");
neuper@42432	1116
neuper@42450	1117	"vvv--- dropped this code WN120730";
neuper@42433	1118	val msg = "fill patterns " ^
neuper@42433	1119	((map ((apsnd term2str) o quad2pair) fillpats) \|> map pair2str_ \|> strs2str_);
neuper@42450	1120	msg =
neuper@42432	1121	"fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
neuper@42432	1122	" =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" ^
neuper@42432	1123	"#fill-both-args#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
neuper@42432	1124	" =\nd_d x (x ^^^ 2) + cos ?_dummy_2 * d_d x ?_dummy_3" ^
neuper@42432	1125	"#fill-d_d#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
neuper@42432	1126	" =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1 x (x ^^^ 4)" ^
neuper@42432	1127	"#fill-inner-deriv#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
neuper@42432	1128	" =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1" ^
neuper@42450	1129	"#fill-all#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) = d_d x (x ^^^ 2) + ?_dummy_1#";
neuper@42450	1130	"^^^--- dropped this code WN120730";
neuper@42450	1131
neuper@42450	1132	if (map #1 fillpats) =
neuper@42450	1133	["fill-d_d-arg", "fill-both-args", "fill-d_d", "fill-inner-deriv", "fill-all"]
neuper@42450	1134	then () else error "find_fillpatterns changed 4b";
wneuper@59252	1135	DEconstrCalcTree 1;
neuper@42450	1136
neuper@42437	1137	"--------- build fun is_exactly_equal, inputFillFormula ----------";
neuper@42437	1138	"--------- build fun is_exactly_equal, inputFillFormula ----------";
neuper@42437	1139	"--------- build fun is_exactly_equal, inputFillFormula ----------";
s1210629013@55445	1140	reset_states ();
neuper@42437	1141	CalcTree
neuper@42437	1142	[(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
wneuper@59592	1143	("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
neuper@42437	1144	Iterator 1;
neuper@42437	1145	moveActiveRoot 1;
wneuper@59248	1146	autoCalculate 1 CompleteCalcHead;
walther@59747	1147	autoCalculate 1 (Steps 1);
walther@59747	1148	autoCalculate 1 (Steps 1);(([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)))
wneuper@59123	1149	appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (\|> Future.join); (<<<<<<<=========================)
neuper@42437	1150	(* the check for errpat is maximally liberal (whole term modulo "nrls" from "type met"),
neuper@42437	1151	would recognize "cos (4 * x ^ (4 - 1)) + 2 * x" as well.
neuper@42437	1152	results in <CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>
neuper@42437	1153	instead of <CALCMESSAGE> no derivation found </CALCMESSAGE> *)
neuper@42437	1154	val ((pt,pos), _) = get_calc 1;
neuper@42437	1155	val p = get_pos 1 1;
neuper@42437	1156	val (Form f, _, asms) = pt_extract (pt, p);
neuper@42437	1157
wneuper@59253	1158	if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
wneuper@59497	1159	case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
wneuper@59253	1160	("diff_sum", thm)) =>
wneuper@59253	1161	if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
wneuper@59253	1162	else error "embed fun get_fillform changed 11"
wneuper@59253	1163	\| _ => error "embed fun get_fillform changed 12"
wneuper@59253	1164	else error "embed fun get_fillform changed 13";
neuper@42437	1165
neuper@42437	1166	findFillpatterns 1 "chain-rule-diff-both"; (<<<<<<<=================================)
neuper@42437	1167	(*<CALCMESSAGE> fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =
neuper@42437	1168	d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1#fill-both-args#...#...#... *)
neuper@42437	1169	val ((pt,pos),_) = get_calc 1;
neuper@42437	1170	val p = get_pos 1 1;
neuper@42437	1171
neuper@42437	1172	val (Form f, _, asms) = pt_extract (pt, p);
wneuper@59253	1173	if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
wneuper@59497	1174	case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
wneuper@59253	1175	("diff_sum", thm)) =>
wneuper@59253	1176	if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
wneuper@59253	1177	else error "embed fun get_fillform changed 21"
wneuper@59253	1178	\| _ => error "embed fun get_fillform changed 22"
wneuper@59253	1179	else error "embed fun get_fillform changed 23";
neuper@42437	1180
neuper@42437	1181	requestFillformula 1 ("chain-rule-diff-both", "fill-both-args");(<<<<<<<============)
neuper@42437	1182	(<AUTOCALC> ([1], Res) ([2], Res) ([2], Res) </AUTOCALC>)
neuper@42437	1183	val ((pt,pos),_) = get_calc 1;
neuper@42437	1184	val p = get_pos 1 1;
neuper@42437	1185	val (Form f, _, asms) = pt_extract (pt, p);
wneuper@59253	1186	if p = ([1], Res) andalso existpt [2] pt
wneuper@59253	1187	andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"
wneuper@59497	1188	then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
wneuper@59253	1189	("diff_sum", thm)) =>
wneuper@59253	1190	if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
wneuper@59253	1191	else error "embed fun get_fillform changed 31"
wneuper@59253	1192	\| _ => error "embed fun get_fillform changed 32"
wneuper@59253	1193	else error "embed fun get_fillform changed 33";
neuper@42437	1194
neuper@42437	1195	(* input a formula which exactly fills the gaps in a "fillformula"
neuper@42437	1196	presented to the learner immediately before by "requestFillformula (errpatID, fillpatID)":
neuper@42437	1197	errpatID: lhs of the respective thm = lhs of fillformula with fillpatID.
neuper@42437	1198	the respective thm is in the ctree ................
neuper@42437	1199	*)
neuper@42437	1200	"~~~~~ fun inputFillFormula, args:"; val (cI, ifo) =
neuper@42437	1201	(1, "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)");
neuper@42437	1202	val ((pt, _), _) = get_calc cI
neuper@42437	1203	val pos = get_pos cI 1;
neuper@42437	1204
neuper@42437	1205	"~~~~~ fun is_exactly_equal, args:"; val ((pt, pos as (p, p_)), istr) = ((pt, pos), ifo);
wneuper@59592	1206	val SOME ifo = parseNEW (assoc_thy "Isac_Knowledge" \|> thy2ctxt) istr
neuper@42437	1207	val p' = lev_on p;
neuper@42437	1208	val tac = get_obj g_tac pt p';
wneuper@59497	1209	val Rewrite_Inst ([bbb as "(''bdv'', x)"], ("diff_sin_chain", ttt)) = tac;
wneuper@59253	1210	if (term2str o Thm.prop_of) ttt = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
wneuper@59252	1211	else error "inputFillFormula changed 10";
neuper@42437	1212	val Appl rew = applicable_in pos pt tac;
neuper@42437	1213	val Rewrite_Inst' (_, _, _, _, _, _, _, (res, _)) = rew;
neuper@42437	1214
neuper@42437	1215	"~~~~~ to inputFillFormula return val:"; val ("ok", tac) = ("ok", tac);
neuper@42437	1216	val ("ok", (_, c, ptp as (_,p'))) = locatetac tac (pt, pos);
neuper@42437	1217	upd_calc cI (ptp, []);
neuper@42437	1218	upd_ipos cI 1 p';
neuper@42437	1219	autocalculateOK2xml cI pos (if null c then p' else last_elem c) p';
neuper@42437	1220
neuper@42437	1221	"~~~~~ final check:";
neuper@42437	1222	val ((pt, _),_) = get_calc 1;
neuper@42437	1223	val p = get_pos 1 1;
neuper@42437	1224	val (Form f, _, asms) = pt_extract (pt, p);
wneuper@59253	1225	if p = ([2], Res) andalso term2str f = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)"
wneuper@59497	1226	then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
wneuper@59253	1227	("diff_sin_chain", thm)) =>
wneuper@59253	1228	if (term2str o Thm.prop_of) thm = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
wneuper@59253	1229	else error "inputFillFormula changed 111"
wneuper@59253	1230	\| _ => error "inputFillFormula changed 112"
wneuper@59253	1231	else error "inputFillFormula changed 113";
neuper@42437	1232
wneuper@59262	1233	"--------- fun appl_adds -----------------------------------------";
wneuper@59262	1234	"--------- fun appl_adds -----------------------------------------";
wneuper@59262	1235	"--------- fun appl_adds -----------------------------------------";
wneuper@59262	1236	(* val (dI, oris, ppc, pbt, selct::ss) =
wneuper@59262	1237	(dI, pors, probl, ppc, map itms2fstr probl);
wneuper@59262	1238	...vvv
wneuper@59262	1239	*)
wneuper@59262	1240	(* val (dI, oris, ppc, pbt, (selct::ss))=
wneuper@59262	1241	(#1 (some_spec ospec spec), oris, []:itm list,
wneuper@59262	1242	((#ppc o get_pbt) (#2 (some_spec ospec spec))),(imodel2fstr imodel));
wneuper@59262	1243	val iii = appl_adds dI oris ppc pbt (selct::ss);
wneuper@59262	1244	tracing(itms2str_ thy iii);
wneuper@59262	1245
wneuper@59262	1246	val itm = appl_add' dI oris ppc pbt selct;
wneuper@59262	1247	val ppc = insert_ppc' itm ppc;
wneuper@59262	1248
wneuper@59262	1249	val _::selct::ss = (selct::ss);
wneuper@59262	1250	val itm = appl_add' dI oris ppc pbt selct;
wneuper@59262	1251	val ppc = insert_ppc' itm ppc;
wneuper@59262	1252
wneuper@59262	1253	val _::selct::ss = (selct::ss);
wneuper@59262	1254	val itm = appl_add' dI oris ppc pbt selct;
wneuper@59262	1255	val ppc = insert_ppc' itm ppc;
wneuper@59262	1256	tracing(itms2str_ thy ppc);
wneuper@59262	1257
wneuper@59262	1258	val _::selct::ss = (selct::ss);
wneuper@59262	1259	val itm = appl_add' dI oris ppc pbt selct;
wneuper@59262	1260	val ppc = insert_ppc' itm ppc;
wneuper@59262	1261	*)
wneuper@59264	1262	"--------- fun concat_deriv --------------------------------------";
wneuper@59264	1263	"--------- fun concat_deriv --------------------------------------";
wneuper@59264	1264	"--------- fun concat_deriv --------------------------------------";
wneuper@59264	1265	(*
wneuper@59264	1266	val ({rew_ord, erls, rules,...}, fo, ifo) =
wneuper@59264	1267	(rep_rls Test_simplify, str2term "x+1+ -12=0", str2term "-21+(x+1)=0");
wneuper@59264	1268	(tracing o trtas2str) fod';
wneuper@59264	1269	> ["
wneuper@59264	1270	(x + 1 + -1 * 2 = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (x + 1) = 0, []))","
wneuper@59264	1271	(-1 * 2 + (x + 1) = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (1 + x) = 0, []))","
wneuper@59264	1272	(-1 * 2 + (1 + x) = 0, Thm ("radd_left_commute","?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (-1 * 2 + x) = 0, []))","
wneuper@59264	1273	(1 + (-1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))","-1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]
wneuper@59264	1274	val it = () : unit
wneuper@59264	1275	(tracing o trtas2str) (map rev_deriv' rifod');
wneuper@59264	1276	> ["
wneuper@59264	1277	(1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))","-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))","
wneuper@59264	1278	(1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute","?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))","
wneuper@59264	1279	(-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute","?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]
wneuper@59264	1280	val it = () : unit
wneuper@59264	1281	*)
wneuper@59264	1282	"--------- handle an input formula -------------------------------";
wneuper@59264	1283	"--------- handle an input formula -------------------------------";
wneuper@59264	1284	"--------- handle an input formula -------------------------------";
wneuper@59264	1285	(*
wneuper@59264	1286	Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:
wneuper@59264	1287	Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden,
wneuper@59264	1288	wenn Abteilungen nur auf gleichem Level gesucht werden ?
wneuper@59264	1289	WN.040216
wneuper@59264	1290
wneuper@59264	1291	Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml
wneuper@59264	1292
wneuper@59264	1293	------------------------------------------------------------------------------
wneuper@59264	1294	"Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
wneuper@59264	1295	------------------------------------------------------------------------------
wneuper@59264	1296	1. "5 * x / (x - 2) - x / (x + 2) = 4"
wneuper@59264	1297	...
wneuper@59367	1298	4. "12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalise", "poly"..
wneuper@59264	1299	...
wneuper@59264	1300	4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..
wneuper@59264	1301	...
wneuper@59264	1302	4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"
wneuper@59264	1303	...
wneuper@59264	1304	"[x = -4 / 3]"
wneuper@59264	1305	------------------------------------------------------------------------------
wneuper@59264	1306	(1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
wneuper@59264	1307
wneuper@59264	1308	(4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
wneuper@59264	1309	------------------------------------------------------------------------------
wneuper@59264	1310
wneuper@59264	1311
wneuper@59264	1312	------------------------------------------------------------------------------
wneuper@59264	1313	"Schalk I s.87 Bsp 55b (x/(x^^^2 - 6x+9) - 1/(x^^^2 - 3x) =1/x)";
wneuper@59264	1314	------------------------------------------------------------------------------
wneuper@59264	1315	1. "x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) = 1 / x"
wneuper@59264	1316	...
wneuper@59264	1317	4. "(3 + (-1 * x + x ^^^ 2)) * x = 1 * (9 * x + (x ^^^ 3 + -6 * x ^^^ 2))"
wneuper@59367	1318	Subproblem["normalise", "polynomial", "univariate"..
wneuper@59264	1319	...
wneuper@59264	1320	4.4. "-6 * x + 5 * x ^^^ 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..
wneuper@59264	1321	...
wneuper@59264	1322	4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
wneuper@59264	1323	4.4.5. "[x = 0, x = 6 / 5]"
wneuper@59264	1324	...
wneuper@59264	1325	5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
wneuper@59264	1326	"[x = 6 / 5]"
wneuper@59264	1327	------------------------------------------------------------------------------
wneuper@59264	1328	(1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]
wneuper@59264	1329
wneuper@59264	1330	(4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]
wneuper@59264	1331	------------------------------------------------------------------------------
wneuper@59264	1332
wneuper@59264	1333
wneuper@59264	1334	------------------------------------------------------------------------------
wneuper@59264	1335	"Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4x+4)=sqrt(9x+9))";
wneuper@59264	1336	------------------------------------------------------------------------------
wneuper@59264	1337	1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"
wneuper@59264	1338	...
wneuper@59264	1339	6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"
wneuper@59489	1340	Subproblem["sq", "rootX", "univariate", "equation"]
wneuper@59264	1341	...
wneuper@59264	1342	6.6. "144 + 288 * x + 144 * x ^^^ 2 = 144 + x ^^^ 2 + 288 * x + 143 * x ^^^ 2"
wneuper@59367	1343	Subproblem["normalise", "polynomial", "univariate", "equation"]
wneuper@59264	1344	...
wneuper@59264	1345	6.6.3 "0 = 0" Subproblem["degree_0", "polynomial", "univariate", "equation"]
wneuper@59264	1346	... Or_to_List
wneuper@59264	1347	6.6.3.2 "UniversalList"
wneuper@59264	1348	------------------------------------------------------------------------------
wneuper@59264	1349	(1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]
wneuper@59264	1350
wneuper@59264	1351	(6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]
wneuper@59264	1352	------------------------------------------------------------------------------
wneuper@59264	1353	*)
wneuper@59264	1354	(sh. comments auf 498)
wneuper@59264	1355	"--------- fun dropwhile' ----------------------------------------";
wneuper@59264	1356	"--------- fun dropwhile' ----------------------------------------";
wneuper@59264	1357	"--------- fun dropwhile' ----------------------------------------";
wneuper@59264	1358	(*
wneuper@59264	1359	fun equal a b = a=b;
wneuper@59264	1360	val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];
wneuper@59264	1361	val r_foder = rev foder; val r_ifoder = rev ifoder;
wneuper@59264	1362	dropwhile' equal r_foder r_ifoder;
wneuper@59264	1363	> vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list
wneuper@59264	1364
wneuper@59264	1365	val foder = [3,4,5]; val ifoder = [11,12,3,4,5];
wneuper@59264	1366	val r_foder = rev foder; val r_ifoder = rev ifoder;
wneuper@59264	1367	dropwhile' equal r_foder r_ifoder;
wneuper@59264	1368	> val it = ([3], [3, 12, 11]) : int list * int list
wneuper@59264	1369
wneuper@59264	1370	val foder = [5]; val ifoder = [11,12,3,4,5];
wneuper@59264	1371	val r_foder = rev foder; val r_ifoder = rev ifoder;
wneuper@59264	1372	dropwhile' equal r_foder r_ifoder;
wneuper@59264	1373	> val it = ([5], [5, 4, 3, 12, 11]) : int list * int list
wneuper@59264	1374
wneuper@59264	1375	val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];
wneuper@59264	1376	val r_foder = rev foder; val r_ifoder = rev ifoder;
wneuper@59264	1377	dropwhile' equal r_foder r_ifoder;
wneuper@59264	1378	> *** dropwhile': did not start with equal elements*)

author	Walther Neuper <walther.neuper@jku.at>
	Wed, 18 Dec 2019 15:33:27 +0100
changeset 59747	8e5335c63475
parent 59719	568ea658e026
child 59749	cc3b1807f72e
permissions	-rw-r--r--