1 (* Title: tests on inform.sml
2 Author: Walther Neuper 060225,
3 (c) due to copyright terms
6 "-----------------------------------------------------------------";
7 "table of contents -----------------------------------------------";
8 "-----------------------------------------------------------------";
9 "appendForm with miniscript with mini-subpbl:";
10 "--------- appendFormula: on Res + equ_nrls ----------------------";
11 "--------- appendFormula: on Frm + equ_nrls ----------------------";
12 "--------- appendFormula: on Res + NO deriv ----------------------";
13 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
14 "replaceForm with miniscript with mini-subpbl:";
15 "--------- replaceFormula: on Res + = ----------------------------";
16 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
17 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
18 "--------- replaceFormula: cut calculation -----------------------";
19 "--------- replaceFormula: cut calculation -----------------------";
20 (* 040307 copied from informtest.sml ... old versions
21 "--------- maximum-example, UC: Modeling / modifyCalcHead --------";*)
22 "--------- syntax error ------------------------------------------";
24 "--------- CAS-command on ([],Pbl) -------------------------------";
25 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
26 "--------- locate_input_term [rational,simplification] ----------------------";
27 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
28 "--------- Take as 1st tac, start from exp -----------------------";
29 "--------- init_form, start with <NEW> (CAS input) ---------------";
30 "--------- build fun check_err_patt ------------------------------";
31 "--------- build fun check_err_patt ?bdv -------------------------";
32 "--------- build fun check_error_patterns ------------------------";
33 "--------- embed fun check_error_patterns ------------------------";
34 "--------- build fun get_fillpats --------------------------------";
35 "--------- embed fun find_fillpatterns ---------------------------";
36 "--------- build fun is_exactly_equal, inputFillFormula ----------";
37 "--------- fun appl_adds -----------------------------------------";
38 "--------- fun concat_deriv --------------------------------------";
39 "--------- handle an input formula -------------------------------";
40 "--------- fun dropwhile' ----------------------------------------";
41 "-----------------------------------------------------------------";
42 "-----------------------------------------------------------------";
43 "-----------------------------------------------------------------";
46 "--------- appendFormula: on Res + equ_nrls ----------------------";
47 "--------- appendFormula: on Res + equ_nrls ----------------------";
48 "--------- appendFormula: on Res + equ_nrls ----------------------";
49 val Prog sc = (#scr o get_met) ["Test","squ-equ-test-subpbl1"];
50 (writeln o term2str) sc;
51 val Prog sc = (#scr o get_met) ["Test","solve_linear"];
52 (writeln o term2str) sc;
55 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
56 ("Test", ["sqroot-test","univariate","equation","test"],
57 ["Test","squ-equ-test-subpbl1"]))];
58 Iterator 1; moveActiveRoot 1;
59 autoCalculate 1 CompleteCalcHead;
60 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
61 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
63 appendFormula 1 "-2 * 1 + (1 + x) = 0" (*|> Future.join*); refFormula 1 (get_pos 1 1);
64 val ((pt,_),_) = get_calc 1;
65 val str = pr_ctree pr_short pt;
67 (". ----- pblobj -----\n" ^
69 "2. x + 1 + -1 * 2 = 0\n" ^
70 "2.1. x + 1 + -1 * 2 = 0\n" ^
71 "2.2. 1 + x + -1 * 2 = 0\n" ^
72 "2.3. 1 + (x + -1 * 2) = 0\n" ^
73 "2.4. 1 + (x + -2) = 0\n" ^
74 "2.5. 1 + (x + -2 * 1) = 0\n" ^
75 "2.6. 1 + x + -2 * 1 = 0\n" ) then ()
76 else error "inform.sml: diff.behav.appendFormula: on Res + equ 1";
78 moveDown 1 ([ ],Pbl); refFormula 1 ([1],Frm); (*x + 1 = 2*)
79 moveDown 1 ([1],Frm); refFormula 1 ([1],Res); (*x + 1 + -1 * 2 = 0*)
81 (*the seven steps of detailed derivation*)
82 moveDown 1 ([1 ],Res); refFormula 1 ([2,1],Frm);
83 moveDown 1 ([2,1],Frm); refFormula 1 ([2,1],Res);
84 moveDown 1 ([2,1],Res); refFormula 1 ([2,2],Res);
85 moveDown 1 ([2,2],Res); refFormula 1 ([2,3],Res);
86 moveDown 1 ([2,3],Res); refFormula 1 ([2,4],Res);
87 moveDown 1 ([2,4],Res); refFormula 1 ([2,5],Res);
88 moveDown 1 ([2,5],Res); refFormula 1 ([2,6],Res);
89 val ((pt,_),_) = get_calc 1;
90 if "-2 * 1 + (1 + x) = 0" = term2str (fst (get_obj g_result pt [2,6])) then()
91 else error "inform.sml: diff.behav.appendFormula: on Res + equ 2";
93 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
94 (* <ERROR> error in kernel </ERROR> ALREADY IN 2009-2*)
95 (*========== inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 =============
96 val (_,(tac,_,_)::_) = get_calc 1;
97 if tac = Rewrite_Set "Test_simplify" then ()
98 else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
99 ============ inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 ============*)
101 autoCalculate 1 CompleteCalc;
102 val ((pt,_),_) = get_calc 1;
103 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
104 else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
105 (* autoCalculate 1 CompleteCalc;
106 val ((pt,p),_) = get_calc 1;
107 (writeln o istates2str) (get_obj g_loc pt [ ]);
108 (writeln o istates2str) (get_obj g_loc pt [1]);
109 (writeln o istates2str) (get_obj g_loc pt [2]);
110 (writeln o istates2str) (get_obj g_loc pt [3]);
111 (writeln o istates2str) (get_obj g_loc pt [3,1]);
112 (writeln o istates2str) (get_obj g_loc pt [3,2]);
113 (writeln o istates2str) (get_obj g_loc pt [4]);
116 "----------------------------------------------------------";
118 val fod = make_deriv (@{theory "Isac_Knowledge"}) Atools_erls
119 ((#rules o rep_rls) Test_simplify)
120 (sqrt_right false (@{theory "Pure"})) NONE
121 (str2term "x + 1 + -1 * 2 = 0");
122 (writeln o trtas2str) fod;
124 val ifod = make_deriv (@{theory "Isac_Knowledge"}) Atools_erls
125 ((#rules o rep_rls) Test_simplify)
126 (sqrt_right false (@{theory "Pure"})) NONE
127 (str2term "-2 * 1 + (1 + x) = 0");
128 (writeln o trtas2str) ifod;
129 fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
130 val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
131 val der = fod' @ (map rev_deriv' rifod');
132 (writeln o trtas2str) der;
133 "----------------------------------------------------------";
136 "--------- appendFormula: on Frm + equ_nrls ----------------------";
137 "--------- appendFormula: on Frm + equ_nrls ----------------------";
138 "--------- appendFormula: on Frm + equ_nrls ----------------------";
140 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
141 ("Test", ["sqroot-test","univariate","equation","test"],
142 ["Test","squ-equ-test-subpbl1"]))];
143 Iterator 1; moveActiveRoot 1;
144 autoCalculate 1 CompleteCalcHead;
145 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
146 appendFormula 1 "2+ -1 + x = 2" (*|> Future.join*); refFormula 1 (get_pos 1 1);
148 moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (*x + 1 = 2*);
150 moveDown 1 ([1 ],Frm); refFormula 1 ([1,1],Frm);
151 moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res);
152 moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res);
153 moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res);
154 moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res);
155 moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res);
156 moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res);
157 val ((pt,_),_) = get_calc 1;
158 if "2 + -1 + x = 2" = term2str (fst (get_obj g_result pt [1,6])) then()
159 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
161 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
162 val (_,(tac,_,_)::_) = get_calc 1;
163 case tac of Rewrite_Set "norm_equation" => ()
164 | _ => error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
165 autoCalculate 1 CompleteCalc;
166 val ((pt,_),_) = get_calc 1;
167 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
168 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
171 "--------- appendFormula: on Res + NO deriv ----------------------";
172 "--------- appendFormula: on Res + NO deriv ----------------------";
173 "--------- appendFormula: on Res + NO deriv ----------------------";
175 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
176 ("Test", ["sqroot-test","univariate","equation","test"],
177 ["Test","squ-equ-test-subpbl1"]))];
178 Iterator 1; moveActiveRoot 1;
179 autoCalculate 1 CompleteCalcHead;
180 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
181 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
183 appendFormula 1 "x = 2" (*|> Future.join*);
184 val ((pt,p),_) = get_calc 1;
185 val str = pr_ctree pr_short pt;
187 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" andalso p = ([1], Res)
189 else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
191 fetchProposedTactic 1;
192 val (_,(tac,_,_)::_) = get_calc 1;
193 case tac of Rewrite_Set "Test_simplify" => ()
194 | _ => error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
195 autoCalculate 1 CompleteCalc;
196 val ((pt,_),_) = get_calc 1;
197 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
198 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
201 "--------- appendFormula: on Res + late deriv --------------------";
202 "--------- appendFormula: on Res + late deriv --------------------";
203 "--------- appendFormula: on Res + late deriv --------------------";
204 (*cp with "fun me" to test/../lucas-interpreter.sml:
205 re-build: fun locate_input_term ---------------------------------------------------";
208 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
209 ("Test", ["sqroot-test","univariate","equation","test"],
210 ["Test","squ-equ-test-subpbl1"]))];
211 Iterator 1; moveActiveRoot 1;
212 autoCalculate 1 CompleteCalcHead;
213 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
214 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
216 appendFormula 1 "x = 1" (*|> Future.join*);
217 val ((pt,p),_) = get_calc 1;
218 val str = pr_ctree pr_short pt;
220 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)
221 then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
222 else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
224 fetchProposedTactic 1;
225 val (_,(tac,_,_)::_) = get_calc 1;
226 case tac of Check_Postcond ["LINEAR", "univariate", "equation", "test"] => ()
227 | _ => error "inform.sml: diff.behav.appendFormula: Res + late d 2";
228 autoCalculate 1 CompleteCalc;
229 val ((pt,_),_) = get_calc 1;
230 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
231 else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
234 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
235 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
236 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
238 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
239 ("Test", ["sqroot-test","univariate","equation","test"],
240 ["Test","squ-equ-test-subpbl1"]))];
241 Iterator 1; moveActiveRoot 1;
242 autoCalculate 1 CompleteCalcHead;
243 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
244 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
245 appendFormula 1 "[x = 3 + -2*1]" (*|> Future.join*);
246 val ((pt,p),_) = get_calc 1;
247 val str = pr_ctree pr_short pt;
249 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 ()
250 else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
251 autoCalculate 1 CompleteCalc;
252 val ((pt,p),_) = get_calc 1;
253 if "[x = 3 + -2 * 1]" = term2str (fst (get_obj g_result pt [])) then ()
254 (* ~~~~~~~~~~ simplify as last step in any script ?!*)
255 else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
258 "--------- replaceFormula: on Res + = ----------------------------";
259 "--------- replaceFormula: on Res + = ----------------------------";
260 "--------- replaceFormula: on Res + = ----------------------------";
262 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
263 ("Test", ["sqroot-test","univariate","equation","test"],
264 ["Test","squ-equ-test-subpbl1"]))];
265 Iterator 1; moveActiveRoot 1;
266 autoCalculate 1 CompleteCalcHead;
267 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
268 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
269 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*-1 + x*);
271 replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
272 val ((pt,_),_) = get_calc 1;
273 val str = pr_ctree pr_short pt;
275 (* before AK110725 this was
276 ". ----- pblobj -----\n
278 2. x + 1 + -1 * 2 = 0\n
279 2.1. x + 1 + -1 * 2 = 0\n
280 2.2. 1 + x + -1 * 2 = 0\n
281 2.3. 1 + (x + -1 * 2) = 0\n
282 2.4. 1 + (x + -2) = 0\n
283 2.5. 1 + (x + -2 * 1) = 0\n
284 2.6. 1 + x + -2 * 1 = 0\n";
287 ". ----- pblobj -----\n"^
289 "2. x + 1 + -1 * 2 = 0\n"^
290 "2.1. x + 1 + -1 * 2 = 0\n"^
291 "2.2. 1 + x + -1 * 2 = 0\n"^
292 "2.3. 1 + (x + -1 * 2) = 0\n"^
293 "2.4. 1 + (x + -2) = 0\n"^
294 "2.5. 1 + (x + -2 * 1) = 0\n"^
295 "2.6. 1 + x + -2 * 1 = 0\n" then()
296 else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
298 autoCalculate 1 CompleteCalc;
299 val ((pt,pos as (p,_)),_) = get_calc 1;
300 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst) (get_obj g_result pt p) then()
301 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
304 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
305 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
306 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
308 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
309 ("Test", ["sqroot-test","univariate","equation","test"],
310 ["Test","squ-equ-test-subpbl1"]))];
311 Iterator 1; moveActiveRoot 1;
312 autoCalculate 1 CompleteCalcHead;
313 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
314 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
316 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
317 val ((pt,_),_) = get_calc 1;
318 val str = pr_ctree pr_short pt;
320 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 ()
321 else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
322 autoCalculate 1 CompleteCalc;
323 val ((pt,pos as (p,_)),_) = get_calc 1;
324 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
325 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
328 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
329 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
330 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
332 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
333 ("Test", ["sqroot-test","univariate","equation","test"],
334 ["Test","squ-equ-test-subpbl1"]))];
335 Iterator 1; moveActiveRoot 1;
336 autoCalculate 1 CompleteCalcHead;
337 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
339 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
340 val ((pt,_),_) = get_calc 1;
341 val str = pr_ctree pr_short pt;
343 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 ()
344 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
345 autoCalculate 1 CompleteCalc;
346 val ((pt,pos as (p,_)),_) = get_calc 1;
347 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
348 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
351 "--------- replaceFormula: cut calculation -----------------------";
352 "--------- replaceFormula: cut calculation -----------------------";
353 "--------- replaceFormula: cut calculation -----------------------";
355 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
356 ("Test", ["sqroot-test","univariate","equation","test"],
357 ["Test","squ-equ-test-subpbl1"]))];
358 Iterator 1; moveActiveRoot 1;
359 autoCalculate 1 CompleteCalc;
360 moveActiveRoot 1; moveActiveDown 1;
361 if get_pos 1 1 = ([1], Frm) then ()
362 else error "inform.sml: diff.behav. cut calculation 1";
364 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
365 val ((pt,p),_) = get_calc 1;
366 val str = pr_ctree pr_short pt;
368 if p = ([1], Res) then ()
369 else error "inform.sml: diff.behav. cut calculation 2";
372 (* 040307 copied from informtest.sml; ... old version
373 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
374 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
375 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
378 val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
379 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
380 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
381 "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos (alpha::real)]",
382 (*^^^ these are the elements for the root-problem (in variants)*)
383 (*vvv these are elements required for subproblems*)
384 "boundVariable a","boundVariable b","boundVariable alpha",
385 "interval {x::real. 0 <= x & x <= 2*r}",
386 "interval {x::real. 0 <= x & x <= 2*r}",
387 "interval {x::real. 0 <= x & x <= pi}",
388 "errorBound (eps=(0::real))"]
389 (*specifying is not interesting for this example*)
390 val spec = ("DiffApp", ["maximum_of","function"],
391 ["DiffApp","max_by_calculus"]);
392 (*the empty model with descriptions for user-guidance by Model_Problem*)
393 val empty_model = [Given ["fixedValues []"],
394 Find ["maximum", "valuesFor"],
395 Relate ["relations []"]];
398 (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
399 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
400 (*val nxt = ("Model_Problem", ...*)
401 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
403 val (p,_,f,nxt,_,pt) = me nxt p c pt;
404 (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
405 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
407 (0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
408 (0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
409 (0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
410 (0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
412 (*the empty CalcHead is checked w.r.t the model and re-established as such*)
413 val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, e_spec);
414 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
415 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";
417 (*there is one input to the model (could be more)*)
419 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
420 Find ["maximum", "valuesFor"],
421 Relate ["relations"]], Pbl, e_spec);
422 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
423 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 ()
424 else error "informtest.sml: diff.behav. max 2";
426 (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
427 val (b,pt''''',ocalhd) =
428 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
429 Find ["maximum A", "valuesFor [a,b]"],
430 Relate ["relations [A=a*b, a/2=r*sin alpha, \
431 \b/2=r*cos alpha]"]], Pbl, e_spec);
432 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
433 if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
435 (*this input is complete in variant 1 (variant 3 does not work yet)*)
436 val (b,pt''''',ocalhd) =
437 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
438 Find ["maximum A", "valuesFor [a,b]"],
439 Relate ["relations [A=a*b, \
440 \(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
442 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
444 modifycalcheadOK2xml 111 (bool2str b) ocalhd;
448 "--------- syntax error ------------------------------------------";
449 "--------- syntax error ------------------------------------------";
450 "--------- syntax error ------------------------------------------";
452 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
453 ("Test", ["sqroot-test","univariate","equation","test"],
454 ["Test","squ-equ-test-subpbl1"]))];
455 Iterator 1; moveActiveRoot 1;
456 autoCalculate 1 CompleteCalcHead;
457 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
458 autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
460 appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
461 val ((pt,_),_) = get_calc 1;
462 val str = pr_ctree pr_short pt;
464 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
465 else error "inform.sml: diff.behav.appendFormula: syntax error";
468 "--------- CAS-command on ([],Pbl) -------------------------------";
469 "--------- CAS-command on ([],Pbl) -------------------------------";
470 "--------- CAS-command on ([],Pbl) -------------------------------";
471 val (p,_,f,nxt,_,pt) =
472 CalcTreeTEST [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
473 val ifo = "solve(x+1=2,x)";
474 val (_,(_,c,(pt,p))) = Step_Solve.by_term (pt,p) "solve(x+1=2,x)";
476 val nxt = (Apply_Method ["Test","squ-equ-test-subpbl1"]);
477 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
478 if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
479 else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
482 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
483 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
484 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
486 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
489 replaceFormula 1 "solve(x+1=2,x)";
490 autoCalculate 1 CompleteCalc;
491 val ((pt,p),_) = get_calc 1;
493 if p = ([], Res) then ()
494 else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
497 "--------- inform [rational,simplification] ----------------------";
498 "--------- inform [rational,simplification] ----------------------";
499 "--------- inform [rational,simplification] ----------------------";
501 CalcTree [(["Term (a * x / (b * x) + c * x / (d * x) + e / f)", "normalform N"],
502 ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
503 Iterator 1; moveActiveRoot 1;
504 autoCalculate 1 CompleteCalcHead;
506 "--- (-1) give a preview on the calculation without any input";
508 autoCalculate 1 CompleteCalc;
509 val ((pt, p), _) = get_calc 1;
512 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
513 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
514 (([1], Res), a / b + c / d + e / f), <--- (1) input arbitrary
515 (([2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
516 (([3], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
517 (([4], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)), <--- (2) input next
518 (([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))] <--- (3) is also final result
521 "--- (0) user input as the *first* step does not work, thus impdo at least 1 step";
522 autoCalculate 1 (Steps 1);
523 autoCalculate 1 (Steps 1);
524 val ((pt, p), _) = get_calc 1;
527 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
528 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
529 (([1], Res), a / b + c / d + e / f)]
531 "--- (1) input an arbitrary next formula";
532 appendFormula 1 "((a * d) + (c * b)) / (b * d) + e / f" (*|> Future.join*);
533 val ((pt, p), _) = get_calc 1;
536 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
537 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
538 (([1], Res), a / b + c / d + e / f),
539 (([2,1], Frm), a / b + c / d + e / f),
540 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
541 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
542 (([2], Res), (a * d + c * b) / (b * d) + e / f)]
544 val ((pt,p),_) = get_calc 1;
545 if p = ([2], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
546 else error ("inform.sml: [rational,simplification] 1");
548 "--- (2) input the next formula that would be presented by mat-engine";
549 (* generate a preview:
550 autoCalculate 1 (Steps 1);
551 val ((pt, p), _) = get_calc 1;
554 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
555 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
556 (([1], Res), a / b + c / d + e / f),
557 (([2,1], Frm), a / b + c / d + e / f),
558 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
559 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
560 (([2], Res), (a * d + c * b) / (b * d) + e / f),
561 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))] <--- input this
563 appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
564 val ((pt, p), _) = get_calc 1;
567 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
568 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
569 (([1], Res), a / b + c / d + e / f),
570 (([2,1], Frm), a / b + c / d + e / f),
571 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
572 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
573 (([2], Res), (a * d + c * b) / (b * d) + e / f),
574 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
576 if p = ([3], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
577 else error ("inform.sml: [rational,simplification] 2");
579 "--- (3) input the exact final result";
580 appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
581 val ((pt, p), _) = get_calc 1;
584 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
585 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
586 (([1], Res), a / b + c / d + e / f),
587 (([2,1], Frm), a / b + c / d + e / f),
588 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
589 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
590 (([2], Res), (a * d + c * b) / (b * d) + e / f),
591 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
592 (([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
593 (([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
594 (([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
595 (([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
597 if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
598 else error ("inform.sml: [rational,simplification] 3");
600 "--- (4) finish the calculation + check the postcondition (in the future)";
601 autoCalculate 1 CompleteCalc;
602 val ((pt, p), _) = get_calc 1;
603 val (t, asm) = get_obj g_result pt [];
604 if term2str t = "(a * d * f + b * c * f + b * d * e) / (b * d * f)" andalso
605 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\"]"
606 then () else error "inform [rational,simplification] changed at end";
609 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
610 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
611 (([1], Res), a / b + c / d + e / f),
612 (([2,1], Frm), a / b + c / d + e / f),
613 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
614 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
615 (([2], Res), (a * d + c * b) / (b * d) + e / f),
616 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
617 (([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
618 (([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
619 (([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
620 (([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
621 (([5], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
622 (([6], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)),
623 (([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))]
627 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
628 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
629 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
630 val t = str2term "Diff (x^^^2 + x + 1, x)";
631 case t of Const ("Diff.Diff", _) $ _ => ()
633 error "diff.sml behav.changed for CAS Diff (..., x)";
635 "-----------------------------------------------------------------";
636 (*1>*)reset_states ();
637 (*2>*)CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
638 (*3>*)Iterator 1;moveActiveRoot 1;
639 "----- here the Headline has been finished";
640 (*4>*)moveActiveFormula 1 ([],Pbl);
641 (*5>*)replaceFormula 1 "Diff (x^2 + x + 1, x)";
642 val ((pt,_),_) = get_calc 1;
643 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
645 val (SOME istate, NONE) = loc;
646 (*default_print_depth 5;*)
647 writeln"-----------------------------------------------------------";
649 writeln (itms2str_ ctxt probl);
650 writeln (itms2str_ ctxt meth);
651 writeln (istate2str (fst istate));
653 refFormula 1 ([],Pbl) (*--> correct CalcHead*);
654 (*081016 NOT necessary (but leave it in Java):*)
655 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
656 "----- here the CalcHead has been completed --- ONCE MORE ?????";
658 (***difference II***)
659 val ((pt,p),_) = get_calc 1;
660 (*val p = ([], Pbl)*)
661 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
663 val (SOME istate, NONE) = loc;
664 (*default_print_depth 5;*) writeln (istate2str (fst istate)); (*default_print_depth 3;*)
667 ??.empty, Sundef, false)*)
668 (*default_print_depth 5;*) spec; (*default_print_depth 3;*)
670 ["derivative_of", "function"],
671 ["diff", "differentiate_on_R"]) : spec*)
672 writeln (itms2str_ ctxt probl);
674 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
675 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
676 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
677 writeln (itms2str_ ctxt meth);
679 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
680 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
681 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
682 writeln"-----------------------------------------------------------";
683 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
684 (*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
685 autoCalculate 1 CompleteCalc;
686 val ((pt,p),_) = get_calc 1;
687 val Form res = (#1 o pt_extract) (pt, ([],Res));
689 if p = ([], Res) andalso term2str res = "1 + 2 * x" then ()
690 else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
693 "--------- Take as 1st tac, start from exp -----------------------";
694 "--------- Take as 1st tac, start from exp -----------------------";
695 "--------- Take as 1st tac, start from exp -----------------------";
696 (*the following input is copied from BridgeLog Java <==> SML,
697 omitting unnecessary inputs*)
698 (*1>*)reset_states ();
699 (*2>*)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac_Knowledge",["derivative_of","function"],["diff","differentiate_on_R"]))];
700 (*3>*)Iterator 1; moveActiveRoot 1;
702 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
703 (***difference II***)
704 val ((pt,_),_) = get_calc 1;
705 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
707 val (SOME istate, NONE) = loc;
708 (*default_print_depth 5;*) writeln (istate2str (fst istate)); (*default_print_depth 3;*)
711 ??.empty, Sundef, false)*)
712 (*default_print_depth 5;*) spec; (*default_print_depth 3;*)
714 ["derivative_of", "function"],
715 ["diff", "differentiate_on_R"]) : spec*)
716 writeln (itms2str_ ctxt probl);
718 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
719 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
720 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
721 writeln (itms2str_ ctxt meth);
723 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
724 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
725 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
726 writeln"-----------------------------------------------------------";
727 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
728 autoCalculate 1 (Steps 1);
729 val ((pt,p),_) = get_calc 1;
730 val Form res = (#1 o pt_extract) (pt, p);
731 if term2str res = "d_d x (x ^^^ 2 + x + 1)" then ()
732 else error "diff.sml Diff (x^2 + x + 1, x) from exp";
735 "--------- init_form, start with <NEW> (CAS input) ---------------";
736 "--------- init_form, start with <NEW> (CAS input) ---------------";
737 "--------- init_form, start with <NEW> (CAS input) ---------------";
739 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
740 (*[[from sml: > @@@@@begin@@@@@
742 [[from sml: <CALCTREE>
743 [[from sml: <CALCID> 1 </CALCID>
744 [[from sml: </CALCTREE>
745 [[from sml: @@@@@end@@@@@*)
747 (*[[from sml: > @@@@@begin@@@@@
749 [[from sml: <ADDUSER>
750 [[from sml: <CALCID> 1 </CALCID>
751 [[from sml: <USERID> 1 </USERID>
752 [[from sml: </ADDUSER>
753 [[from sml: @@@@@end@@@@@*)
755 (*[[from sml: > @@@@@begin@@@@@
757 [[from sml: <CALCITERATOR>
758 [[from sml: <CALCID> 1 </CALCID>
759 [[from sml: <POSITION>
760 [[from sml: <INTLIST>
761 [[from sml: </INTLIST>
762 [[from sml: <POS> Pbl </POS>
763 [[from sml: </POSITION>
764 [[from sml: </CALCITERATOR>
765 [[from sml: @@@@@end@@@@@*)
766 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
767 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
769 [[from sml: <GETELEMENTSFROMTO>
770 [[from sml: <CALCID> 1 </CALCID>
771 [[from sml: <FORMHEADS>
772 [[from sml: <CALCFORMULA>
773 [[from sml: <POSITION>
774 [[from sml: <INTLIST>
775 [[from sml: </INTLIST>
776 [[from sml: <POS> Pbl </POS>
777 [[from sml: </POSITION>
778 [[from sml: <FORMULA>
780 [[from sml: <ISA> ________________________________________________ </ISA>
781 [[from sml: </MATHML>
783 [[from sml: </FORMULA>
784 [[from sml: </CALCFORMULA>
785 [[from sml: </FORMHEADS>
786 [[from sml: </GETELEMENTSFROMTO>
787 [[from sml: @@@@@end@@@@@*)
788 refFormula 1 ([],Pbl);
789 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
791 [[from sml: <REFFORMULA>
792 [[from sml: <CALCID> 1 </CALCID>
793 [[from sml: <CALCHEAD status = "incorrect">
794 [[from sml: <POSITION>
795 [[from sml: <INTLIST>
796 [[from sml: </INTLIST>
797 [[from sml: <POS> Pbl </POS>
798 [[from sml: </POSITION>
801 [[from sml: <ISA> Problem (e_domID, [e_pblID]) </ISA>
802 [[from sml: </MATHML>
805 [[from sml: <GIVEN> </GIVEN>
806 [[from sml: <WHERE> </WHERE>
807 [[from sml: <FIND> </FIND>
808 [[from sml: <RELATE> </RELATE>
810 [[from sml: <BELONGSTO> Pbl </BELONGSTO>
811 [[from sml: <SPECIFICATION>
812 [[from sml: <THEORYID> e_domID </THEORYID>
813 [[from sml: <PROBLEMID>
814 [[from sml: <STRINGLIST>
815 [[from sml: <STRING> e_pblID </STRING>
816 [[from sml: </STRINGLIST>
817 [[from sml: </PROBLEMID>
818 [[from sml: <METHODID>
819 [[from sml: <STRINGLIST>
820 [[from sml: <STRING> e_metID </STRING>
821 [[from sml: </STRINGLIST>
822 [[from sml: </METHODID>
823 [[from sml: </SPECIFICATION>
824 [[from sml: </CALCHEAD>
825 [[from sml: </REFFORMULA>
826 [[from sml: @@@@@end@@@@@*)
827 moveActiveFormula 1 ([],Pbl);
828 (*[[from sml: > @@@@@begin@@@@@
830 [[from sml: <CALCITERATOR>
831 [[from sml: <CALCID> 1 </CALCID>
832 [[from sml: <POSITION>
833 [[from sml: <INTLIST>
834 [[from sml: </INTLIST>
835 [[from sml: <POS> Pbl </POS>
836 [[from sml: </POSITION>
837 [[from sml: </CALCITERATOR>
838 [[from sml: @@@@@end@@@@@*)
839 replaceFormula 1 "Simplify (1+2)";
840 (*[[from sml: > @@@@@begin@@@@@
842 [[from sml: <REPLACEFORMULA>
843 [[from sml: <CALCID> 1 </CALCID>
844 [[from sml: <CALCCHANGED>
845 [[from sml: <UNCHANGED>
846 [[from sml: <INTLIST>
847 [[from sml: </INTLIST>
848 [[from sml: <POS> Pbl </POS>
849 [[from sml: </UNCHANGED>
850 [[from sml: <DELETED>
851 [[from sml: <INTLIST>
852 [[from sml: </INTLIST>
853 [[from sml: <POS> Pbl </POS>
854 [[from sml: </DELETED>
855 [[from sml: <GENERATED>
856 [[from sml: <INTLIST>
857 [[from sml: </INTLIST>
858 [[from sml: <POS> Met </POS> DIFFERENCE: Pbl
859 [[from sml: </GENERATED>
860 [[from sml: </CALCCHANGED>
861 [[from sml: </REPLACEFORMULA>
862 [[from sml: @@@@@end@@@@@*)
863 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
877 <ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
884 getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
885 (*[[from sml: > @@@@@begin@@@@@
887 [[from sml: <SYSERROR>
888 [[from sml: <CALCID> 1 </CALCID>
889 [[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
890 [[from sml: </SYSERROR>
891 [[from sml: @@@@@end@@@@@*)
892 (*step into getFormulaeFromTo --- bug corrected...*)
894 "--------- build fun check_err_patt ------------------------------";
895 "--------- build fun check_err_patt ------------------------------";
896 "--------- build fun check_err_patt ------------------------------";
897 val subst = [(str2term "bdv", str2term "x")]: subst;
898 val rls = norm_Rational
899 val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
900 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
901 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "1 / 2");
903 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
904 rew_sub thy 1 [] e_rew_ord e_rls false [] (HOLogic.Trueprop $ pat) res;
905 if rewritten then NONE else SOME "e_errpatID";
907 val norm_res = case rewrite_set_ (Isac()) false rls res' of
909 | SOME (norm_res, _) => norm_res
911 val norm_inf = case rewrite_set_ (Isac()) false rls inf of
913 | SOME (norm_inf, _) => norm_inf;
918 val pat = parse_patt @{theory} "(?a + ?b)/?a = ?b";
919 val (res, inf) = (str2term "(2 + 3)/2", str2term "3");
920 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
921 then () else error "error patt example1 changed";
923 val pat = parse_patt @{theory} "(?a + ?b)/(?a + ?c) = ?b / ?c";
924 val (res, inf) = (str2term "(2 + 3)/(2 + 4)", str2term "3 / 4");
925 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
926 then () else error "error patt example2 changed";
928 val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
929 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
930 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
931 then () else error "error patt example3 changed";
933 val inf = str2term "1 / 2";
934 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
935 then () else error "error patt example3 changed";
937 "--------- build fun check_err_patt ?bdv -------------------------";
938 "--------- build fun check_err_patt ?bdv -------------------------";
939 "--------- build fun check_err_patt ?bdv -------------------------";
940 val subst = [(str2term "bdv", str2term "x")]: subst;
941 val t = str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))";
942 val SOME (t, _) = rewrite_set_inst_ thy false subst norm_diff t;
943 if term2str t = "2 * x + cos (x ^^^ 4) * 4 * x ^^^ 3" then ()
944 else error "build fun check_err_patt ?bdv changed 1";
947 val pat = parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)";
948 val (res, inf) = (str2term "2 * x + d_d x (sin (x ^^^ 4))", str2term "2 * x + cos (4 * x ^^^ 3)");
950 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
951 rew_sub thy 1 subst e_rew_ord e_rls false [] (HOLogic.Trueprop $ pat) res;
952 if term2str res' = "2 * x + cos (d_d x (x ^^^ 4))" andalso rewritten then ()
953 else error "build fun check_err_patt ?bdv changed 2";
955 val norm_res = case rewrite_set_inst_ (Isac()) false subst rls res' of
957 | SOME (norm_res, _) => norm_res;
958 if term2str norm_res = "2 * x + cos (4 * x ^^^ 3)" then ()
959 else error "build fun check_err_patt ?bdv changed 3";
961 val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of
963 | SOME (norm_inf, _) => norm_inf;
964 if term2str norm_inf = "2 * x + cos (4 * x ^^^ 3)" then ()
965 else error "build fun check_err_patt ?bdv changed 4";
968 if norm_res = norm_inf then ()
969 else error "build fun check_err_patt ?bdv changed 5";
971 if check_err_patt (res, inf) (subst: subst) ("errpatID": errpatID, pat) rls = SOME "errpatID"
972 then () else error "error patt example1 changed";
974 "--------- build fun check_error_patterns ------------------------";
975 "--------- build fun check_error_patterns ------------------------";
976 "--------- build fun check_error_patterns ------------------------";
978 (str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))",
979 str2term "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)");
980 val {errpats, nrls = rls, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
982 val env = [(str2term "v_v", str2term "x")];
984 [e_errpat, (*generalised for testing*)
985 ("chain-rule-diff-both",
986 [parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)",
987 parse_patt @{theory} "d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)",
988 parse_patt @{theory} "d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1)",
989 parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / ?u",
990 parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u"],
991 [@{thm diff_sin_chain}, @{thm diff_cos_chain}, @{thm diff_pow_chain},
992 @{thm diff_ln_chain}, @{thm diff_exp_chain}])]: errpat list;
993 case check_error_patterns (res, inf) (prog, env) (errpats, rls) of SOME _ => ()
994 | NONE => error "check_error_patterns broken";
997 "--------- embed fun check_error_patterns ------------------------";
998 "--------- embed fun check_error_patterns ------------------------";
999 "--------- embed fun check_error_patterns ------------------------";
1002 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1003 ("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1006 autoCalculate 1 CompleteCalcHead;
1007 autoCalculate 1 (Steps 1);
1008 autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1009 (*autoCalculate 1 (Steps 1);([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)*)
1011 "~~~~~ fun appendFormula , args:"; val (cI, (ifo:cterm')) = (1, "d_d x (x ^ 2) + cos (4 * x ^ 3)");
1012 "~~~~~ fun appendFormula' , args:"; val (cI, (ifo: Rule.cterm')) = (cI, ifo);
1013 val cs = get_calc cI
1014 val pos = get_pos cI 1;
1015 (*+*)if pos = ([1], Res) then () else error "inform with (positive) check_error_patterns broken 1";
1016 val ("ok", cs' as (_, _, ptp)) = (*case*) Step.do_next pos cs (*of*);
1017 (*case*) Step_Solve.by_term ptp (encode ifo) (*of*); (*ERROR WAS: "no derivation found"*)
1018 "~~~~~ fun Step_Solve.by_term , args:"; val (((*next_*)cs as (_, _, (pt, pos as (p, _))): Chead.calcstate'), istr)
1019 = (cs', (encode ifo));
1020 val ctxt = get_ctxt pt pos (*see TODO.thy*)
1021 val SOME f_in = (*case*) TermC.parse (Celem.assoc_thy "Isac_Knowledge") istr (*of*);
1022 val f_in = Thm.term_of f_in
1023 val pos_pred = lev_back' pos
1024 val f_pred = Ctree.get_curr_formula (pt, pos_pred);
1025 (*if*) f_pred = f_in; (*else*)
1026 val NONE = (*case*) In_Chead.cas_input f_in (*of*);
1027 (*old* )val (_, _, metID) = get_obj g_spec pt (par_pblobj pt p)
1028 (*old*)val {scr = prog, ...} = Specify.get_met metID
1029 (*old*)val istate = get_istate_LI pt pos
1030 (*old*)val ctxt = get_ctxt pt pos
1032 val LI.Not_Derivable =
1033 (*case*) LI.locate_input_term (pt, pos) f_in (*of*);
1034 val pp = Ctree.par_pblobj pt p
1035 val (errpats, nrls, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of
1036 {errpats, nrls, scr = Rule.Prog prog, ...} => (errpats, nrls, prog)
1037 | _ => error "inform: uncovered case of get_met"
1039 (*+*)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\"]]"
1040 (*+*)then () else error "inform with (positive) check_error_patterns broken 3";
1042 val {env, ...} = Ctree.get_istate_LI pt pos |> Istate.the_pstate
1044 (*+*)if term2str f_pred = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" andalso
1045 (*+*) term2str f_in = "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)"
1046 (*+*)then () else error "inform with (positive) check_error_patterns broken 2";
1048 val SOME "chain-rule-diff-both" = (*case*) Error_Pattern.check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) (*of*);
1051 (*+*)val (_, _, ptp') = cs';
1052 case Step_Solve.by_term ptp' (encode ifo) of
1053 ("error pattern #chain-rule-diff-both#", calcstate') => ()
1054 | _ => error "inform with (positive) check_error_patterns broken"
1057 "--------- embed fun find_fillpatterns ---------------------------";
1058 "--------- embed fun find_fillpatterns ---------------------------";
1059 "--------- embed fun find_fillpatterns ---------------------------";
1062 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1063 ("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1066 autoCalculate 1 CompleteCalcHead;
1067 autoCalculate 1 (Steps 1);
1068 autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1069 appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (*|> Future.join*);
1070 (*<CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>*)
1072 <CALCMESSAGE> no derivation found </CALCMESSAGE>*)
1074 "~~~~~ fun findFillpatterns, args:"; val (cI, errpatID) = (1, "chain-rule-diff-both");
1075 val ((pt, _), _) = get_calc cI
1076 val pos = get_pos cI 1;
1077 "~~~~~ fun find_fillpatterns , args:"; val ((pt, pos as (p, _)), errpatID) = ((pt, pos), errpatID);
1078 val f_curr = Ctree.get_curr_formula (pt, pos);
1079 val pp = Ctree.par_pblobj pt p
1080 val (errpats, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of
1081 {errpats, scr = Rule.Prog prog, ...} => (errpats, prog)
1082 | _ => error "find_fillpatterns: uncovered case of get_met"
1083 val {env, ...} = Ctree.get_istate_LI pt pos |> Istate.the_pstate
1084 val subst = Rtools.get_bdv_subst prog env
1085 val errpatthms = errpats
1086 |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
1087 |> map (#3: errpat -> thm list)
1090 case map (get_fillpats subst f_curr errpatID) errpatthms |> flat of
1091 ("fill-d_d-arg", tm, thm, subs_opt) :: _ => if term2str tm =
1092 "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1093 then () else error "find_fillpatterns changed 1a"
1094 | _ => error "find_fillpatterns changed 1b"
1096 "~~~~~ fun get_fillpats, args:"; val (subst, form, errpatID, thm) =
1097 (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
1098 val thmDeriv = Thm.get_name_hint thm
1099 val (part, thyID) = thy_containing_thm thmDeriv
1100 val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]
1101 val Hthm {fillpats, ...} = get_the theID
1102 val some = map (get_fillform subst (thm, form) errpatID) fillpats;
1104 case some |> filter is_some |> map the of
1105 ("fill-d_d-arg", tm, thm, subsopt) :: _ => if term2str tm =
1106 "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1107 then () else error "find_fillpatterns changed 2a"
1108 | _ => error "find_fillpatterns changed 2b"
1110 "~~~~~ fun get_fillform, args:";
1111 val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
1112 (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
1113 val (form', _, _, rewritten) =
1114 rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (HOLogic.Trueprop $ pat) form;
1116 if term2str form' = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
1117 else error "find_fillpatterns changed 3";
1119 "~~~~~ to findFillpatterns return val:"; val (fillpats) =
1120 (map (get_fillpats (subs_opt, subst) f_curr errpatID) errpatthms |> flat) (*only from "hd errpatthms"*);
1122 "vvv--- dropped this code WN120730";
1123 val msg = "fill patterns " ^
1124 ((map ((apsnd term2str) o quad2pair) fillpats) |> map pair2str_ |> strs2str_);
1126 "fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1127 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" ^
1128 "#fill-both-args#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1129 " =\nd_d x (x ^^^ 2) + cos ?_dummy_2 * d_d x ?_dummy_3" ^
1130 "#fill-d_d#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1131 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1 x (x ^^^ 4)" ^
1132 "#fill-inner-deriv#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1133 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1" ^
1134 "#fill-all#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) = d_d x (x ^^^ 2) + ?_dummy_1#";
1135 "^^^--- dropped this code WN120730";
1137 if (map #1 fillpats) =
1138 ["fill-d_d-arg", "fill-both-args", "fill-d_d", "fill-inner-deriv", "fill-all"]
1139 then () else error "find_fillpatterns changed 4b";
1142 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1143 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1144 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1147 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1148 ("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1151 autoCalculate 1 CompleteCalcHead;
1152 autoCalculate 1 (Steps 1);
1153 autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1154 appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (*|> Future.join*); (*<<<<<<<=========================*)
1155 (* the check for errpat is maximally liberal (whole term modulo "nrls" from "type met"),
1156 would recognize "cos (4 * x ^ (4 - 1)) + 2 * x" as well.
1157 results in <CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>
1158 instead of <CALCMESSAGE> no derivation found </CALCMESSAGE> *)
1159 val ((pt,pos), _) = get_calc 1;
1160 val p = get_pos 1 1;
1161 val (Form f, _, asms) = pt_extract (pt, p);
1163 if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
1164 case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1165 ("diff_sum", thm)) =>
1166 if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1167 else error "embed fun get_fillform changed 11"
1168 | _ => error "embed fun get_fillform changed 12"
1169 else error "embed fun get_fillform changed 13";
1171 findFillpatterns 1 "chain-rule-diff-both"; (*<<<<<<<=================================*)
1172 (*<CALCMESSAGE> fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =
1173 d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1#fill-both-args#...#...#... *)
1174 val ((pt,pos),_) = get_calc 1;
1175 val p = get_pos 1 1;
1177 val (Form f, _, asms) = pt_extract (pt, p);
1178 if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
1179 case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1180 ("diff_sum", thm)) =>
1181 if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1182 else error "embed fun get_fillform changed 21"
1183 | _ => error "embed fun get_fillform changed 22"
1184 else error "embed fun get_fillform changed 23";
1186 requestFillformula 1 ("chain-rule-diff-both", "fill-both-args");(*<<<<<<<============*)
1187 (*<AUTOCALC> ([1], Res) ([2], Res) ([2], Res) </AUTOCALC>*)
1188 val ((pt,pos),_) = get_calc 1;
1189 val p = get_pos 1 1;
1190 val (Form f, _, asms) = pt_extract (pt, p);
1191 if p = ([1], Res) andalso existpt [2] pt
1192 andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"
1193 then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1194 ("diff_sum", thm)) =>
1195 if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1196 else error "embed fun get_fillform changed 31"
1197 | _ => error "embed fun get_fillform changed 32"
1198 else error "embed fun get_fillform changed 33";
1200 (* input a formula which exactly fills the gaps in a "fillformula"
1201 presented to the learner immediately before by "requestFillformula (errpatID, fillpatID)":
1202 errpatID: lhs of the respective thm = lhs of fillformula with fillpatID.
1203 the respective thm is in the ctree ................
1205 "~~~~~ fun inputFillFormula, args:"; val (cI, ifo) =
1206 (1, "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)");
1207 val ((pt, _), _) = get_calc cI
1208 val pos = get_pos cI 1;
1210 "~~~~~ fun is_exactly_equal, args:"; val ((pt, pos as (p, p_)), istr) = ((pt, pos), ifo);
1211 val SOME ifo = parseNEW (assoc_thy "Isac_Knowledge" |> thy2ctxt) istr
1213 val tac = get_obj g_tac pt p';
1214 val Rewrite_Inst ([bbb as "(''bdv'', x)"], ("diff_sin_chain", ttt)) = tac;
1215 if (term2str o Thm.prop_of) ttt = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
1216 else error "inputFillFormula changed 10";
1217 val Appl rew = applicable_in pos pt tac;
1218 val Rewrite_Inst' (_, _, _, _, _, _, _, (res, _)) = rew;
1220 "~~~~~ to inputFillFormula return val:"; val ("ok", tac) = ("ok", tac);
1221 val ("ok", (_, c, ptp as (_,p'))) = Step.by_tactic tac (pt, pos);
1222 upd_calc cI (ptp, []);
1224 autocalculateOK2xml cI pos (if null c then p' else last_elem c) p';
1226 "~~~~~ final check:";
1227 val ((pt, _),_) = get_calc 1;
1228 val p = get_pos 1 1;
1229 val (Form f, _, asms) = pt_extract (pt, p);
1230 if p = ([2], Res) andalso term2str f = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)"
1231 then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1232 ("diff_sin_chain", thm)) =>
1233 if (term2str o Thm.prop_of) thm = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
1234 else error "inputFillFormula changed 111"
1235 | _ => error "inputFillFormula changed 112"
1236 else error "inputFillFormula changed 113";
1238 "--------- fun appl_adds -----------------------------------------";
1239 "--------- fun appl_adds -----------------------------------------";
1240 "--------- fun appl_adds -----------------------------------------";
1241 (* val (dI, oris, ppc, pbt, selct::ss) =
1242 (dI, pors, probl, ppc, map itms2fstr probl);
1245 (* val (dI, oris, ppc, pbt, (selct::ss))=
1246 (#1 (some_spec ospec spec), oris, []:itm list,
1247 ((#ppc o get_pbt) (#2 (some_spec ospec spec))),(imodel2fstr imodel));
1248 val iii = appl_adds dI oris ppc pbt (selct::ss);
1249 tracing(itms2str_ thy iii);
1251 val itm = appl_add' dI oris ppc pbt selct;
1252 val ppc = insert_ppc' itm ppc;
1254 val _::selct::ss = (selct::ss);
1255 val itm = appl_add' dI oris ppc pbt selct;
1256 val ppc = insert_ppc' itm ppc;
1258 val _::selct::ss = (selct::ss);
1259 val itm = appl_add' dI oris ppc pbt selct;
1260 val ppc = insert_ppc' itm ppc;
1261 tracing(itms2str_ thy ppc);
1263 val _::selct::ss = (selct::ss);
1264 val itm = appl_add' dI oris ppc pbt selct;
1265 val ppc = insert_ppc' itm ppc;
1267 "--------- fun concat_deriv --------------------------------------";
1268 "--------- fun concat_deriv --------------------------------------";
1269 "--------- fun concat_deriv --------------------------------------";
1271 val ({rew_ord, erls, rules,...}, fo, ifo) =
1272 (rep_rls Test_simplify, str2term "x+1+ -1*2=0", str2term "-2*1+(x+1)=0");
1273 (tracing o trtas2str) fod';
1275 (x + 1 + -1 * 2 = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (x + 1) = 0, []))","
1276 (-1 * 2 + (x + 1) = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (1 + x) = 0, []))","
1277 (-1 * 2 + (1 + x) = 0, Thm ("radd_left_commute","?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (-1 * 2 + x) = 0, []))","
1278 (1 + (-1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))","-1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]
1280 (tracing o trtas2str) (map rev_deriv' rifod');
1282 (1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))","-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))","
1283 (1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute","?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))","
1284 (-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute","?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]
1287 "--------- handle an input formula -------------------------------";
1288 "--------- handle an input formula -------------------------------";
1289 "--------- handle an input formula -------------------------------";
1291 Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:
1292 Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden,
1293 wenn Abteilungen nur auf gleichem Level gesucht werden ?
1296 Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml
1298 ------------------------------------------------------------------------------
1299 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
1300 ------------------------------------------------------------------------------
1301 1. "5 * x / (x - 2) - x / (x + 2) = 4"
1303 4. "12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalise", "poly"..
1305 4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..
1307 4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"
1310 ------------------------------------------------------------------------------
1311 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
1313 (4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
1314 ------------------------------------------------------------------------------
1317 ------------------------------------------------------------------------------
1318 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
1319 ------------------------------------------------------------------------------
1320 1. "x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) = 1 / x"
1322 4. "(3 + (-1 * x + x ^^^ 2)) * x = 1 * (9 * x + (x ^^^ 3 + -6 * x ^^^ 2))"
1323 Subproblem["normalise", "polynomial", "univariate"..
1325 4.4. "-6 * x + 5 * x ^^^ 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..
1327 4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
1328 4.4.5. "[x = 0, x = 6 / 5]"
1330 5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
1332 ------------------------------------------------------------------------------
1333 (1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]
1335 (4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]
1336 ------------------------------------------------------------------------------
1339 ------------------------------------------------------------------------------
1340 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
1341 ------------------------------------------------------------------------------
1342 1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"
1344 6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"
1345 Subproblem["sq", "rootX", "univariate", "equation"]
1347 6.6. "144 + 288 * x + 144 * x ^^^ 2 = 144 + x ^^^ 2 + 288 * x + 143 * x ^^^ 2"
1348 Subproblem["normalise", "polynomial", "univariate", "equation"]
1350 6.6.3 "0 = 0" Subproblem["degree_0", "polynomial", "univariate", "equation"]
1352 6.6.3.2 "UniversalList"
1353 ------------------------------------------------------------------------------
1354 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]
1356 (6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]
1357 ------------------------------------------------------------------------------
1359 (*sh. comments auf 498*)
1360 "--------- fun dropwhile' ----------------------------------------";
1361 "--------- fun dropwhile' ----------------------------------------";
1362 "--------- fun dropwhile' ----------------------------------------";
1364 fun equal a b = a=b;
1365 val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];
1366 val r_foder = rev foder; val r_ifoder = rev ifoder;
1367 dropwhile' equal r_foder r_ifoder;
1368 > vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list
1370 val foder = [3,4,5]; val ifoder = [11,12,3,4,5];
1371 val r_foder = rev foder; val r_ifoder = rev ifoder;
1372 dropwhile' equal r_foder r_ifoder;
1373 > val it = ([3], [3, 12, 11]) : int list * int list
1375 val foder = [5]; val ifoder = [11,12,3,4,5];
1376 val r_foder = rev foder; val r_ifoder = rev ifoder;
1377 dropwhile' equal r_foder r_ifoder;
1378 > val it = ([5], [5, 4, 3, 12, 11]) : int list * int list
1380 val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];
1381 val r_foder = rev foder; val r_ifoder = rev ifoder;
1382 dropwhile' equal r_foder r_ifoder;
1383 > *** dropwhile': did not start with equal elements*)