1 (* Title: tests on inform.sml
2 Author: Walther Neuper 060225,
3 (c) due to copyright terms
5 use"../smltest/ME/inform.sml";
9 "-----------------------------------------------------------------";
10 "table of contents -----------------------------------------------";
11 "-----------------------------------------------------------------";
12 "appendForm with miniscript with mini-subpbl:";
13 "--------- appendFormula: on Res + equ_nrls ----------------------";
14 "--------- appendFormula: on Frm + equ_nrls ----------------------";
15 "--------- appendFormula: on Res + NO deriv ----------------------";
16 "--------- appendFormula: on Res + late deriv --------------------";
17 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
18 "replaceForm with miniscript with mini-subpbl:";
19 "--------- replaceFormula: on Res + = ----------------------------";
20 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
21 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
22 "--------- replaceFormula: cut calculation -----------------------";
23 "--------- replaceFormula: cut calculation -----------------------";
24 (* 040307 copied from informtest.sml ... old versions
25 "--------- maximum-example, UC: Modeling / modifyCalcHead --------";*)
26 "--------- syntax error ------------------------------------------";
28 "--------- CAS-command on ([],Pbl) -------------------------------";
29 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
30 "--------- inform [rational,simplification] ----------------------";
31 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
32 "--------- Take as 1st tac, start from exp -----------------------";
33 "--------- init_form, start with <NEW> (CAS input) ---------------";
34 "--------- build fun check_err_patt ------------------------------";
35 "--------- build fun check_err_patt ?bdv -------------------------";
36 "--------- build fun check_error_patterns ------------------------";
37 "--------- embed fun check_error_patterns ------------------------";
38 "--------- build fun get_fillpats --------------------------------";
39 "--------- embed fun find_fillpatterns ---------------------------";
40 "--------- build fun is_exactly_equal, inputFillFormula ----------";
41 "--------- fun appl_adds -----------------------------------------";
42 "--------- fun concat_deriv --------------------------------------";
43 "--------- handle an input formula -------------------------------";
44 "--------- fun dropwhile' ----------------------------------------";
45 "-----------------------------------------------------------------";
46 "-----------------------------------------------------------------";
47 "-----------------------------------------------------------------";
50 "--------- appendFormula: on Res + equ_nrls ----------------------";
51 "--------- appendFormula: on Res + equ_nrls ----------------------";
52 "--------- appendFormula: on Res + equ_nrls ----------------------";
53 val Prog sc = (#scr o get_met) ["Test","squ-equ-test-subpbl1"];
54 (writeln o term2str) sc;
55 val Prog sc = (#scr o get_met) ["Test","solve_linear"];
56 (writeln o term2str) sc;
59 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
60 ("Test", ["sqroot-test","univariate","equation","test"],
61 ["Test","squ-equ-test-subpbl1"]))];
62 Iterator 1; moveActiveRoot 1;
63 autoCalculate 1 CompleteCalcHead;
64 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
65 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
67 appendFormula 1 "-2 * 1 + (1 + x) = 0" (*|> Future.join*); refFormula 1 (get_pos 1 1);
68 val ((pt,_),_) = get_calc 1;
69 val str = pr_ptree pr_short pt;
71 (". ----- pblobj -----\n" ^
73 "2. x + 1 + -1 * 2 = 0\n" ^
74 "2.1. x + 1 + -1 * 2 = 0\n" ^
75 "2.2. 1 + x + -1 * 2 = 0\n" ^
76 "2.3. 1 + (x + -1 * 2) = 0\n" ^
77 "2.4. 1 + (x + -2) = 0\n" ^
78 "2.5. 1 + (x + -2 * 1) = 0\n" ^
79 "2.6. 1 + x + -2 * 1 = 0\n" ) then ()
80 else error "inform.sml: diff.behav.appendFormula: on Res + equ 1";
82 moveDown 1 ([ ],Pbl); refFormula 1 ([1],Frm); (*x + 1 = 2*)
83 moveDown 1 ([1],Frm); refFormula 1 ([1],Res); (*x + 1 + -1 * 2 = 0*)
85 (*the seven steps of detailed derivation*)
86 moveDown 1 ([1 ],Res); refFormula 1 ([2,1],Frm);
87 moveDown 1 ([2,1],Frm); refFormula 1 ([2,1],Res);
88 moveDown 1 ([2,1],Res); refFormula 1 ([2,2],Res);
89 moveDown 1 ([2,2],Res); refFormula 1 ([2,3],Res);
90 moveDown 1 ([2,3],Res); refFormula 1 ([2,4],Res);
91 moveDown 1 ([2,4],Res); refFormula 1 ([2,5],Res);
92 moveDown 1 ([2,5],Res); refFormula 1 ([2,6],Res);
93 val ((pt,_),_) = get_calc 1;
94 if "-2 * 1 + (1 + x) = 0" = term2str (fst (get_obj g_result pt [2,6])) then()
95 else error "inform.sml: diff.behav.appendFormula: on Res + equ 2";
97 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
98 (* <ERROR> error in kernel </ERROR> ALREADY IN 2009-2*)
99 (*========== inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 =============
100 val (_,(tac,_,_)::_) = get_calc 1;
101 if tac = Rewrite_Set "Test_simplify" then ()
102 else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
103 ============ inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 ============*)
105 autoCalculate 1 CompleteCalc;
106 val ((pt,_),_) = get_calc 1;
107 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
108 else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
109 (* autoCalculate 1 CompleteCalc;
110 val ((pt,p),_) = get_calc 1;
111 (writeln o istates2str) (get_obj g_loc pt [ ]);
112 (writeln o istates2str) (get_obj g_loc pt [1]);
113 (writeln o istates2str) (get_obj g_loc pt [2]);
114 (writeln o istates2str) (get_obj g_loc pt [3]);
115 (writeln o istates2str) (get_obj g_loc pt [3,1]);
116 (writeln o istates2str) (get_obj g_loc pt [3,2]);
117 (writeln o istates2str) (get_obj g_loc pt [4]);
120 "----------------------------------------------------------";
122 val fod = make_deriv (@{theory "Isac"}) Atools_erls
123 ((#rules o rep_rls) Test_simplify)
124 (sqrt_right false (@{theory "Pure"})) NONE
125 (str2term "x + 1 + -1 * 2 = 0");
126 (writeln o trtas2str) fod;
128 val ifod = make_deriv (@{theory "Isac"}) Atools_erls
129 ((#rules o rep_rls) Test_simplify)
130 (sqrt_right false (@{theory "Pure"})) NONE
131 (str2term "-2 * 1 + (1 + x) = 0");
132 (writeln o trtas2str) ifod;
133 fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
134 val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
135 val der = fod' @ (map rev_deriv' rifod');
136 (writeln o trtas2str) der;
137 "----------------------------------------------------------";
140 "--------- appendFormula: on Frm + equ_nrls ----------------------";
141 "--------- appendFormula: on Frm + equ_nrls ----------------------";
142 "--------- appendFormula: on Frm + equ_nrls ----------------------";
144 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
145 ("Test", ["sqroot-test","univariate","equation","test"],
146 ["Test","squ-equ-test-subpbl1"]))];
147 Iterator 1; moveActiveRoot 1;
148 autoCalculate 1 CompleteCalcHead;
149 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
150 appendFormula 1 "2+ -1 + x = 2" (*|> Future.join*); refFormula 1 (get_pos 1 1);
152 moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (*x + 1 = 2*);
154 moveDown 1 ([1 ],Frm); refFormula 1 ([1,1],Frm);
155 moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res);
156 moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res);
157 moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res);
158 moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res);
159 moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res);
160 moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res);
161 val ((pt,_),_) = get_calc 1;
162 if "2 + -1 + x = 2" = term2str (fst (get_obj g_result pt [1,6])) then()
163 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
165 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
166 val (_,(tac,_,_)::_) = get_calc 1;
167 case tac of Rewrite_Set "norm_equation" => ()
168 | _ => error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
169 autoCalculate 1 CompleteCalc;
170 val ((pt,_),_) = get_calc 1;
171 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
172 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
175 "--------- appendFormula: on Res + NO deriv ----------------------";
176 "--------- appendFormula: on Res + NO deriv ----------------------";
177 "--------- appendFormula: on Res + NO deriv ----------------------";
179 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
180 ("Test", ["sqroot-test","univariate","equation","test"],
181 ["Test","squ-equ-test-subpbl1"]))];
182 Iterator 1; moveActiveRoot 1;
183 autoCalculate 1 CompleteCalcHead;
184 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
185 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
187 appendFormula 1 "x = 2" (*|> Future.join*);
188 val ((pt,p),_) = get_calc 1;
189 val str = pr_ptree pr_short pt;
191 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" andalso p = ([1], Res)
193 else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
195 fetchProposedTactic 1;
196 val (_,(tac,_,_)::_) = get_calc 1;
197 case tac of Rewrite_Set "Test_simplify" => ()
198 | _ => error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
199 autoCalculate 1 CompleteCalc;
200 val ((pt,_),_) = get_calc 1;
201 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
202 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
205 "--------- appendFormula: on Res + late deriv --------------------";
206 "--------- appendFormula: on Res + late deriv --------------------";
207 "--------- appendFormula: on Res + late deriv --------------------";
209 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
210 ("Test", ["sqroot-test","univariate","equation","test"],
211 ["Test","squ-equ-test-subpbl1"]))];
212 Iterator 1; moveActiveRoot 1;
213 autoCalculate 1 CompleteCalcHead;
214 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
215 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
217 appendFormula 1 "x = 1" (*|> Future.join*);
218 val ((pt,p),_) = get_calc 1;
219 val str = pr_ptree pr_short pt;
221 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)
222 then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
223 else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
225 fetchProposedTactic 1;
226 val (_,(tac,_,_)::_) = get_calc 1;
227 case tac of Check_Postcond ["LINEAR", "univariate", "equation", "test"] => ()
228 | _ => error "inform.sml: diff.behav.appendFormula: Res + late d 2";
229 autoCalculate 1 CompleteCalc;
230 val ((pt,_),_) = get_calc 1;
231 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
232 else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
235 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
236 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
237 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
239 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
240 ("Test", ["sqroot-test","univariate","equation","test"],
241 ["Test","squ-equ-test-subpbl1"]))];
242 Iterator 1; moveActiveRoot 1;
243 autoCalculate 1 CompleteCalcHead;
244 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
245 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
246 appendFormula 1 "[x = 3 + -2*1]" (*|> Future.join*);
247 val ((pt,p),_) = get_calc 1;
248 val str = pr_ptree pr_short pt;
250 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 ()
251 else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
252 autoCalculate 1 CompleteCalc;
253 val ((pt,p),_) = get_calc 1;
254 if "[x = 3 + -2 * 1]" = term2str (fst (get_obj g_result pt [])) then ()
255 (* ~~~~~~~~~~ simplify as last step in any script ?!*)
256 else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
259 "--------- replaceFormula: on Res + = ----------------------------";
260 "--------- replaceFormula: on Res + = ----------------------------";
261 "--------- replaceFormula: on Res + = ----------------------------";
263 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
264 ("Test", ["sqroot-test","univariate","equation","test"],
265 ["Test","squ-equ-test-subpbl1"]))];
266 Iterator 1; moveActiveRoot 1;
267 autoCalculate 1 CompleteCalcHead;
268 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
269 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
270 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*-1 + x*);
272 replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
273 val ((pt,_),_) = get_calc 1;
274 val str = pr_ptree pr_short pt;
276 (* before AK110725 this was
277 ". ----- pblobj -----\n
279 2. x + 1 + -1 * 2 = 0\n
280 2.1. x + 1 + -1 * 2 = 0\n
281 2.2. 1 + x + -1 * 2 = 0\n
282 2.3. 1 + (x + -1 * 2) = 0\n
283 2.4. 1 + (x + -2) = 0\n
284 2.5. 1 + (x + -2 * 1) = 0\n
285 2.6. 1 + x + -2 * 1 = 0\n";
288 ". ----- pblobj -----\n"^
290 "2. x + 1 + -1 * 2 = 0\n"^
291 "2.1. x + 1 + -1 * 2 = 0\n"^
292 "2.2. 1 + x + -1 * 2 = 0\n"^
293 "2.3. 1 + (x + -1 * 2) = 0\n"^
294 "2.4. 1 + (x + -2) = 0\n"^
295 "2.5. 1 + (x + -2 * 1) = 0\n"^
296 "2.6. 1 + x + -2 * 1 = 0\n" then()
297 else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
299 autoCalculate 1 CompleteCalc;
300 val ((pt,pos as (p,_)),_) = get_calc 1;
301 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst) (get_obj g_result pt p) then()
302 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
305 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
306 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
307 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
309 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
310 ("Test", ["sqroot-test","univariate","equation","test"],
311 ["Test","squ-equ-test-subpbl1"]))];
312 Iterator 1; moveActiveRoot 1;
313 autoCalculate 1 CompleteCalcHead;
314 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
315 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
317 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
318 val ((pt,_),_) = get_calc 1;
319 val str = pr_ptree pr_short pt;
321 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 ()
322 else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
323 autoCalculate 1 CompleteCalc;
324 val ((pt,pos as (p,_)),_) = get_calc 1;
325 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
326 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
329 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
330 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
331 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
333 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
334 ("Test", ["sqroot-test","univariate","equation","test"],
335 ["Test","squ-equ-test-subpbl1"]))];
336 Iterator 1; moveActiveRoot 1;
337 autoCalculate 1 CompleteCalcHead;
338 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
340 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
341 val ((pt,_),_) = get_calc 1;
342 val str = pr_ptree pr_short pt;
344 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 ()
345 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
346 autoCalculate 1 CompleteCalc;
347 val ((pt,pos as (p,_)),_) = get_calc 1;
348 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
349 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
352 "--------- replaceFormula: cut calculation -----------------------";
353 "--------- replaceFormula: cut calculation -----------------------";
354 "--------- replaceFormula: cut calculation -----------------------";
356 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
357 ("Test", ["sqroot-test","univariate","equation","test"],
358 ["Test","squ-equ-test-subpbl1"]))];
359 Iterator 1; moveActiveRoot 1;
360 autoCalculate 1 CompleteCalc;
361 moveActiveRoot 1; moveActiveDown 1;
362 if get_pos 1 1 = ([1], Frm) then ()
363 else error "inform.sml: diff.behav. cut calculation 1";
365 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
366 val ((pt,p),_) = get_calc 1;
367 val str = pr_ptree pr_short pt;
369 if p = ([1], Res) then ()
370 else error "inform.sml: diff.behav. cut calculation 2";
373 (* 040307 copied from informtest.sml; ... old version
374 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
375 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
376 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
379 val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
380 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
381 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
382 "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
383 (*^^^ these are the elements for the root-problem (in variants)*)
384 (*vvv these are elements required for subproblems*)
385 "boundVariable a","boundVariable b","boundVariable alpha",
386 "interval {x::real. 0 <= x & x <= 2*r}",
387 "interval {x::real. 0 <= x & x <= 2*r}",
388 "interval {x::real. 0 <= x & x <= pi}",
389 "errorBound (eps=(0::real))"]
390 (*specifying is not interesting for this example*)
391 val spec = ("DiffApp", ["maximum_of","function"],
392 ["DiffApp","max_by_calculus"]);
393 (*the empty model with descriptions for user-guidance by Model_Problem*)
394 val empty_model = [Given ["fixedValues []"],
395 Find ["maximum", "valuesFor"],
396 Relate ["relations []"]];
399 (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
400 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
401 (*val nxt = ("Model_Problem", ...*)
402 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
404 val (p,_,f,nxt,_,pt) = me nxt p c pt;
405 (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
406 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
408 (0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
409 (0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
410 (0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
411 (0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
413 (*the empty CalcHead is checked w.r.t the model and re-established as such*)
414 val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, e_spec);
415 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
416 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";
418 (*there is one input to the model (could be more)*)
420 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
421 Find ["maximum", "valuesFor"],
422 Relate ["relations"]], Pbl, e_spec);
423 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
424 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 ()
425 else error "informtest.sml: diff.behav. max 2";
427 (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
428 val (b,pt''''',ocalhd) =
429 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
430 Find ["maximum A", "valuesFor [a,b]"],
431 Relate ["relations [A=a*b, a/2=r*sin alpha, \
432 \b/2=r*cos alpha]"]], Pbl, e_spec);
433 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
434 if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
436 (*this input is complete in variant 1 (variant 3 does not work yet)*)
437 val (b,pt''''',ocalhd) =
438 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
439 Find ["maximum A", "valuesFor [a,b]"],
440 Relate ["relations [A=a*b, \
441 \(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
443 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
445 modifycalcheadOK2xml 111 (bool2str b) ocalhd;
449 "--------- syntax error ------------------------------------------";
450 "--------- syntax error ------------------------------------------";
451 "--------- syntax error ------------------------------------------";
453 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
454 ("Test", ["sqroot-test","univariate","equation","test"],
455 ["Test","squ-equ-test-subpbl1"]))];
456 Iterator 1; moveActiveRoot 1;
457 autoCalculate 1 CompleteCalcHead;
458 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
459 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
461 appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
462 val ((pt,_),_) = get_calc 1;
463 val str = pr_ptree pr_short pt;
465 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
466 else error "inform.sml: diff.behav.appendFormula: syntax error";
469 "--------- CAS-command on ([],Pbl) -------------------------------";
470 "--------- CAS-command on ([],Pbl) -------------------------------";
471 "--------- CAS-command on ([],Pbl) -------------------------------";
472 val (p,_,f,nxt,_,pt) =
473 CalcTreeTEST [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
474 val ifo = "solve(x+1=2,x)";
475 val (_,(_,c,(pt,p))) = inform ([],[],(pt,p)) "solve(x+1=2,x)";
477 val nxt = ("Apply_Method",Apply_Method ["Test","squ-equ-test-subpbl1"]);
478 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
479 if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
480 else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
483 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
484 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
485 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
487 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
490 replaceFormula 1 "solve(x+1=2,x)";
491 autoCalculate 1 CompleteCalc;
492 val ((pt,p),_) = get_calc 1;
494 if p = ([], Res) then ()
495 else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
498 "--------- inform [rational,simplification] ----------------------";
499 "--------- inform [rational,simplification] ----------------------";
500 "--------- inform [rational,simplification] ----------------------";
502 CalcTree [(["Term (a * x / (b * x) + c * x / (d * x) + e / f)", "normalform N"],
503 ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
504 Iterator 1; moveActiveRoot 1;
505 autoCalculate 1 CompleteCalcHead;
507 "--- (-1) give a preview on the calculation without any input";
509 autoCalculate 1 CompleteCalc;
510 val ((pt, p), _) = get_calc 1;
513 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
514 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
515 (([1], Res), a / b + c / d + e / f), <--- (1) input arbitrary
516 (([2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
517 (([3], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
518 (([4], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)), <--- (2) input next
519 (([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))] <--- (3) is also final result
522 "--- (0) user input as the *first* step does not work, thus impdo at least 1 step";
523 autoCalculate 1 (Step 1);
524 autoCalculate 1 (Step 1);
525 val ((pt, p), _) = get_calc 1;
528 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
529 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
530 (([1], Res), a / b + c / d + e / f)]
532 "--- (1) input an arbitrary next formula";
533 appendFormula 1 "((a * d) + (c * b)) / (b * d) + e / f" (*|> Future.join*);
534 val ((pt, p), _) = get_calc 1;
537 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
538 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
539 (([1], Res), a / b + c / d + e / f),
540 (([2,1], Frm), a / b + c / d + e / f),
541 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
542 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
543 (([2], Res), (a * d + c * b) / (b * d) + e / f)]
545 val ((pt,p),_) = get_calc 1;
546 if p = ([2], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
547 else error ("inform.sml: [rational,simplification] 1");
549 "--- (2) input the next formula that would be presented by mat-engine";
550 (* generate a preview:
551 autoCalculate 1 (Step 1);
552 val ((pt, p), _) = get_calc 1;
555 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
556 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
557 (([1], Res), a / b + c / d + e / f),
558 (([2,1], Frm), a / b + c / d + e / f),
559 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
560 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
561 (([2], Res), (a * d + c * b) / (b * d) + e / f),
562 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))] <--- input this
564 appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
565 val ((pt, p), _) = get_calc 1;
568 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
569 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
570 (([1], Res), a / b + c / d + e / f),
571 (([2,1], Frm), a / b + c / d + e / f),
572 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
573 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
574 (([2], Res), (a * d + c * b) / (b * d) + e / f),
575 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
577 if p = ([3], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
578 else error ("inform.sml: [rational,simplification] 2");
580 "--- (3) input the exact final result";
581 appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
582 val ((pt, p), _) = get_calc 1;
585 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
586 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
587 (([1], Res), a / b + c / d + e / f),
588 (([2,1], Frm), a / b + c / d + e / f),
589 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
590 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
591 (([2], Res), (a * d + c * b) / (b * d) + e / f),
592 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
593 (([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
594 (([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
595 (([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
596 (([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
598 if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
599 else error ("inform.sml: [rational,simplification] 3");
601 "--- (4) finish the calculation + check the postcondition (in the future)";
602 autoCalculate 1 CompleteCalc;
603 val ((pt, p), _) = get_calc 1;
604 val (t, asm) = get_obj g_result pt [];
605 if term2str t = "(a * d * f + b * c * f + b * d * e) / (b * d * f)" andalso
606 terms2str asm = "[\"b * d * f ~= 0\",\"d ~= 0\",\"b ~= 0\"," ^
607 "\"a * x / (b * x) + c * x / (d * x) + e / f is_ratpolyexp\"]"
608 then () else error "inform [rational,simplification] changed at end";
611 (([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
612 (([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
613 (([1], Res), a / b + c / d + e / f),
614 (([2,1], Frm), a / b + c / d + e / f),
615 (([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
616 (([2,2], Res), (a * d + c * b) / (b * d) + e / f),
617 (([2], Res), (a * d + c * b) / (b * d) + e / f),
618 (([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
619 (([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
620 (([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
621 (([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
622 (([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
623 (([5], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
624 (([6], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)),
625 (([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))]
629 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
630 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
631 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
632 val t = str2term "Diff (x^^^2 + x + 1, x)";
633 case t of Const ("Diff.Diff", _) $ _ => ()
635 error "diff.sml behav.changed for CAS Diff (..., x)";
637 "-----------------------------------------------------------------";
638 (*1>*)reset_states ();
639 (*2>*)CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
640 (*3>*)Iterator 1;moveActiveRoot 1;
641 "----- here the Headline has been finished";
642 (*4>*)moveActiveFormula 1 ([],Pbl);
643 (*5>*)replaceFormula 1 "Diff (x^2 + x + 1, x)";
644 val ((pt,_),_) = get_calc 1;
645 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
647 val (SOME istate, NONE) = loc;
648 default_print_depth 5;
649 writeln"-----------------------------------------------------------";
651 writeln (itms2str_ ctxt probl);
652 writeln (itms2str_ ctxt meth);
653 writeln (istate2str (fst istate));
655 refFormula 1 ([],Pbl) (*--> correct CalcHead*);
656 (*081016 NOT necessary (but leave it in Java):*)
657 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
658 "----- here the CalcHead has been completed --- ONCE MORE ?????";
660 (***difference II***)
661 val ((pt,p),_) = get_calc 1;
662 (*val p = ([], Pbl)*)
663 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
665 val (SOME istate, NONE) = loc;
666 default_print_depth 5; writeln (istate2str (fst istate)); default_print_depth 3;
669 ??.empty, Sundef, false)*)
670 default_print_depth 5; spec; default_print_depth 3;
672 ["derivative_of", "function"],
673 ["diff", "differentiate_on_R"]) : spec*)
674 writeln (itms2str_ ctxt probl);
676 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
677 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
678 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
679 writeln (itms2str_ ctxt meth);
681 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
682 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
683 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
684 writeln"-----------------------------------------------------------";
685 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
686 (*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
687 autoCalculate 1 CompleteCalc;
688 val ((pt,p),_) = get_calc 1;
689 val Form res = (#1 o pt_extract) (pt, ([],Res));
691 if p = ([], Res) andalso term2str res = "1 + 2 * x" then ()
692 else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
695 "--------- Take as 1st tac, start from exp -----------------------";
696 "--------- Take as 1st tac, start from exp -----------------------";
697 "--------- Take as 1st tac, start from exp -----------------------";
698 (*the following input is copied from BridgeLog Java <==> SML,
699 omitting unnecessary inputs*)
700 (*1>*)reset_states ();
701 (*2>*)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac",["derivative_of","function"],["diff","differentiate_on_R"]))];
702 (*3>*)Iterator 1; moveActiveRoot 1;
704 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
705 (***difference II***)
706 val ((pt,_),_) = get_calc 1;
707 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
709 val (SOME istate, NONE) = loc;
710 default_print_depth 5; writeln (istate2str (fst istate)); default_print_depth 3;
713 ??.empty, Sundef, false)*)
714 default_print_depth 5; spec; default_print_depth 3;
716 ["derivative_of", "function"],
717 ["diff", "differentiate_on_R"]) : spec*)
718 writeln (itms2str_ ctxt probl);
720 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
721 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
722 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
723 writeln (itms2str_ ctxt meth);
725 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
726 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
727 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
728 writeln"-----------------------------------------------------------";
729 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
730 autoCalculate 1 (Step 1);
731 val ((pt,p),_) = get_calc 1;
732 val Form res = (#1 o pt_extract) (pt, p);
733 if term2str res = "d_d x (x ^^^ 2 + x + 1)" then ()
734 else error "diff.sml Diff (x^2 + x + 1, x) from exp";
737 "--------- init_form, start with <NEW> (CAS input) ---------------";
738 "--------- init_form, start with <NEW> (CAS input) ---------------";
739 "--------- init_form, start with <NEW> (CAS input) ---------------";
741 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
742 (*[[from sml: > @@@@@begin@@@@@
744 [[from sml: <CALCTREE>
745 [[from sml: <CALCID> 1 </CALCID>
746 [[from sml: </CALCTREE>
747 [[from sml: @@@@@end@@@@@*)
749 (*[[from sml: > @@@@@begin@@@@@
751 [[from sml: <ADDUSER>
752 [[from sml: <CALCID> 1 </CALCID>
753 [[from sml: <USERID> 1 </USERID>
754 [[from sml: </ADDUSER>
755 [[from sml: @@@@@end@@@@@*)
757 (*[[from sml: > @@@@@begin@@@@@
759 [[from sml: <CALCITERATOR>
760 [[from sml: <CALCID> 1 </CALCID>
761 [[from sml: <POSITION>
762 [[from sml: <INTLIST>
763 [[from sml: </INTLIST>
764 [[from sml: <POS> Pbl </POS>
765 [[from sml: </POSITION>
766 [[from sml: </CALCITERATOR>
767 [[from sml: @@@@@end@@@@@*)
768 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
769 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
771 [[from sml: <GETELEMENTSFROMTO>
772 [[from sml: <CALCID> 1 </CALCID>
773 [[from sml: <FORMHEADS>
774 [[from sml: <CALCFORMULA>
775 [[from sml: <POSITION>
776 [[from sml: <INTLIST>
777 [[from sml: </INTLIST>
778 [[from sml: <POS> Pbl </POS>
779 [[from sml: </POSITION>
780 [[from sml: <FORMULA>
782 [[from sml: <ISA> ________________________________________________ </ISA>
783 [[from sml: </MATHML>
785 [[from sml: </FORMULA>
786 [[from sml: </CALCFORMULA>
787 [[from sml: </FORMHEADS>
788 [[from sml: </GETELEMENTSFROMTO>
789 [[from sml: @@@@@end@@@@@*)
790 refFormula 1 ([],Pbl);
791 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
793 [[from sml: <REFFORMULA>
794 [[from sml: <CALCID> 1 </CALCID>
795 [[from sml: <CALCHEAD status = "incorrect">
796 [[from sml: <POSITION>
797 [[from sml: <INTLIST>
798 [[from sml: </INTLIST>
799 [[from sml: <POS> Pbl </POS>
800 [[from sml: </POSITION>
803 [[from sml: <ISA> Problem (e_domID, [e_pblID]) </ISA>
804 [[from sml: </MATHML>
807 [[from sml: <GIVEN> </GIVEN>
808 [[from sml: <WHERE> </WHERE>
809 [[from sml: <FIND> </FIND>
810 [[from sml: <RELATE> </RELATE>
812 [[from sml: <BELONGSTO> Pbl </BELONGSTO>
813 [[from sml: <SPECIFICATION>
814 [[from sml: <THEORYID> e_domID </THEORYID>
815 [[from sml: <PROBLEMID>
816 [[from sml: <STRINGLIST>
817 [[from sml: <STRING> e_pblID </STRING>
818 [[from sml: </STRINGLIST>
819 [[from sml: </PROBLEMID>
820 [[from sml: <METHODID>
821 [[from sml: <STRINGLIST>
822 [[from sml: <STRING> e_metID </STRING>
823 [[from sml: </STRINGLIST>
824 [[from sml: </METHODID>
825 [[from sml: </SPECIFICATION>
826 [[from sml: </CALCHEAD>
827 [[from sml: </REFFORMULA>
828 [[from sml: @@@@@end@@@@@*)
829 moveActiveFormula 1 ([],Pbl);
830 (*[[from sml: > @@@@@begin@@@@@
832 [[from sml: <CALCITERATOR>
833 [[from sml: <CALCID> 1 </CALCID>
834 [[from sml: <POSITION>
835 [[from sml: <INTLIST>
836 [[from sml: </INTLIST>
837 [[from sml: <POS> Pbl </POS>
838 [[from sml: </POSITION>
839 [[from sml: </CALCITERATOR>
840 [[from sml: @@@@@end@@@@@*)
841 replaceFormula 1 "Simplify (1+2)";
842 (*[[from sml: > @@@@@begin@@@@@
844 [[from sml: <REPLACEFORMULA>
845 [[from sml: <CALCID> 1 </CALCID>
846 [[from sml: <CALCCHANGED>
847 [[from sml: <UNCHANGED>
848 [[from sml: <INTLIST>
849 [[from sml: </INTLIST>
850 [[from sml: <POS> Pbl </POS>
851 [[from sml: </UNCHANGED>
852 [[from sml: <DELETED>
853 [[from sml: <INTLIST>
854 [[from sml: </INTLIST>
855 [[from sml: <POS> Pbl </POS>
856 [[from sml: </DELETED>
857 [[from sml: <GENERATED>
858 [[from sml: <INTLIST>
859 [[from sml: </INTLIST>
860 [[from sml: <POS> Met </POS> DIFFERENCE: Pbl
861 [[from sml: </GENERATED>
862 [[from sml: </CALCCHANGED>
863 [[from sml: </REPLACEFORMULA>
864 [[from sml: @@@@@end@@@@@*)
865 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
879 <ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
886 getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
887 (*[[from sml: > @@@@@begin@@@@@
889 [[from sml: <SYSERROR>
890 [[from sml: <CALCID> 1 </CALCID>
891 [[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
892 [[from sml: </SYSERROR>
893 [[from sml: @@@@@end@@@@@*)
894 (*step into getFormulaeFromTo --- bug corrected...*)
896 "--------- build fun check_err_patt ------------------------------";
897 "--------- build fun check_err_patt ------------------------------";
898 "--------- build fun check_err_patt ------------------------------";
899 val subst = [(str2term "bdv", str2term "x")]: subst;
900 val rls = norm_Rational
901 val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
902 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
903 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "1 / 2");
905 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
906 rew_sub thy 1 [] e_rew_ord e_rls false [] (Trueprop $ pat) res;
907 if rewritten then NONE else SOME "e_errpatID";
909 val norm_res = case rewrite_set_ (Isac()) false rls res' of
911 | SOME (norm_res, _) => norm_res
913 val norm_inf = case rewrite_set_ (Isac()) false rls inf of
915 | SOME (norm_inf, _) => norm_inf;
920 val pat = parse_patt @{theory} "(?a + ?b)/?a = ?b";
921 val (res, inf) = (str2term "(2 + 3)/2", str2term "3");
922 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
923 then () else error "error patt example1 changed";
925 val pat = parse_patt @{theory} "(?a + ?b)/(?a + ?c) = ?b / ?c";
926 val (res, inf) = (str2term "(2 + 3)/(2 + 4)", str2term "3 / 4");
927 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
928 then () else error "error patt example2 changed";
930 val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
931 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
932 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
933 then () else error "error patt example3 changed";
935 val inf = str2term "1 / 2";
936 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
937 then () else error "error patt example3 changed";
939 "--------- build fun check_err_patt ?bdv -------------------------";
940 "--------- build fun check_err_patt ?bdv -------------------------";
941 "--------- build fun check_err_patt ?bdv -------------------------";
942 val subst = [(str2term "bdv", str2term "x")]: subst;
943 val t = str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))";
944 val SOME (t, _) = rewrite_set_inst_ thy false subst norm_diff t;
945 if term2str t = "2 * x + cos (x ^^^ 4) * 4 * x ^^^ 3" then ()
946 else error "build fun check_err_patt ?bdv changed 1";
949 val pat = parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)";
950 val (res, inf) = (str2term "2 * x + d_d x (sin (x ^^^ 4))", str2term "2 * x + cos (4 * x ^^^ 3)");
952 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
953 rew_sub thy 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) res;
954 if term2str res' = "2 * x + cos (d_d x (x ^^^ 4))" andalso rewritten then ()
955 else error "build fun check_err_patt ?bdv changed 2";
957 val norm_res = case rewrite_set_inst_ (Isac()) false subst rls res' of
959 | SOME (norm_res, _) => norm_res;
960 if term2str norm_res = "2 * x + cos (4 * x ^^^ 3)" then ()
961 else error "build fun check_err_patt ?bdv changed 3";
963 val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of
965 | SOME (norm_inf, _) => norm_inf;
966 if term2str norm_inf = "2 * x + cos (4 * x ^^^ 3)" then ()
967 else error "build fun check_err_patt ?bdv changed 4";
970 if norm_res = norm_inf then ()
971 else error "build fun check_err_patt ?bdv changed 5";
973 if check_err_patt (res, inf) (subst: subst) ("errpatID": errpatID, pat) rls = SOME "errpatID"
974 then () else error "error patt example1 changed";
976 "--------- build fun check_error_patterns ------------------------";
977 "--------- build fun check_error_patterns ------------------------";
978 "--------- build fun check_error_patterns ------------------------";
980 (str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))",
981 str2term "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)");
982 val {errpats, nrls = rls, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
984 val env = [(str2term "v_v", str2term "x")];
986 [e_errpat, (*generalised for testing*)
987 ("chain-rule-diff-both",
988 [parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)",
989 parse_patt @{theory} "d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)",
990 parse_patt @{theory} "d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1)",
991 parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / ?u",
992 parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u"],
993 [@{thm diff_sin_chain}, @{thm diff_cos_chain}, @{thm diff_pow_chain},
994 @{thm diff_ln_chain}, @{thm diff_exp_chain}])]: errpat list;
995 case check_error_patterns (res, inf) (prog, env) (errpats, rls) of SOME _ => ()
996 | NONE => error "check_error_patterns broken";
999 "--------- embed fun check_error_patterns ------------------------";
1000 "--------- embed fun check_error_patterns ------------------------";
1001 "--------- embed fun check_error_patterns ------------------------";
1004 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1005 ("Isac", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1008 autoCalculate 1 CompleteCalcHead;
1009 autoCalculate 1 (Step 1);
1010 autoCalculate 1 (Step 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1011 (*autoCalculate 1 (Step 1);([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)*)
1013 "~~~~~ fun appendFormula, args:"; val (cI, (ifo:cterm')) = (1, "d_d x (x ^ 2) + cos (4 * x ^ 3)");
1014 val cs = get_calc cI
1015 val pos as (_,p_) = get_pos cI 1; (*pos = ([1], Res)*)
1020 val (_, _, (pt, ([2], Res))) = cs';
1022 [(([], Frm), Diff (x ^^^ 2 + sin (x ^^^ 4), x)),
1023 (([1], Frm), d_d x (x ^^^ 2 + sin (x ^^^ 4))),
1024 (([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))), <<=== input follos: "...+ cos(4.x^3)"
1025 (([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4))] *)
1027 "~~~~~ fun inform, args:"; val ((cs as (_, _, ptp as (pt, pos as (p, p_))): calcstate'), istr) =
1028 (cs', (encode ifo));
1029 val SOME f_in = parse (assoc_thy "Isac") istr
1030 val f_in = Thm.term_of f_in
1031 val pos_pred = lev_back' pos
1032 (* f_pred ---"step pos cs"---> f_succ in appendFormula
1033 TODO.WN120517: one starting point for redesign of pos' *)
1034 val (f_pred, f_succ) = (get_curr_formula (pt, pos_pred), get_curr_formula (pt, pos));
1036 term2str f_pred = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))";
1037 term2str f_succ = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)";
1039 f_succ = f_in; (* = false*)
1040 cas_input f_in; (* = NONE*)
1041 val msg_calcstate' = compare_step ([], [], (pt, pos_pred)) f_in
1042 val ("no derivation found", calcstate') = msg_calcstate';
1043 val pp = par_pblobj pt p
1044 val {errpats, nrls, scr = Prog prog, ...} = get_met (get_obj g_metID pt pp)
1045 val ScrState (env, _, _, _, _, _) = get_istate pt pos;
1046 case check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) of
1047 SOME errpatID => ("error pattern #" ^ errpatID ^ "#", calcstate')
1048 | NONE => msg_calcstate';
1050 "~~~~~ from inform return val:"; val () = ();
1051 case check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) of
1053 | NONE => error "check_error_patterns broken";
1056 case inform cs' (encode ifo) of
1057 ("error pattern #chain-rule-diff-both#", calcstate') => ()
1058 | _ => error "inform with (positive) check_error_patterns broken"
1060 "--------- build fun get_fillpats --------------------------------";
1061 "--------- build fun get_fillpats --------------------------------";
1062 "--------- build fun get_fillpats --------------------------------";
1063 (*cause for this test was: wrong thy in Build_Thydata.thy in
1064 insert_fillpats ["IsacKnowledge", "Diff", "Theorems", "diff_sin_chain"]*)
1065 val f_curr = str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"
1066 val errpatID = "chain-rule-diff-both"
1067 val {errpats, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
1069 [(str2term "f_f", str2term "x ^^^ 2 + sin (x ^^^ 4)"),
1070 (str2term "v_v", str2term "x"),
1071 (str2term "f_f'", str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))")]
1072 val subst = get_bdv_subst prog env
1073 val errpatthms = errpats
1074 |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
1075 |> map (#3: errpat -> thm list)
1077 "~~~~~ fun get_fillpats, args:"; val (subst, form, errpatID, thm) =
1078 (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
1079 val thmDeriv = Thm.get_name_hint thm
1080 val (part, thyID) = thy_containing_thm thmDeriv
1081 val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]
1082 val Hthm {fillpats, ...} = get_the theID
1083 val some = map (get_fillform subst (thm, form) errpatID) fillpats;
1084 "~~~~~ fun get_fillform, args:";
1085 val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
1086 (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
1087 val (form', _, _, rewritten) =
1088 rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) form;
1089 "~~~~~ fun rew_sub, args:"; val (thy, i, bdv, tless, rls, put_asm, lrd:lrd list, r, t) =
1090 ((Isac()), 1, subst, e_rew_ord, e_rls, false, [], (Trueprop $ pat), form);
1091 val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop
1092 o Logic.strip_imp_concl) r;
1093 (*/-------------catch the planned exception*)
1095 val r' = Envir.subst_term (Pattern.match thy (lhs, t)
1096 (Vartab.empty, Vartab.empty)) r;
1098 ) handle PATTERN (*because only a subterm matches*) => 111;
1099 case t of t1 $ t2 =>
1100 let val (t2', asm2, lrd, rew2) = rew_sub thy i bdv tless rls put_asm (lrd@[R]) r t2
1102 if rew2 then (t1 $ t2', asm2, lrd, true) else
1103 let val (t1', asm1, lrd, rew1) = rew_sub thy i bdv tless rls put_asm (lrd@[L]) r t1
1104 in if rew1 then (t1' $ t2, asm1, lrd, true) else (t1 $ t2,[], lrd, false) end
1106 (*catch the planned exception-------------/*)
1109 val (t2', asm2, lrd, rew2) = rew_sub thy i bdv tless rls put_asm (lrd@[R]) r t2;
1110 "~~~~~ fun rew_sub, args:"; val (thy, i, bdv, tless, rls, put_asm, lrd:lrd list, r, t) =
1111 (thy, i, bdv, tless, rls, put_asm, (lrd@[R]), r, t2);
1112 val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r;
1113 val r' = Envir.subst_term (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) r;
1114 val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems) (Logic.count_prems r', [], r'));
1115 val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r';
1116 if term2str t' = "cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
1117 else error "get_fillpats changed 1"
1120 "--------- embed fun find_fillpatterns ---------------------------";
1121 "--------- embed fun find_fillpatterns ---------------------------";
1122 "--------- embed fun find_fillpatterns ---------------------------";
1125 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1126 ("Isac", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1129 autoCalculate 1 CompleteCalcHead;
1130 autoCalculate 1 (Step 1);
1131 autoCalculate 1 (Step 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1132 appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (*|> Future.join*);
1133 (*<CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>*)
1135 <CALCMESSAGE> no derivation found </CALCMESSAGE>*)
1137 "~~~~~ fun findFillpatterns, args:"; val (cI, errpatID) = (1, "chain-rule-diff-both");
1138 val ((pt, _), _) = get_calc cI
1139 val pos = get_pos cI 1;
1140 "~~~~~ fun find_fillpatterns, args:"; val ((pt, pos as (p, _)), errpatID) = ((pt, pos), errpatID);
1141 val f_curr = get_curr_formula (pt, pos); (* = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"*)
1142 val pp = par_pblobj pt p
1143 val {errpats, scr = Prog prog, ...} = get_met (get_obj g_metID pt pp)
1144 val ScrState (env, _, _, _, _, _) = get_istate pt pos
1145 val subst = get_bdv_subst prog env
1146 val errpatthms = errpats
1147 |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
1148 |> map (#3: errpat -> thm list)
1151 case map (get_fillpats subst f_curr errpatID) errpatthms |> flat of
1152 ("fill-d_d-arg", tm, thm, subs_opt) :: _ => if term2str tm =
1153 "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1154 then () else error "find_fillpatterns changed 1a"
1155 | _ => error "find_fillpatterns changed 1b"
1157 "~~~~~ fun get_fillpats, args:"; val (subst, form, errpatID, thm) =
1158 (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
1159 val thmDeriv = Thm.get_name_hint thm
1160 val (part, thyID) = thy_containing_thm thmDeriv
1161 val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]
1162 val Hthm {fillpats, ...} = get_the theID
1163 val some = map (get_fillform subst (thm, form) errpatID) fillpats;
1165 case some |> filter is_some |> map the of
1166 ("fill-d_d-arg", tm, thm, subsopt) :: _ => if term2str tm =
1167 "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1168 then () else error "find_fillpatterns changed 2a"
1169 | _ => error "find_fillpatterns changed 2b"
1171 "~~~~~ fun get_fillform, args:";
1172 val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
1173 (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
1174 val (form', _, _, rewritten) =
1175 rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) form;
1177 if term2str form' = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
1178 else error "find_fillpatterns changed 3";
1180 "~~~~~ to findFillpatterns return val:"; val (fillpats) =
1181 (map (get_fillpats (subs_opt, subst) f_curr errpatID) errpatthms |> flat) (*only from "hd errpatthms"*);
1183 "vvv--- dropped this code WN120730";
1184 val msg = "fill patterns " ^
1185 ((map ((apsnd term2str) o quad2pair) fillpats) |> map pair2str_ |> strs2str_);
1187 "fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1188 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" ^
1189 "#fill-both-args#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1190 " =\nd_d x (x ^^^ 2) + cos ?_dummy_2 * d_d x ?_dummy_3" ^
1191 "#fill-d_d#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1192 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1 x (x ^^^ 4)" ^
1193 "#fill-inner-deriv#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1194 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1" ^
1195 "#fill-all#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) = d_d x (x ^^^ 2) + ?_dummy_1#";
1196 "^^^--- dropped this code WN120730";
1198 if (map #1 fillpats) =
1199 ["fill-d_d-arg", "fill-both-args", "fill-d_d", "fill-inner-deriv", "fill-all"]
1200 then () else error "find_fillpatterns changed 4b";
1203 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1204 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1205 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1208 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1209 ("Isac", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1212 autoCalculate 1 CompleteCalcHead;
1213 autoCalculate 1 (Step 1);
1214 autoCalculate 1 (Step 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1215 appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (*|> Future.join*); (*<<<<<<<=========================*)
1216 (* the check for errpat is maximally liberal (whole term modulo "nrls" from "type met"),
1217 would recognize "cos (4 * x ^ (4 - 1)) + 2 * x" as well.
1218 results in <CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>
1219 instead of <CALCMESSAGE> no derivation found </CALCMESSAGE> *)
1220 val ((pt,pos), _) = get_calc 1;
1221 val p = get_pos 1 1;
1222 val (Form f, _, asms) = pt_extract (pt, p);
1224 if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
1225 case get_obj g_tac pt (fst p) of Rewrite_Inst (["(bdv, x)"],
1226 ("diff_sum", thm)) =>
1227 if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1228 else error "embed fun get_fillform changed 11"
1229 | _ => error "embed fun get_fillform changed 12"
1230 else error "embed fun get_fillform changed 13";
1232 findFillpatterns 1 "chain-rule-diff-both"; (*<<<<<<<=================================*)
1233 (*<CALCMESSAGE> fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =
1234 d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1#fill-both-args#...#...#... *)
1235 val ((pt,pos),_) = get_calc 1;
1236 val p = get_pos 1 1;
1238 val (Form f, _, asms) = pt_extract (pt, p);
1239 if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
1240 case get_obj g_tac pt (fst p) of Rewrite_Inst (["(bdv, x)"],
1241 ("diff_sum", thm)) =>
1242 if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1243 else error "embed fun get_fillform changed 21"
1244 | _ => error "embed fun get_fillform changed 22"
1245 else error "embed fun get_fillform changed 23";
1247 requestFillformula 1 ("chain-rule-diff-both", "fill-both-args");(*<<<<<<<============*)
1248 (*<AUTOCALC> ([1], Res) ([2], Res) ([2], Res) </AUTOCALC>*)
1249 val ((pt,pos),_) = get_calc 1;
1250 val p = get_pos 1 1;
1251 val (Form f, _, asms) = pt_extract (pt, p);
1252 if p = ([1], Res) andalso existpt [2] pt
1253 andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"
1254 then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(bdv, x)"],
1255 ("diff_sum", thm)) =>
1256 if (term2str o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1257 else error "embed fun get_fillform changed 31"
1258 | _ => error "embed fun get_fillform changed 32"
1259 else error "embed fun get_fillform changed 33";
1261 (* input a formula which exactly fills the gaps in a "fillformula"
1262 presented to the learner immediately before by "requestFillformula (errpatID, fillpatID)":
1263 errpatID: lhs of the respective thm = lhs of fillformula with fillpatID.
1264 the respective thm is in the ctree ................
1266 "~~~~~ fun inputFillFormula, args:"; val (cI, ifo) =
1267 (1, "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)");
1268 val ((pt, _), _) = get_calc cI
1269 val pos = get_pos cI 1;
1271 "~~~~~ fun is_exactly_equal, args:"; val ((pt, pos as (p, p_)), istr) = ((pt, pos), ifo);
1272 val SOME ifo = parseNEW (assoc_thy "Isac" |> thy2ctxt) istr
1274 val tac = get_obj g_tac pt p';
1275 val Rewrite_Inst ([bbb as "(bdv, x)"], ("diff_sin_chain", ttt)) = tac;
1276 if (term2str o Thm.prop_of) ttt = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
1277 else error "inputFillFormula changed 10";
1278 val Appl rew = applicable_in pos pt tac;
1279 val Rewrite_Inst' (_, _, _, _, _, _, _, (res, _)) = rew;
1281 "~~~~~ to inputFillFormula return val:"; val ("ok", tac) = ("ok", tac);
1282 val ("ok", (_, c, ptp as (_,p'))) = locatetac tac (pt, pos);
1283 upd_calc cI (ptp, []);
1285 autocalculateOK2xml cI pos (if null c then p' else last_elem c) p';
1287 "~~~~~ final check:";
1288 val ((pt, _),_) = get_calc 1;
1289 val p = get_pos 1 1;
1290 val (Form f, _, asms) = pt_extract (pt, p);
1291 if p = ([2], Res) andalso term2str f = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)"
1292 then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(bdv, x)"],
1293 ("diff_sin_chain", thm)) =>
1294 if (term2str o Thm.prop_of) thm = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
1295 else error "inputFillFormula changed 111"
1296 | _ => error "inputFillFormula changed 112"
1297 else error "inputFillFormula changed 113";
1299 "--------- fun appl_adds -----------------------------------------";
1300 "--------- fun appl_adds -----------------------------------------";
1301 "--------- fun appl_adds -----------------------------------------";
1302 (* val (dI, oris, ppc, pbt, selct::ss) =
1303 (dI, pors, probl, ppc, map itms2fstr probl);
1306 (* val (dI, oris, ppc, pbt, (selct::ss))=
1307 (#1 (some_spec ospec spec), oris, []:itm list,
1308 ((#ppc o get_pbt) (#2 (some_spec ospec spec))),(imodel2fstr imodel));
1309 val iii = appl_adds dI oris ppc pbt (selct::ss);
1310 tracing(itms2str_ thy iii);
1312 val itm = appl_add' dI oris ppc pbt selct;
1313 val ppc = insert_ppc' itm ppc;
1315 val _::selct::ss = (selct::ss);
1316 val itm = appl_add' dI oris ppc pbt selct;
1317 val ppc = insert_ppc' itm ppc;
1319 val _::selct::ss = (selct::ss);
1320 val itm = appl_add' dI oris ppc pbt selct;
1321 val ppc = insert_ppc' itm ppc;
1322 tracing(itms2str_ thy ppc);
1324 val _::selct::ss = (selct::ss);
1325 val itm = appl_add' dI oris ppc pbt selct;
1326 val ppc = insert_ppc' itm ppc;
1328 "--------- fun concat_deriv --------------------------------------";
1329 "--------- fun concat_deriv --------------------------------------";
1330 "--------- fun concat_deriv --------------------------------------";
1332 val ({rew_ord, erls, rules,...}, fo, ifo) =
1333 (rep_rls Test_simplify, str2term "x+1+ -1*2=0", str2term "-2*1+(x+1)=0");
1334 (tracing o trtas2str) fod';
1336 (x + 1 + -1 * 2 = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (x + 1) = 0, []))","
1337 (-1 * 2 + (x + 1) = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (1 + x) = 0, []))","
1338 (-1 * 2 + (1 + x) = 0, Thm ("radd_left_commute","?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (-1 * 2 + x) = 0, []))","
1339 (1 + (-1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))","-1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]
1341 (tracing o trtas2str) (map rev_deriv' rifod');
1343 (1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))","-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))","
1344 (1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute","?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))","
1345 (-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute","?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]
1348 "--------- handle an input formula -------------------------------";
1349 "--------- handle an input formula -------------------------------";
1350 "--------- handle an input formula -------------------------------";
1352 Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:
1353 Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden,
1354 wenn Abteilungen nur auf gleichem Level gesucht werden ?
1357 Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml
1359 ------------------------------------------------------------------------------
1360 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
1361 ------------------------------------------------------------------------------
1362 1. "5 * x / (x - 2) - x / (x + 2) = 4"
1364 4. "12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalize", "poly"..
1366 4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..
1368 4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"
1371 ------------------------------------------------------------------------------
1372 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
1374 (4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
1375 ------------------------------------------------------------------------------
1378 ------------------------------------------------------------------------------
1379 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
1380 ------------------------------------------------------------------------------
1381 1. "x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) = 1 / x"
1383 4. "(3 + (-1 * x + x ^^^ 2)) * x = 1 * (9 * x + (x ^^^ 3 + -6 * x ^^^ 2))"
1384 Subproblem["normalize", "polynomial", "univariate"..
1386 4.4. "-6 * x + 5 * x ^^^ 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..
1388 4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
1389 4.4.5. "[x = 0, x = 6 / 5]"
1391 5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
1393 ------------------------------------------------------------------------------
1394 (1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]
1396 (4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]
1397 ------------------------------------------------------------------------------
1400 ------------------------------------------------------------------------------
1401 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
1402 ------------------------------------------------------------------------------
1403 1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"
1405 6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"
1406 Subproblem["sq", "root'", "univariate", "equation"]
1408 6.6. "144 + 288 * x + 144 * x ^^^ 2 = 144 + x ^^^ 2 + 288 * x + 143 * x ^^^ 2"
1409 Subproblem["normalize", "polynomial", "univariate", "equation"]
1411 6.6.3 "0 = 0" Subproblem["degree_0", "polynomial", "univariate", "equation"]
1413 6.6.3.2 "UniversalList"
1414 ------------------------------------------------------------------------------
1415 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]
1417 (6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]
1418 ------------------------------------------------------------------------------
1420 (*sh. comments auf 498*)
1421 "--------- fun dropwhile' ----------------------------------------";
1422 "--------- fun dropwhile' ----------------------------------------";
1423 "--------- fun dropwhile' ----------------------------------------";
1425 fun equal a b = a=b;
1426 val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];
1427 val r_foder = rev foder; val r_ifoder = rev ifoder;
1428 dropwhile' equal r_foder r_ifoder;
1429 > vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list
1431 val foder = [3,4,5]; val ifoder = [11,12,3,4,5];
1432 val r_foder = rev foder; val r_ifoder = rev ifoder;
1433 dropwhile' equal r_foder r_ifoder;
1434 > val it = ([3], [3, 12, 11]) : int list * int list
1436 val foder = [5]; val ifoder = [11,12,3,4,5];
1437 val r_foder = rev foder; val r_ifoder = rev ifoder;
1438 dropwhile' equal r_foder r_ifoder;
1439 > val it = ([5], [5, 4, 3, 12, 11]) : int list * int list
1441 val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];
1442 val r_foder = rev foder; val r_ifoder = rev ifoder;
1443 dropwhile' equal r_foder r_ifoder;
1444 > *** dropwhile': did not start with equal elements*)