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 "-----------------------------------------------------------------";
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 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
61 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
63 appendFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
64 val ((pt,_),_) = get_calc 1;
65 val str = pr_ptree 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"}) 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"}) 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 (Step 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
146 appendFormula 1 "2+ -1 + x = 2"; 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 if tac = Rewrite_Set "norm_equation" then ()
164 else 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 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
181 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
183 appendFormula 1 "x = 2";
184 val ((pt,p),_) = get_calc 1;
185 val str = pr_ptree 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 if tac = Rewrite_Set "Test_simplify" then ()
194 else 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 --------------------";
205 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
206 ("Test", ["sqroot-test","univariate","equation","test"],
207 ["Test","squ-equ-test-subpbl1"]))];
208 Iterator 1; moveActiveRoot 1;
209 autoCalculate 1 CompleteCalcHead;
210 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
211 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
213 appendFormula 1 "x = 1";
214 val ((pt,p),_) = get_calc 1;
215 val str = pr_ptree pr_short pt;
217 if str = ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n3. ----- pblobj -----\n3.1. -1 + x = 0\n3.2. x = 0 + -1 * -1\n3.2.1. x = 0 + -1 * -1\n3.2.2. x = 0 + 1\n" andalso p = ([3,2], Res)
218 then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
219 else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
221 fetchProposedTactic 1;
222 val (_,(tac,_,_)::_) = get_calc 1;
223 if tac = Check_Postcond ["linear", "univariate", "equation", "test"] then ()
224 else error "inform.sml: diff.behav.appendFormula: Res + late d 2";
225 autoCalculate 1 CompleteCalc;
226 val ((pt,_),_) = get_calc 1;
227 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
228 else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
231 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
232 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
233 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
235 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
236 ("Test", ["sqroot-test","univariate","equation","test"],
237 ["Test","squ-equ-test-subpbl1"]))];
238 Iterator 1; moveActiveRoot 1;
239 autoCalculate 1 CompleteCalcHead;
240 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
241 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
242 appendFormula 1 "[x = 3 + -2*1]";
243 val ((pt,p),_) = get_calc 1;
244 val str = pr_ptree pr_short pt;
246 if str=". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n3. ----- pblobj -----\n3.1. -1 + x = 0\n3.2. x = 0 + -1 * -1\n4. [x = 1]\n4.1. [x = 1]\n4.2. [x = -2 + 3]\n4.3. [x = 3 + -2]\n" then ()
247 else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
248 autoCalculate 1 CompleteCalc;
249 val ((pt,p),_) = get_calc 1;
250 if "[x = 3 + -2 * 1]" = term2str (fst (get_obj g_result pt [])) then ()
251 (* ~~~~~~~~~~ simplify as last step in any script ?!*)
252 else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
256 "--------- replaceFormula: on Res + = ----------------------------";
257 "--------- replaceFormula: on Res + = ----------------------------";
258 "--------- replaceFormula: on Res + = ----------------------------";
260 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
261 ("Test", ["sqroot-test","univariate","equation","test"],
262 ["Test","squ-equ-test-subpbl1"]))];
263 Iterator 1; moveActiveRoot 1;
264 autoCalculate 1 CompleteCalcHead;
265 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
266 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
267 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*-1 + x*);
269 replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
270 val ((pt,_),_) = get_calc 1;
271 val str = pr_ptree pr_short pt;
273 (* before AK110725 this was
274 ". ----- pblobj -----\n
276 2. x + 1 + -1 * 2 = 0\n
277 2.1. x + 1 + -1 * 2 = 0\n
278 2.2. 1 + x + -1 * 2 = 0\n
279 2.3. 1 + (x + -1 * 2) = 0\n
280 2.4. 1 + (x + -2) = 0\n
281 2.5. 1 + (x + -2 * 1) = 0\n
282 2.6. 1 + x + -2 * 1 = 0\n";
285 ". ----- pblobj -----\n"^
287 "2. x + 1 + -1 * 2 = 0\n"^
288 "2.1. x + 1 + -1 * 2 = 0\n"^
289 "2.2. 1 + x + -1 * 2 = 0\n"^
290 "2.3. 1 + (x + -1 * 2) = 0\n"^
291 "2.4. 1 + (x + -2) = 0\n"^
292 "2.5. 1 + (x + -2 * 1) = 0\n"^
293 "2.6. 1 + x + -2 * 1 = 0\n" then()
294 else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
296 autoCalculate 1 CompleteCalc;
297 val ((pt,pos as (p,_)),_) = get_calc 1;
298 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst) (get_obj g_result pt p) then()
299 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
301 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
302 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
303 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
305 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
306 ("Test", ["sqroot-test","univariate","equation","test"],
307 ["Test","squ-equ-test-subpbl1"]))];
308 Iterator 1; moveActiveRoot 1;
309 autoCalculate 1 CompleteCalcHead;
310 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
311 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
313 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
314 val ((pt,_),_) = get_calc 1;
315 val str = pr_ptree pr_short pt;
317 if str= ". ----- pblobj -----\n1. x + 1 = 2\n1.1. x + 1 = 2\n1.2. 1 + x = 2\n1.3. 1 + x = -2 + 4\n1.4. x + 1 = -2 + 4\n" then ()
318 else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
319 autoCalculate 1 CompleteCalc;
320 val ((pt,pos as (p,_)),_) = get_calc 1;
321 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
322 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
325 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
326 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
327 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
329 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
330 ("Test", ["sqroot-test","univariate","equation","test"],
331 ["Test","squ-equ-test-subpbl1"]))];
332 Iterator 1; moveActiveRoot 1;
333 autoCalculate 1 CompleteCalcHead;
334 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
336 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
337 val ((pt,_),_) = get_calc 1;
338 val str = pr_ptree pr_short pt;
340 if str= ". ----- pblobj -----\n1. x + 1 = 2\n1.1. x + 1 = 2\n1.2. 1 + x = 2\n1.3. 1 + x = -2 + 4\n1.4. x + 1 = -2 + 4\n" then ()
341 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
342 autoCalculate 1 CompleteCalc;
343 val ((pt,pos as (p,_)),_) = get_calc 1;
344 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
345 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
348 "--------- replaceFormula: cut calculation -----------------------";
349 "--------- replaceFormula: cut calculation -----------------------";
350 "--------- replaceFormula: cut calculation -----------------------";
352 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
353 ("Test", ["sqroot-test","univariate","equation","test"],
354 ["Test","squ-equ-test-subpbl1"]))];
355 Iterator 1; moveActiveRoot 1;
356 autoCalculate 1 CompleteCalc;
357 moveActiveRoot 1; moveActiveDown 1;
358 if get_pos 1 1 = ([1], Frm) then ()
359 else error "inform.sml: diff.behav. cut calculation 1";
361 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
362 val ((pt,p),_) = get_calc 1;
363 val str = pr_ptree pr_short pt;
365 if p = ([1], Res) then ()
366 else error "inform.sml: diff.behav. cut calculation 2";
369 (* 040307 copied from informtest.sml; ... old version
370 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
371 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
372 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
375 val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
376 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
377 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
378 "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
379 (*^^^ these are the elements for the root-problem (in variants)*)
380 (*vvv these are elements required for subproblems*)
381 "boundVariable a","boundVariable b","boundVariable alpha",
382 "interval {x::real. 0 <= x & x <= 2*r}",
383 "interval {x::real. 0 <= x & x <= 2*r}",
384 "interval {x::real. 0 <= x & x <= pi}",
385 "errorBound (eps=(0::real))"]
386 (*specifying is not interesting for this example*)
387 val spec = ("DiffApp", ["maximum_of","function"],
388 ["DiffApp","max_by_calculus"]);
389 (*the empty model with descriptions for user-guidance by Model_Problem*)
390 val empty_model = [Given ["fixedValues []"],
391 Find ["maximum", "valuesFor"],
392 Relate ["relations []"]];
395 (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
396 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
397 (*val nxt = ("Model_Problem", ...*)
398 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
400 val (p,_,f,nxt,_,pt) = me nxt p c pt;
401 (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
402 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
404 (0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
405 (0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
406 (0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
407 (0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
409 (*the empty CalcHead is checked w.r.t the model and re-established as such*)
410 val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, e_spec);
411 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
412 if ocalhd2str ocalhd = "(Pbl, ??.empty, [\n(0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),\n(0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),\n(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),\n(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))], [], \n(\"e_domID\", [\"e_pblID\"], [\"e_metID\"]) )" then () else error "informtest.sml: diff.behav. max 1";
414 (*there is one input to the model (could be more)*)
416 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
417 Find ["maximum", "valuesFor"],
418 Relate ["relations"]], Pbl, e_spec);
419 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
420 if ocalhd2str ocalhd = "(Pbl, ??.empty, [\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),\n(0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),\n(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),\n(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))], [], \n(\"e_domID\", [\"e_pblID\"], [\"e_metID\"]) )" then ()
421 else error "informtest.sml: diff.behav. max 2";
423 (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
424 val (b,pt''''',ocalhd) =
425 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
426 Find ["maximum A", "valuesFor [a,b]"],
427 Relate ["relations [A=a*b, a/2=r*sin alpha, \
428 \b/2=r*cos alpha]"]], Pbl, e_spec);
429 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
430 if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
432 (*this input is complete in variant 1 (variant 3 does not work yet)*)
433 val (b,pt''''',ocalhd) =
434 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
435 Find ["maximum A", "valuesFor [a,b]"],
436 Relate ["relations [A=a*b, \
437 \(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
439 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
441 modifycalcheadOK2xml 111 (bool2str b) ocalhd;
444 "--------- syntax error ------------------------------------------";
445 "--------- syntax error ------------------------------------------";
446 "--------- syntax error ------------------------------------------";
448 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
449 ("Test", ["sqroot-test","univariate","equation","test"],
450 ["Test","squ-equ-test-subpbl1"]))];
451 Iterator 1; moveActiveRoot 1;
452 autoCalculate 1 CompleteCalcHead;
453 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
454 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
456 appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
457 val ((pt,_),_) = get_calc 1;
458 val str = pr_ptree pr_short pt;
460 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
461 else error "inform.sml: diff.behav.appendFormula: syntax error";
464 "--------- CAS-command on ([],Pbl) -------------------------------";
465 "--------- CAS-command on ([],Pbl) -------------------------------";
466 "--------- CAS-command on ([],Pbl) -------------------------------";
467 val (p,_,f,nxt,_,pt) =
468 CalcTreeTEST [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
469 val ifo = "solve(x+1=2,x)";
470 val (_,(_,c,(pt,p))) = inform ([],[],(pt,p)) "solve(x+1=2,x)";
472 val nxt = ("Apply_Method",Apply_Method ["Test","squ-equ-test-subpbl1"]);
473 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
474 if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
475 else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
478 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
479 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
480 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
482 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
485 replaceFormula 1 "solve(x+1=2,x)";
486 autoCalculate 1 CompleteCalc;
487 val ((pt,p),_) = get_calc 1;
489 if p = ([], Res) then ()
490 else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
493 "--------- inform [rational,simplification] ----------------------";
494 "--------- inform [rational,simplification] ----------------------";
495 "--------- inform [rational,simplification] ----------------------";
497 CalcTree [(["Term (4/x - 3/y - 1)", "normalform N"],
498 ("Rational",["rational","simplification"],
499 ["simplification","of_rationals"]))];
500 Iterator 1; moveActiveRoot 1;
501 autoCalculate 1 CompleteCalcHead;
502 autoCalculate 1 (Step 1);
503 autoCalculate 1 (Step 1);
504 autoCalculate 1 (Step 1);
505 autoCalculate 1 (Step 1);
506 "--- input the next formula that _should_ be presented by mat-engine";
507 appendFormula 1 "(4 * y + -3 * x) / (x * y) + -1";
508 val ((pt,p),_) = get_calc 1;
509 if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
510 else error ("inform.sml: [rational,simplification] 1");
512 "--- input the next formula that would be presented by mat-engine";
513 (*autoCalculate 1 (Step 1);*)
514 appendFormula 1 "(4 * y + -3 * x + -1 * (x * y)) / (x * y)";
515 val ((pt,p),_) = get_calc 1;
516 if p = ([5], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
517 else error ("inform.sml: [rational,simplification] 2");
519 "--- input the exact final result";(*TODO: Exception- LIST "last_elem" raised*)
520 appendFormula 1 "(-3 * x + 4 * y + -1 * x * y) / (x * y)";
521 val ((pt,p),_) = get_calc 1;
522 if p = ([6], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
523 else error ("inform.sml: [rational,simplification] 3");
526 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
527 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
528 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
529 val t = str2term "Diff (x^^^2 + x + 1, x)";
530 case t of Const ("Diff.Diff", _) $ _ => ()
532 error "diff.sml behav.changed for CAS Diff (..., x)";
534 "-----------------------------------------------------------------";
536 (*2>*)CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
537 (*3>*)Iterator 1;moveActiveRoot 1;
538 "----- here the Headline has been finished";
539 (*4>*)moveActiveFormula 1 ([],Pbl);
540 (*5>*)replaceFormula 1 "Diff (x^2 + x + 1, x)";
541 val ((pt,_),_) = get_calc 1;
542 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
544 val (SOME istate, NONE) = loc;
546 writeln"-----------------------------------------------------------";
548 writeln (itms2str_ ctxt probl);
549 writeln (itms2str_ ctxt meth);
550 writeln (istate2str (fst istate));
552 refFormula 1 ([],Pbl) (*--> correct CalcHead*);
553 (*081016 NOT necessary (but leave it in Java):*)
554 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
555 "----- here the CalcHead has been completed --- ONCE MORE ?????";
557 (***difference II***)
558 val ((pt,p),_) = get_calc 1;
559 (*val p = ([], Pbl)*)
560 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
562 val (SOME istate, NONE) = loc;
563 print_depth 5; writeln (istate2str (fst istate)); print_depth 3;
566 ??.empty, Sundef, false)*)
567 print_depth 5; spec; print_depth 3;
569 ["derivative_of", "function"],
570 ["diff", "differentiate_on_R"]) : spec*)
571 writeln (itms2str_ ctxt probl);
573 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
574 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
575 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
576 writeln (itms2str_ ctxt meth);
578 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
579 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
580 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
581 writeln"-----------------------------------------------------------";
582 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
583 (*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
584 autoCalculate 1 CompleteCalc;
585 val ((pt,p),_) = get_calc 1;
586 val Form res = (#1 o pt_extract) (pt, ([],Res));
588 if p = ([], Res) andalso term2str res = "1 + 2 * x" then ()
589 else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
591 "--------- Take as 1st tac, start from exp -----------------------";
592 "--------- Take as 1st tac, start from exp -----------------------";
593 "--------- Take as 1st tac, start from exp -----------------------";
594 (*the following input is copied from BridgeLog Java <==> SML,
595 omitting unnecessary inputs*)
597 (*2>*)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac",["derivative_of","function"],["diff","differentiate_on_R"]))];
598 (*3>*)Iterator 1; moveActiveRoot 1;
600 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
601 (***difference II***)
602 val ((pt,_),_) = get_calc 1;
603 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
605 val (SOME istate, NONE) = loc;
606 print_depth 5; writeln (istate2str (fst istate)); print_depth 3;
609 ??.empty, Sundef, false)*)
610 print_depth 5; spec; print_depth 3;
612 ["derivative_of", "function"],
613 ["diff", "differentiate_on_R"]) : spec*)
614 writeln (itms2str_ ctxt probl);
616 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
617 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
618 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
619 writeln (itms2str_ ctxt meth);
621 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
622 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
623 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
624 writeln"-----------------------------------------------------------";
625 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
626 autoCalculate 1 (Step 1);
627 val ((pt,p),_) = get_calc 1;
628 val Form res = (#1 o pt_extract) (pt, p);
629 if term2str res = "d_d x (x ^^^ 2 + x + 1)" then ()
630 else error "diff.sml Diff (x^2 + x + 1, x) from exp";
632 "--------- init_form, start with <NEW> (CAS input) ---------------";
633 "--------- init_form, start with <NEW> (CAS input) ---------------";
634 "--------- init_form, start with <NEW> (CAS input) ---------------";
636 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
637 (*[[from sml: > @@@@@begin@@@@@
639 [[from sml: <CALCTREE>
640 [[from sml: <CALCID> 1 </CALCID>
641 [[from sml: </CALCTREE>
642 [[from sml: @@@@@end@@@@@*)
644 (*[[from sml: > @@@@@begin@@@@@
646 [[from sml: <ADDUSER>
647 [[from sml: <CALCID> 1 </CALCID>
648 [[from sml: <USERID> 1 </USERID>
649 [[from sml: </ADDUSER>
650 [[from sml: @@@@@end@@@@@*)
652 (*[[from sml: > @@@@@begin@@@@@
654 [[from sml: <CALCITERATOR>
655 [[from sml: <CALCID> 1 </CALCID>
656 [[from sml: <POSITION>
657 [[from sml: <INTLIST>
658 [[from sml: </INTLIST>
659 [[from sml: <POS> Pbl </POS>
660 [[from sml: </POSITION>
661 [[from sml: </CALCITERATOR>
662 [[from sml: @@@@@end@@@@@*)
663 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
664 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
666 [[from sml: <GETELEMENTSFROMTO>
667 [[from sml: <CALCID> 1 </CALCID>
668 [[from sml: <FORMHEADS>
669 [[from sml: <CALCFORMULA>
670 [[from sml: <POSITION>
671 [[from sml: <INTLIST>
672 [[from sml: </INTLIST>
673 [[from sml: <POS> Pbl </POS>
674 [[from sml: </POSITION>
675 [[from sml: <FORMULA>
677 [[from sml: <ISA> ________________________________________________ </ISA>
678 [[from sml: </MATHML>
680 [[from sml: </FORMULA>
681 [[from sml: </CALCFORMULA>
682 [[from sml: </FORMHEADS>
683 [[from sml: </GETELEMENTSFROMTO>
684 [[from sml: @@@@@end@@@@@*)
685 refFormula 1 ([],Pbl);
686 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
688 [[from sml: <REFFORMULA>
689 [[from sml: <CALCID> 1 </CALCID>
690 [[from sml: <CALCHEAD status = "incorrect">
691 [[from sml: <POSITION>
692 [[from sml: <INTLIST>
693 [[from sml: </INTLIST>
694 [[from sml: <POS> Pbl </POS>
695 [[from sml: </POSITION>
698 [[from sml: <ISA> Problem (e_domID, [e_pblID]) </ISA>
699 [[from sml: </MATHML>
702 [[from sml: <GIVEN> </GIVEN>
703 [[from sml: <WHERE> </WHERE>
704 [[from sml: <FIND> </FIND>
705 [[from sml: <RELATE> </RELATE>
707 [[from sml: <BELONGSTO> Pbl </BELONGSTO>
708 [[from sml: <SPECIFICATION>
709 [[from sml: <THEORYID> e_domID </THEORYID>
710 [[from sml: <PROBLEMID>
711 [[from sml: <STRINGLIST>
712 [[from sml: <STRING> e_pblID </STRING>
713 [[from sml: </STRINGLIST>
714 [[from sml: </PROBLEMID>
715 [[from sml: <METHODID>
716 [[from sml: <STRINGLIST>
717 [[from sml: <STRING> e_metID </STRING>
718 [[from sml: </STRINGLIST>
719 [[from sml: </METHODID>
720 [[from sml: </SPECIFICATION>
721 [[from sml: </CALCHEAD>
722 [[from sml: </REFFORMULA>
723 [[from sml: @@@@@end@@@@@*)
724 moveActiveFormula 1 ([],Pbl);
725 (*[[from sml: > @@@@@begin@@@@@
727 [[from sml: <CALCITERATOR>
728 [[from sml: <CALCID> 1 </CALCID>
729 [[from sml: <POSITION>
730 [[from sml: <INTLIST>
731 [[from sml: </INTLIST>
732 [[from sml: <POS> Pbl </POS>
733 [[from sml: </POSITION>
734 [[from sml: </CALCITERATOR>
735 [[from sml: @@@@@end@@@@@*)
736 replaceFormula 1 "Simplify (1+2)";
737 (*[[from sml: > @@@@@begin@@@@@
739 [[from sml: <REPLACEFORMULA>
740 [[from sml: <CALCID> 1 </CALCID>
741 [[from sml: <CALCCHANGED>
742 [[from sml: <UNCHANGED>
743 [[from sml: <INTLIST>
744 [[from sml: </INTLIST>
745 [[from sml: <POS> Pbl </POS>
746 [[from sml: </UNCHANGED>
747 [[from sml: <DELETED>
748 [[from sml: <INTLIST>
749 [[from sml: </INTLIST>
750 [[from sml: <POS> Pbl </POS>
751 [[from sml: </DELETED>
752 [[from sml: <GENERATED>
753 [[from sml: <INTLIST>
754 [[from sml: </INTLIST>
755 [[from sml: <POS> Met </POS> DIFFERENCE: Pbl
756 [[from sml: </GENERATED>
757 [[from sml: </CALCCHANGED>
758 [[from sml: </REPLACEFORMULA>
759 [[from sml: @@@@@end@@@@@*)
760 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
774 <ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
781 getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
782 (*[[from sml: > @@@@@begin@@@@@
784 [[from sml: <SYSERROR>
785 [[from sml: <CALCID> 1 </CALCID>
786 [[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
787 [[from sml: </SYSERROR>
788 [[from sml: @@@@@end@@@@@*)
789 (*step into getFormulaeFromTo --- bug corrected...*)
791 "--------- build fun check_err_patt ------------------------------";
792 "--------- build fun check_err_patt ------------------------------";
793 "--------- build fun check_err_patt ------------------------------";
794 val subst = [(str2term "bdv", str2term "x")]: subst;
795 val rls = norm_Rational
796 val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
797 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
798 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "1 / 2");
800 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
801 rew_sub thy 1 [] e_rew_ord e_rls false [] (Trueprop $ pat) res;
802 if rewritten then NONE else SOME "e_errpatID";
804 val norm_res = case rewrite_set_ (Isac()) false rls res' of
806 | SOME (norm_res, _) => norm_res
808 val norm_inf = case rewrite_set_ (Isac()) false rls inf of
810 | SOME (norm_inf, _) => norm_inf;
815 val pat = parse_patt @{theory} "(?a + ?b)/?a = ?b";
816 val (res, inf) = (str2term "(2 + 3)/2", str2term "3");
817 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
818 then () else error "error patt example1 changed";
820 val pat = parse_patt @{theory} "(?a + ?b)/(?a + ?c) = ?b / ?c";
821 val (res, inf) = (str2term "(2 + 3)/(2 + 4)", str2term "3 / 4");
822 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
823 then () else error "error patt example2 changed";
825 val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
826 val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
827 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
828 then () else error "error patt example3 changed";
830 val inf = str2term "1 / 2";
831 if check_err_patt (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
832 then () else error "error patt example3 changed";
834 "--------- build fun check_err_patt ?bdv -------------------------";
835 "--------- build fun check_err_patt ?bdv -------------------------";
836 "--------- build fun check_err_patt ?bdv -------------------------";
837 val subst = [(str2term "bdv", str2term "x")]: subst;
838 val t = str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))";
839 val SOME (t, _) = rewrite_set_inst_ thy false subst norm_diff t;
840 if term2str t = "2 * x + cos (x ^^^ 4) * 4 * x ^^^ 3" then ()
841 else error "build fun check_err_patt ?bdv changed 1";
844 val pat = parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)";
845 val (res, inf) = (str2term "2 * x + d_d x (sin (x ^^^ 4))", str2term "2 * x + cos (4 * x ^^^ 3)");
847 val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
848 rew_sub thy 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) res;
849 if term2str res' = "2 * x + cos (d_d x (x ^^^ 4))" andalso rewritten then ()
850 else error "build fun check_err_patt ?bdv changed 2";
852 val norm_res = case rewrite_set_inst_ (Isac()) false subst rls res' of
854 | SOME (norm_res, _) => norm_res;
855 if term2str norm_res = "2 * x + cos (4 * x ^^^ 3)" then ()
856 else error "build fun check_err_patt ?bdv changed 3";
858 val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of
860 | SOME (norm_inf, _) => norm_inf;
861 if term2str norm_inf = "2 * x + cos (4 * x ^^^ 3)" then ()
862 else error "build fun check_err_patt ?bdv changed 4";
865 if norm_res = norm_inf then ()
866 else error "build fun check_err_patt ?bdv changed 5";
868 if check_err_patt (res, inf) (subst: subst) ("errpatID": errpatID, pat) rls = SOME "errpatID"
869 then () else error "error patt example1 changed";
871 "--------- build fun check_error_patterns ------------------------";
872 "--------- build fun check_error_patterns ------------------------";
873 "--------- build fun check_error_patterns ------------------------";
875 (str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))",
876 str2term "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)");
877 val {errpats, nrls = rls, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
879 val env = [(str2term "v_v", str2term "x")];
881 [e_errpat, (*generalised for testing*)
882 ("chain-rule-diff-both",
883 [parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)",
884 parse_patt @{theory} "d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)",
885 parse_patt @{theory} "d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1)",
886 parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / ?u",
887 parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u"],
888 [@{thm diff_sin_chain}, @{thm diff_cos_chain}, @{thm diff_pow_chain},
889 @{thm diff_ln_chain}, @{thm diff_exp_chain}])]: errpat list;
890 case check_error_patterns (res, inf) (prog, env) (errpats, rls) of SOME _ => ()
891 | NONE => error "check_error_patterns broken";
893 "--------- embed fun check_error_patterns ------------------------";
894 "--------- embed fun check_error_patterns ------------------------";
895 "--------- embed fun check_error_patterns ------------------------";
898 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
899 ("Isac", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
902 autoCalculate 1 CompleteCalcHead;
903 autoCalculate 1 (Step 1);
904 autoCalculate 1 (Step 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
905 (*autoCalculate 1 (Step 1);([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)*)
907 "~~~~~ fun appendFormula, args:"; val (cI, (ifo:cterm')) = (1, "d_d x (x ^ 2) + cos (4 * x ^ 3)");
909 val pos as (_,p_) = get_pos cI 1; (*pos = ([1], Res)*)
914 val (_, _, (pt, ([2], Res))) = cs';
916 [(([], Frm), Diff (x ^^^ 2 + sin (x ^^^ 4), x)),
917 (([1], Frm), d_d x (x ^^^ 2 + sin (x ^^^ 4))),
918 (([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))), <<=== input follos: "...+ cos(4.x^3)"
919 (([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4))] *)
921 "~~~~~ fun inform, args:"; val ((cs as (_, _, ptp as (pt, pos as (p, p_))): calcstate'), istr) =
923 val SOME f_in = parse (assoc_thy "Isac") istr
924 val f_in = term_of f_in
925 val pos_pred = lev_back' pos
926 (* f_pred ---"step pos cs"---> f_succ in appendFormula
927 TODO.WN120517: one starting point for redesign of pos' *)
928 val (f_pred, f_succ) = (get_curr_formula (pt, pos_pred), get_curr_formula (pt, pos));
930 term2str f_pred = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))";
931 term2str f_succ = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)";
933 f_succ = f_in; (* = false*)
934 cas_input f_in; (* = NONE*)
935 val msg_calcstate' = compare_step ([], [], (pt, pos_pred)) f_in
936 val ("no derivation found", calcstate') = msg_calcstate';
937 val pp = par_pblobj pt p
938 val {errpats, nrls, scr = Prog prog, ...} = get_met (get_obj g_metID pt pp)
939 val ScrState (env, _, _, _, _, _) = get_istate pt pos;
940 case check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) of
941 SOME errpatID => ("error pattern #" ^ errpatID ^ "#", calcstate')
942 | NONE => msg_calcstate';
944 "~~~~~ from inform return val:"; val () = ();
945 case check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) of
947 | NONE => error "check_error_patterns broken";
950 case inform cs' (encode ifo) of
951 ("error pattern #chain-rule-diff-both#", calcstate') => ()
952 | _ => error "inform with (positive) check_error_patterns broken"
954 "--------- build fun get_fillpats --------------------------------";
955 "--------- build fun get_fillpats --------------------------------";
956 "--------- build fun get_fillpats --------------------------------";
957 (*cause for this test was: wrong thy in Build_Thydata.thy in
958 insert_fillpats ["IsacKnowledge", "Diff", "Theorems", "diff_sin_chain"]*)
959 val f_curr = str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"
960 val errpatID = "chain-rule-diff-both"
961 val {errpats, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
963 [(str2term "f_f", str2term "x ^^^ 2 + sin (x ^^^ 4)"),
964 (str2term "v_v", str2term "x"),
965 (str2term "f_f'", str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))")]
966 val subst = get_bdv_subst prog env
967 val errpatthms = errpats
968 |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
969 |> map (#3: errpat -> thm list)
971 "~~~~~ fun get_fillpats, args:"; val (subst, form, errpatID, thm) =
972 (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
973 val thmDeriv = Thm.get_name_hint thm
974 val (part, thyID) = thy_containing_thm thmDeriv
975 val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]
976 val Hthm {fillpats, ...} = get_the theID
977 val some = map (get_fillform subst (thm, form) errpatID) fillpats;
978 "~~~~~ fun get_fillform, args:";
979 val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
980 (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
981 val (form', _, _, rewritten) =
982 rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) form;
983 "~~~~~ fun rew_sub, args:"; val (thy, i, bdv, tless, rls, put_asm, lrd:lrd list, r, t) =
984 ((Isac()), 1, subst, e_rew_ord, e_rls, false, [], (Trueprop $ pat), form);
985 val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop
986 o Logic.strip_imp_concl) r;
987 (*/-------------catch the planned exception*)
989 val r' = Envir.subst_term (Pattern.match thy (lhs, t)
990 (Vartab.empty, Vartab.empty)) r;
992 ) handle PATTERN (*because only a subterm matches*) => 111;
994 let val (t2', asm2, lrd, rew2) = rew_sub thy i bdv tless rls put_asm (lrd@[R]) r t2
996 if rew2 then (t1 $ t2', asm2, lrd, true) else
997 let val (t1', asm1, lrd, rew1) = rew_sub thy i bdv tless rls put_asm (lrd@[L]) r t1
998 in if rew1 then (t1' $ t2, asm1, lrd, true) else (t1 $ t2,[], lrd, false) end
1000 (*catch the planned exception-------------/*)
1003 val (t2', asm2, lrd, rew2) = rew_sub thy i bdv tless rls put_asm (lrd@[R]) r t2;
1004 "~~~~~ fun rew_sub, args:"; val (thy, i, bdv, tless, rls, put_asm, lrd:lrd list, r, t) =
1005 (thy, i, bdv, tless, rls, put_asm, (lrd@[R]), r, t2);
1006 val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r;
1007 val r' = Envir.subst_term (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) r;
1008 val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems) (Logic.count_prems r', [], r'));
1009 val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r';
1010 if term2str t' = "cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
1011 else error "get_fillpats changed 1"
1013 "--------- embed fun find_fillpatterns ---------------------------";
1014 "--------- embed fun find_fillpatterns ---------------------------";
1015 "--------- embed fun find_fillpatterns ---------------------------";
1018 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1019 ("Isac", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1022 autoCalculate 1 CompleteCalcHead;
1023 autoCalculate 1 (Step 1);
1024 autoCalculate 1 (Step 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1025 appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)";
1026 (*<CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>*)
1028 <CALCMESSAGE> no derivation found </CALCMESSAGE>*)
1030 "~~~~~ fun findFillpatterns, args:"; val (cI, errpatID) = (1, "chain-rule-diff-both");
1031 val ((pt, _), _) = get_calc cI
1032 val pos = get_pos cI 1;
1033 "~~~~~ fun find_fillpatterns, args:"; val ((pt, pos as (p, _)), errpatID) = ((pt, pos), errpatID);
1034 val f_curr = get_curr_formula (pt, pos); (* = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"*)
1035 val pp = par_pblobj pt p
1036 val {errpats, scr = Prog prog, ...} = get_met (get_obj g_metID pt pp)
1037 val ScrState (env, _, _, _, _, _) = get_istate pt pos
1038 val subst = get_bdv_subst prog env
1039 val errpatthms = errpats
1040 |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
1041 |> map (#3: errpat -> thm list)
1044 case map (get_fillpats subst f_curr errpatID) errpatthms |> flat of
1045 ("fill-d_d-arg", tm, thm, subs_opt) :: _ => if term2str tm =
1046 "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1047 then () else error "find_fillpatterns changed 1a"
1048 | _ => error "find_fillpatterns changed 1b"
1050 "~~~~~ fun get_fillpats, args:"; val (subst, form, errpatID, thm) =
1051 (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
1052 val thmDeriv = Thm.get_name_hint thm
1053 val (part, thyID) = thy_containing_thm thmDeriv
1054 val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]
1055 val Hthm {fillpats, ...} = get_the theID
1056 val some = map (get_fillform subst (thm, form) errpatID) fillpats;
1058 case some |> filter is_some |> map the of
1059 ("fill-d_d-arg", tm, thm, subsopt) :: _ => if term2str tm =
1060 "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1061 then () else error "find_fillpatterns changed 2a"
1062 | _ => error "find_fillpatterns changed 2b"
1064 "~~~~~ fun get_fillform, args:";
1065 val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
1066 (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
1067 val (form', _, _, rewritten) =
1068 rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) form;
1070 if term2str form' = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
1071 else error "find_fillpatterns changed 3";
1073 "~~~~~ to findFillpatterns return val:"; val (fillpats) =
1074 (map (get_fillpats (subs_opt, subst) f_curr errpatID) errpatthms |> flat) (*only from "hd errpatthms"*);
1076 "vvv--- dropped this code WN120730";
1077 val msg = "fill patterns " ^
1078 ((map ((apsnd term2str) o quad2pair) fillpats) |> map pair2str_ |> strs2str_);
1080 "fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1081 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" ^
1082 "#fill-both-args#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1083 " =\nd_d x (x ^^^ 2) + cos ?_dummy_2 * d_d x ?_dummy_3" ^
1084 "#fill-d_d#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1085 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1 x (x ^^^ 4)" ^
1086 "#fill-inner-deriv#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1087 " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1" ^
1088 "#fill-all#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) = d_d x (x ^^^ 2) + ?_dummy_1#";
1089 "^^^--- dropped this code WN120730";
1091 if (map #1 fillpats) =
1092 ["fill-d_d-arg", "fill-both-args", "fill-d_d", "fill-inner-deriv", "fill-all"]
1093 then () else error "find_fillpatterns changed 4b";
1095 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1096 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1097 "--------- build fun is_exactly_equal, inputFillFormula ----------";
1100 [(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1101 ("Isac", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1104 autoCalculate 1 CompleteCalcHead;
1105 autoCalculate 1 (Step 1);
1106 autoCalculate 1 (Step 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1107 appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)"; (*<<<<<<<=========================*)
1108 (* the check for errpat is maximally liberal (whole term modulo "nrls" from "type met"),
1109 would recognize "cos (4 * x ^ (4 - 1)) + 2 * x" as well.
1110 results in <CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>
1111 instead of <CALCMESSAGE> no derivation found </CALCMESSAGE> *)
1112 val ((pt,pos), _) = get_calc 1;
1113 val p = get_pos 1 1;
1114 val (Form f, _, asms) = pt_extract (pt, p);
1116 if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" andalso
1117 get_obj g_tac pt (fst p) = Rewrite_Inst (["(bdv, x)"], ("diff_sum", "Diff.diff_sum"(*?!?*)))
1118 then () else error "embed fun get_fillform changed 1";
1120 findFillpatterns 1 "chain-rule-diff-both"; (*<<<<<<<=================================*)
1121 (*<CALCMESSAGE> fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =
1122 d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1#fill-both-args#...#...#... *)
1123 val ((pt,pos),_) = get_calc 1;
1124 val p = get_pos 1 1;
1126 val (Form f, _, asms) = pt_extract (pt, p);
1127 if p = ([1], Res) andalso term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" andalso
1128 get_obj g_tac pt (fst p) = Rewrite_Inst (["(bdv, x)"], ("diff_sum", "Diff.diff_sum"(*?!?*)))
1130 else error "embed fun get_fillform changed 2";
1132 requestFillformula 1 ("chain-rule-diff-both", "fill-both-args");(*<<<<<<<============*)
1133 (*<AUTOCALC> ([1], Res) ([2], Res) ([2], Res) </AUTOCALC>*)
1134 val ((pt,pos),_) = get_calc 1;
1135 val p = get_pos 1 1;
1136 val (Form f, _, asms) = pt_extract (pt, p);
1137 if p = ([1], Res) andalso existpt [2] pt andalso
1138 term2str f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" andalso
1139 get_obj g_tac pt (fst p) = Rewrite_Inst (["(bdv, x)"], ("diff_sum", "Diff.diff_sum"))
1140 then () else error "embed fun get_fillform changed 3";
1142 (* input a formula which exactly fills the gaps in a "fillformula"
1143 presented to the learner immediately before by "requestFillformula (errpatID, fillpatID)":
1144 errpatID: lhs of the respective thm = lhs of fillformula with fillpatID.
1145 the respective thm is in the ctree ................
1147 "~~~~~ fun inputFillFormula, args:"; val (cI, ifo) =
1148 (1, "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)");
1149 val ((pt, _), _) = get_calc cI
1150 val pos = get_pos cI 1;
1152 "~~~~~ fun is_exactly_equal, args:"; val ((pt, pos as (p, p_)), istr) = ((pt, pos), ifo);
1153 val SOME ifo = parseNEW (assoc_thy "Isac" |> thy2ctxt) istr
1155 val tac = get_obj g_tac pt p';
1156 if tac = Rewrite_Inst (["(bdv, x)"], ("diff_sin_chain", "")) then ()
1157 else error "inputFillFormula changed 10";
1158 val Appl rew = applicable_in pos pt tac;
1159 val Rewrite_Inst' (_, _, _, _, _, _, _, (res, _)) = rew;
1161 "~~~~~ to inputFillFormula return val:"; val ("ok", tac) = ("ok", tac);
1162 val ("ok", (_, c, ptp as (_,p'))) = locatetac tac (pt, pos);
1163 upd_calc cI (ptp, []);
1165 autocalculateOK2xml cI pos (if null c then p' else last_elem c) p';
1167 "~~~~~ final check:";
1168 val ((pt, _),_) = get_calc 1;
1169 val p = get_pos 1 1;
1170 val (Form f, _, asms) = pt_extract (pt, p);
1171 if p = ([2], Res) andalso
1172 term2str f = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)" andalso
1173 get_obj g_tac pt (fst p) = Rewrite_Inst (["(bdv, x)"], ("diff_sin_chain", ""))
1174 then () else error "inputFillFormula changed 11";