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 "-----------------------------------------------------------------";
35 "-----------------------------------------------------------------";
36 "-----------------------------------------------------------------";
43 "--------- appendFormula: on Res + equ_nrls ----------------------";
44 "--------- appendFormula: on Res + equ_nrls ----------------------";
45 "--------- appendFormula: on Res + equ_nrls ----------------------";
47 val Script sc = (#scr o get_met) ["Test","squ-equ-test-subpbl1"];
48 (writeln o term2str) sc;
49 val Script sc = (#scr o get_met) ["Test","solve_linear"];
50 (writeln o term2str) sc;
53 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
54 ("Test", ["sqroot-test","univariate","equation","test"],
55 ["Test","squ-equ-test-subpbl1"]))];
56 Iterator 1; moveActiveRoot 1;
57 autoCalculate 1 CompleteCalcHead;
58 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
59 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
61 appendFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
62 val ((pt,_),_) = get_calc 1;
63 val str = pr_ptree pr_short pt;
66 (*============ inhibit exn AK110726 ==============================================
67 (* 2nd string should be the same as 1st one *)
68 ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n2.1. x + 1 + -1 * 2 = 0\n2.2. 1 + x + -1 * 2 = 0\n2.3. 1 + (x + -1 * 2) = 0\n2.4. 1 + (x + -2) = 0\n2.5. 1 + (x + -2 * 1) = 0\n2.6. 1 + x + -2 * 1 = 0\n";
69 ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n2.1. x + 1 + -1 * 2 = 0\n2.2. -1 * 2 + (x + 1) = 0\n2.3. -1 * 2 + (1 + x) = 0\n2.4. 1 + (-1 * 2 + x) = 0\n2.5. 1 + (-2 + x) = 0\n2.6. 1 + (-2 * 1 + x) = 0\n";
70 if str = ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n2.1. x + 1 + -1 * 2 = 0\n2.2. -1 * 2 + (x + 1) = 0\n2.3. -1 * 2 + (1 + x) = 0\n2.4. 1 + (-1 * 2 + x) = 0\n2.5. 1 + (-2 + x) = 0\n2.6. 1 + (-2 * 1 + x) = 0\n" then ()
71 else error "inform.sml: diff.behav.appendFormula: on Res + equ 1";
72 ============ inhibit exn AK110726 ==============================================*)
74 moveDown 1 ([ ],Pbl); refFormula 1 ([1],Frm); (*x + 1 = 2*)
75 moveDown 1 ([1],Frm); refFormula 1 ([1],Res); (*x + 1 + -1 * 2 = 0*)
77 (*the seven steps of detailed derivation*)
78 moveDown 1 ([1 ],Res); refFormula 1 ([2,1],Frm);
79 moveDown 1 ([2,1],Frm); refFormula 1 ([2,1],Res);
80 moveDown 1 ([2,1],Res); refFormula 1 ([2,2],Res);
81 moveDown 1 ([2,2],Res); refFormula 1 ([2,3],Res);
82 moveDown 1 ([2,3],Res); refFormula 1 ([2,4],Res);
83 moveDown 1 ([2,4],Res); refFormula 1 ([2,5],Res);
84 moveDown 1 ([2,5],Res); refFormula 1 ([2,6],Res);
85 val ((pt,_),_) = get_calc 1;
86 if "-2 * 1 + (1 + x) = 0" = term2str (fst (get_obj g_result pt [2,6])) then()
87 else error "inform.sml: diff.behav.appendFormula: on Res + equ 2";
89 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
91 (*============ inhibit exn AK110725 ==============================================
92 (* ERROR: exception Bind raised *)
93 val (_,(tac,_,_)::_) = get_calc 1;
94 if tac = Rewrite_Set "Test_simplify" then ()
95 else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
96 ============ inhibit exn AK110725 ==============================================*)
98 autoCalculate 1 CompleteCalc;
99 val ((pt,_),_) = get_calc 1;
100 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
101 else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
102 (* autoCalculate 1 CompleteCalc;
103 val ((pt,p),_) = get_calc 1;
104 (writeln o istates2str) (get_obj g_loc pt [ ]);
105 (writeln o istates2str) (get_obj g_loc pt [1]);
106 (writeln o istates2str) (get_obj g_loc pt [2]);
107 (writeln o istates2str) (get_obj g_loc pt [3]);
108 (writeln o istates2str) (get_obj g_loc pt [3,1]);
109 (writeln o istates2str) (get_obj g_loc pt [3,2]);
110 (writeln o istates2str) (get_obj g_loc pt [4]);
113 "----------------------------------------------------------";
115 val fod = make_deriv (@{theory "Isac"}) Atools_erls
116 ((#rules o rep_rls) Test_simplify)
117 (sqrt_right false (@{theory "Pure"})) NONE
118 (str2term "x + 1 + -1 * 2 = 0");
119 (writeln o trtas2str) fod;
121 val ifod = make_deriv (@{theory "Isac"}) Atools_erls
122 ((#rules o rep_rls) Test_simplify)
123 (sqrt_right false (@{theory "Pure"})) NONE
124 (str2term "-2 * 1 + (1 + x) = 0");
125 (writeln o trtas2str) ifod;
126 fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
127 val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
128 val der = fod' @ (map rev_deriv' rifod');
129 (writeln o trtas2str) der;
130 "----------------------------------------------------------";
133 "--------- appendFormula: on Frm + equ_nrls ----------------------";
134 "--------- appendFormula: on Frm + equ_nrls ----------------------";
135 "--------- appendFormula: on Frm + equ_nrls ----------------------";
137 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
138 ("Test", ["sqroot-test","univariate","equation","test"],
139 ["Test","squ-equ-test-subpbl1"]))];
140 Iterator 1; moveActiveRoot 1;
141 autoCalculate 1 CompleteCalcHead;
142 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
143 appendFormula 1 "2+ -1 + x = 2"; refFormula 1 (get_pos 1 1);
145 moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (*x + 1 = 2*);
147 moveDown 1 ([1 ],Frm); refFormula 1 ([1,1],Frm);
148 moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res);
149 moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res);
150 moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res);
151 moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res);
152 moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res);
153 moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res);
154 val ((pt,_),_) = get_calc 1;
155 if "2 + -1 + x = 2" = term2str (fst (get_obj g_result pt [1,6])) then()
156 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
158 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
159 val (_,(tac,_,_)::_) = get_calc 1;
160 if tac = Rewrite_Set "norm_equation" then ()
161 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
162 autoCalculate 1 CompleteCalc;
163 val ((pt,_),_) = get_calc 1;
164 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
165 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
168 "--------- appendFormula: on Res + NO deriv ----------------------";
169 "--------- appendFormula: on Res + NO deriv ----------------------";
170 "--------- appendFormula: on Res + NO deriv ----------------------";
172 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
173 ("Test", ["sqroot-test","univariate","equation","test"],
174 ["Test","squ-equ-test-subpbl1"]))];
175 Iterator 1; moveActiveRoot 1;
176 autoCalculate 1 CompleteCalcHead;
177 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
178 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
180 appendFormula 1 "x = 2";
181 val ((pt,p),_) = get_calc 1;
182 val str = pr_ptree pr_short pt;
184 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" andalso p = ([1], Res)
186 else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
188 fetchProposedTactic 1;
189 val (_,(tac,_,_)::_) = get_calc 1;
190 if tac = Rewrite_Set "Test_simplify" then ()
191 else error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
192 autoCalculate 1 CompleteCalc;
193 val ((pt,_),_) = get_calc 1;
194 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
195 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
198 "--------- appendFormula: on Res + late deriv --------------------";
199 "--------- appendFormula: on Res + late deriv --------------------";
200 "--------- appendFormula: on Res + late deriv --------------------";
202 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
203 ("Test", ["sqroot-test","univariate","equation","test"],
204 ["Test","squ-equ-test-subpbl1"]))];
205 Iterator 1; moveActiveRoot 1;
206 autoCalculate 1 CompleteCalcHead;
207 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
208 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
210 appendFormula 1 "x = 1";
211 val ((pt,p),_) = get_calc 1;
212 val str = pr_ptree pr_short pt;
214 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)
215 then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
216 else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
218 fetchProposedTactic 1;
219 val (_,(tac,_,_)::_) = get_calc 1;
220 if tac = Check_Postcond ["linear", "univariate", "equation", "test"] then ()
221 else error "inform.sml: diff.behav.appendFormula: Res + late d 2";
222 autoCalculate 1 CompleteCalc;
223 val ((pt,_),_) = get_calc 1;
224 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
225 else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
228 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
229 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
230 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
232 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
233 ("Test", ["sqroot-test","univariate","equation","test"],
234 ["Test","squ-equ-test-subpbl1"]))];
235 Iterator 1; moveActiveRoot 1;
236 autoCalculate 1 CompleteCalcHead;
237 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
238 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
239 appendFormula 1 "[x = 3 + -2*1]";
240 val ((pt,p),_) = get_calc 1;
241 val str = pr_ptree pr_short pt;
243 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 ()
244 else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
245 autoCalculate 1 CompleteCalc;
246 val ((pt,p),_) = get_calc 1;
247 if "[x = 3 + -2 * 1]" = term2str (fst (get_obj g_result pt [])) then ()
248 (* ~~~~~~~~~~ simplify as last step in any script ?!*)
249 else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
253 "--------- replaceFormula: on Res + = ----------------------------";
254 "--------- replaceFormula: on Res + = ----------------------------";
255 "--------- replaceFormula: on Res + = ----------------------------";
257 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
258 ("Test", ["sqroot-test","univariate","equation","test"],
259 ["Test","squ-equ-test-subpbl1"]))];
260 Iterator 1; moveActiveRoot 1;
261 autoCalculate 1 CompleteCalcHead;
262 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
263 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
264 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*-1 + x*);
266 replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
267 val ((pt,_),_) = get_calc 1;
268 val str = pr_ptree pr_short pt;
271 (*============ inhibit exn AK110725 ==============================================
272 (* 2nd string should be the same as 1st one *)
273 ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n2.1. x + 1 + -1 * 2 = 0\n2.2. 1 + x + -1 * 2 = 0\n2.3. 1 + (x + -1 * 2) = 0\n2.4. 1 + (x + -2) = 0\n2.5. 1 + (x + -2 * 1) = 0\n2.6. 1 + x + -2 * 1 = 0\n";
274 ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n2.1. x + 1 + -1 * 2 = 0\n2.2. -1 * 2 + (x + 1) = 0\n2.3. -1 * 2 + (1 + x) = 0\n2.4. 1 + (-1 * 2 + x) = 0\n2.5. 1 + (-2 + x) = 0\n2.6. 1 + (-2 * 1 + x) = 0\n";
275 if str = ". ----- pblobj -----\n1. x + 1 = 2\n2. x + 1 + -1 * 2 = 0\n2.1. x + 1 + -1 * 2 = 0\n2.2. -1 * 2 + (x + 1) = 0\n2.3. -1 * 2 + (1 + x) = 0\n2.4. 1 + (-1 * 2 + x) = 0\n2.5. 1 + (-2 + x) = 0\n2.6. 1 + (-2 * 1 + x) = 0\n" then()
276 else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
277 ============ inhibit exn AK110725 ==============================================*)
279 autoCalculate 1 CompleteCalc;
280 val ((pt,pos as (p,_)),_) = get_calc 1;
281 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst) (get_obj g_result pt p) then()
282 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
285 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
286 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
287 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
289 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
290 ("Test", ["sqroot-test","univariate","equation","test"],
291 ["Test","squ-equ-test-subpbl1"]))];
292 Iterator 1; moveActiveRoot 1;
293 autoCalculate 1 CompleteCalcHead;
294 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
295 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
297 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
298 val ((pt,_),_) = get_calc 1;
299 val str = pr_ptree pr_short pt;
301 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 ()
302 else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
303 autoCalculate 1 CompleteCalc;
304 val ((pt,pos as (p,_)),_) = get_calc 1;
305 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
306 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
309 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
310 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
311 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
313 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
314 ("Test", ["sqroot-test","univariate","equation","test"],
315 ["Test","squ-equ-test-subpbl1"]))];
316 Iterator 1; moveActiveRoot 1;
317 autoCalculate 1 CompleteCalcHead;
318 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
320 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
321 val ((pt,_),_) = get_calc 1;
322 val str = pr_ptree pr_short pt;
324 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 ()
325 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
326 autoCalculate 1 CompleteCalc;
327 val ((pt,pos as (p,_)),_) = get_calc 1;
328 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
329 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
332 "--------- replaceFormula: cut calculation -----------------------";
333 "--------- replaceFormula: cut calculation -----------------------";
334 "--------- replaceFormula: cut calculation -----------------------";
336 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
337 ("Test", ["sqroot-test","univariate","equation","test"],
338 ["Test","squ-equ-test-subpbl1"]))];
339 Iterator 1; moveActiveRoot 1;
340 autoCalculate 1 CompleteCalc;
341 moveActiveRoot 1; moveActiveDown 1;
342 if get_pos 1 1 = ([1], Frm) then ()
343 else error "inform.sml: diff.behav. cut calculation 1";
345 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
346 val ((pt,p),_) = get_calc 1;
347 val str = pr_ptree pr_short pt;
349 if p = ([1], Res) then ()
350 else error "inform.sml: diff.behav. cut calculation 2";
353 (* 040307 copied from informtest.sml; ... old version
354 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
355 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
356 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
359 val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
360 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
361 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
362 "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
363 (*^^^ these are the elements for the root-problem (in variants)*)
364 (*vvv these are elements required for subproblems*)
365 "boundVariable a","boundVariable b","boundVariable alpha",
366 "interval {x::real. 0 <= x & x <= 2*r}",
367 "interval {x::real. 0 <= x & x <= 2*r}",
368 "interval {x::real. 0 <= x & x <= pi}",
369 "errorBound (eps=(0::real))"]
370 (*specifying is not interesting for this example*)
371 val spec = ("DiffApp", ["maximum_of","function"],
372 ["DiffApp","max_by_calculus"]);
373 (*the empty model with descriptions for user-guidance by Model_Problem*)
374 val empty_model = [Given ["fixedValues []"],
375 Find ["maximum", "valuesFor"],
376 Relate ["relations []"]];
379 (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
380 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
381 (*val nxt = ("Model_Problem", ...*)
382 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
384 val (p,_,f,nxt,_,pt) = me nxt p c pt;
385 (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
386 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
388 (0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
389 (0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
390 (0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
391 (0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
393 (*the empty CalcHead is checked w.r.t the model and re-established as such*)
394 val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, e_spec);
395 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
396 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";
398 (*there is one input to the model (could be more)*)
400 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
401 Find ["maximum", "valuesFor"],
402 Relate ["relations"]], Pbl, e_spec);
403 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
404 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 ()
405 else error "informtest.sml: diff.behav. max 2";
407 (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
408 val (b,pt''''',ocalhd) =
409 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
410 Find ["maximum A", "valuesFor [a,b]"],
411 Relate ["relations [A=a*b, a/2=r*sin alpha, \
412 \b/2=r*cos alpha]"]], Pbl, e_spec);
413 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
414 if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
416 (*this input is complete in variant 1 (variant 3 does not work yet)*)
417 val (b,pt''''',ocalhd) =
418 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
419 Find ["maximum A", "valuesFor [a,b]"],
420 Relate ["relations [A=a*b, \
421 \(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
423 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
425 modifycalcheadOK2xml 111 (bool2str b) ocalhd;
428 "--------- syntax error ------------------------------------------";
429 "--------- syntax error ------------------------------------------";
430 "--------- syntax error ------------------------------------------";
432 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
433 ("Test", ["sqroot-test","univariate","equation","test"],
434 ["Test","squ-equ-test-subpbl1"]))];
435 Iterator 1; moveActiveRoot 1;
436 autoCalculate 1 CompleteCalcHead;
437 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
438 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
440 appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
441 val ((pt,_),_) = get_calc 1;
442 val str = pr_ptree pr_short pt;
444 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
445 else error "inform.sml: diff.behav.appendFormula: syntax error";
448 "--------- CAS-command on ([],Pbl) -------------------------------";
449 "--------- CAS-command on ([],Pbl) -------------------------------";
450 "--------- CAS-command on ([],Pbl) -------------------------------";
451 val (p,_,f,nxt,_,pt) =
452 CalcTreeTEST [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
453 val ifo = "solve(x+1=2,x)";
454 val (_,(_,c,(pt,p))) = inform ([],[],(pt,p)) "solve(x+1=2,x)";
456 val nxt = ("Apply_Method",Apply_Method ["Test","squ-equ-test-subpbl1"]);
457 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
458 if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
459 else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
462 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
463 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
464 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
466 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
469 replaceFormula 1 "solve(x+1=2,x)";
470 autoCalculate 1 CompleteCalc;
471 val ((pt,p),_) = get_calc 1;
473 if p = ([], Res) then ()
474 else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
477 "--------- inform [rational,simplification] ----------------------";
478 "--------- inform [rational,simplification] ----------------------";
479 "--------- inform [rational,simplification] ----------------------";
481 CalcTree [(["Term (4/x - 3/y - 1)", "normalform N"],
482 ("Rational",["rational","simplification"],
483 ["simplification","of_rationals"]))];
484 Iterator 1; moveActiveRoot 1;
485 autoCalculate 1 CompleteCalcHead;
486 autoCalculate 1 (Step 1);
487 autoCalculate 1 (Step 1);
488 autoCalculate 1 (Step 1);
489 autoCalculate 1 (Step 1);
490 "--- input the next formula that _should_ be presented by mat-engine";
491 appendFormula 1 "(4 * y + -3 * x) / (x * y) + -1";
492 val ((pt,p),_) = get_calc 1;
493 if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
494 else error ("inform.sml: [rational,simplification] 1");
496 "--- input the next formula that would be presented by mat-engine";
497 (*autoCalculate 1 (Step 1);*)
498 appendFormula 1 "(4 * y + -3 * x + -1 * (x * y)) / (x * y)";
499 val ((pt,p),_) = get_calc 1;
500 if p = ([5], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
501 else error ("inform.sml: [rational,simplification] 2");
503 "--- input the exact final result";(*TODO: Exception- LIST "last_elem" raised*)
504 appendFormula 1 "(-3 * x + 4 * y + -1 * x * y) / (x * y)";
505 val ((pt,p),_) = get_calc 1;
506 if p = ([6], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
507 else error ("inform.sml: [rational,simplification] 3");
510 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
511 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
512 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
513 val t = str2term "Diff (x^^^2 + x + 1, x)";
514 case t of Const ("Diff.Diff", _) $ _ => ()
516 error "diff.sml behav.changed for CAS Diff (..., x)";
518 "-----------------------------------------------------------------";
520 (*2>*)CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
521 (*3>*)Iterator 1;moveActiveRoot 1;
522 "----- here the Headline has been finished";
523 (*4>*)moveActiveFormula 1 ([],Pbl);
524 (*5>*)replaceFormula 1 "Diff (x^2 + x + 1, x)";
525 val ((pt,_),_) = get_calc 1;
526 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
528 val (SOME istate, NONE) = loc;
530 writeln"-----------------------------------------------------------";
532 writeln (itms2str_ ctxt probl);
533 writeln (itms2str_ ctxt meth);
535 (*============ inhibit exn AK110725 ==============================================
536 (* ERROR: Argument: istate : istate * Proof.context Reason:
537 Can't unify istate to istate * Proof.context *)
538 writeln (istate2str istate);
539 ============ inhibit exn AK110725 ==============================================*)
543 refFormula 1 ([],Pbl) (*--> correct CalcHead*);
544 (*081016 NOT necessary (but leave it in Java):*)
545 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
546 "----- here the CalcHead has been completed --- ONCE MORE ?????";
548 (***difference II***)
549 val ((pt,p),_) = get_calc 1;
550 (*val p = ([], Pbl)*)
551 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
553 val (SOME istate, NONE) = loc;
554 (*============ inhibit exn AK110725 ==============================================
555 (* ERROR: Argument: istate : istate * Proof.context Reason: Can't unify istate to istate * Proof.context *)
556 print_depth 5; writeln (istate2str istate); print_depth 3;
557 ============ inhibit exn AK110725 ==============================================*)
560 ??.empty, Sundef, false)*)
561 print_depth 5; spec; print_depth 3;
563 ["derivative_of", "function"],
564 ["diff", "differentiate_on_R"]) : spec*)
565 writeln (itms2str_ ctxt probl);
567 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
568 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
569 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
570 writeln (itms2str_ ctxt meth);
572 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
573 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
574 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
575 writeln"-----------------------------------------------------------";
576 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
577 (*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
578 autoCalculate 1 CompleteCalc;
579 val ((pt,p),_) = get_calc 1;
580 val Form res = (#1 o pt_extract) (pt, ([],Res));
582 if p = ([], Res) andalso term2str res = "1 + 2 * x" then ()
583 else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
586 "--------- Take as 1st tac, start from exp -----------------------";
587 "--------- Take as 1st tac, start from exp -----------------------";
588 "--------- Take as 1st tac, start from exp -----------------------";
589 (*the following input is copied from BridgeLog Java <==> SML,
590 omitting unnecessary inputs*)
592 (*2>*)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac",["derivative_of","function"],["diff","differentiate_on_R"]))];
593 (*3>*)Iterator 1; moveActiveRoot 1;
595 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
596 (***difference II***)
597 val ((pt,_),_) = get_calc 1;
598 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
600 val (SOME istate, NONE) = loc;
601 (*============ inhibit exn AK110725 ==============================================
602 (* ERROR: Argument: istate : istate * Proof.context Reason: Can't unify istate to istate * Proof.context *)
603 print_depth 5; writeln (istate2str istate); print_depth 3;
604 ============ inhibit exn AK110725 ==============================================*)
607 ??.empty, Sundef, false)*)
608 print_depth 5; spec; print_depth 3;
610 ["derivative_of", "function"],
611 ["diff", "differentiate_on_R"]) : spec*)
612 writeln (itms2str_ ctxt probl);
614 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
615 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
616 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
617 writeln (itms2str_ ctxt meth);
619 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
620 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
621 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
622 writeln"-----------------------------------------------------------";
623 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
624 autoCalculate 1 (Step 1);
625 val ((pt,p),_) = get_calc 1;
626 val Form res = (#1 o pt_extract) (pt, p);
627 if term2str res = "d_d x (x ^^^ 2 + x + 1)" then ()
628 else error "diff.sml Diff (x^2 + x + 1, x) from exp";
631 "--------- init_form, start with <NEW> (CAS input) ---------------";
632 "--------- init_form, start with <NEW> (CAS input) ---------------";
633 "--------- init_form, start with <NEW> (CAS input) ---------------";
635 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
636 (*[[from sml: > @@@@@begin@@@@@
638 [[from sml: <CALCTREE>
639 [[from sml: <CALCID> 1 </CALCID>
640 [[from sml: </CALCTREE>
641 [[from sml: @@@@@end@@@@@*)
643 (*[[from sml: > @@@@@begin@@@@@
645 [[from sml: <ADDUSER>
646 [[from sml: <CALCID> 1 </CALCID>
647 [[from sml: <USERID> 1 </USERID>
648 [[from sml: </ADDUSER>
649 [[from sml: @@@@@end@@@@@*)
651 (*[[from sml: > @@@@@begin@@@@@
653 [[from sml: <CALCITERATOR>
654 [[from sml: <CALCID> 1 </CALCID>
655 [[from sml: <POSITION>
656 [[from sml: <INTLIST>
657 [[from sml: </INTLIST>
658 [[from sml: <POS> Pbl </POS>
659 [[from sml: </POSITION>
660 [[from sml: </CALCITERATOR>
661 [[from sml: @@@@@end@@@@@*)
662 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
663 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
665 [[from sml: <GETELEMENTSFROMTO>
666 [[from sml: <CALCID> 1 </CALCID>
667 [[from sml: <FORMHEADS>
668 [[from sml: <CALCFORMULA>
669 [[from sml: <POSITION>
670 [[from sml: <INTLIST>
671 [[from sml: </INTLIST>
672 [[from sml: <POS> Pbl </POS>
673 [[from sml: </POSITION>
674 [[from sml: <FORMULA>
676 [[from sml: <ISA> ________________________________________________ </ISA>
677 [[from sml: </MATHML>
679 [[from sml: </FORMULA>
680 [[from sml: </CALCFORMULA>
681 [[from sml: </FORMHEADS>
682 [[from sml: </GETELEMENTSFROMTO>
683 [[from sml: @@@@@end@@@@@*)
684 refFormula 1 ([],Pbl);
685 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
687 [[from sml: <REFFORMULA>
688 [[from sml: <CALCID> 1 </CALCID>
689 [[from sml: <CALCHEAD status = "incorrect">
690 [[from sml: <POSITION>
691 [[from sml: <INTLIST>
692 [[from sml: </INTLIST>
693 [[from sml: <POS> Pbl </POS>
694 [[from sml: </POSITION>
697 [[from sml: <ISA> Problem (e_domID, [e_pblID]) </ISA>
698 [[from sml: </MATHML>
701 [[from sml: <GIVEN> </GIVEN>
702 [[from sml: <WHERE> </WHERE>
703 [[from sml: <FIND> </FIND>
704 [[from sml: <RELATE> </RELATE>
706 [[from sml: <BELONGSTO> Pbl </BELONGSTO>
707 [[from sml: <SPECIFICATION>
708 [[from sml: <THEORYID> e_domID </THEORYID>
709 [[from sml: <PROBLEMID>
710 [[from sml: <STRINGLIST>
711 [[from sml: <STRING> e_pblID </STRING>
712 [[from sml: </STRINGLIST>
713 [[from sml: </PROBLEMID>
714 [[from sml: <METHODID>
715 [[from sml: <STRINGLIST>
716 [[from sml: <STRING> e_metID </STRING>
717 [[from sml: </STRINGLIST>
718 [[from sml: </METHODID>
719 [[from sml: </SPECIFICATION>
720 [[from sml: </CALCHEAD>
721 [[from sml: </REFFORMULA>
722 [[from sml: @@@@@end@@@@@*)
723 moveActiveFormula 1 ([],Pbl);
724 (*[[from sml: > @@@@@begin@@@@@
726 [[from sml: <CALCITERATOR>
727 [[from sml: <CALCID> 1 </CALCID>
728 [[from sml: <POSITION>
729 [[from sml: <INTLIST>
730 [[from sml: </INTLIST>
731 [[from sml: <POS> Pbl </POS>
732 [[from sml: </POSITION>
733 [[from sml: </CALCITERATOR>
734 [[from sml: @@@@@end@@@@@*)
735 replaceFormula 1 "Simplify (1+2)";
736 (*[[from sml: > @@@@@begin@@@@@
738 [[from sml: <REPLACEFORMULA>
739 [[from sml: <CALCID> 1 </CALCID>
740 [[from sml: <CALCCHANGED>
741 [[from sml: <UNCHANGED>
742 [[from sml: <INTLIST>
743 [[from sml: </INTLIST>
744 [[from sml: <POS> Pbl </POS>
745 [[from sml: </UNCHANGED>
746 [[from sml: <DELETED>
747 [[from sml: <INTLIST>
748 [[from sml: </INTLIST>
749 [[from sml: <POS> Pbl </POS>
750 [[from sml: </DELETED>
751 [[from sml: <GENERATED>
752 [[from sml: <INTLIST>
753 [[from sml: </INTLIST>
754 [[from sml: <POS> Met </POS> DIFFERENCE: Pbl
755 [[from sml: </GENERATED>
756 [[from sml: </CALCCHANGED>
757 [[from sml: </REPLACEFORMULA>
758 [[from sml: @@@@@end@@@@@*)
759 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
773 <ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
780 getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
781 (*[[from sml: > @@@@@begin@@@@@
783 [[from sml: <SYSERROR>
784 [[from sml: <CALCID> 1 </CALCID>
785 [[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
786 [[from sml: </SYSERROR>
787 [[from sml: @@@@@end@@@@@*)
788 (*step into getFormulaeFromTo --- bug corrected...*)