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 AK110725 ==============================================
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 AK110725 ==============================================*)
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_*)
90 (*============ inhibit exn AK110725 ==============================================
91 (* ERROR: exception Bind raised *)
92 val (_,(tac,_,_)::_) = get_calc 1;
93 if tac = Rewrite_Set "Test_simplify" then ()
94 else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
95 ============ inhibit exn AK110725 ==============================================*)
96 autoCalculate 1 CompleteCalc;
97 val ((pt,_),_) = get_calc 1;
98 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
99 else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
100 (* autoCalculate 1 CompleteCalc;
101 val ((pt,p),_) = get_calc 1;
102 (writeln o istates2str) (get_obj g_loc pt [ ]);
103 (writeln o istates2str) (get_obj g_loc pt [1]);
104 (writeln o istates2str) (get_obj g_loc pt [2]);
105 (writeln o istates2str) (get_obj g_loc pt [3]);
106 (writeln o istates2str) (get_obj g_loc pt [3,1]);
107 (writeln o istates2str) (get_obj g_loc pt [3,2]);
108 (writeln o istates2str) (get_obj g_loc pt [4]);
111 "----------------------------------------------------------";
113 val fod = make_deriv (@{theory "Isac"}) Atools_erls
114 ((#rules o rep_rls) Test_simplify)
115 (sqrt_right false (@{theory "Pure"})) NONE
116 (str2term "x + 1 + -1 * 2 = 0");
117 (writeln o trtas2str) fod;
119 val ifod = make_deriv (@{theory "Isac"}) Atools_erls
120 ((#rules o rep_rls) Test_simplify)
121 (sqrt_right false (@{theory "Pure"})) NONE
122 (str2term "-2 * 1 + (1 + x) = 0");
123 (writeln o trtas2str) ifod;
124 fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
125 val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
126 val der = fod' @ (map rev_deriv' rifod');
127 (writeln o trtas2str) der;
128 "----------------------------------------------------------";
131 "--------- appendFormula: on Frm + equ_nrls ----------------------";
132 "--------- appendFormula: on Frm + equ_nrls ----------------------";
133 "--------- appendFormula: on Frm + equ_nrls ----------------------";
135 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
136 ("Test", ["sqroot-test","univariate","equation","test"],
137 ["Test","squ-equ-test-subpbl1"]))];
138 Iterator 1; moveActiveRoot 1;
139 autoCalculate 1 CompleteCalcHead;
140 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
141 appendFormula 1 "2+ -1 + x = 2"; refFormula 1 (get_pos 1 1);
143 moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (*x + 1 = 2*);
145 moveDown 1 ([1 ],Frm); refFormula 1 ([1,1],Frm);
146 moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res);
147 moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res);
148 moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res);
149 moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res);
150 moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res);
151 moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res);
152 val ((pt,_),_) = get_calc 1;
153 if "2 + -1 + x = 2" = term2str (fst (get_obj g_result pt [1,6])) then()
154 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
156 fetchProposedTactic 1; (*takes Iterator 1 _1_*)
157 val (_,(tac,_,_)::_) = get_calc 1;
158 if tac = Rewrite_Set "norm_equation" then ()
159 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
160 autoCalculate 1 CompleteCalc;
161 val ((pt,_),_) = get_calc 1;
162 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
163 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
166 "--------- appendFormula: on Res + NO deriv ----------------------";
167 "--------- appendFormula: on Res + NO deriv ----------------------";
168 "--------- appendFormula: on Res + NO deriv ----------------------";
170 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
171 ("Test", ["sqroot-test","univariate","equation","test"],
172 ["Test","squ-equ-test-subpbl1"]))];
173 Iterator 1; moveActiveRoot 1;
174 autoCalculate 1 CompleteCalcHead;
175 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
176 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
178 appendFormula 1 "x = 2";
179 val ((pt,p),_) = get_calc 1;
180 val str = pr_ptree pr_short pt;
182 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" andalso p = ([1], Res)
184 else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
186 fetchProposedTactic 1;
187 val (_,(tac,_,_)::_) = get_calc 1;
188 if tac = Rewrite_Set "Test_simplify" then ()
189 else error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
190 autoCalculate 1 CompleteCalc;
191 val ((pt,_),_) = get_calc 1;
192 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
193 else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
196 "--------- appendFormula: on Res + late deriv --------------------";
197 "--------- appendFormula: on Res + late deriv --------------------";
198 "--------- appendFormula: on Res + late deriv --------------------";
200 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
201 ("Test", ["sqroot-test","univariate","equation","test"],
202 ["Test","squ-equ-test-subpbl1"]))];
203 Iterator 1; moveActiveRoot 1;
204 autoCalculate 1 CompleteCalcHead;
205 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
206 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
208 appendFormula 1 "x = 1";
209 val ((pt,p),_) = get_calc 1;
210 val str = pr_ptree pr_short pt;
212 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)
213 then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
214 else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
216 fetchProposedTactic 1;
217 val (_,(tac,_,_)::_) = get_calc 1;
218 if tac = Check_Postcond ["linear", "univariate", "equation", "test"] then ()
219 else error "inform.sml: diff.behav.appendFormula: Res + late d 2";
220 autoCalculate 1 CompleteCalc;
221 val ((pt,_),_) = get_calc 1;
222 if "[x = 1]" = term2str (fst (get_obj g_result pt [])) then ()
223 else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
226 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
227 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
228 "--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
230 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
231 ("Test", ["sqroot-test","univariate","equation","test"],
232 ["Test","squ-equ-test-subpbl1"]))];
233 Iterator 1; moveActiveRoot 1;
234 autoCalculate 1 CompleteCalcHead;
235 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
236 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
237 appendFormula 1 "[x = 3 + -2*1]";
238 val ((pt,p),_) = get_calc 1;
239 val str = pr_ptree pr_short pt;
241 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 ()
242 else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
243 autoCalculate 1 CompleteCalc;
244 val ((pt,p),_) = get_calc 1;
245 if "[x = 3 + -2 * 1]" = term2str (fst (get_obj g_result pt [])) then ()
246 (* ~~~~~~~~~~ simplify as last step in any script ?!*)
247 else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
251 "--------- replaceFormula: on Res + = ----------------------------";
252 "--------- replaceFormula: on Res + = ----------------------------";
253 "--------- replaceFormula: on Res + = ----------------------------";
255 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
256 ("Test", ["sqroot-test","univariate","equation","test"],
257 ["Test","squ-equ-test-subpbl1"]))];
258 Iterator 1; moveActiveRoot 1;
259 autoCalculate 1 CompleteCalcHead;
260 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
261 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
262 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*-1 + x*);
264 replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
265 val ((pt,_),_) = get_calc 1;
266 val str = pr_ptree pr_short pt;
269 (*============ inhibit exn AK110725 ==============================================
270 (* 2nd string should be the same as 1st one *)
271 ". ----- 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";
272 ". ----- 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";
273 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()
274 else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
275 ============ inhibit exn AK110725 ==============================================*)
277 autoCalculate 1 CompleteCalc;
278 val ((pt,pos as (p,_)),_) = get_calc 1;
279 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst) (get_obj g_result pt p) then()
280 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
283 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
284 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
285 "--------- replaceFormula: on Res + = 1st Nd ---------------------";
287 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
288 ("Test", ["sqroot-test","univariate","equation","test"],
289 ["Test","squ-equ-test-subpbl1"]))];
290 Iterator 1; moveActiveRoot 1;
291 autoCalculate 1 CompleteCalcHead;
292 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
293 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
295 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
296 val ((pt,_),_) = get_calc 1;
297 val str = pr_ptree pr_short pt;
299 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 ()
300 else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
301 autoCalculate 1 CompleteCalc;
302 val ((pt,pos as (p,_)),_) = get_calc 1;
303 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
304 else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
307 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
308 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
309 "--------- replaceFormula: on Frm + = 1st Nd ---------------------";
311 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
312 ("Test", ["sqroot-test","univariate","equation","test"],
313 ["Test","squ-equ-test-subpbl1"]))];
314 Iterator 1; moveActiveRoot 1;
315 autoCalculate 1 CompleteCalcHead;
316 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
318 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
319 val ((pt,_),_) = get_calc 1;
320 val str = pr_ptree pr_short pt;
322 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 ()
323 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
324 autoCalculate 1 CompleteCalc;
325 val ((pt,pos as (p,_)),_) = get_calc 1;
326 if pos = ([],Res) andalso "[x = 1]" = (term2str o fst)(get_obj g_result pt p) then()
327 else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
330 "--------- replaceFormula: cut calculation -----------------------";
331 "--------- replaceFormula: cut calculation -----------------------";
332 "--------- replaceFormula: cut calculation -----------------------";
334 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
335 ("Test", ["sqroot-test","univariate","equation","test"],
336 ["Test","squ-equ-test-subpbl1"]))];
337 Iterator 1; moveActiveRoot 1;
338 autoCalculate 1 CompleteCalc;
339 moveActiveRoot 1; moveActiveDown 1;
340 if get_pos 1 1 = ([1], Frm) then ()
341 else error "inform.sml: diff.behav. cut calculation 1";
343 replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
344 val ((pt,p),_) = get_calc 1;
345 val str = pr_ptree pr_short pt;
347 if p = ([1], Res) then ()
348 else error "inform.sml: diff.behav. cut calculation 2";
351 (* 040307 copied from informtest.sml; ... old version
352 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
353 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
354 "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
357 val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
358 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
359 "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
360 "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
361 (*^^^ these are the elements for the root-problem (in variants)*)
362 (*vvv these are elements required for subproblems*)
363 "boundVariable a","boundVariable b","boundVariable alpha",
364 "interval {x::real. 0 <= x & x <= 2*r}",
365 "interval {x::real. 0 <= x & x <= 2*r}",
366 "interval {x::real. 0 <= x & x <= pi}",
367 "errorBound (eps=(0::real))"]
368 (*specifying is not interesting for this example*)
369 val spec = ("DiffApp", ["maximum_of","function"],
370 ["DiffApp","max_by_calculus"]);
371 (*the empty model with descriptions for user-guidance by Model_Problem*)
372 val empty_model = [Given ["fixedValues []"],
373 Find ["maximum", "valuesFor"],
374 Relate ["relations []"]];
377 (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
378 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
379 (*val nxt = ("Model_Problem", ...*)
380 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
382 val (p,_,f,nxt,_,pt) = me nxt p c pt;
383 (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
384 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
386 (0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
387 (0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
388 (0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
389 (0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
391 (*the empty CalcHead is checked w.r.t the model and re-established as such*)
392 val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, e_spec);
393 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
394 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";
396 (*there is one input to the model (could be more)*)
398 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
399 Find ["maximum", "valuesFor"],
400 Relate ["relations"]], Pbl, e_spec);
401 val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
402 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 ()
403 else error "informtest.sml: diff.behav. max 2";
405 (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
406 val (b,pt''''',ocalhd) =
407 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
408 Find ["maximum A", "valuesFor [a,b]"],
409 Relate ["relations [A=a*b, a/2=r*sin alpha, \
410 \b/2=r*cos alpha]"]], Pbl, e_spec);
411 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
412 if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
414 (*this input is complete in variant 1 (variant 3 does not work yet)*)
415 val (b,pt''''',ocalhd) =
416 input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
417 Find ["maximum A", "valuesFor [a,b]"],
418 Relate ["relations [A=a*b, \
419 \(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
421 val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
423 modifycalcheadOK2xml 111 (bool2str b) ocalhd;
426 "--------- syntax error ------------------------------------------";
427 "--------- syntax error ------------------------------------------";
428 "--------- syntax error ------------------------------------------";
430 CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
431 ("Test", ["sqroot-test","univariate","equation","test"],
432 ["Test","squ-equ-test-subpbl1"]))];
433 Iterator 1; moveActiveRoot 1;
434 autoCalculate 1 CompleteCalcHead;
435 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
436 autoCalculate 1 (Step 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
438 appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
439 val ((pt,_),_) = get_calc 1;
440 val str = pr_ptree pr_short pt;
442 if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
443 else error "inform.sml: diff.behav.appendFormula: syntax error";
446 "--------- CAS-command on ([],Pbl) -------------------------------";
447 "--------- CAS-command on ([],Pbl) -------------------------------";
448 "--------- CAS-command on ([],Pbl) -------------------------------";
449 val (p,_,f,nxt,_,pt) =
450 CalcTreeTEST [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
451 val ifo = "solve(x+1=2,x)";
452 val (_,(_,c,(pt,p))) = inform ([],[],(pt,p)) "solve(x+1=2,x)";
454 val nxt = ("Apply_Method",Apply_Method ["Test","squ-equ-test-subpbl1"]);
455 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
456 if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
457 else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
460 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
461 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
462 "--------- CAS-command on ([],Pbl) FE-interface ------------------";
464 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
467 replaceFormula 1 "solve(x+1=2,x)";
468 autoCalculate 1 CompleteCalc;
469 val ((pt,p),_) = get_calc 1;
471 if p = ([], Res) then ()
472 else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
475 "--------- inform [rational,simplification] ----------------------";
476 "--------- inform [rational,simplification] ----------------------";
477 "--------- inform [rational,simplification] ----------------------";
479 CalcTree [(["Term (4/x - 3/y - 1)", "normalform N"],
480 ("Rational",["rational","simplification"],
481 ["simplification","of_rationals"]))];
482 Iterator 1; moveActiveRoot 1;
483 autoCalculate 1 CompleteCalcHead;
484 autoCalculate 1 (Step 1);
485 autoCalculate 1 (Step 1);
486 autoCalculate 1 (Step 1);
487 autoCalculate 1 (Step 1);
488 "--- input the next formula that _should_ be presented by mat-engine";
489 appendFormula 1 "(4 * y + -3 * x) / (x * y) + -1";
490 val ((pt,p),_) = get_calc 1;
491 if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
492 else error ("inform.sml: [rational,simplification] 1");
494 "--- input the next formula that would be presented by mat-engine";
495 (*autoCalculate 1 (Step 1);*)
496 appendFormula 1 "(4 * y + -3 * x + -1 * (x * y)) / (x * y)";
497 val ((pt,p),_) = get_calc 1;
498 if p = ([5], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
499 else error ("inform.sml: [rational,simplification] 2");
501 "--- input the exact final result";(*TODO: Exception- LIST "last_elem" raised*)
502 appendFormula 1 "(-3 * x + 4 * y + -1 * x * y) / (x * y)";
503 val ((pt,p),_) = get_calc 1;
504 if p = ([6], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
505 else error ("inform.sml: [rational,simplification] 3");
508 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
509 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
510 "--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
511 val t = str2term "Diff (x^^^2 + x + 1, x)";
512 case t of Const ("Diff.Diff", _) $ _ => ()
514 error "diff.sml behav.changed for CAS Diff (..., x)";
516 "-----------------------------------------------------------------";
518 (*2>*)CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
519 (*3>*)Iterator 1;moveActiveRoot 1;
520 "----- here the Headline has been finished";
521 (*4>*)moveActiveFormula 1 ([],Pbl);
522 (*5>*)replaceFormula 1 "Diff (x^2 + x + 1, x)";
523 val ((pt,_),_) = get_calc 1;
524 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
526 val (SOME istate, NONE) = loc;
528 writeln"-----------------------------------------------------------";
530 writeln (itms2str_ ctxt probl);
531 writeln (itms2str_ ctxt meth);
532 (*============ inhibit exn AK110725 ==============================================
533 (* ERROR: Argument: istate : istate * Proof.context Reason: Can't unify istate to istate * Proof.context *)
534 writeln (istate2str istate);
535 ============ inhibit exn AK110725 ==============================================*)
539 refFormula 1 ([],Pbl) (*--> correct CalcHead*);
540 (*081016 NOT necessary (but leave it in Java):*)
541 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
542 "----- here the CalcHead has been completed --- ONCE MORE ?????";
544 (***difference II***)
545 val ((pt,p),_) = get_calc 1;
546 (*val p = ([], Pbl)*)
547 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
549 val (SOME istate, NONE) = loc;
550 (*============ inhibit exn AK110725 ==============================================
551 (* ERROR: Argument: istate : istate * Proof.context Reason: Can't unify istate to istate * Proof.context *)
552 print_depth 5; writeln (istate2str istate); print_depth 3;
553 ============ inhibit exn AK110725 ==============================================*)
556 ??.empty, Sundef, false)*)
557 print_depth 5; spec; print_depth 3;
559 ["derivative_of", "function"],
560 ["diff", "differentiate_on_R"]) : spec*)
561 writeln (itms2str_ ctxt probl);
563 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
564 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
565 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
566 writeln (itms2str_ ctxt meth);
568 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
569 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
570 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
571 writeln"-----------------------------------------------------------";
572 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
573 (*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
574 autoCalculate 1 CompleteCalc;
575 val ((pt,p),_) = get_calc 1;
576 val Form res = (#1 o pt_extract) (pt, ([],Res));
578 if p = ([], Res) andalso term2str res = "1 + 2 * x" then ()
579 else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
582 "--------- Take as 1st tac, start from exp -----------------------";
583 "--------- Take as 1st tac, start from exp -----------------------";
584 "--------- Take as 1st tac, start from exp -----------------------";
585 (*the following input is copied from BridgeLog Java <==> SML,
586 omitting unnecessary inputs*)
588 (*2>*)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac",["derivative_of","function"],["diff","differentiate_on_R"]))];
589 (*3>*)Iterator 1; moveActiveRoot 1;
591 (*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
592 (***difference II***)
593 val ((pt,_),_) = get_calc 1;
594 val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
596 val (SOME istate, NONE) = loc;
597 (*============ inhibit exn AK110725 ==============================================
598 (* ERROR: Argument: istate : istate * Proof.context Reason: Can't unify istate to istate * Proof.context *)
599 print_depth 5; writeln (istate2str istate); print_depth 3;
600 ============ inhibit exn AK110725 ==============================================*)
603 ??.empty, Sundef, false)*)
604 print_depth 5; spec; print_depth 3;
606 ["derivative_of", "function"],
607 ["diff", "differentiate_on_R"]) : spec*)
608 writeln (itms2str_ ctxt probl);
610 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
611 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
612 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
613 writeln (itms2str_ ctxt meth);
615 (1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
616 (2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
617 (3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
618 writeln"-----------------------------------------------------------";
619 (*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
620 autoCalculate 1 (Step 1);
621 val ((pt,p),_) = get_calc 1;
622 val Form res = (#1 o pt_extract) (pt, p);
623 if term2str res = "d_d x (x ^^^ 2 + x + 1)" then ()
624 else error "diff.sml Diff (x^2 + x + 1, x) from exp";
627 "--------- init_form, start with <NEW> (CAS input) ---------------";
628 "--------- init_form, start with <NEW> (CAS input) ---------------";
629 "--------- init_form, start with <NEW> (CAS input) ---------------";
631 CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
632 (*[[from sml: > @@@@@begin@@@@@
634 [[from sml: <CALCTREE>
635 [[from sml: <CALCID> 1 </CALCID>
636 [[from sml: </CALCTREE>
637 [[from sml: @@@@@end@@@@@*)
639 (*[[from sml: > @@@@@begin@@@@@
641 [[from sml: <ADDUSER>
642 [[from sml: <CALCID> 1 </CALCID>
643 [[from sml: <USERID> 1 </USERID>
644 [[from sml: </ADDUSER>
645 [[from sml: @@@@@end@@@@@*)
647 (*[[from sml: > @@@@@begin@@@@@
649 [[from sml: <CALCITERATOR>
650 [[from sml: <CALCID> 1 </CALCID>
651 [[from sml: <POSITION>
652 [[from sml: <INTLIST>
653 [[from sml: </INTLIST>
654 [[from sml: <POS> Pbl </POS>
655 [[from sml: </POSITION>
656 [[from sml: </CALCITERATOR>
657 [[from sml: @@@@@end@@@@@*)
658 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
659 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
661 [[from sml: <GETELEMENTSFROMTO>
662 [[from sml: <CALCID> 1 </CALCID>
663 [[from sml: <FORMHEADS>
664 [[from sml: <CALCFORMULA>
665 [[from sml: <POSITION>
666 [[from sml: <INTLIST>
667 [[from sml: </INTLIST>
668 [[from sml: <POS> Pbl </POS>
669 [[from sml: </POSITION>
670 [[from sml: <FORMULA>
672 [[from sml: <ISA> ________________________________________________ </ISA>
673 [[from sml: </MATHML>
675 [[from sml: </FORMULA>
676 [[from sml: </CALCFORMULA>
677 [[from sml: </FORMHEADS>
678 [[from sml: </GETELEMENTSFROMTO>
679 [[from sml: @@@@@end@@@@@*)
680 refFormula 1 ([],Pbl);
681 (*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
683 [[from sml: <REFFORMULA>
684 [[from sml: <CALCID> 1 </CALCID>
685 [[from sml: <CALCHEAD status = "incorrect">
686 [[from sml: <POSITION>
687 [[from sml: <INTLIST>
688 [[from sml: </INTLIST>
689 [[from sml: <POS> Pbl </POS>
690 [[from sml: </POSITION>
693 [[from sml: <ISA> Problem (e_domID, [e_pblID]) </ISA>
694 [[from sml: </MATHML>
697 [[from sml: <GIVEN> </GIVEN>
698 [[from sml: <WHERE> </WHERE>
699 [[from sml: <FIND> </FIND>
700 [[from sml: <RELATE> </RELATE>
702 [[from sml: <BELONGSTO> Pbl </BELONGSTO>
703 [[from sml: <SPECIFICATION>
704 [[from sml: <THEORYID> e_domID </THEORYID>
705 [[from sml: <PROBLEMID>
706 [[from sml: <STRINGLIST>
707 [[from sml: <STRING> e_pblID </STRING>
708 [[from sml: </STRINGLIST>
709 [[from sml: </PROBLEMID>
710 [[from sml: <METHODID>
711 [[from sml: <STRINGLIST>
712 [[from sml: <STRING> e_metID </STRING>
713 [[from sml: </STRINGLIST>
714 [[from sml: </METHODID>
715 [[from sml: </SPECIFICATION>
716 [[from sml: </CALCHEAD>
717 [[from sml: </REFFORMULA>
718 [[from sml: @@@@@end@@@@@*)
719 moveActiveFormula 1 ([],Pbl);
720 (*[[from sml: > @@@@@begin@@@@@
722 [[from sml: <CALCITERATOR>
723 [[from sml: <CALCID> 1 </CALCID>
724 [[from sml: <POSITION>
725 [[from sml: <INTLIST>
726 [[from sml: </INTLIST>
727 [[from sml: <POS> Pbl </POS>
728 [[from sml: </POSITION>
729 [[from sml: </CALCITERATOR>
730 [[from sml: @@@@@end@@@@@*)
731 replaceFormula 1 "Simplify (1+2)";
732 (*[[from sml: > @@@@@begin@@@@@
734 [[from sml: <REPLACEFORMULA>
735 [[from sml: <CALCID> 1 </CALCID>
736 [[from sml: <CALCCHANGED>
737 [[from sml: <UNCHANGED>
738 [[from sml: <INTLIST>
739 [[from sml: </INTLIST>
740 [[from sml: <POS> Pbl </POS>
741 [[from sml: </UNCHANGED>
742 [[from sml: <DELETED>
743 [[from sml: <INTLIST>
744 [[from sml: </INTLIST>
745 [[from sml: <POS> Pbl </POS>
746 [[from sml: </DELETED>
747 [[from sml: <GENERATED>
748 [[from sml: <INTLIST>
749 [[from sml: </INTLIST>
750 [[from sml: <POS> Met </POS> DIFFERENCE: Pbl
751 [[from sml: </GENERATED>
752 [[from sml: </CALCCHANGED>
753 [[from sml: </REPLACEFORMULA>
754 [[from sml: @@@@@end@@@@@*)
755 getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
769 <ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
776 getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
777 (*[[from sml: > @@@@@begin@@@@@
779 [[from sml: <SYSERROR>
780 [[from sml: <CALCID> 1 </CALCID>
781 [[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
782 [[from sml: </SYSERROR>
783 [[from sml: @@@@@end@@@@@*)
784 (*step into getFormulaeFromTo --- bug corrected...*)