1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/test/Tools/isac/Interpret/error-pattern.sml Fri Apr 24 08:51:05 2020 +0200
1.3 @@ -0,0 +1,1384 @@
1.4 +(* Title: "Interpret/error-pattern.sml"
1.5 + Author: Walther Neuper 060225,
1.6 + (c) due to copyright terms
1.7 +
1.8 +Strange ERROR "Undefined fact: "all_left""
1.9 +*)
1.10 +
1.11 +"-----------------------------------------------------------------";
1.12 +"table of contents -----------------------------------------------";
1.13 +"-----------------------------------------------------------------";
1.14 +"appendForm with miniscript with mini-subpbl:";
1.15 +"--------- appendFormula: on Res + equ_nrls ----------------------";
1.16 +"--------- appendFormula: on Frm + equ_nrls ----------------------";
1.17 +"--------- appendFormula: on Res + NO deriv ----------------------";
1.18 +"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
1.19 +"replaceForm with miniscript with mini-subpbl:";
1.20 +"--------- replaceFormula: on Res + = ----------------------------";
1.21 +"--------- replaceFormula: on Res + = 1st Nd ---------------------";
1.22 +"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
1.23 +"--------- replaceFormula: cut calculation -----------------------";
1.24 +"--------- replaceFormula: cut calculation -----------------------";
1.25 +(* 040307 copied from informtest.sml ... old versions
1.26 +"--------- maximum-example, UC: Modeling / modifyCalcHead --------";*)
1.27 +"--------- syntax error ------------------------------------------";
1.28 +"CAS-command:";
1.29 +"--------- CAS-command on ([],Pbl) -------------------------------";
1.30 +"--------- CAS-command on ([],Pbl) FE-interface ------------------";
1.31 +"--------- locate_input_term [rational,simplification] ----------------------";
1.32 +"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
1.33 +"--------- Take as 1st tac, start from exp -----------------------";
1.34 +"--------- implicit_take, start with <NEW> (CAS input) ---------------";
1.35 +"--------- build fun check_for' ------------------------------";
1.36 +"--------- build fun check_for' ?bdv -------------------------";
1.37 +"--------- build fun check_for ------------------------";
1.38 +"--------- embed fun check_for ------------------------";
1.39 +"--------- embed fun find_fill_patterns ---------------------------";
1.40 +"--------- build fun is_exactly_equal, inputFillFormula ----------";
1.41 +"--------- fun appl_adds -----------------------------------------";
1.42 +"--------- fun concat_deriv --------------------------------------";
1.43 +"--------- handle an input formula -------------------------------";
1.44 +"--------- fun dropwhile' ----------------------------------------";
1.45 +"-----------------------------------------------------------------";
1.46 +"-----------------------------------------------------------------";
1.47 +"-----------------------------------------------------------------";
1.48 +
1.49 +
1.50 +"--------- appendFormula: on Res + equ_nrls ----------------------";
1.51 +"--------- appendFormula: on Res + equ_nrls ----------------------";
1.52 +"--------- appendFormula: on Res + equ_nrls ----------------------";
1.53 + val Prog sc = (#scr o get_met) ["Test","squ-equ-test-subpbl1"];
1.54 + (writeln o UnparseC.term) sc;
1.55 + val Prog sc = (#scr o get_met) ["Test","solve_linear"];
1.56 + (writeln o UnparseC.term) sc;
1.57 +
1.58 + reset_states ();
1.59 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.60 + ("Test", ["sqroot-test","univariate","equation","test"],
1.61 + ["Test","squ-equ-test-subpbl1"]))];
1.62 + Iterator 1; moveActiveRoot 1;
1.63 + autoCalculate 1 CompleteCalcHead;
1.64 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.65 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.66 +
1.67 + appendFormula 1 "-2 * 1 + (1 + x) = 0" (*|> Future.join*); refFormula 1 (get_pos 1 1);
1.68 + val ((pt,_),_) = get_calc 1;
1.69 + val str = pr_ctree pr_short pt;
1.70 +if str =
1.71 +(". ----- pblobj -----\n" ^
1.72 +"1. x + 1 = 2\n" ^
1.73 +"2. x + 1 + -1 * 2 = 0\n" ^
1.74 +"2.1. x + 1 + -1 * 2 = 0\n" ^
1.75 +"2.2. 1 + x + -1 * 2 = 0\n" ^
1.76 +"2.3. 1 + (x + -1 * 2) = 0\n" ^
1.77 +"2.4. 1 + (x + -2) = 0\n" ^
1.78 +"2.5. 1 + (x + -2 * 1) = 0\n" ^
1.79 +"2.6. 1 + x + -2 * 1 = 0\n" ) then ()
1.80 +else error "inform.sml: diff.behav.appendFormula: on Res + equ 1";
1.81 +
1.82 + moveDown 1 ([ ],Pbl); refFormula 1 ([1],Frm); (*x + 1 = 2*)
1.83 + moveDown 1 ([1],Frm); refFormula 1 ([1],Res); (*x + 1 + -1 * 2 = 0*)
1.84 +
1.85 + (*the seven steps of detailed derivation*)
1.86 + moveDown 1 ([1 ],Res); refFormula 1 ([2,1],Frm);
1.87 + moveDown 1 ([2,1],Frm); refFormula 1 ([2,1],Res);
1.88 + moveDown 1 ([2,1],Res); refFormula 1 ([2,2],Res);
1.89 + moveDown 1 ([2,2],Res); refFormula 1 ([2,3],Res);
1.90 + moveDown 1 ([2,3],Res); refFormula 1 ([2,4],Res);
1.91 + moveDown 1 ([2,4],Res); refFormula 1 ([2,5],Res);
1.92 + moveDown 1 ([2,5],Res); refFormula 1 ([2,6],Res);
1.93 + val ((pt,_),_) = get_calc 1;
1.94 + if "-2 * 1 + (1 + x) = 0" = UnparseC.term (fst (get_obj g_result pt [2,6])) then()
1.95 + else error "inform.sml: diff.behav.appendFormula: on Res + equ 2";
1.96 +
1.97 + fetchProposedTactic 1; (*takes Iterator 1 _1_*)
1.98 +(* <ERROR> error in kernel </ERROR> ALREADY IN 2009-2*)
1.99 +(*========== inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 =============
1.100 + val (_,(tac,_,_)::_) = get_calc 1;
1.101 + if tac = Rewrite_Set "Test_simplify" then ()
1.102 + else error "inform.sml: diff.behav.appendFormula: on Res + equ 3";
1.103 +============ inhibit exn WN1130701 broken at Isabelle2002 --> 2009-2 ============*)
1.104 +
1.105 + autoCalculate 1 CompleteCalc;
1.106 + val ((pt,_),_) = get_calc 1;
1.107 + if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
1.108 + else error "inform.sml: diff.behav.appendFormula: on Res + equ 4";
1.109 + (* autoCalculate 1 CompleteCalc;
1.110 + val ((pt,p),_) = get_calc 1;
1.111 + (writeln o istates2str) (get_obj g_loc pt [ ]);
1.112 + (writeln o istates2str) (get_obj g_loc pt [1]);
1.113 + (writeln o istates2str) (get_obj g_loc pt [2]);
1.114 + (writeln o istates2str) (get_obj g_loc pt [3]);
1.115 + (writeln o istates2str) (get_obj g_loc pt [3,1]);
1.116 + (writeln o istates2str) (get_obj g_loc pt [3,2]);
1.117 + (writeln o istates2str) (get_obj g_loc pt [4]);
1.118 +
1.119 + *)
1.120 +"----------------------------------------------------------";
1.121 +
1.122 + val fod = Derive.do_one (@{theory "Isac_Knowledge"}) Atools_erls
1.123 + ((#rules o Rule_Set.rep) Test_simplify)
1.124 + (sqrt_right false (@{theory "Pure"})) NONE
1.125 + (str2term "x + 1 + -1 * 2 = 0");
1.126 + (writeln o Derive.trtas2str) fod;
1.127 +
1.128 + val ifod = Derive.do_one (@{theory "Isac_Knowledge"}) Atools_erls
1.129 + ((#rules o Rule_Set.rep) Test_simplify)
1.130 + (sqrt_right false (@{theory "Pure"})) NONE
1.131 + (str2term "-2 * 1 + (1 + x) = 0");
1.132 + (writeln o Derive.trtas2str) ifod;
1.133 + fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1 = t2;
1.134 + val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod);
1.135 + val der = fod' @ (map Derive.rev_deriv' rifod');
1.136 + (writeln o Derive.trtas2str) der;
1.137 + "----------------------------------------------------------";
1.138 +DEconstrCalcTree 1;
1.139 +
1.140 +"--------- appendFormula: on Frm + equ_nrls ----------------------";
1.141 +"--------- appendFormula: on Frm + equ_nrls ----------------------";
1.142 +"--------- appendFormula: on Frm + equ_nrls ----------------------";
1.143 + reset_states ();
1.144 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.145 + ("Test", ["sqroot-test","univariate","equation","test"],
1.146 + ["Test","squ-equ-test-subpbl1"]))];
1.147 + Iterator 1; moveActiveRoot 1;
1.148 + autoCalculate 1 CompleteCalcHead;
1.149 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1) (*x + 1 = 2*);
1.150 + appendFormula 1 "2+ -1 + x = 2" (*|> Future.join*); refFormula 1 (get_pos 1 1);
1.151 +
1.152 + moveDown 1 ([],Pbl); refFormula 1 ([1],Frm) (*x + 1 = 2*);
1.153 +
1.154 + moveDown 1 ([1 ],Frm); refFormula 1 ([1,1],Frm);
1.155 + moveDown 1 ([1,1],Frm); refFormula 1 ([1,1],Res);
1.156 + moveDown 1 ([1,1],Res); refFormula 1 ([1,2],Res);
1.157 + moveDown 1 ([1,2],Res); refFormula 1 ([1,3],Res);
1.158 + moveDown 1 ([1,3],Res); refFormula 1 ([1,4],Res);
1.159 + moveDown 1 ([1,4],Res); refFormula 1 ([1,5],Res);
1.160 + moveDown 1 ([1,5],Res); refFormula 1 ([1,6],Res);
1.161 + val ((pt,_),_) = get_calc 1;
1.162 + if "2 + -1 + x = 2" = UnparseC.term (fst (get_obj g_result pt [1,6])) then()
1.163 + else error "inform.sml: diff.behav.appendFormula: on Frm + equ 1";
1.164 +
1.165 + fetchProposedTactic 1; (*takes Iterator 1 _1_*)
1.166 + val (_,(tac,_,_)::_) = get_calc 1;
1.167 + case tac of Rewrite_Set "norm_equation" => ()
1.168 + | _ => error "inform.sml: diff.behav.appendFormula: on Frm + equ 2";
1.169 + autoCalculate 1 CompleteCalc;
1.170 + val ((pt,_),_) = get_calc 1;
1.171 + if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
1.172 + else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
1.173 +DEconstrCalcTree 1;
1.174 +
1.175 +"--------- appendFormula: on Res + NO deriv ----------------------";
1.176 +"--------- appendFormula: on Res + NO deriv ----------------------";
1.177 +"--------- appendFormula: on Res + NO deriv ----------------------";
1.178 + reset_states ();
1.179 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.180 + ("Test", ["sqroot-test","univariate","equation","test"],
1.181 + ["Test","squ-equ-test-subpbl1"]))];
1.182 + Iterator 1; moveActiveRoot 1;
1.183 + autoCalculate 1 CompleteCalcHead;
1.184 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.185 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.186 +
1.187 + appendFormula 1 "x = 2" (*|> Future.join*);
1.188 + val ((pt,p),_) = get_calc 1;
1.189 + val str = pr_ctree pr_short pt;
1.190 + writeln str;
1.191 + if str = ". ----- pblobj -----\n1. x + 1 = 2\n" andalso p = ([1], Res)
1.192 + then ()
1.193 + else error "inform.sml: diff.behav.appendFormula: Res + NOder 1";
1.194 +
1.195 + fetchProposedTactic 1;
1.196 + val (_,(tac,_,_)::_) = get_calc 1;
1.197 + case tac of Rewrite_Set "Test_simplify" => ()
1.198 + | _ => error "inform.sml: diff.behav.appendFormula: Res + NOder 2";
1.199 + autoCalculate 1 CompleteCalc;
1.200 + val ((pt,_),_) = get_calc 1;
1.201 + if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
1.202 + else error "inform.sml: diff.behav.appendFormula: on Frm + equ 3";
1.203 +DEconstrCalcTree 1;
1.204 +
1.205 +"--------- appendFormula: on Res + late deriv --------------------";
1.206 +"--------- appendFormula: on Res + late deriv --------------------";
1.207 +"--------- appendFormula: on Res + late deriv --------------------";
1.208 +(*cp with "fun me" to test/../lucas-interpreter.sml:
1.209 + re-build: fun locate_input_term ---------------------------------------------------";
1.210 +*)
1.211 + reset_states ();
1.212 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.213 + ("Test", ["sqroot-test","univariate","equation","test"],
1.214 + ["Test","squ-equ-test-subpbl1"]))];
1.215 + Iterator 1; moveActiveRoot 1;
1.216 + autoCalculate 1 CompleteCalcHead;
1.217 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.218 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.219 +
1.220 + appendFormula 1 "x = 1" (*|> Future.join*);
1.221 + val ((pt,p),_) = get_calc 1;
1.222 + val str = pr_ctree pr_short pt;
1.223 + writeln str;
1.224 + 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)
1.225 + then () (*finds 1 step too early: ([3,2], Res) "x = 1" also by script !!!*)
1.226 + else error "inform.sml: diff.behav.appendFormula: Res + late d 1";
1.227 +
1.228 + fetchProposedTactic 1;
1.229 + val (_,(tac,_,_)::_) = get_calc 1;
1.230 + case tac of Check_Postcond ["LINEAR", "univariate", "equation", "test"] => ()
1.231 + | _ => error "inform.sml: diff.behav.appendFormula: Res + late d 2";
1.232 + autoCalculate 1 CompleteCalc;
1.233 + val ((pt,_),_) = get_calc 1;
1.234 + if "[x = 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
1.235 + else error "inform.sml: diff.behav.appendFormula: Res + late d 3";
1.236 +DEconstrCalcTree 1;
1.237 +
1.238 +"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
1.239 +"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
1.240 +"--------- appendFormula: on Res + late deriv [x = 3 + -2]---///--";
1.241 + reset_states ();
1.242 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.243 + ("Test", ["sqroot-test","univariate","equation","test"],
1.244 + ["Test","squ-equ-test-subpbl1"]))];
1.245 + Iterator 1; moveActiveRoot 1;
1.246 + autoCalculate 1 CompleteCalcHead;
1.247 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.248 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.249 + appendFormula 1 "[x = 3 + -2*1]" (*|> Future.join*);
1.250 + val ((pt,p),_) = get_calc 1;
1.251 + val str = pr_ctree pr_short pt;
1.252 + writeln str;
1.253 + 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 ()
1.254 + else error "inform.sml: diff.behav.appendFormula: Res + latEE 1";
1.255 + autoCalculate 1 CompleteCalc;
1.256 + val ((pt,p),_) = get_calc 1;
1.257 + if "[x = 3 + -2 * 1]" = UnparseC.term (fst (get_obj g_result pt [])) then ()
1.258 + (* ~~~~~~~~~~ simplify as last step in any script ?!*)
1.259 + else error "inform.sml: diff.behav.appendFormula: Res + latEE 2";
1.260 +DEconstrCalcTree 1;
1.261 +
1.262 +"--------- replaceFormula: on Res + = ----------------------------";
1.263 +"--------- replaceFormula: on Res + = ----------------------------";
1.264 +"--------- replaceFormula: on Res + = ----------------------------";
1.265 + reset_states ();
1.266 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.267 + ("Test", ["sqroot-test","univariate","equation","test"],
1.268 + ["Test","squ-equ-test-subpbl1"]))];
1.269 + Iterator 1; moveActiveRoot 1;
1.270 + autoCalculate 1 CompleteCalcHead;
1.271 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.272 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.273 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*-1 + x*);
1.274 +
1.275 + replaceFormula 1 "-2 * 1 + (1 + x) = 0"; refFormula 1 (get_pos 1 1);
1.276 + val ((pt,_),_) = get_calc 1;
1.277 + val str = pr_ctree pr_short pt;
1.278 +
1.279 +(* before AK110725 this was
1.280 +". ----- pblobj -----\n
1.281 +1. x + 1 = 2\n
1.282 +2. x + 1 + -1 * 2 = 0\n
1.283 +2.1. x + 1 + -1 * 2 = 0\n
1.284 +2.2. 1 + x + -1 * 2 = 0\n
1.285 +2.3. 1 + (x + -1 * 2) = 0\n
1.286 +2.4. 1 + (x + -2) = 0\n
1.287 +2.5. 1 + (x + -2 * 1) = 0\n
1.288 +2.6. 1 + x + -2 * 1 = 0\n";
1.289 +*)
1.290 +if str =
1.291 +". ----- pblobj -----\n"^
1.292 +"1. x + 1 = 2\n"^
1.293 +"2. x + 1 + -1 * 2 = 0\n"^
1.294 +"2.1. x + 1 + -1 * 2 = 0\n"^
1.295 +"2.2. 1 + x + -1 * 2 = 0\n"^
1.296 +"2.3. 1 + (x + -1 * 2) = 0\n"^
1.297 +"2.4. 1 + (x + -2) = 0\n"^
1.298 +"2.5. 1 + (x + -2 * 1) = 0\n"^
1.299 +"2.6. 1 + x + -2 * 1 = 0\n" then()
1.300 +else error "inform.sml: diff.behav.replaceFormula: on Res += 1";
1.301 +
1.302 + autoCalculate 1 CompleteCalc;
1.303 + val ((pt,pos as (p,_)),_) = get_calc 1;
1.304 + if pos = ([],Res) andalso "[x = 1]" = (UnparseC.term o fst) (get_obj g_result pt p) then()
1.305 + else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
1.306 +DEconstrCalcTree 1;
1.307 +
1.308 +"--------- replaceFormula: on Res + = 1st Nd ---------------------";
1.309 +"--------- replaceFormula: on Res + = 1st Nd ---------------------";
1.310 +"--------- replaceFormula: on Res + = 1st Nd ---------------------";
1.311 + reset_states ();
1.312 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.313 + ("Test", ["sqroot-test","univariate","equation","test"],
1.314 + ["Test","squ-equ-test-subpbl1"]))];
1.315 + Iterator 1; moveActiveRoot 1;
1.316 + autoCalculate 1 CompleteCalcHead;
1.317 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.318 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.319 +
1.320 + replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
1.321 + val ((pt,_),_) = get_calc 1;
1.322 + val str = pr_ctree pr_short pt;
1.323 + writeln str;
1.324 + 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 ()
1.325 + else error "inform.sml: diff.behav.replaceFormula: on Res 1 + = 1";
1.326 + autoCalculate 1 CompleteCalc;
1.327 + val ((pt,pos as (p,_)),_) = get_calc 1;
1.328 + if pos = ([],Res) andalso "[x = 1]" = (UnparseC.term o fst)(get_obj g_result pt p) then()
1.329 + else error "inform.sml: diff.behav.replaceFormula: on Res + = 2";
1.330 +DEconstrCalcTree 1;
1.331 +
1.332 +"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
1.333 +"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
1.334 +"--------- replaceFormula: on Frm + = 1st Nd ---------------------";
1.335 + reset_states ();
1.336 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.337 + ("Test", ["sqroot-test","univariate","equation","test"],
1.338 + ["Test","squ-equ-test-subpbl1"]))];
1.339 + Iterator 1; moveActiveRoot 1;
1.340 + autoCalculate 1 CompleteCalcHead;
1.341 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.342 +
1.343 + replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
1.344 + val ((pt,_),_) = get_calc 1;
1.345 + val str = pr_ctree pr_short pt;
1.346 + writeln str;
1.347 + 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 ()
1.348 + else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 1";
1.349 + autoCalculate 1 CompleteCalc;
1.350 + val ((pt,pos as (p,_)),_) = get_calc 1;
1.351 + if pos = ([],Res) andalso "[x = 1]" = (UnparseC.term o fst)(get_obj g_result pt p) then()
1.352 + else error "inform.sml: diff.behav.replaceFormula: on Frm 1 + = 2";
1.353 +DEconstrCalcTree 1;
1.354 +
1.355 +"--------- replaceFormula: cut calculation -----------------------";
1.356 +"--------- replaceFormula: cut calculation -----------------------";
1.357 +"--------- replaceFormula: cut calculation -----------------------";
1.358 + reset_states ();
1.359 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.360 + ("Test", ["sqroot-test","univariate","equation","test"],
1.361 + ["Test","squ-equ-test-subpbl1"]))];
1.362 + Iterator 1; moveActiveRoot 1;
1.363 + autoCalculate 1 CompleteCalc;
1.364 + moveActiveRoot 1; moveActiveDown 1;
1.365 + if get_pos 1 1 = ([1], Frm) then ()
1.366 + else error "inform.sml: diff.behav. cut calculation 1";
1.367 +
1.368 + replaceFormula 1 "x + 1 = 4 + -2"; refFormula 1 (get_pos 1 1);
1.369 + val ((pt,p),_) = get_calc 1;
1.370 + val str = pr_ctree pr_short pt;
1.371 + writeln str;
1.372 + if p = ([1], Res) then ()
1.373 + else error "inform.sml: diff.behav. cut calculation 2";
1.374 +
1.375 +
1.376 +(* 040307 copied from informtest.sml; ... old version
1.377 + "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
1.378 + "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
1.379 + "---------------- maximum-example, UC: Modeling / modifyCalcHead -";
1.380 +
1.381 + val p = ([],Pbl);
1.382 + val elems = ["fixedValues [r=Arbfix]","maximum A","valuesFor [a,b]",
1.383 + "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.384 + "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.385 + "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos (alpha::real)]",
1.386 + (*^^^ these are the elements for the root-problem (in variants)*)
1.387 + (*vvv these are elements required for subproblems*)
1.388 + "boundVariable a","boundVariable b","boundVariable alpha",
1.389 + "interval {x::real. 0 <= x & x <= 2*r}",
1.390 + "interval {x::real. 0 <= x & x <= 2*r}",
1.391 + "interval {x::real. 0 <= x & x <= pi}",
1.392 + "errorBound (eps=(0::real))"]
1.393 + (*specifying is not interesting for this example*)
1.394 + val spec = ("DiffApp", ["maximum_of","function"],
1.395 + ["DiffApp","max_by_calculus"]);
1.396 + (*the empty model with descriptions for user-guidance by Model_Problem*)
1.397 + val empty_model = [Given ["fixedValues []"],
1.398 + Find ["maximum", "valuesFor"],
1.399 + Relate ["relations []"]];
1.400 +
1.401 +
1.402 + (*!!!!!!!!!!!!!!!!! DON'T USE me FOR FINDING nxt !!!!!!!!!!!!!!!!!!*)
1.403 + val (p,_,f,nxt,_,pt) = CalcTreeTEST [(elems, spec)];
1.404 + (*val nxt = ("Model_Problem", ...*)
1.405 + val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
1.406 +
1.407 + val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.408 + (*nxt = Add_Given "fixedValues [r = Arbfix]"*)
1.409 + val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
1.410 +(*[
1.411 +(0 ,[] ,false ,#Given ,Inc fixedValues [] ,(??.empty, [])),
1.412 +(0 ,[] ,false ,#Find ,Inc maximum ,(??.empty, [])),
1.413 +(0 ,[] ,false ,#Find ,Inc valuesFor ,(??.empty, [])),
1.414 +(0 ,[] ,false ,#Relate ,Inc relations [] ,(??.empty, []))]*)
1.415 +
1.416 + (*the empty CalcHead is checked w.r.t the model and re-established as such*)
1.417 + val (b,pt,ocalhd) = input_icalhd pt (p,"", empty_model, Pbl, Spec.empty);
1.418 + val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
1.419 + 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(\"ThyC.id_empty\", [\"e_pblID\"], [\"e_metID\"]) )" then () else error "informtest.sml: diff.behav. max 1";
1.420 +
1.421 + (*there is one input to the model (could be more)*)
1.422 + val (b,pt,ocalhd) =
1.423 + input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
1.424 + Find ["maximum", "valuesFor"],
1.425 + Relate ["relations"]], Pbl, Spec.empty);
1.426 + val pbl = get_obj g_pbl pt (fst p); (writeln o (itms2str_ ctxt)) pbl;
1.427 + 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(\"ThyC.id_empty\", [\"e_pblID\"], [\"e_metID\"]) )" then ()
1.428 + else error "informtest.sml: diff.behav. max 2";
1.429 +
1.430 + (*this input is complete in variant 3, but the ME doesn't recognize FIXXXXME
1.431 + val (b,pt''''',ocalhd) =
1.432 + input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
1.433 + Find ["maximum A", "valuesFor [a,b]"],
1.434 + Relate ["relations [A=a*b, a/2=r*sin alpha, \
1.435 + \b/2=r*cos alpha]"]], Pbl, Spec.empty);
1.436 + val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
1.437 + if ocalhd2str ocalhd = ------------^^^^^^^^^^ missing !!!*)
1.438 +
1.439 + (*this input is complete in variant 1 (variant 3 does not work yet)*)
1.440 + val (b,pt''''',ocalhd) =
1.441 + input_icalhd pt (p,"", [Given ["fixedValues [r=Arbfix]"],
1.442 + Find ["maximum A", "valuesFor [a,b]"],
1.443 + Relate ["relations [A=a*b, \
1.444 + \(a/2)^^^2 + (b/2)^^^2 = r^^^2]"]],
1.445 + Pbl, Spec.empty);
1.446 + val pbl = get_obj g_pbl pt''''' (fst p); (writeln o (itms2str_ ctxt)) pbl;
1.447 +
1.448 + modifycalcheadOK2xml 111 (bool2str b) ocalhd;
1.449 +*)
1.450 +DEconstrCalcTree 1;
1.451 +
1.452 +"--------- syntax error ------------------------------------------";
1.453 +"--------- syntax error ------------------------------------------";
1.454 +"--------- syntax error ------------------------------------------";
1.455 + reset_states ();
1.456 + CalcTree [(["equality (x+1=(2::real))", "solveFor x","solutions L"],
1.457 + ("Test", ["sqroot-test","univariate","equation","test"],
1.458 + ["Test","squ-equ-test-subpbl1"]))];
1.459 + Iterator 1; moveActiveRoot 1;
1.460 + autoCalculate 1 CompleteCalcHead;
1.461 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 = 2*)
1.462 + autoCalculate 1 (Steps 1); refFormula 1 (get_pos 1 1);(*x + 1 + -1 * 2 = 0*);
1.463 +
1.464 + appendFormula 1 " x - "; (*<ERROR> syntax error in ' x - ' </ERROR>*)
1.465 + val ((pt,_),_) = get_calc 1;
1.466 + val str = pr_ctree pr_short pt;
1.467 + writeln str;
1.468 + if str = ". ----- pblobj -----\n1. x + 1 = 2\n" then ()
1.469 + else error "inform.sml: diff.behav.appendFormula: syntax error";
1.470 +DEconstrCalcTree 1;
1.471 +
1.472 +"--------- CAS-command on ([],Pbl) -------------------------------";
1.473 +"--------- CAS-command on ([],Pbl) -------------------------------";
1.474 +"--------- CAS-command on ([],Pbl) -------------------------------";
1.475 +val (p,_,f,nxt,_,pt) =
1.476 + CalcTreeTEST [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
1.477 +val ifo = "solve(x+1=2,x)";
1.478 +val (_,(_,c,(pt,p))) = Step_Solve.by_term (pt,p) "solve(x+1=2,x)";
1.479 +show_pt pt;
1.480 +val nxt = (Apply_Method ["Test","squ-equ-test-subpbl1"]);
1.481 +val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1.482 +if p = ([1], Frm) andalso f2str f = "x + 1 = 2" then ()
1.483 +else error "inform.sml: diff.behav. CAScmd ([],Pbl)";
1.484 +DEconstrCalcTree 1;
1.485 +
1.486 +"--------- CAS-command on ([],Pbl) FE-interface ------------------";
1.487 +"--------- CAS-command on ([],Pbl) FE-interface ------------------";
1.488 +"--------- CAS-command on ([],Pbl) FE-interface ------------------";
1.489 +reset_states ();
1.490 +CalcTree [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
1.491 +Iterator 1;
1.492 +moveActiveRoot 1;
1.493 +replaceFormula 1 "solve(x+1=2,x)";
1.494 +autoCalculate 1 CompleteCalc;
1.495 +val ((pt,p),_) = get_calc 1;
1.496 +show_pt pt;
1.497 +if p = ([], Res) then ()
1.498 +else error "inform.sml: diff.behav. CAScmd ([],Pbl) FE-interface";
1.499 +DEconstrCalcTree 1;
1.500 +
1.501 +"--------- inform [rational,simplification] ----------------------";
1.502 +"--------- inform [rational,simplification] ----------------------";
1.503 +"--------- inform [rational,simplification] ----------------------";
1.504 +reset_states ();
1.505 +CalcTree [(["Term (a * x / (b * x) + c * x / (d * x) + e / f)", "normalform N"],
1.506 + ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1.507 +Iterator 1; moveActiveRoot 1;
1.508 +autoCalculate 1 CompleteCalcHead;
1.509 +
1.510 +"--- (-1) give a preview on the calculation without any input";
1.511 +(*
1.512 +autoCalculate 1 CompleteCalc;
1.513 +val ((pt, p), _) = get_calc 1;
1.514 +show_pt pt;
1.515 +[
1.516 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.517 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.518 +(([1], Res), a / b + c / d + e / f), <--- (1) input arbitrary
1.519 +(([2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.520 +(([3], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
1.521 +(([4], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)), <--- (2) input next
1.522 +(([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))] <--- (3) is also final result
1.523 + EXAMPLE NOT OPTIMAL
1.524 +*)
1.525 +"--- (0) user input as the *first* step does not work, thus impdo at least 1 step";
1.526 +autoCalculate 1 (Steps 1);
1.527 +autoCalculate 1 (Steps 1);
1.528 +val ((pt, p), _) = get_calc 1;
1.529 +(*show_pt pt;
1.530 +[
1.531 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.532 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.533 +(([1], Res), a / b + c / d + e / f)]
1.534 +*)
1.535 +"--- (1) input an arbitrary next formula";
1.536 +appendFormula 1 "((a * d) + (c * b)) / (b * d) + e / f" (*|> Future.join*);
1.537 +val ((pt, p), _) = get_calc 1;
1.538 +(*show_pt pt;
1.539 +[
1.540 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.541 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.542 +(([1], Res), a / b + c / d + e / f),
1.543 +(([2,1], Frm), a / b + c / d + e / f),
1.544 +(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.545 +(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
1.546 +(([2], Res), (a * d + c * b) / (b * d) + e / f)]
1.547 +*)
1.548 +val ((pt,p),_) = get_calc 1;
1.549 +if p = ([2], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
1.550 +else error ("inform.sml: [rational,simplification] 1");
1.551 +
1.552 +"--- (2) input the next formula that would be presented by mat-engine";
1.553 +(* generate a preview:
1.554 +autoCalculate 1 (Steps 1);
1.555 +val ((pt, p), _) = get_calc 1;
1.556 +show_pt pt;
1.557 +[
1.558 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.559 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.560 +(([1], Res), a / b + c / d + e / f),
1.561 +(([2,1], Frm), a / b + c / d + e / f),
1.562 +(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.563 +(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
1.564 +(([2], Res), (a * d + c * b) / (b * d) + e / f),
1.565 +(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))] <--- input this
1.566 +*)
1.567 +appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
1.568 +val ((pt, p), _) = get_calc 1;
1.569 +(*show_pt pt;
1.570 +[
1.571 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.572 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.573 +(([1], Res), a / b + c / d + e / f),
1.574 +(([2,1], Frm), a / b + c / d + e / f),
1.575 +(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.576 +(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
1.577 +(([2], Res), (a * d + c * b) / (b * d) + e / f),
1.578 +(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
1.579 +*)
1.580 +if p = ([3], Res) andalso (length o children o (get_nd pt)) (fst p) = 0 then ()
1.581 +else error ("inform.sml: [rational,simplification] 2");
1.582 +
1.583 +"--- (3) input the exact final result";
1.584 +appendFormula 1 "(b * d * e + b * c * f + a * d * f) / (b * d * f)" (*|> Future.join*);
1.585 +val ((pt, p), _) = get_calc 1;
1.586 +(*show_pt pt;
1.587 +[
1.588 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.589 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.590 +(([1], Res), a / b + c / d + e / f),
1.591 +(([2,1], Frm), a / b + c / d + e / f),
1.592 +(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.593 +(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
1.594 +(([2], Res), (a * d + c * b) / (b * d) + e / f),
1.595 +(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.596 +(([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.597 +(([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
1.598 +(([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.599 +(([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f))]
1.600 +*)
1.601 +if p = ([4], Res) andalso (length o children o (get_nd pt)) (fst p) = 2 then ()
1.602 +else error ("inform.sml: [rational,simplification] 3");
1.603 +
1.604 +"--- (4) finish the calculation + check the postcondition (in the future)";
1.605 +autoCalculate 1 CompleteCalc;
1.606 +val ((pt, p), _) = get_calc 1;
1.607 +val (t, asm) = get_obj g_result pt [];
1.608 +if UnparseC.term t = "(a * d * f + b * c * f + b * d * e) / (b * d * f)" andalso
1.609 +UnparseC.terms asm = "[\"b * d * f \<noteq> 0\",\"d \<noteq> 0\",\"b \<noteq> 0\",\"a * x / (b * x) + c * x / (d * x) + e / f is_ratpolyexp\"]"
1.610 +then () else error "inform [rational,simplification] changed at end";
1.611 +(*show_pt pt;
1.612 +[
1.613 +(([], Frm), Simplify (a * x / (b * x) + c * x / (d * x) + e / f)),
1.614 +(([1], Frm), a * x / (b * x) + c * x / (d * x) + e / f),
1.615 +(([1], Res), a / b + c / d + e / f),
1.616 +(([2,1], Frm), a / b + c / d + e / f),
1.617 +(([2,1], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.618 +(([2,2], Res), (a * d + c * b) / (b * d) + e / f),
1.619 +(([2], Res), (a * d + c * b) / (b * d) + e / f),
1.620 +(([3], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.621 +(([4,1], Frm), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.622 +(([4,1], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
1.623 +(([4,2], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.624 +(([4], Res), (b * d * e + b * c * f + a * d * f) / (b * d * f)),
1.625 +(([5], Res), (a * (d * f) + b * (c * f) + b * (d * e)) / (b * (d * f))),
1.626 +(([6], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f)),
1.627 +(([], Res), (a * d * f + b * c * f + b * d * e) / (b * d * f))]
1.628 +*)
1.629 +DEconstrCalcTree 1;
1.630 +
1.631 +"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
1.632 +"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
1.633 +"--------- Take as 1st tac, start with <NEW> (CAS input) ---------";
1.634 +val t = str2term "Diff (x^^^2 + x + 1, x)";
1.635 +case t of Const ("Diff.Diff", _) $ _ => ()
1.636 + | _ => raise
1.637 + error "diff.sml behav.changed for CAS Diff (..., x)";
1.638 +atomty t;
1.639 +"-----------------------------------------------------------------";
1.640 +(*1>*)reset_states ();
1.641 +(*2>*)CalcTree [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
1.642 +(*3>*)Iterator 1;moveActiveRoot 1;
1.643 +"----- here the Headline has been finished";
1.644 +(*4>*)moveActiveFormula 1 ([],Pbl);
1.645 +(*5>*)replaceFormula 1 "Diff (x^2 + x + 1, x)";
1.646 +val ((pt,_),_) = get_calc 1;
1.647 +val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
1.648 +val NONE = env;
1.649 +val (SOME istate, NONE) = loc;
1.650 +(*default_print_depth 5;*)
1.651 +writeln"-----------------------------------------------------------";
1.652 +spec;
1.653 +writeln (itms2str_ ctxt probl);
1.654 +writeln (itms2str_ ctxt meth);
1.655 +writeln (Istate.string_of (fst istate));
1.656 +
1.657 +refFormula 1 ([],Pbl) (*--> correct CalcHead*);
1.658 + (*081016 NOT necessary (but leave it in Java):*)
1.659 +(*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
1.660 +"----- here the CalcHead has been completed --- ONCE MORE ?????";
1.661 +
1.662 +(***difference II***)
1.663 +val ((pt,p),_) = get_calc 1;
1.664 +(*val p = ([], Pbl)*)
1.665 +val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
1.666 +val NONE = env;
1.667 +val (SOME istate, NONE) = loc;
1.668 +(*default_print_depth 5;*) writeln (Istate.string_of (fst istate)); (*default_print_depth 3;*)
1.669 +(*Pstate ([],
1.670 + [], NONE,
1.671 + ??.empty, Sundef, false)*)
1.672 +(*default_print_depth 5;*) spec; (*default_print_depth 3;*)
1.673 +(*("Isac_Knowledge",
1.674 + ["derivative_of", "function"],
1.675 + ["diff", "differentiate_on_R"]) : spec*)
1.676 +writeln (itms2str_ ctxt probl);
1.677 +(*[
1.678 +(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
1.679 +(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
1.680 +(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
1.681 +writeln (itms2str_ ctxt meth);
1.682 +(*[
1.683 +(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
1.684 +(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
1.685 +(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
1.686 +writeln"-----------------------------------------------------------";
1.687 +(*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
1.688 +(*WN081028 fixed <ERROR> helpless </ERROR> by inform returning ...(.,Met)*)
1.689 +autoCalculate 1 CompleteCalc;
1.690 +val ((pt,p),_) = get_calc 1;
1.691 +val Form res = (#1 o pt_extract) (pt, ([],Res));
1.692 +show_pt pt;
1.693 +if p = ([], Res) andalso UnparseC.term res = "1 + 2 * x" then ()
1.694 +else error "diff.sml behav.changed for Diff (x^2 + x + 1, x)";
1.695 +DEconstrCalcTree 1;
1.696 +
1.697 +"--------- Take as 1st tac, start from exp -----------------------";
1.698 +"--------- Take as 1st tac, start from exp -----------------------";
1.699 +"--------- Take as 1st tac, start from exp -----------------------";
1.700 +(*the following input is copied from BridgeLog Java <==> SML,
1.701 + omitting unnecessary inputs*)
1.702 +(*1>*)reset_states ();
1.703 +(*2>*)CalcTree [(["functionTerm (x^2 + x + 1)", "differentiateFor x", "derivative f_'_f"],("Isac_Knowledge",["derivative_of","function"],["diff","differentiate_on_R"]))];
1.704 +(*3>*)Iterator 1; moveActiveRoot 1;
1.705 +
1.706 +(*6>*)(*completeCalcHead*)autoCalculate 1 CompleteCalcHead;
1.707 +(***difference II***)
1.708 +val ((pt,_),_) = get_calc 1;
1.709 +val PblObj {probl, meth, spec, fmz, env, loc, ...} = get_obj I pt [];
1.710 +val NONE = env;
1.711 +val (SOME istate, NONE) = loc;
1.712 +(*default_print_depth 5;*) writeln (Istate.string_of (fst istate)); (*default_print_depth 3;*)
1.713 +(*Pstate ([],
1.714 + [], NONE,
1.715 + ??.empty, Sundef, false)*)
1.716 +(*default_print_depth 5;*) spec; (*default_print_depth 3;*)
1.717 +(*("Isac_Knowledge",
1.718 + ["derivative_of", "function"],
1.719 + ["diff", "differentiate_on_R"]) : spec*)
1.720 +writeln (itms2str_ ctxt probl);
1.721 +(*[
1.722 +(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
1.723 +(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
1.724 +(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
1.725 +writeln (itms2str_ ctxt meth);
1.726 +(*[
1.727 +(1 ,[1] ,true ,#Given ,Cor functionTerm (x ^^^ 2 + x + 1) ,(f_, [x ^^^ 2 + x + 1])),
1.728 +(2 ,[1] ,true ,#Given ,Cor differentiateFor x ,(v_, [x])),
1.729 +(3 ,[1] ,true ,#Find ,Cor derivative f_'_f ,(f_'_f, [f_'_f]))]*)
1.730 +writeln"-----------------------------------------------------------";
1.731 +(*7>*)fetchProposedTactic 1 (*--> Apply_Method*);
1.732 +autoCalculate 1 (Steps 1);
1.733 +val ((pt,p),_) = get_calc 1;
1.734 +val Form res = (#1 o pt_extract) (pt, p);
1.735 +if UnparseC.term res = "d_d x (x ^^^ 2 + x + 1)" then ()
1.736 +else error "diff.sml Diff (x^2 + x + 1, x) from exp";
1.737 +DEconstrCalcTree 1;
1.738 +
1.739 +"--------- implicit_take, start with <NEW> (CAS input) ---------------";
1.740 +"--------- implicit_take, start with <NEW> (CAS input) ---------------";
1.741 +"--------- implicit_take, start with <NEW> (CAS input) ---------------";
1.742 +reset_states ();
1.743 +CalcTree [([], ("empty_thy_id", ["empty_probl_id"], ["empty_meth_id"]))];
1.744 +(*[[from sml: > @@@@@begin@@@@@
1.745 +[[from sml: 1
1.746 +[[from sml: <CALCTREE>
1.747 +[[from sml: <CALCID> 1 </CALCID>
1.748 +[[from sml: </CALCTREE>
1.749 +[[from sml: @@@@@end@@@@@*)
1.750 +Iterator 1;
1.751 +(*[[from sml: > @@@@@begin@@@@@
1.752 +[[from sml: 1
1.753 +[[from sml: <ADDUSER>
1.754 +[[from sml: <CALCID> 1 </CALCID>
1.755 +[[from sml: <USERID> 1 </USERID>
1.756 +[[from sml: </ADDUSER>
1.757 +[[from sml: @@@@@end@@@@@*)
1.758 +moveActiveRoot 1;
1.759 +(*[[from sml: > @@@@@begin@@@@@
1.760 +[[from sml: 1
1.761 +[[from sml: <CALCITERATOR>
1.762 +[[from sml: <CALCID> 1 </CALCID>
1.763 +[[from sml: <POSITION>
1.764 +[[from sml: <INTLIST>
1.765 +[[from sml: </INTLIST>
1.766 +[[from sml: <POS> Pbl </POS>
1.767 +[[from sml: </POSITION>
1.768 +[[from sml: </CALCITERATOR>
1.769 +[[from sml: @@@@@end@@@@@*)
1.770 +getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false;
1.771 +(*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
1.772 +[[from sml: 1
1.773 +[[from sml: <GETELEMENTSFROMTO>
1.774 +[[from sml: <CALCID> 1 </CALCID>
1.775 +[[from sml: <FORMHEADS>
1.776 +[[from sml: <CALCFORMULA>
1.777 +[[from sml: <POSITION>
1.778 +[[from sml: <INTLIST>
1.779 +[[from sml: </INTLIST>
1.780 +[[from sml: <POS> Pbl </POS>
1.781 +[[from sml: </POSITION>
1.782 +[[from sml: <FORMULA>
1.783 +[[from sml: <MATHML>
1.784 +[[from sml: <ISA> ________________________________________________ </ISA>
1.785 +[[from sml: </MATHML>
1.786 +[[from sml:
1.787 +[[from sml: </FORMULA>
1.788 +[[from sml: </CALCFORMULA>
1.789 +[[from sml: </FORMHEADS>
1.790 +[[from sml: </GETELEMENTSFROMTO>
1.791 +[[from sml: @@@@@end@@@@@*)
1.792 +refFormula 1 ([],Pbl);
1.793 +(*[[from sml: > @@@@@begin@@@@@ STILL CORRECT
1.794 +[[from sml: 1
1.795 +[[from sml: <REFFORMULA>
1.796 +[[from sml: <CALCID> 1 </CALCID>
1.797 +[[from sml: <CALCHEAD status = "incorrect">
1.798 +[[from sml: <POSITION>
1.799 +[[from sml: <INTLIST>
1.800 +[[from sml: </INTLIST>
1.801 +[[from sml: <POS> Pbl </POS>
1.802 +[[from sml: </POSITION>
1.803 +[[from sml: <HEAD>
1.804 +[[from sml: <MATHML>
1.805 +[[from sml: <ISA> Problem (ThyC.id_empty, [e_pblID]) </ISA>
1.806 +[[from sml: </MATHML>
1.807 +[[from sml: </HEAD>
1.808 +[[from sml: <MODEL>
1.809 +[[from sml: <GIVEN> </GIVEN>
1.810 +[[from sml: <WHERE> </WHERE>
1.811 +[[from sml: <FIND> </FIND>
1.812 +[[from sml: <RELATE> </RELATE>
1.813 +[[from sml: </MODEL>
1.814 +[[from sml: <BELONGSTO> Pbl </BELONGSTO>
1.815 +[[from sml: <SPECIFICATION>
1.816 +[[from sml: <THEORYID> ThyC.id_empty </THEORYID>
1.817 +[[from sml: <PROBLEMID>
1.818 +[[from sml: <STRINGLIST>
1.819 +[[from sml: <STRING> Problem.id_empty </STRING>
1.820 +[[from sml: </STRINGLIST>
1.821 +[[from sml: </PROBLEMID>
1.822 +[[from sml: <METHODID>
1.823 +[[from sml: <STRINGLIST>
1.824 +[[from sml: <STRING> e_metID </STRING>
1.825 +[[from sml: </STRINGLIST>
1.826 +[[from sml: </METHODID>
1.827 +[[from sml: </SPECIFICATION>
1.828 +[[from sml: </CALCHEAD>
1.829 +[[from sml: </REFFORMULA>
1.830 +[[from sml: @@@@@end@@@@@*)
1.831 +moveActiveFormula 1 ([],Pbl);
1.832 +(*[[from sml: > @@@@@begin@@@@@
1.833 +[[from sml: 1
1.834 +[[from sml: <CALCITERATOR>
1.835 +[[from sml: <CALCID> 1 </CALCID>
1.836 +[[from sml: <POSITION>
1.837 +[[from sml: <INTLIST>
1.838 +[[from sml: </INTLIST>
1.839 +[[from sml: <POS> Pbl </POS>
1.840 +[[from sml: </POSITION>
1.841 +[[from sml: </CALCITERATOR>
1.842 +[[from sml: @@@@@end@@@@@*)
1.843 +replaceFormula 1 "Simplify (1+2)";
1.844 +(*[[from sml: > @@@@@begin@@@@@
1.845 +[[from sml: 1
1.846 +[[from sml: <REPLACEFORMULA>
1.847 +[[from sml: <CALCID> 1 </CALCID>
1.848 +[[from sml: <CALCCHANGED>
1.849 +[[from sml: <UNCHANGED>
1.850 +[[from sml: <INTLIST>
1.851 +[[from sml: </INTLIST>
1.852 +[[from sml: <POS> Pbl </POS>
1.853 +[[from sml: </UNCHANGED>
1.854 +[[from sml: <DELETED>
1.855 +[[from sml: <INTLIST>
1.856 +[[from sml: </INTLIST>
1.857 +[[from sml: <POS> Pbl </POS>
1.858 +[[from sml: </DELETED>
1.859 +[[from sml: <GENERATED>
1.860 +[[from sml: <INTLIST>
1.861 +[[from sml: </INTLIST>
1.862 +[[from sml: <POS> Met </POS> DIFFERENCE: Pbl
1.863 +[[from sml: </GENERATED>
1.864 +[[from sml: </CALCCHANGED>
1.865 +[[from sml: </REPLACEFORMULA>
1.866 +[[from sml: @@@@@end@@@@@*)
1.867 +getFormulaeFromTo 1 ([],Pbl) ([],Pbl) 0 false(* DIFFERENCE: Pbl*);
1.868 +(*@@@@@begin@@@@@
1.869 + 1
1.870 +<GETELEMENTSFROMTO>
1.871 + <CALCID> 1 </CALCID>
1.872 + <FORMHEADS>
1.873 + <CALCFORMULA>
1.874 + <POSITION>
1.875 + <INTLIST>
1.876 + </INTLIST>
1.877 + <POS> Pbl </POS>
1.878 + </POSITION>
1.879 + <FORMULA>
1.880 + <MATHML>
1.881 + <ISA> Simplify (1 + 2) </ISA> WORKS !!!!!
1.882 + </MATHML>
1.883 + </FORMULA>
1.884 + </CALCFORMULA>
1.885 + </FORMHEADS>
1.886 +</GETELEMENTSFROMTO>
1.887 +@@@@@end@@@@@*)
1.888 +getFormulaeFromTo 1 ([],Pbl) ([],Met) 0 false;
1.889 +(*[[from sml: > @@@@@begin@@@@@
1.890 +[[from sml: 1
1.891 +[[from sml: <SYSERROR>
1.892 +[[from sml: <CALCID> 1 </CALCID>
1.893 +[[from sml: <ERROR> error in getFormulaeFromTo </ERROR>
1.894 +[[from sml: </SYSERROR>
1.895 +[[from sml: @@@@@end@@@@@*)
1.896 +(*step into getFormulaeFromTo --- bug corrected...*)
1.897 +
1.898 +"--------- build fun check_for' ------------------------------";
1.899 +"--------- build fun check_for' ------------------------------";
1.900 +"--------- build fun check_for' ------------------------------";
1.901 +val subst = [(str2term "bdv", str2term "x")]: subst;
1.902 +val rls = norm_Rational
1.903 +val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
1.904 +val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
1.905 +val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "1 / 2");
1.906 +
1.907 +val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
1.908 + rew_sub thy 1 [] e_rew_ord Rule_Set.empty false [] (HOLogic.Trueprop $ pat) res;
1.909 +if rewritten then NONE else SOME "e_errpatID";
1.910 +
1.911 +val norm_res = case rewrite_set_ (Isac()) false rls res' of
1.912 + NONE => res'
1.913 +| SOME (norm_res, _) => norm_res
1.914 +
1.915 +val norm_inf = case rewrite_set_ (Isac()) false rls inf of
1.916 + NONE => inf
1.917 +| SOME (norm_inf, _) => norm_inf;
1.918 +
1.919 +res' = inf;
1.920 +norm_res = norm_inf;
1.921 +
1.922 +val pat = parse_patt @{theory} "(?a + ?b)/?a = ?b";
1.923 +val (res, inf) = (str2term "(2 + 3)/2", str2term "3");
1.924 +if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
1.925 +then () else error "error patt example1 changed";
1.926 +
1.927 +val pat = parse_patt @{theory} "(?a + ?b)/(?a + ?c) = ?b / ?c";
1.928 +val (res, inf) = (str2term "(2 + 3)/(2 + 4)", str2term "3 / 4");
1.929 +if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
1.930 +then () else error "error patt example2 changed";
1.931 +
1.932 +val pat = parse_patt @{theory} "(?a + ?b)/(?b + ?c) = ?a / ?c";
1.933 +val (res, inf) = (str2term "(2 + 3)/(3 + 4)", str2term "2 / 4");
1.934 +if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
1.935 +then () else error "error patt example3 changed";
1.936 +
1.937 +val inf = str2term "1 / 2";
1.938 +if check_for' (res, inf) subst ("errpatID", pat) rls = SOME "errpatID"
1.939 +then () else error "error patt example3 changed";
1.940 +
1.941 +"--------- build fun check_for' ?bdv -------------------------";
1.942 +"--------- build fun check_for' ?bdv -------------------------";
1.943 +"--------- build fun check_for' ?bdv -------------------------";
1.944 +val subst = [(str2term "bdv", str2term "x")]: subst;
1.945 +val t = str2term "d_d x (x ^^^ 2 + sin (x ^^^ 4))";
1.946 +val SOME (t, _) = rewrite_set_inst_ thy false subst norm_diff t;
1.947 +if UnparseC.term t = "2 * x + cos (x ^^^ 4) * 4 * x ^^^ 3" then ()
1.948 +else error "build fun check_for' ?bdv changed 1";
1.949 +
1.950 +val rls = norm_diff
1.951 +val pat = parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)";
1.952 +val (res, inf) = (str2term "2 * x + d_d x (sin (x ^^^ 4))", str2term "2 * x + cos (4 * x ^^^ 3)");
1.953 +
1.954 +val (res', _, _, rewritten) = (*rewritten: the lhs of the pattern matches in res*)
1.955 + rew_sub thy 1 subst e_rew_ord Rule_Set.empty false [] (HOLogic.Trueprop $ pat) res;
1.956 +if UnparseC.term res' = "2 * x + cos (d_d x (x ^^^ 4))" andalso rewritten then ()
1.957 +else error "build fun check_for' ?bdv changed 2";
1.958 +
1.959 +val norm_res = case rewrite_set_inst_ (Isac()) false subst rls res' of
1.960 + NONE => res'
1.961 +| SOME (norm_res, _) => norm_res;
1.962 +if UnparseC.term norm_res = "2 * x + cos (4 * x ^^^ 3)" then ()
1.963 +else error "build fun check_for' ?bdv changed 3";
1.964 +
1.965 +val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of
1.966 + NONE => inf
1.967 +| SOME (norm_inf, _) => norm_inf;
1.968 +if UnparseC.term norm_inf = "2 * x + cos (4 * x ^^^ 3)" then ()
1.969 +else error "build fun check_for' ?bdv changed 4";
1.970 +
1.971 +res' = inf;
1.972 +if norm_res = norm_inf then ()
1.973 +else error "build fun check_for' ?bdv changed 5";
1.974 +
1.975 +if Error_Pattern.check_for' (res, inf) (subst: subst) ("errpatID": errpatID, pat) rls = SOME "errpatID"
1.976 +then () else error "error patt example1 changed";
1.977 +
1.978 +"--------- build fun check_for ------------------------";
1.979 +"--------- build fun check_for ------------------------";
1.980 +"--------- build fun check_for ------------------------";
1.981 +val (res, inf) =
1.982 + (str2term "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))",
1.983 + str2term "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)");
1.984 +val {errpats, nrls = rls, scr = Prog prog, ...} = get_met ["diff", "differentiate_on_R"]
1.985 +
1.986 +val env = [(str2term "v_v", str2term "x")];
1.987 +val errpats =
1.988 + [e_errpat, (*generalised for testing*)
1.989 + ("chain-rule-diff-both",
1.990 + [parse_patt @{theory} "d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)",
1.991 + parse_patt @{theory} "d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)",
1.992 + parse_patt @{theory} "d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1)",
1.993 + parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / ?u",
1.994 + parse_patt @{theory} "d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u"],
1.995 + [@{thm diff_sin_chain}, @{thm diff_cos_chain}, @{thm diff_pow_chain},
1.996 + @{thm diff_ln_chain}, @{thm diff_exp_chain}])]: errpat list;
1.997 +case Error_Pattern.check_for (res, inf) (prog, env) (errpats, rls) of SOME _ => ()
1.998 +| NONE => error "Error_Pattern.check_for broken";
1.999 +DEconstrCalcTree 1;
1.1000 +
1.1001 +"--------- embed fun check_for ------------------------";
1.1002 +"--------- embed fun check_for ------------------------";
1.1003 +"--------- embed fun check_for ------------------------";
1.1004 +reset_states ();
1.1005 +CalcTree
1.1006 +[(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1.1007 + ("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1.1008 +Iterator 1;
1.1009 +moveActiveRoot 1;
1.1010 +autoCalculate 1 CompleteCalcHead;
1.1011 +autoCalculate 1 (Steps 1);
1.1012 +autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1.1013 +(*autoCalculate 1 (Steps 1);([2], Res), d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)*)
1.1014 +
1.1015 +"~~~~~ fun appendFormula , args:"; val (cI, (ifo:TermC.as_string)) = (1, "d_d x (x ^ 2) + cos (4 * x ^ 3)");
1.1016 +"~~~~~ fun appendFormula' , args:"; val (cI, (ifo: TermC.as_string)) = (cI, ifo);
1.1017 + val cs = get_calc cI
1.1018 + val pos = get_pos cI 1;
1.1019 +(*+*)if pos = ([1], Res) then () else error "inform with (positive) Error_Pattern.check_for broken 1";
1.1020 + val ("ok", cs' as (_, _, ptp)) = (*case*) Step.do_next pos cs (*of*);
1.1021 + (*case*) Step_Solve.by_term ptp (encode ifo) (*of*); (*ERROR WAS: "no derivation found"*)
1.1022 +"~~~~~ fun Step_Solve.by_term , args:"; val (((*next_*)cs as (_, _, (pt, pos as (p, _))): Chead.calcstate'), istr)
1.1023 + = (cs', (encode ifo));
1.1024 + val ctxt = get_ctxt pt pos (*see TODO.thy*)
1.1025 + val SOME f_in = (*case*) TermC.parse (ThyC.get_theory "Isac_Knowledge") istr (*of*);
1.1026 + val f_in = Thm.term_of f_in
1.1027 + val pos_pred = lev_back' pos
1.1028 + val f_pred = Ctree.get_curr_formula (pt, pos_pred);
1.1029 + (*if*) f_pred = f_in; (*else*)
1.1030 + val NONE = (*case*) In_Chead.cas_input f_in (*of*);
1.1031 + (*old* )val (_, _, metID) = get_obj g_spec pt (par_pblobj pt p)
1.1032 + (*old*)val {scr = prog, ...} = Specify.get_met metID
1.1033 + (*old*)val istate = get_istate_LI pt pos
1.1034 + (*old*)val ctxt = get_ctxt pt pos
1.1035 + ( *old*)
1.1036 + val LI.Not_Derivable =
1.1037 + (*case*) LI.locate_input_term (pt, pos) f_in (*of*);
1.1038 + val pp = Ctree.par_pblobj pt p
1.1039 + val (errpats, nrls, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of
1.1040 + {errpats, nrls, scr = Rule.Prog prog, ...} => (errpats, nrls, prog)
1.1041 + | _ => error "inform: uncovered case of get_met"
1.1042 +;
1.1043 +(*+*)if errpats2str errpats = "[(\"chain-rule-diff-both\",\n[\"d_d ?bdv (sin ?u) = cos (d_d ?bdv ?u)\",\"d_d ?bdv (cos ?u) = - sin (d_d ?bdv ?u)\",\"d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1)\",\"d_d ?bdv (LogExp.ln ?u) = 1 / ?u\",\"d_d ?bdv (LogExp.ln ?u) = 1 / d_d ?bdv ?u\"],\n[\"d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u\",\"d_d ?bdv (cos ?u) = - sin ?u * d_d ?bdv ?u\",\"d_d ?bdv (?u ^^^ ?n) = ?n * ?u ^^^ (?n - 1) * d_d ?bdv ?u\",\"d_d ?bdv (LogExp.ln ?u) = d_d ?bdv ?u / ?u\",\"d_d ?bdv (E_ ^^^ ?u) = E_ ^^^ ?u * d_d ?x ?u\"]]"
1.1044 +(*+*)then () else error "inform with (positive) Error_Pattern.check_for broken 3";
1.1045 +
1.1046 + val {env, ...} = Ctree.get_istate_LI pt pos |> Istate.the_pstate
1.1047 +;
1.1048 +(*+*)if UnparseC.term f_pred = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" andalso
1.1049 +(*+*) UnparseC.term f_in = "d_d x (x ^^^ 2) + cos (4 * x ^^^ 3)"
1.1050 +(*+*)then () else error "inform with (positive) Error_Pattern.check_for broken 2";
1.1051 +
1.1052 + val SOME "chain-rule-diff-both" = (*case*) Error_Pattern.check_for (f_pred, f_in) (prog, env) (errpats, nrls) (*of*);
1.1053 +
1.1054 +"--- final check:";
1.1055 +(*+*)val (_, _, ptp') = cs';
1.1056 +case Step_Solve.by_term ptp' (encode ifo) of
1.1057 + ("error pattern #chain-rule-diff-both#", calcstate') => ()
1.1058 +| _ => error "inform with (positive) Error_Pattern.check_for broken"
1.1059 +
1.1060 +
1.1061 +"--------- embed fun find_fill_patterns ---------------------------";
1.1062 +"--------- embed fun find_fill_patterns ---------------------------";
1.1063 +"--------- embed fun find_fill_patterns ---------------------------";
1.1064 +reset_states ();
1.1065 +CalcTree
1.1066 +[(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1.1067 + ("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1.1068 +Iterator 1;
1.1069 +moveActiveRoot 1;
1.1070 +autoCalculate 1 CompleteCalcHead;
1.1071 +autoCalculate 1 (Steps 1);
1.1072 +autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1.1073 +appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (*|> Future.join*);
1.1074 + (*<CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>*)
1.1075 + (*or
1.1076 + <CALCMESSAGE> no derivation found </CALCMESSAGE>*)
1.1077 +
1.1078 +"~~~~~ fun findFillpatterns, args:"; val (cI, errpatID) = (1, "chain-rule-diff-both");
1.1079 + val ((pt, _), _) = get_calc cI
1.1080 + val pos = get_pos cI 1;
1.1081 +"~~~~~ fun find_fill_patterns , args:"; val ((pt, pos as (p, _)), errpatID) = ((pt, pos), errpatID);
1.1082 + val f_curr = Ctree.get_curr_formula (pt, pos);
1.1083 + val pp = Ctree.par_pblobj pt p
1.1084 + val (errpats, prog) = case Specify.get_met (Ctree.get_obj Ctree.g_metID pt pp) of
1.1085 + {errpats, scr = Rule.Prog prog, ...} => (errpats, prog)
1.1086 + | _ => error "find_fill_patterns: uncovered case of get_met"
1.1087 + val {env, ...} = Ctree.get_istate_LI pt pos |> Istate.the_pstate
1.1088 + val subst = Rtools.get_bdv_subst prog env
1.1089 + val errpatthms = errpats
1.1090 + |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))
1.1091 + |> map (#3: errpat -> thm list)
1.1092 + |> flat;
1.1093 +
1.1094 +case map (Error_Pattern.fill_from_store subst f_curr errpatID) errpatthms |> flat of
1.1095 + ("fill-d_d-arg", tm, thm, subs_opt) :: _ => if UnparseC.term tm =
1.1096 + "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1.1097 + then () else error "find_fill_patterns changed 1a"
1.1098 +| _ => error "find_fill_patterns changed 1b"
1.1099 +
1.1100 +"~~~~~ fun fill_from_store, args:"; val (subst, form, errpatID, thm) =
1.1101 + (subst, f_curr, errpatID, hd (*simulate beginning of "map"*) errpatthms);
1.1102 + val thmDeriv = Thm.get_name_hint thm
1.1103 + val (part, thyID) = thy_containing_thm thmDeriv
1.1104 + val theID = [part, thyID, "Theorems", ThmC.cut_id thmDeriv]
1.1105 + val Hthm {fillpats, ...} = get_the theID
1.1106 + val some = map (Error_Pattern.fill_form subst (thm, form) errpatID) fillpats;
1.1107 +
1.1108 +case some |> filter is_some |> map the of
1.1109 + ("fill-d_d-arg", tm, thm, subsopt) :: _ => if UnparseC.term tm =
1.1110 + "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1"
1.1111 + then () else error "find_fill_patterns changed 2a"
1.1112 +| _ => error "find_fill_patterns changed 2b"
1.1113 +
1.1114 +"~~~~~ fun fill_form, args:";
1.1115 + val ((subs_opt, subst), (thm, form), errpatID, (fillpatID, pat, erpaID)) =
1.1116 + (subst, (thm, form), errpatID, hd (*simulate beginning of "map"*) fillpats);
1.1117 +val (form', _, _, rewritten) =
1.1118 + rew_sub (Isac()) 1 subst e_rew_ord Rule_Set.empty false [] (HOLogic.Trueprop $ pat) form;
1.1119 +
1.1120 +if UnparseC.term form' = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" then ()
1.1121 +else error "find_fill_patterns changed 3";
1.1122 +
1.1123 +"~~~~~ to findFillpatterns return val:"; val (fillpats) =
1.1124 + (map (Error_Pattern.fill_from_store (subs_opt, subst) f_curr errpatID) errpatthms |> flat) (*only from "hd errpatthms"*);
1.1125 +
1.1126 +"vvv--- dropped this code WN120730";
1.1127 +val msg = "fill patterns " ^
1.1128 + ((map ((apsnd UnparseC.term) o quad2pair) fillpats) |> map pair2str_ |> strs2str_);
1.1129 +msg =
1.1130 + "fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1.1131 + " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1" ^
1.1132 + "#fill-both-args#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1.1133 + " =\nd_d x (x ^^^ 2) + cos ?_dummy_2 * d_d x ?_dummy_3" ^
1.1134 + "#fill-d_d#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1.1135 + " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1 x (x ^^^ 4)" ^
1.1136 + "#fill-inner-deriv#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" ^
1.1137 + " =\nd_d x (x ^^^ 2) + cos (x ^^^ 4) * ?_dummy_1" ^
1.1138 + "#fill-all#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) = d_d x (x ^^^ 2) + ?_dummy_1#";
1.1139 +"^^^--- dropped this code WN120730";
1.1140 +
1.1141 +if (map #1 fillpats) =
1.1142 + ["fill-d_d-arg", "fill-both-args", "fill-d_d", "fill-inner-deriv", "fill-all"]
1.1143 +then () else error "find_fill_patterns changed 4b";
1.1144 +DEconstrCalcTree 1;
1.1145 +
1.1146 +"--------- build fun is_exactly_equal, inputFillFormula ----------";
1.1147 +"--------- build fun is_exactly_equal, inputFillFormula ----------";
1.1148 +"--------- build fun is_exactly_equal, inputFillFormula ----------";
1.1149 +reset_states ();
1.1150 +CalcTree
1.1151 +[(["functionTerm (x ^ 2 + sin (x ^ 4))", "differentiateFor x", "derivative f_f'"],
1.1152 + ("Isac_Knowledge", ["derivative_of","function"], ["diff","differentiate_on_R"]))];
1.1153 +Iterator 1;
1.1154 +moveActiveRoot 1;
1.1155 +autoCalculate 1 CompleteCalcHead;
1.1156 +autoCalculate 1 (Steps 1);
1.1157 +autoCalculate 1 (Steps 1);(*([1], Res), d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))*)
1.1158 +appendFormula 1 "d_d x (x ^ 2) + cos (4 * x ^ 3)" (*|> Future.join*); (*<<<<<<<=========================*)
1.1159 +(* the check for errpat is maximally liberal (whole term modulo "nrls" from "type met"),
1.1160 + would recognize "cos (4 * x ^ (4 - 1)) + 2 * x" as well.
1.1161 + results in <CALCMESSAGE> error pattern #chain-rule-diff-both# </CALCMESSAGE>
1.1162 + instead of <CALCMESSAGE> no derivation found </CALCMESSAGE> *)
1.1163 + val ((pt,pos), _) = get_calc 1;
1.1164 + val p = get_pos 1 1;
1.1165 + val (Form f, _, asms) = pt_extract (pt, p);
1.1166 +
1.1167 + if p = ([1], Res) andalso UnparseC.term f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
1.1168 + case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1.1169 + ("diff_sum", thm)) =>
1.1170 + if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1.1171 + else error "embed fun fill_form changed 11"
1.1172 + | _ => error "embed fun fill_form changed 12"
1.1173 + else error "embed fun fill_form changed 13";
1.1174 +
1.1175 +findFillpatterns 1 "chain-rule-diff-both"; (*<<<<<<<=================================*)
1.1176 +(*<CALCMESSAGE> fill patterns #fill-d_d-arg#d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4)) =
1.1177 + d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x ?_dummy_1#fill-both-args#...#...#... *)
1.1178 + val ((pt,pos),_) = get_calc 1;
1.1179 + val p = get_pos 1 1;
1.1180 +
1.1181 + val (Form f, _, asms) = pt_extract (pt, p);
1.1182 + if p = ([1], Res) andalso UnparseC.term f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))" then
1.1183 + case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1.1184 + ("diff_sum", thm)) =>
1.1185 + if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1.1186 + else error "embed fun fill_form changed 21"
1.1187 + | _ => error "embed fun fill_form changed 22"
1.1188 + else error "embed fun fill_form changed 23";
1.1189 +
1.1190 +requestFillformula 1 ("chain-rule-diff-both", "fill-both-args");(*<<<<<<<============*)
1.1191 + (*<AUTOCALC> ([1], Res) ([2], Res) ([2], Res) </AUTOCALC>*)
1.1192 + val ((pt,pos),_) = get_calc 1;
1.1193 + val p = get_pos 1 1;
1.1194 + val (Form f, _, asms) = pt_extract (pt, p);
1.1195 + if p = ([1], Res) andalso existpt [2] pt
1.1196 + andalso UnparseC.term f = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"
1.1197 + then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1.1198 + ("diff_sum", thm)) =>
1.1199 + if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" then ()
1.1200 + else error "embed fun fill_form changed 31"
1.1201 + | _ => error "embed fun fill_form changed 32"
1.1202 + else error "embed fun fill_form changed 33";
1.1203 +
1.1204 +(* input a formula which exactly fills the gaps in a "fillformula"
1.1205 + presented to the learner immediately before by "requestFillformula (errpatID, fillpatID)":
1.1206 + errpatID: lhs of the respective thm = lhs of fillformula with fillpatID.
1.1207 + the respective thm is in the ctree ................
1.1208 +*)
1.1209 +"~~~~~ fun inputFillFormula, args:"; val (cI, ifo) =
1.1210 + (1, "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)");
1.1211 + val ((pt, _), _) = get_calc cI
1.1212 + val pos = get_pos cI 1;
1.1213 +
1.1214 +"~~~~~ fun is_exactly_equal, args:"; val ((pt, pos as (p, p_)), istr) = ((pt, pos), ifo);
1.1215 + val SOME ifo = parseNEW (ThyC.get_theory "Isac_Knowledge" |> ThyC.to_ctxt) istr
1.1216 + val p' = lev_on p;
1.1217 + val tac = get_obj g_tac pt p';
1.1218 +val Rewrite_Inst ([bbb as "(''bdv'', x)"], ("diff_sin_chain", ttt)) = tac;
1.1219 +if (UnparseC.term o Thm.prop_of) ttt = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
1.1220 +else error "inputFillFormula changed 10";
1.1221 + val Appl rew = applicable_in pos pt tac;
1.1222 + val Rewrite_Inst' (_, _, _, _, _, _, _, (res, _)) = rew;
1.1223 +
1.1224 +"~~~~~ to inputFillFormula return val:"; val ("ok", tac) = ("ok", tac);
1.1225 + val ("ok", (_, c, ptp as (_,p'))) = Step.by_tactic tac (pt, pos);
1.1226 + upd_calc cI (ptp, []);
1.1227 + upd_ipos cI 1 p';
1.1228 + autocalculateOK2xml cI pos (if null c then p' else last_elem c) p';
1.1229 +
1.1230 +"~~~~~ final check:";
1.1231 +val ((pt, _),_) = get_calc 1;
1.1232 +val p = get_pos 1 1;
1.1233 +val (Form f, _, asms) = pt_extract (pt, p);
1.1234 + if p = ([2], Res) andalso UnparseC.term f = "d_d x (x ^^^ 2) + cos (x ^^^ 4) * d_d x (x ^^^ 4)"
1.1235 + then case get_obj g_tac pt (fst p) of Rewrite_Inst (["(''bdv'', x)"],
1.1236 + ("diff_sin_chain", thm)) =>
1.1237 + if (UnparseC.term o Thm.prop_of) thm = "d_d ?bdv (sin ?u) = cos ?u * d_d ?bdv ?u" then ()
1.1238 + else error "inputFillFormula changed 111"
1.1239 + | _ => error "inputFillFormula changed 112"
1.1240 + else error "inputFillFormula changed 113";
1.1241 +
1.1242 +"--------- fun appl_adds -----------------------------------------";
1.1243 +"--------- fun appl_adds -----------------------------------------";
1.1244 +"--------- fun appl_adds -----------------------------------------";
1.1245 +(* val (dI, oris, ppc, pbt, selct::ss) =
1.1246 + (dI, pors, probl, ppc, map itms2fstr probl);
1.1247 + ...vvv
1.1248 + *)
1.1249 +(* val (dI, oris, ppc, pbt, (selct::ss))=
1.1250 + (#1 (some_spec ospec spec), oris, []:itm list,
1.1251 + ((#ppc o get_pbt) (#2 (some_spec ospec spec))),(imodel2fstr imodel));
1.1252 + val iii = appl_adds dI oris ppc pbt (selct::ss);
1.1253 + tracing(itms2str_ thy iii);
1.1254 +
1.1255 + val itm = appl_add' dI oris ppc pbt selct;
1.1256 + val ppc = insert_ppc' itm ppc;
1.1257 +
1.1258 + val _::selct::ss = (selct::ss);
1.1259 + val itm = appl_add' dI oris ppc pbt selct;
1.1260 + val ppc = insert_ppc' itm ppc;
1.1261 +
1.1262 + val _::selct::ss = (selct::ss);
1.1263 + val itm = appl_add' dI oris ppc pbt selct;
1.1264 + val ppc = insert_ppc' itm ppc;
1.1265 + tracing(itms2str_ thy ppc);
1.1266 +
1.1267 + val _::selct::ss = (selct::ss);
1.1268 + val itm = appl_add' dI oris ppc pbt selct;
1.1269 + val ppc = insert_ppc' itm ppc;
1.1270 + *)
1.1271 +"--------- fun concat_deriv --------------------------------------";
1.1272 +"--------- fun concat_deriv --------------------------------------";
1.1273 +"--------- fun concat_deriv --------------------------------------";
1.1274 +(*
1.1275 + val ({rew_ord, erls, rules,...}, fo, ifo) =
1.1276 + (Rule_Set.rep Test_simplify, str2term "x+1+ -1*2=0", str2term "-2*1+(x+1)=0");
1.1277 + (tracing o Derive.trtas2str) fod';
1.1278 +> ["
1.1279 +(x + 1 + -1 * 2 = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (x + 1) = 0, []))","
1.1280 +(-1 * 2 + (x + 1) = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (1 + x) = 0, []))","
1.1281 +(-1 * 2 + (1 + x) = 0, Thm ("radd_left_commute","?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (-1 * 2 + x) = 0, []))","
1.1282 +(1 + (-1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))","-1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]
1.1283 +val it = () : unit
1.1284 + (tracing o Derive.trtas2str) (map Derive.rev_deriv' rifod');
1.1285 +> ["
1.1286 +(1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))","-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))","
1.1287 +(1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute","?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))","
1.1288 +(-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute","?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]
1.1289 +val it = () : unit
1.1290 +*)
1.1291 +"--------- handle an input formula -------------------------------";
1.1292 +"--------- handle an input formula -------------------------------";
1.1293 +"--------- handle an input formula -------------------------------";
1.1294 +(*
1.1295 +Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:
1.1296 +Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden,
1.1297 +wenn Abteilungen nur auf gleichem Level gesucht werden ?
1.1298 +WN.040216
1.1299 +
1.1300 +Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml
1.1301 +
1.1302 +------------------------------------------------------------------------------
1.1303 +"Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
1.1304 +------------------------------------------------------------------------------
1.1305 +1. "5 * x / (x - 2) - x / (x + 2) = 4"
1.1306 +...
1.1307 +4. "12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalise", "poly"..
1.1308 +...
1.1309 +4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..
1.1310 +...
1.1311 +4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"
1.1312 +...
1.1313 +"[x = -4 / 3]"
1.1314 +------------------------------------------------------------------------------
1.1315 +(1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
1.1316 +
1.1317 +(4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]
1.1318 +------------------------------------------------------------------------------
1.1319 +
1.1320 +
1.1321 +------------------------------------------------------------------------------
1.1322 +"Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
1.1323 +------------------------------------------------------------------------------
1.1324 +1. "x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) = 1 / x"
1.1325 +...
1.1326 +4. "(3 + (-1 * x + x ^^^ 2)) * x = 1 * (9 * x + (x ^^^ 3 + -6 * x ^^^ 2))"
1.1327 + Subproblem["normalise", "polynomial", "univariate"..
1.1328 +...
1.1329 +4.4. "-6 * x + 5 * x ^^^ 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..
1.1330 +...
1.1331 +4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
1.1332 +4.4.5. "[x = 0, x = 6 / 5]"
1.1333 +...
1.1334 +5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"
1.1335 + "[x = 6 / 5]"
1.1336 +------------------------------------------------------------------------------
1.1337 +(1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]
1.1338 +
1.1339 +(4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]
1.1340 +------------------------------------------------------------------------------
1.1341 +
1.1342 +
1.1343 +------------------------------------------------------------------------------
1.1344 +"Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
1.1345 +------------------------------------------------------------------------------
1.1346 +1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"
1.1347 +...
1.1348 +6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"
1.1349 + Subproblem["sq", "rootX", "univariate", "equation"]
1.1350 +...
1.1351 +6.6. "144 + 288 * x + 144 * x ^^^ 2 = 144 + x ^^^ 2 + 288 * x + 143 * x ^^^ 2"
1.1352 + Subproblem["normalise", "polynomial", "univariate", "equation"]
1.1353 +...
1.1354 +6.6.3 "0 = 0" Subproblem["degree_0", "polynomial", "univariate", "equation"]
1.1355 +... Or_to_List
1.1356 +6.6.3.2 "UniversalList"
1.1357 +------------------------------------------------------------------------------
1.1358 +(1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]
1.1359 +
1.1360 +(6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]
1.1361 +------------------------------------------------------------------------------
1.1362 +*)
1.1363 +(*sh. comments auf 498*)
1.1364 +"--------- fun dropwhile' ----------------------------------------";
1.1365 +"--------- fun dropwhile' ----------------------------------------";
1.1366 +"--------- fun dropwhile' ----------------------------------------";
1.1367 +(*
1.1368 + fun equal a b = a=b;
1.1369 + val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];
1.1370 + val r_foder = rev foder; val r_ifoder = rev ifoder;
1.1371 + dropwhile' equal r_foder r_ifoder;
1.1372 +> vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list
1.1373 +
1.1374 + val foder = [3,4,5]; val ifoder = [11,12,3,4,5];
1.1375 + val r_foder = rev foder; val r_ifoder = rev ifoder;
1.1376 + dropwhile' equal r_foder r_ifoder;
1.1377 +> val it = ([3], [3, 12, 11]) : int list * int list
1.1378 +
1.1379 + val foder = [5]; val ifoder = [11,12,3,4,5];
1.1380 + val r_foder = rev foder; val r_ifoder = rev ifoder;
1.1381 + dropwhile' equal r_foder r_ifoder;
1.1382 +> val it = ([5], [5, 4, 3, 12, 11]) : int list * int list
1.1383 +
1.1384 + val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];
1.1385 + val r_foder = rev foder; val r_ifoder = rev ifoder;
1.1386 + dropwhile' equal r_foder r_ifoder;
1.1387 +> *** dropwhile': did not start with equal elements*)