wneuper/isa: test/Tools/isac/Knowledge/polyminus.sml@c3acf9c442ac

     1 (* title:  Knowledge/polyminus.sml

     2    author: Walther Neuper

     3    WN071207,

     4    (c) due to copyright terms

     5 *)

     6 "--------------------------------------------------------";

     7 "--------------------------------------------------------";

     8 "table of contents --------------------------------------";

     9 "--------------------------------------------------------";

    10 "----------- fun identifier --------------------------------------------------------------------";

    11 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    12 "----------- fun ist_monom ---------------------------------------------------------------------";

    13 "----------- fun eval_ist_monom -------------------------";

    14 "----------- watch order_add_mult  ----------------------";

    15 "----------- build predicate for +- ordering ------------";

    16 "----------- build fasse_zusammen -----------------------";

    17 "----------- build verschoenere -------------------------";

    18 "----------- met simplification for_polynomials with_minu";

    19 "----------- me simplification.for_polynomials.with_minus";

    20 "----------- pbl polynom vereinfachen p.33 --------------";

    21 "----------- met probe fuer_polynom ---------------------";

    22 "----------- pbl polynom probe --------------------------";

    23 "----------- pbl klammer polynom vereinfachen p.34 ------";

    24 "----------- try fun applyTactics -----------------------";

    25 "----------- pbl binom polynom vereinfachen p.39 --------";

    26 "----------- pbl binom polynom vereinfachen: cube -------";

    27 "----------- Refine.refine Vereinfache -------------------------";

    28 "----------- *** Problem.prep_input: syntax error in '#Where' of [v";

    29 "--------------------------------------------------------";

    30 "--------------------------------------------------------";

    31 "--------------------------------------------------------";

    33 val thy = @{theory "PolyMinus"};

    34 val ctxt = Proof_Context.init_global thy;

    36 "----------- fun identifier --------------------------------------------------------------------";

    37 "----------- fun identifier --------------------------------------------------------------------";

    38 "----------- fun identifier --------------------------------------------------------------------";

    39 if identifier (TermC.str2term "12 ::real") = "12"     then () else error "identifier 1";

    40 if identifier (TermC.str2term

    41   "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g ::real") = "|||||||||||||"

    42                                                       then () else error "identifier 1a";

    44 if identifier (TermC.str2term "a ::real") = "a"       then () else error "identifier 2";

    45 if identifier (TermC.str2term "3 * a ::real") = "a"   then () else error "identifier 3";

    47 if identifier (TermC.str2term "a \<up> 2 ::real") = "a"   then () else error "identifier 4";

    48 if identifier (TermC.str2term "3*a \<up> 2 ::real") = "a" then () else error "identifier 5";

    49 if identifier (TermC.str2term "a * b ::real") = "b"   then () else error "identifier 5b";

    51 (*these are strange (see "specific monomials" in comment to fun.def.)..*)

    52 if identifier (TermC.str2term "a*b ::real") = "b"     then () else error "identifier 6";

    53 if identifier (TermC.str2term "(3*a*b) ::real") = "b" then () else error "identifier 7";

    56 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    57 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    58 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    59 "a" < "b";

    60 "ba" < "ab";

    61 "123" < "a"; (*unused due to ---vvv*)

    62 "12" < "3"; (*true !!!*)

    64 " a kleiner b ==> (b + a) = (a + b)";

    65 TermC.str2term "aaa";

    66 TermC.str2term "222 * aaa";

    68 case eval_kleiner 0 0 (TermC.str2term "123 kleiner 32") 0 of

    69     SOME ("123 kleiner 32 = False", _) => ()

    70   | _ => error "polyminus.sml: 12 kleiner 9 = False";

    71 case eval_kleiner 0 0 (TermC.str2term "a kleiner b") 0 of

    72     SOME ("a kleiner b = True", _) => ()

    73   | _ => error "polyminus.sml: a kleiner b = True";

    74 case eval_kleiner 0 0 (TermC.str2term "(10*g) kleiner f") 0 of

    75     SOME ("10 * g kleiner f = False", _) => ()

    76   | _ => error "polyminus.sml: 10 * g kleiner f = False";

    77 case eval_kleiner 0 0 (TermC.str2term "(a \<up> 2) kleiner b") 0 of

    78     SOME ("a \<up> 2 kleiner b = True", _) => ()

    79   | _ => error "polyminus.sml: a \<up> 2 kleiner b = True";

    80 case eval_kleiner 0 0 (TermC.str2term "(3*a \<up> 2) kleiner b") 0 of

    81     SOME ("3 * a \<up> 2 kleiner b = True", _) => ()

    82   | _ => error "polyminus.sml: 3 * a \<up> 2 kleiner b = True";

    83 case eval_kleiner 0 0 (TermC.str2term "(a*b) kleiner c") 0 of

    84     SOME ("a * b kleiner c = True", _) => ()

    85   | _ => error "polyminus.sml: a * b kleiner b = True";

    86 case eval_kleiner 0 0 (TermC.str2term "(3*a*b) kleiner c") 0 of

    87     SOME ("3 * a * b kleiner c = True", _) => ()

    88   | _ => error "polyminus.sml: 3 * a * b kleiner b = True";

    91 val t = TermC.str2term "12 kleiner 5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * (g::real)";

    92 val SOME ("12 kleiner 5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g = True", _) =

    93            eval_kleiner "aaa" "bbb" t "ccc";

    94 "~~~~~ fun eval_kleiner , args:"; val (_, _, (p as (Const (\<^const_name>\<open>kleiner\<close>,_) $ a $ b)), _) =

    95   ("aaa", "bbb", t, "ccc");

    96     (*if*) TermC.is_num b (*else*);

    98    	(*if*) identifier a < identifier b  (*else*);

    99 "~~~~~ fun identifier , args:"; val (t) = (a);

   100 (*+*)case a of

   101   Const (\<^const_name>\<open>numeral\<close>, _) $ (Const (\<^const_name>\<open>num.Bit0\<close>, _) $

   102     (Const (\<^const_name>\<open>num.Bit0\<close>, _) $ (Const (\<^const_name>\<open>num.Bit1\<close>, _) $ Const (\<^const_name>\<open>num.One\<close>, _)))) => ()

   103 | _ => error "eval_kleiner CHANGED";                                                 (*isa*)

   106 "----------- fun ist_monom ---------------------------------------------------------------------";

   107 "----------- fun ist_monom ---------------------------------------------------------------------";

   108 "----------- fun ist_monom ---------------------------------------------------------------------";

   109 val t = TermC.str2term "0 ::real";

   110  if ist_monom t then () else error "ist_monom 1";

   112 val t = TermC.str2term "a";

   113 if ist_monom t then () else error "ist_monom 2";

   115 val t = TermC.str2term "2 * a";

   116 if ist_monom t then () else error "ist_monom 3";

   118 val t = TermC.str2term "2 * a * b";

   119 if ist_monom t then () else error "ist_monom 4";

   121 val t = TermC.str2term "a * b";

   122 if ist_monom t then () else error "ist_monom 5";

   124 (*not covered before NEW numerals*)

   125 val t = TermC.str2term "2 * a \<up> 2 * b";

   126 if ist_monom t then () else error "ist_monom 6";

   128 (*not covered before NEW numerals*)

   129 val t = TermC.str2term "a \<up> 2 * b \<up> 3";

   130 if ist_monom t then () else error "ist_monom 7";

   132 val t = TermC.str2term "a \<up> 2 * 4 * b \<up> 3 * 5";

   133 if ist_monom t then () else error "ist_monom 8";

   136 "----------- fun eval_ist_monom ----------------------------------";

   137 "----------- fun eval_ist_monom ----------------------------------";

   138 "----------- fun eval_ist_monom ----------------------------------";

   139 case eval_ist_monom 0 0 (TermC.str2term "12 ist_monom") 0 of

   140     SOME ("12 ist_monom = True", _) => ()

   141   | _ => error "polyminus.sml: 12 ist_monom = True";

   143 case eval_ist_monom 0 0 (TermC.str2term "a ist_monom") 0 of

   144     SOME ("a ist_monom = True", _) => ()

   145   | _ => error "polyminus.sml: a ist_monom = True";

   147 case eval_ist_monom 0 0 (TermC.str2term "(3*a) ist_monom") 0 of

   148     SOME ("3 * a ist_monom = True", _) => ()

   149   | _ => error "polyminus.sml: 3 * a ist_monom = True";

   151 case eval_ist_monom 0 0 (TermC.str2term "(a \<up> 2) ist_monom") 0 of

   152    SOME ("a \<up> 2 ist_monom = True", _) => ()

   153   | _ => error "polyminus.sml: a \<up> 2 ist_monom = True";

   155 case eval_ist_monom 0 0 (TermC.str2term "(3*a \<up> 2) ist_monom") 0 of

   156     SOME ("3 * a \<up> 2 ist_monom = True", _) => ()

   157   | _ => error "polyminus.sml: 3*a \<up> 2 ist_monom = True";

   159 case eval_ist_monom 0 0 (TermC.str2term "(a*b) ist_monom") 0 of

   160     SOME ("a * b ist_monom = True", _) => ()

   161   | _ => error "polyminus.sml: a*b ist_monom = True";

   163 case eval_ist_monom 0 0 (TermC.str2term "(3*a*b) ist_monom") 0 of

   164     SOME ("3 * a * b ist_monom = True", _) => ()

   165   | _ => error "polyminus.sml: 3*a*b ist_monom = True";

   168 "----------- watch order_add_mult  -------------------------------";

   169 "----------- watch order_add_mult  -------------------------------";

   170 "----------- watch order_add_mult  -------------------------------";

   171 "----- with these simple variables it works...";

   172 (*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

   173 Rewrite.trace_on:=false; (*true false*)

   174 val t = TermC.str2term "((a + d) + c) + b";

   175 val SOME (t,_) = rewrite_set_ thy false order_add_mult t; UnparseC.term t;

   176 if UnparseC.term t = "a + (b + (c + d))" then ()

   177 else error "polyminus.sml 1 watch order_add_mult";

   178 Rewrite.trace_on:=false; (*true false*)

   180 "----- the same stepwise...";

   181 val od = ord_make_polynomial true (@{theory "Poly"});

   182 val t = TermC.str2term "((a + d) + c) + b";

   183 "((a + d) + c) + b";

   184 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.commute} t; UnparseC.term t;

   185 "b + ((a + d) + c)";

   186 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.commute} t; UnparseC.term t;

   187 "b + (c + (a + d))";

   188 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

   189 "b + (a + (c + d))";

   190 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

   191 "a + (b + (c + d))";

   192 if UnparseC.term t = "a + (b + (c + d))" then ()

   193 else error "polyminus.sml 2 watch order_add_mult";

   195 "----- if parentheses are right, left_commute is (almost) sufficient...";

   196 val t = TermC.str2term "a + (d + (c + b))";

   197 "a + (d + (c + b))";

   198 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

   199 "a + (c + (d + b))";

   200 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.commute} t;UnparseC.term t;

   201 "a + (c + (b + d))";

   202 val SOME (t,_) = rewrite_ thy od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

   203 "a + (b + (c + d))";

   205 "----- but we do not want the parentheses at right; thus: cond.rew.";

   206 "WN0712707 complicated monomials do not yet work ...";

   207 val t = TermC.str2term "((5*a + 4*d) + 3*c) + 2*b";

   208 val SOME (t,_) = rewrite_set_ thy false order_add_mult t; UnparseC.term t;

   209 if UnparseC.term t = "2 * b + (3 * c + (4 * d + 5 * a))" then ()

   210 else error "polyminus.sml: order_add_mult changed";

   212 "----- here we see rew_sub going into subterm with ord.rew....";

   213 val od = ord_make_polynomial false (@{theory "Poly"});

   214 val t = TermC.str2term "b + a + c + d";

   215 val SOME (t,_) = rewrite_ thy od Rule_Set.empty false @{thm add.commute} t; UnparseC.term t;

   216 val SOME (t,_) = rewrite_ thy od Rule_Set.empty false @{thm add.commute} t; UnparseC.term t;

   217 (*@@@ rew_sub gosub: t = d + (b + a + c)

   218   @@@ rew_sub begin: t = b + a + c*)

   221 "----------- build predicate for +- ordering ---------------------";

   222 "----------- build predicate for +- ordering ---------------------";

   223 "----------- build predicate for +- ordering ---------------------";

   224 "a" < "b";

   225 "ba" < "ab";

   226 "123" < "a"; (*unused due to ---vvv*)

   227 "12" < "3"; (*true !!!*)

   229 " a kleiner b ==> (b + a) = (a + b)";

   230 TermC.str2term "aaa";

   231 TermC.str2term "222 * aaa";

   233 case eval_kleiner 0 0 (TermC.str2term "123 kleiner 32") 0 of

   234     SOME ("123 kleiner 32 = False", _) => ()

   235   | _ => error "polyminus.sml: 12 kleiner 9 = False";

   237 case eval_kleiner 0 0 (TermC.str2term "a kleiner b") 0 of

   238     SOME ("a kleiner b = True", _) => ()

   239   | _ => error "polyminus.sml: a kleiner b = True";

   241 case eval_kleiner 0 0 (TermC.str2term "(10*g) kleiner f") 0 of

   242     SOME ("10 * g kleiner f = False", _) => ()

   243   | _ => error "polyminus.sml: 10 * g kleiner f = False";

   245 case eval_kleiner 0 0 (TermC.str2term "(a \<up> 2) kleiner b") 0 of

   246     SOME ("a \<up> 2 kleiner b = True", _) => ()

   247   | _ => error "polyminus.sml: a \<up> 2 kleiner b = True";

   249 case eval_kleiner 0 0 (TermC.str2term "(3*a \<up> 2) kleiner b") 0 of

   250     SOME ("3 * a \<up> 2 kleiner b = True", _) => ()

   251   | _ => error "polyminus.sml: 3 * a \<up> 2 kleiner b = True";

   253 case eval_kleiner 0 0 (TermC.str2term "(a*b) kleiner c") 0 of

   254     SOME ("a * b kleiner c = True", _) => ()

   255   | _ => error "polyminus.sml: a * b kleiner b = True";

   257 case eval_kleiner 0 0 (TermC.str2term "(3*a*b) kleiner c") 0 of

   258     SOME ("3 * a * b kleiner c = True", _) => ()

   259   | _ => error "polyminus.sml: 3 * a * b kleiner b = True";

   261 "======= compare tausche_plus with real_num_collect";

   262 val od = dummy_ord;

   264 val erls = erls_ordne_alphabetisch;

   265 val t = TermC.str2term "b + a";

   266 val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; UnparseC.term t;

   267 if UnparseC.term t = "a + b" then ()

   268 else error "polyminus.sml: ordne_alphabetisch1 b + a";

   270 val erls = Atools_erls;

   271 val t = TermC.str2term "2*a + 3*a";

   272 val SOME (t,_) = rewrite_ thy od erls false @{thm real_num_collect} t; UnparseC.term t;

   274 "======= test rewrite_, rewrite_set_";

   275 (*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

   276 val erls = erls_ordne_alphabetisch;

   277 val t = TermC.str2term "b + a";

   278 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; UnparseC.term t;

   279 if UnparseC.term t = "a + b" then ()

   280 else error "polyminus.sml: ordne_alphabetisch a + b";

   282 val t = TermC.str2term "2*b + a";

   283 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; UnparseC.term t;

   284 if UnparseC.term t = "a + 2 * b" then ()

   285 else error "polyminus.sml: ordne_alphabetisch a + 2 * b";

   287 val t = TermC.str2term "a + c + b";

   288 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; UnparseC.term t;

   289 if UnparseC.term t = "a + b + c" then ()

   290 else error "polyminus.sml: ordne_alphabetisch a + b + c";

   292 "======= rewrite goes into subterms";

   293 val t = TermC.str2term "a + c + b + d ::real";

   294 val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus_plus} t; UnparseC.term t;

   295 if UnparseC.term t = "a + b + c + d" then ()

   296 else error "polyminus.sml: ordne_alphabetisch1 a + b + c + d";

   298 val t = TermC.str2term "a + c + d + b";

   299 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; UnparseC.term t;

   300 if UnparseC.term t = "a + b + c + d" then ()

   301 else error "polyminus.sml: ordne_alphabetisch2 a + b + c + d";

   303 "======= here we see rew_sub going into subterm with cond.rew....";

   304 val t = TermC.str2term "b + a + c + d";

   305 val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; UnparseC.term t;

   306 if UnparseC.term t = "a + b + c + d" then ()

   307 else error "polyminus.sml: ordne_alphabetisch3 a + b + c + d";

   309 "======= compile rls for the most complicated terms";

   310 val t = TermC.str2term "5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12";

   311 "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

   312 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t;

   313 if UnparseC.term t = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g"

   314 then () else error "polyminus.sml: ordne_alphabetisch finished";

   318 "----------- build fasse_zusammen --------------------------------";

   319 "----------- build fasse_zusammen --------------------------------";

   320 "----------- build fasse_zusammen --------------------------------";

   321 val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";

   322 val SOME (t,_) = rewrite_set_ thy false fasse_zusammen t;

   323 if UnparseC.term t = "3 + - 2 * e + 2 * f + 2 * g" then ()

   324 else error "polyminus.sml: fasse_zusammen finished";

   326 "----------- build verschoenere ----------------------------------";

   327 "----------- build verschoenere ----------------------------------";

   328 "----------- build verschoenere ----------------------------------";

   329 val t = TermC.str2term "3 + - 2 * e + 2 * f + 2 * g";

   330 val SOME (t,_) = rewrite_set_ thy false verschoenere t;

   331 if UnparseC.term t = "3 - 2 * e + 2 * f + 2 * g" then ()

   332 else error "polyminus.sml: verschoenere 3 + - 2 * e ...";

   334 (*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

   335 Rewrite.trace_on:=false; (*true false*)

   337 "----------- met simplification for_polynomials with_minus -------";

   338 "----------- met simplification for_polynomials with_minus -------";

   339 "----------- met simplification for_polynomials with_minus -------";

   340 val str =

   341 "Program SimplifyScript (t_t::real) =                \

   342 \  (((Try (Rewrite_Set ordne_alphabetisch False)) #>     \

   343 \    (Try (Rewrite_Set fasse_zusammen False)) #>     \

   344 \    (Try (Rewrite_Set verschoenere False))) t_t)"

   345 val sc = (inst_abs o (TermC.parseNEW' ctxt)) str;

   346 TermC.atomty sc;

   348 "----------- me simplification.for_polynomials.with_minus";

   349 "----------- me simplification.for_polynomials.with_minus";

   350 "----------- me simplification.for_polynomials.with_minus";

   351 val c = [];

   352 val (p,_,f,nxt,_,pt) =

   353       CalcTreeTEST

   354         [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

   355            "normalform N"],

   356 	          ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   357 	           ["simplification", "for_polynomials", "with_minus"]))];

   358 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   359 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   360 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   361 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   362 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   363 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   365 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   366 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   367 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   368 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   369 val (p,_,f,nxt,_,pt) = me nxt p c pt;

   370 if f2str f = "3 - 2 * e + 2 * f + 2 * g"

   371 then case nxt of End_Proof' => () | _ =>  error "me simplification.for_polynomials.with_minus 1"

   372 else error "polyminus.sml: me simplification.for_polynomials.with_minus 2";

   374 "----------- pbl polynom vereinfachen p.33 -----------------------";

   375 "----------- pbl polynom vereinfachen p.33 -----------------------";

   376 "----------- pbl polynom vereinfachen p.33 -----------------------";

   377 "----------- 140 c ---";

   378 reset_states ();

   379 CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

   380 	    "normalform N"],

   381 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   382 	    ["simplification", "for_polynomials", "with_minus"]))];

   383 moveActiveRoot 1;

   384 autoCalculate 1 CompleteCalc;

   385 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   386 if p = ([], Res) andalso

   387    UnparseC.term (get_obj g_res pt (fst p)) = "3 - 2 * e + 2 * f + 2 * g"

   388 then () else error "polyminus.sml: Vereinfache (3 - 2 * e + 2 * f...";

   390 "======= 140 d ---";

   391 reset_states ();

   392 CalcTree [(["Term (-r - 2*s - 3*t + 5 + 4*r + 8*s - 5*t - 2)",

   393 	    "normalform N"],

   394 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   395 	    ["simplification", "for_polynomials", "with_minus"]))];

   396 moveActiveRoot 1;

   397 autoCalculate 1 CompleteCalc;

   398 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   399 if p = ([], Res) andalso

   400    UnparseC.term (get_obj g_res pt (fst p)) = "3 + 3 * r + 6 * s - 8 * t"

   401 then () else error "polyminus.sml: Vereinfache 140 d)";

   403 "======= 139 c ---";

   404 reset_states ();

   405 CalcTree [(["Term (3*e - 6*f - 8*e - 4*f + 5*e + 7*f)",

   406 	    "normalform N"],

   407 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   408 	    ["simplification", "for_polynomials", "with_minus"]))];

   409 moveActiveRoot 1;

   410 autoCalculate 1 CompleteCalc;

   411 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   412 if p = ([], Res) andalso

   413    UnparseC.term (get_obj g_res pt (fst p)) = "- (3 * f)"

   414 then () else error "polyminus.sml: Vereinfache 139 c)";

   416 "======= 139 b ---";

   417 reset_states ();

   418 CalcTree [(["Term (8*u - 5*v - 5*u + 7*v - 6*u - 3*v)",

   419 	    "normalform N"],

   420 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   421 	    ["simplification", "for_polynomials", "with_minus"]))];

   422 moveActiveRoot 1;

   423 autoCalculate 1 CompleteCalc;

   424 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   425 if p = ([], Res) andalso

   426    UnparseC.term (get_obj g_res pt (fst p)) = "- 3 * u - v"

   427 then () else error "polyminus.sml: Vereinfache 139 b)";

   429 "======= 138 a ---";

   430 reset_states ();

   431 CalcTree [(["Term (2*u - 3*v - 6*u + 5*v)",

   432 	    "normalform N"],

   433 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   434 	    ["simplification", "for_polynomials", "with_minus"]))];

   435 moveActiveRoot 1;

   436 autoCalculate 1 CompleteCalc;

   437 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   438 if p = ([], Res) andalso

   439    UnparseC.term (get_obj g_res pt (fst p)) = "- 4 * u + 2 * v"

   440 then () else error "polyminus.sml: Vereinfache 138 a)";

   442 "----------- met probe fuer_polynom ------------------------------";

   443 "----------- met probe fuer_polynom ------------------------------";

   444 "----------- met probe fuer_polynom ------------------------------";

   445 val str =

   446 "Program ProbeScript (e_e::bool) (w_s::bool list) =\

   447 \ (let e_e = Take e_e;                             \

   448 \      e_e = Substitute w_s e_e                    \

   449 \ in (Repeat((Try (Repeat (Calculate ''TIMES''))) #>  \

   450 \            (Try (Repeat (Calculate ''PLUS''))) #>  \

   451 \            (Try (Repeat (Calculate ''MINUS''))))) e_e)"

   452 val sc = (inst_abs o (TermC.parseNEW' ctxt)) str;

   453 TermC.atomty sc;

   455 "----------- pbl polynom probe -----------------------------------";

   456 "----------- pbl polynom probe -----------------------------------";

   457 "----------- pbl polynom probe -----------------------------------";

   458 reset_states ();

   459 CalcTree [(["Pruefe ((5::int)*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12 =\

   460 	    \3 - 2 * e + 2 * f + 2 * (g::int))",

   461 	    "mitWert [e = (1::int), f = (2::int), g = (3::int)]",

   462 	    "Geprueft b"],

   463 	   ("PolyMinus",["polynom", "probe"],

   464 	    ["probe", "fuer_polynom"]))];

   465 moveActiveRoot 1;

   466 autoCalculate 1 CompleteCalc;

   467 (* autoCalculate 1 CompleteCalcHead;

   468    autoCalculate 1 (Steps 1);

   469    autoCalculate 1 (Steps 1);

   470    val ((pt,p),_) = get_calc 1; UnparseC.term (get_obj g_res pt (fst p));

   471 @@@@@WN081114 gives "??.empty", all "Pruefe" are the same,

   472 although analogies work in interface.sml: FIXME.WN081114 in "Pruefe"*)

   473 val ((pt,p),_) = get_calc 1;

   474 if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "11 = 11"

   475 then () else error "polyminus.sml: Probe 11 = 11";

   476 Test_Tool.show_pt pt;

   479 "----------- pbl klammer polynom vereinfachen p.34 ---------------";

   480 "----------- pbl klammer polynom vereinfachen p.34 ---------------";

   481 "----------- pbl klammer polynom vereinfachen p.34 ---------------";

   482 reset_states ();

   483 CalcTree [(["Term (2*u - 5 - (3 - 4*u) + (8*u + 9))",

   484 	    "normalform N"],

   485 	   ("PolyMinus",["klammer", "polynom", "vereinfachen"],

   486 	    ["simplification", "for_polynomials", "with_parentheses"]))];

   487 moveActiveRoot 1;

   488 autoCalculate 1 CompleteCalc;

   489 val ((pt,p),_) = get_calc 1;

   490 if p = ([], Res) andalso

   491    UnparseC.term (get_obj g_res pt (fst p)) = "1 + 14 * u"

   492 then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";

   493 Test_Tool.show_pt pt;

   495 "======= probe p.34 -----";

   496 reset_states ();

   497 CalcTree [(["Pruefe (2*u - 5 - (3 - 4*u) + (8*u + 9) = 1 + 14 * (u::int))",

   498 	    "mitWert [u = (2::int)]",

   499 	    "Geprueft b"],

   500 	   ("PolyMinus",["polynom", "probe"],

   501 	    ["probe", "fuer_polynom"]))];

   502 moveActiveRoot 1;

   503 autoCalculate 1 CompleteCalc;

   504 val ((pt,p),_) = get_calc 1;

   505 if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "29 = 29"

   506 then () else error "polyminus.sml: Probe 29 = 29";

   507 Test_Tool.show_pt pt;

   510 "----------- try fun applyTactics --------------------------------";

   511 "----------- try fun applyTactics --------------------------------";

   512 "----------- try fun applyTactics --------------------------------";

   513 reset_states ();

   514 CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

   515 	    "normalform N"],

   516 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   517 	    ["simplification", "for_polynomials", "with_minus"]))];

   518 moveActiveRoot 1;

   519 autoCalculate 1 CompleteCalcHead;

   520 autoCalculate 1 (Steps 1);

   521 autoCalculate 1 (Steps 1);

   522 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   523 "----- 1  \<up> ";

   524 fetchApplicableTactics 1 0 p;

   525 val appltacs = specific_from_prog pt p;

   526 applyTactic 1 p (hd appltacs) (*addiere_x_plus_minus*);

   527 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   528 "----- 2  \<up> ";

   529 (*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

   530 val erls = erls_ordne_alphabetisch;

   531 val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

   532 val SOME (t',_) =

   533     rewrite_ (@{theory "Isac_Knowledge"}) e_rew_ord erls false @{thm tausche_minus} t;

   534 UnparseC.term t';     "- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f - 8 * g + 10 * g";

   536 val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

   537 val NONE =

   538     rewrite_ (@{theory "Isac_Knowledge"}) e_rew_ord erls false @{thm tausche_minus_plus} t;

   540 val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

   541 val SOME (t',_) =

   542     rewrite_set_ (@{theory "Isac_Knowledge"}) false ordne_alphabetisch t;

   543 UnparseC.term t';     "- 9 + 12 + 5 * e - 7 * e - 8 * g + 10 * g + (- 4 + 6) * f";

   544 Rewrite.trace_on := false; (*true false*)

   547 applyTactic 1 p (hd (specific_from_prog pt p)) (*tausche_minus*);

   548 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   549 "----- 3  \<up> ";

   550 applyTactic 1 p (hd (specific_from_prog pt p)) (**);

   551 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   552 "----- 4  \<up> ";

   553 applyTactic 1 p (hd (specific_from_prog pt p)) (**);

   554 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   555 "----- 5  \<up> ";

   556 applyTactic 1 p (hd (specific_from_prog pt p)) (**);

   557 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   558 "----- 6  \<up> ";

   560 (*<CALCMESSAGE> failure </CALCMESSAGE>

   561 applyTactic 1 p (hd (specific_from_prog pt p)) (**);

   562 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   563 "----- 7  \<up> ";

   564 *)

   565 autoCalculate 1 CompleteCalc;

   566 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   567 (*independent from failure above: met_simp_poly_minus not confluent:

   568 (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

   569 (([], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f))]

   570 ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

   571 val ([], Res) = p;

   572 val "2 * g + (3 - 2 * e + 2 * f)" = get_obj g_res pt (fst p) |> UnparseC.term;

   573 (* ---------^^^--- not quite perfect*)

   576 "#############################################################################";

   577 reset_states ();

   578 CalcTree [(["Term (- (8 * g) + 10 * g + h)",

   579 	    "normalform N"],

   580 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   581 	    ["simplification", "for_polynomials", "with_minus"]))];

   582 moveActiveRoot 1;

   583 autoCalculate 1 CompleteCalc;

   584 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   585 if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "2 * g + h"

   586 then () else error "polyminus.sml: addiere_vor_minus";

   589 "#############################################################################";

   590 reset_states ();

   591 CalcTree [(["Term (- (8 * g) + 10 * g + f)",

   592 	    "normalform N"],

   593 	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

   594 	    ["simplification", "for_polynomials", "with_minus"]))];

   595 moveActiveRoot 1;

   596 autoCalculate 1 CompleteCalc;

   597 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   598 if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "f + 2 * g"

   599 then () else error "polyminus.sml: tausche_vor_plus";

   601 "----------- pbl binom polynom vereinfachen p.39 -----------------";

   602 "----------- pbl binom polynom vereinfachen p.39 -----------------";

   603 "----------- pbl binom polynom vereinfachen p.39 -----------------";

   604 val thy = @{theory};

   605 val rls = klammern_ausmultiplizieren;

   606 val t = TermC.str2term "(3 * a + 2) * (4 * a - 1::real)";

   607 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   608 "3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

   609 val rls = discard_parentheses;

   610 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   611 "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

   612 val rls = ordne_monome;

   613 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   614 "3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

   615 (*

   616 val t = TermC.str2term "3 * a * 4 * a";

   617 val rls = ordne_monome;

   618 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   619 *)

   620 val rls = klammern_aufloesen;

   621 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   622 "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

   623 val rls = ordne_alphabetisch;

   624 (*TODO: make is_monom more general, a*a=a^2, ...*)

   625 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   626 "3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

   627 (*STOPPED.WN080104

   628 val rls = fasse_zusammen;

   629 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   630 val rls = verschoenere;

   631 val SOME (t,_) = rewrite_set_ thy false rls t; UnparseC.term t;

   632 *)

   634 (*@@@@@@@*)

   635 reset_states ();

   636 CalcTree [(["Term ((3*a + 2) * (4*a - 1))",

   637 	    "normalform N"],

   638 	   ("PolyMinus",["binom_klammer", "polynom", "vereinfachen"],

   639 	    ["simplification", "for_polynomials", "with_parentheses_mult"]))];

   640 moveActiveRoot 1;

   641 autoCalculate 1 CompleteCalc;

   642 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   644 if p = ([], Res) andalso

   645    UnparseC.term (get_obj g_res pt (fst p)) =(*"- 2 + 12 * a \<up> 2 + 5 * a" with OLD numerals*)

   646                                                "- 2 + 5 * a + 12 * a \<up> 2"

   647 then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";

   649 "----------- pbl binom polynom vereinfachen: cube ----------------";

   650 "----------- pbl binom polynom vereinfachen: cube ----------------";

   651 "----------- pbl binom polynom vereinfachen: cube ----------------";

   652 reset_states ();

   653 CalcTree [(["Term (8*(a - q) + a - 2*q + 3*(a - 2*q))", "normalform N"],

   654 	   ("PolyMinus",["binom_klammer", "polynom", "vereinfachen"],

   655 	    ["simplification", "for_polynomials", "with_parentheses_mult"]))];

   656 moveActiveRoot 1;

   657 autoCalculate 1 CompleteCalc;

   658 val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

   659 if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "12 * a - 16 * q"

   660 then () else error "pbl binom polynom vereinfachen: cube";

   662 "----------- Refine.refine Vereinfache ----------------------------------";

   663 "----------- Refine.refine Vereinfache ----------------------------------";

   664 "----------- Refine.refine Vereinfache ----------------------------------";

   665 val fmz = ["Term (8*(a - q) + a - 2*q + 3*(a - 2*(q::real)))", "normalform (N::real)"];

   666 (*default_print_depth 11;*)

   667 val matches = Refine.refine fmz ["vereinfachen"];

   668 (*default_print_depth 3;*)

   670 "----- go into details, if it seems not to work -----";

   671 "--- does the predicate evaluate correctly ?";

   672 val t = TermC.str2term

   673 	    "matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q + 3 * (a - 2 * (q::real)))";

   674 val ma = eval_matchsub "" "Prog_Expr.matchsub" t thy;

   675 case ma of

   676     SOME ("matchsub (?a * (?b - ?c)) (8 * (a - q) + \

   677 	  \a - 2 * q + 3 * (a - 2 * q)) = True", _) => ()

   678   | _ => error "polyminus.sml matchsub (?a * (?b - ?c)...A";

   680 "--- does the respective prls rewrite ?";

   681 val prls = Rule_Set.append_rules "prls_pbl_vereinf_poly" Rule_Set.empty

   682 	     [Eval ("Poly.is_polyexp", eval_is_polyexp ""),

   683 	      Eval ("Prog_Expr.matchsub", eval_matchsub ""),

   684 	      Thm ("or_true",@{thm or_true}),

   685 	      (*"(?a | True) = True"*)

   686 	      Thm ("or_false",@{thm or_false}),

   687 	      (*"(?a | False) = ?a"*)

   688 	      Thm ("not_true", @{thm not_true}),

   689 	      (*"(~ True) = False"*)

   690 	      Thm ("not_false", @{thm not_false})

   691 	      (*"(~ False) = True"*)];

   692 (*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

   693 val SOME (t', _) = rewrite_set_ thy false prls t;

   694 Rewrite.trace_on := false; (*true false*)

   696 "--- does the respective prls rewrite the whole predicate ?";

   697 val t = TermC.str2term

   698 	    "Not (matchsub (?a * (?b + ?c)) (8 * (a - q) + a - 2 * q) | \

   699 	    \     matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q) | \

   700 	    \     matchsub ((?b + ?c) * ?a) (8 * (a - q) + a - 2 * q) | \

   701 	    \     matchsub ((?b - ?c) * ?a) (8 * (a - q) + a - 2 * q) )";

   702 (*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

   703 val SOME (t', _) = rewrite_set_ thy false prls t;

   704 Rewrite.trace_on := false; (*true false*)

   705 if UnparseC.term t' = "False" then ()

   706 else error "polyminus.sml Not (matchsub (?a * (?b + ?c)) (8 ...";

   708 "----------- *** Problem.prep_input: syntax error in '#Where' of [v";

   709 "----------- *** Problem.prep_input: syntax error in '#Where' of [v";

   710 "----------- *** Problem.prep_input: syntax error in '#Where' of [v";

   711 (*see test/../termC.sml for details*)

   712 val t = TermC.parse_patt thy "t_t is_polyexp";

   713 val t = TermC.parse_patt thy ("Not (matchsub (?a + (?b + ?c)) t_t | " ^

   714 	                "     matchsub (?a + (?b - ?c)) t_t | " ^

   715 	                "     matchsub (?a - (?b + ?c)) t_t | " ^

   716 	                "     matchsub (?a + (?b - ?c)) t_t )");

   717 (*show_types := true;

   718 if UnparseC.term t = "~ (matchsub ((?a::real) + ((?b::real) + (?c::real))) (t_t::real) |\n   matchsub (?a + (?b - ?c)) t_t |\n   matchsub (?a - (?b + ?c)) t_t | matchsub (?a + (?b - ?c)) t_t)"

   719 then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";

   720 show_types := false;*)

   721 if UnparseC.term t =

   722   "\<not> (matchsub (?a + (?b + ?c)) t_t \<or>\n        " ^

   723   "matchsub (?a + (?b - ?c)) t_t \<or>\n        " ^

   724   "matchsub (?a - (?b + ?c)) t_t \<or> " ^

   725   "matchsub (?a + (?b - ?c)) t_t)"

   726 then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";

author	wneuper <Walther.Neuper@jku.at>
	Thu, 26 May 2022 12:44:51 +0200
changeset 60424	c3acf9c442ac
parent 60352	3c0a46d36530
child 60500	59a3af532717
permissions	-rw-r--r--