wneuper/isa: test/Tools/isac/Knowledge/polyminus.sml@3c0a46d36530

     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"};

    35 "----------- fun identifier --------------------------------------------------------------------";

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

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

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

    39 if identifier (TermC.str2term

    40   "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g ::real") = "|||||||||||||"

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

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

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

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

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

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

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

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

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

    55 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

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

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

    58 "a" < "b";

    59 "ba" < "ab";

    60 "123" < "a"; (*unused due to ---vvv*)

    61 "12" < "3"; (*true !!!*)

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

    64 TermC.str2term "aaa";

    65 TermC.str2term "222 * aaa";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    92            eval_kleiner "aaa" "bbb" t "ccc";

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

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

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

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

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

    99 (*+*)case a of

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

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

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

   105 "----------- fun ist_monom ---------------------------------------------------------------------";

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

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

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

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

   111 val t = TermC.str2term "a";

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

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

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

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

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

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

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

   123 (*not covered before NEW numerals*)

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

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

   127 (*not covered before NEW numerals*)

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

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

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

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

   135 "----------- fun eval_ist_monom ----------------------------------";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   167 "----------- watch order_add_mult  -------------------------------";

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

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

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

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

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

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

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

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

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

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

   179 "----- the same stepwise...";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   223 "a" < "b";

   224 "ba" < "ab";

   225 "123" < "a"; (*unused due to ---vvv*)

   226 "12" < "3"; (*true !!!*)

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

   229 TermC.str2term "aaa";

   230 TermC.str2term "222 * aaa";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   260 "======= compare tausche_plus with real_num_collect";

   261 val od = dummy_ord;

   263 val erls = erls_ordne_alphabetisch;

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

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

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

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

   269 val erls = Atools_erls;

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

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

   273 "======= test rewrite_, rewrite_set_";

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

   275 val erls = erls_ordne_alphabetisch;

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

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

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

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

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

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

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

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

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

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

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

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

   291 "======= rewrite goes into subterms";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   310 "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

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

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

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

   317 "----------- build fasse_zusammen --------------------------------";

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

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

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

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

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

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

   325 "----------- build verschoenere ----------------------------------";

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

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

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

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

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

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

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

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

   336 "----------- met simplification for_polynomials with_minus -------";

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

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

   339 val str =

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

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

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

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

   344 val sc = (inst_abs o Thm.term_of o the o (TermC.parse thy)) str;

   345 TermC.atomty sc;

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

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

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

   350 val c = [];

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

   352       CalcTreeTEST

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

   354            "normalform N"],

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

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

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

   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;

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

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

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

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

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

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

   376 "----------- 140 c ---";

   377 reset_states ();

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

   379 	    "normalform N"],

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

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

   382 moveActiveRoot 1;

   383 autoCalculate 1 CompleteCalc;

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

   385 if p = ([], Res) andalso

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

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

   389 "======= 140 d ---";

   390 reset_states ();

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

   392 	    "normalform N"],

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

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

   395 moveActiveRoot 1;

   396 autoCalculate 1 CompleteCalc;

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

   398 if p = ([], Res) andalso

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

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

   402 "======= 139 c ---";

   403 reset_states ();

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

   405 	    "normalform N"],

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

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

   408 moveActiveRoot 1;

   409 autoCalculate 1 CompleteCalc;

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

   411 if p = ([], Res) andalso

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

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

   415 "======= 139 b ---";

   416 reset_states ();

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

   418 	    "normalform N"],

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

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

   421 moveActiveRoot 1;

   422 autoCalculate 1 CompleteCalc;

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

   424 if p = ([], Res) andalso

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

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

   428 "======= 138 a ---";

   429 reset_states ();

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

   431 	    "normalform N"],

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

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

   434 moveActiveRoot 1;

   435 autoCalculate 1 CompleteCalc;

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

   437 if p = ([], Res) andalso

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

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

   441 "----------- met probe fuer_polynom ------------------------------";

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

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

   444 val str =

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

   446 \ (let e_e = Take e_e;                             \

   447 \      e_e = Substitute w_s e_e                    \

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

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

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

   451 val sc = (inst_abs o Thm.term_of o the o (TermC.parse thy)) str;

   452 TermC.atomty sc;

   454 "----------- pbl polynom probe -----------------------------------";

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

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

   457 reset_states ();

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

   459 	    \3 - 2 * e + 2 * f + 2 * (g::int))",

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

   461 	    "Geprueft b"],

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

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

   464 moveActiveRoot 1;

   465 autoCalculate 1 CompleteCalc;

   466 (* autoCalculate 1 CompleteCalcHead;

   467    autoCalculate 1 (Steps 1);

   468    autoCalculate 1 (Steps 1);

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

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

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

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

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

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

   475 Test_Tool.show_pt pt;

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

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

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

   481 reset_states ();

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

   483 	    "normalform N"],

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

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

   486 moveActiveRoot 1;

   487 autoCalculate 1 CompleteCalc;

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

   489 if p = ([], Res) andalso

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

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

   492 Test_Tool.show_pt pt;

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

   495 reset_states ();

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

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

   498 	    "Geprueft b"],

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

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

   501 moveActiveRoot 1;

   502 autoCalculate 1 CompleteCalc;

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

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

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

   506 Test_Tool.show_pt pt;

   509 "----------- try fun applyTactics --------------------------------";

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

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

   512 reset_states ();

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

   514 	    "normalform N"],

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

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

   517 moveActiveRoot 1;

   518 autoCalculate 1 CompleteCalcHead;

   519 autoCalculate 1 (Steps 1);

   520 autoCalculate 1 (Steps 1);

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

   522 "----- 1  \<up> ";

   523 fetchApplicableTactics 1 0 p;

   524 val appltacs = specific_from_prog pt p;

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

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

   527 "----- 2  \<up> ";

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

   529 val erls = erls_ordne_alphabetisch;

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

   531 val SOME (t',_) =

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

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

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

   536 val NONE =

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

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

   540 val SOME (t',_) =

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

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

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

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

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

   548 "----- 3  \<up> ";

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

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

   551 "----- 4  \<up> ";

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

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

   554 "----- 5  \<up> ";

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

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

   557 "----- 6  \<up> ";

   559 (*<CALCMESSAGE> failure </CALCMESSAGE>

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

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

   562 "----- 7  \<up> ";

   563 *)

   564 autoCalculate 1 CompleteCalc;

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

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

   567 (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

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

   569 ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

   570 val ([], Res) = p;

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

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

   575 "#############################################################################";

   576 reset_states ();

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

   578 	    "normalform N"],

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

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

   581 moveActiveRoot 1;

   582 autoCalculate 1 CompleteCalc;

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

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

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

   588 "#############################################################################";

   589 reset_states ();

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

   591 	    "normalform N"],

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

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

   594 moveActiveRoot 1;

   595 autoCalculate 1 CompleteCalc;

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

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

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

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

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

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

   603 val thy = @{theory};

   604 val rls = klammern_ausmultiplizieren;

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

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

   607 "3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

   608 val rls = discard_parentheses;

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

   610 "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

   611 val rls = ordne_monome;

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

   613 "3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

   614 (*

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

   616 val rls = ordne_monome;

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

   618 *)

   619 val rls = klammern_aufloesen;

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

   621 "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

   622 val rls = ordne_alphabetisch;

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

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

   625 "3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

   626 (*STOPPED.WN080104

   627 val rls = fasse_zusammen;

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

   629 val rls = verschoenere;

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

   631 *)

   633 (*@@@@@@@*)

   634 reset_states ();

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

   636 	    "normalform N"],

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

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

   639 moveActiveRoot 1;

   640 autoCalculate 1 CompleteCalc;

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

   643 if p = ([], Res) andalso

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

   645                                                "- 2 + 5 * a + 12 * a \<up> 2"

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

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

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

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

   651 reset_states ();

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

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

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

   655 moveActiveRoot 1;

   656 autoCalculate 1 CompleteCalc;

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

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

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

   661 "----------- Refine.refine Vereinfache ----------------------------------";

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

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

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

   665 (*default_print_depth 11;*)

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

   667 (*default_print_depth 3;*)

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

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

   671 val t = TermC.str2term

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

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

   674 case ma of

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   696 val t = TermC.str2term

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   716 (*show_types := true;

   717 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)"

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

   719 show_types := false;*)

   720 if UnparseC.term t =

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

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

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

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

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

author	wneuper <walther.neuper@jku.at>
	Fri, 06 Aug 2021 11:13:20 +0200
changeset 60352	3c0a46d36530
parent 60351	d74e7e33db35
child 60424	c3acf9c442ac
permissions	-rw-r--r--