wneuper/isa: test/Tools/isac/Knowledge/polyminus.sml@0ee698b0a703

     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 (*+*)identifier (TermC.str2term "12 ::real") = "|||||||||||||";

    39 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

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

    41 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

    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 (*+*)identifier (TermC.str2term "a \<up> 2 ::real") = "|||||||||||||";(*TOODOO <-- START HERE*)

    47 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

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

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

    50 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

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

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

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

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

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

    59 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    60 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    61 "a" < "b";

    62 "ba" < "ab";

    63 "123" < "a"; (*unused due to ---vvv*)

    64 "12" < "3"; (*true !!!*)

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

    67 TermC.str2term "aaa";

    68 TermC.str2term "222 * aaa";

    70 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

    71 (*TOODOO eval_kleiner *)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    97            eval_kleiner "aaa" "bbb" t "ccc";

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

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

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

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

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

   104 (*+*)case a of

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

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

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

   108 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

   111 "----------- fun ist_monom ---------------------------------------------------------------------";

   112 "----------- fun ist_monom ---------------------------------------------------------------------";

   113 "----------- fun ist_monom ---------------------------------------------------------------------";

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

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

   117 val t = TermC.str2term "a";

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

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

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

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

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

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

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

   129 (*not covered before NEW numerals*)

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

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

   133 (*not covered before NEW numerals*)

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

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

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

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

   141 "----------- fun eval_ist_monom ----------------------------------";

   142 "----------- fun eval_ist_monom ----------------------------------";

   143 "----------- fun eval_ist_monom ----------------------------------";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   173 "----------- watch order_add_mult  -------------------------------";

   174 "----------- watch order_add_mult  -------------------------------";

   175 "----------- watch order_add_mult  -------------------------------";

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

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

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

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

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

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

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

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

   185 "----- the same stepwise...";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   229 "a" < "b";

   230 "ba" < "ab";

   231 "123" < "a"; (*unused due to ---vvv*)

   232 "12" < "3"; (*true !!!*)

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

   235 TermC.str2term "aaa";

   236 TermC.str2term "222 * aaa";

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

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

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

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

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

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

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

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

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

   250 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

   251 (*TOODOO eval_kleiner 0 0 (TermC.str2term "(a \<up> 2) kleiner b") 0 \<longrightarrow> False*)

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

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

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

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

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

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

   259 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

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

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

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

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

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

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

   269 "======= compare tausche_plus with real_num_collect";

   270 val od = dummy_ord;

   272 val erls = erls_ordne_alphabetisch;

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

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

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

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

   278 val erls = Atools_erls;

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

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

   282 "======= test rewrite_, rewrite_set_";

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

   284 val erls = erls_ordne_alphabetisch;

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

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

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

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

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

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

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

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

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

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

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

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

   300 "======= rewrite goes into subterms";

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

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

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

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

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

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

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

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

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

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

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

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

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

   317 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

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

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

   320 "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

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

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

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

   324 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

   327 "----------- build fasse_zusammen --------------------------------";

   328 "----------- build fasse_zusammen --------------------------------";

   329 "----------- build fasse_zusammen --------------------------------";

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

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

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

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

   335 "----------- build verschoenere ----------------------------------";

   336 "----------- build verschoenere ----------------------------------";

   337 "----------- build verschoenere ----------------------------------";

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

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

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

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

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

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

   346 "----------- met simplification for_polynomials with_minus -------";

   347 "----------- met simplification for_polynomials with_minus -------";

   348 "----------- met simplification for_polynomials with_minus -------";

   349 val str =

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

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

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

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

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

   355 TermC.atomty sc;

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

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

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

   360 val c = [];

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

   362       CalcTreeTEST

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

   364            "normalform N"],

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

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

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

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

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

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

   375    f2str f = "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";      (*isa == isa2*)

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

   377    val                 Check_Postcond ["plus_minus", "polynom", "vereinfachen"] = nxt;

   378 nxt;

   379 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

   380    val                              (*TOODOO*) Rewrite_Set "ordne_alphabetisch" = nxt;

   381    f2str f = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";    (*isa2*)

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

   383    f2str f = "3 + - 2 * e + 2 * f + 2 * g";                                  (*isa2*)

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

   385    f2str f = "3 - 2 * e + 2 * f + 2 * g";                                    (*isa2*)

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

   387    f2str f = "3 - 2 * e + 2 * f + 2 * g";                                    (*isa2*)

   388 if f2str f = "3 - 2 * e + 2 * f + 2 * g"                                     (*isa2*)

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

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

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

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

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

   395 "----------- 140 c ---";

   396 reset_states ();

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

   398 	    "normalform N"],

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

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

   401 moveActiveRoot 1;

   402 autoCalculate 1 CompleteCalc;

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

   404 if p = ([], Res) andalso

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

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

   408 "======= 140 d ---";

   409 reset_states ();

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

   411 	    "normalform N"],

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

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

   414 moveActiveRoot 1;

   415 autoCalculate 1 CompleteCalc;

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

   417 if p = ([], Res) andalso

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

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

   420 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

   422 "======= 139 c ---";

   423 reset_states ();

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

   425 	    "normalform N"],

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

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

   428 moveActiveRoot 1;

   429 autoCalculate 1 CompleteCalc;

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

   431 if p = ([], Res) andalso

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

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

   435 "======= 139 b ---";

   436 reset_states ();

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

   438 	    "normalform N"],

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

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

   441 moveActiveRoot 1;

   442 autoCalculate 1 CompleteCalc;

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

   444 if p = ([], Res) andalso

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

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

   448 "======= 138 a ---";

   449 reset_states ();

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

   451 	    "normalform N"],

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

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

   454 moveActiveRoot 1;

   455 autoCalculate 1 CompleteCalc;

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

   457 if p = ([], Res) andalso

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

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

   461 "----------- met probe fuer_polynom ------------------------------";

   462 "----------- met probe fuer_polynom ------------------------------";

   463 "----------- met probe fuer_polynom ------------------------------";

   464 val str =

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

   466 \ (let e_e = Take e_e;                             \

   467 \      e_e = Substitute w_s e_e                    \

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

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

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

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

   472 TermC.atomty sc;

   474 "----------- pbl polynom probe -----------------------------------";

   475 "----------- pbl polynom probe -----------------------------------";

   476 "----------- pbl polynom probe -----------------------------------";

   477 reset_states ();

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

   479 	    \3 - 2 * e + 2 * f + 2 * (g::int))",

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

   481 	    "Geprueft b"],

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

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

   484 moveActiveRoot 1;

   485 autoCalculate 1 CompleteCalc;

   486 (* autoCalculate 1 CompleteCalcHead;

   487    autoCalculate 1 (Steps 1);

   488    autoCalculate 1 (Steps 1);

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

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

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

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

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

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

   495 Test_Tool.show_pt pt;

   497 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

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

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

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

   501 reset_states ();

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

   503 	    "normalform N"],

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

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

   506 moveActiveRoot 1;

   507 autoCalculate 1 CompleteCalc;

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

   509 if p = ([], Res) andalso

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

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

   512 Test_Tool.show_pt pt;

   513 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

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

   516 reset_states ();

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

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

   519 	    "Geprueft b"],

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

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

   522 moveActiveRoot 1;

   523 autoCalculate 1 CompleteCalc;

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

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

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

   527 Test_Tool.show_pt pt;

   529 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

   530 "----------- try fun applyTactics --------------------------------";

   531 "----------- try fun applyTactics --------------------------------";

   532 "----------- try fun applyTactics --------------------------------";

   533 reset_states ();

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

   535 	    "normalform N"],

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

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

   538 moveActiveRoot 1;

   539 autoCalculate 1 CompleteCalcHead;

   540 autoCalculate 1 (Steps 1);

   541 autoCalculate 1 (Steps 1);

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

   543 "----- 1  \<up> ";

   544 fetchApplicableTactics 1 0 p;

   545 val appltacs = specific_from_prog pt p;

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

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

   548 "----- 2  \<up> ";

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

   550 val erls = erls_ordne_alphabetisch;

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

   552 val SOME (t',_) =

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

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

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

   557 val NONE =

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

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

   561 val SOME (t',_) =

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

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

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

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

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

   569 "----- 3  \<up> ";

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

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

   572 "----- 4  \<up> ";

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

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

   575 "----- 5  \<up> ";

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

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

   578 "----- 6  \<up> ";

   580 (*<CALCMESSAGE> failure </CALCMESSAGE>

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

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

   583 "----- 7  \<up> ";

   584 *)

   585 autoCalculate 1 CompleteCalc;

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

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

   588 (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

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

   590 ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

   591 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

   594 "#############################################################################";

   595 reset_states ();

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

   597 	    "normalform N"],

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

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

   600 moveActiveRoot 1;

   601 autoCalculate 1 CompleteCalc;

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

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

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

   607 "#############################################################################";

   608 reset_states ();

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

   610 	    "normalform N"],

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

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

   613 moveActiveRoot 1;

   614 autoCalculate 1 CompleteCalc;

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

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

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

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

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

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

   622 val thy = @{theory};

   623 val rls = klammern_ausmultiplizieren;

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

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

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

   627 val rls = discard_parentheses;

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

   629 "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

   630 val rls = ordne_monome;

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

   632 "3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

   633 (*

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

   635 val rls = ordne_monome;

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

   637 *)

   638 val rls = klammern_aufloesen;

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

   640 "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

   641 val rls = ordne_alphabetisch;

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

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

   644 "3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

   645 (*STOPPED.WN080104

   646 val rls = fasse_zusammen;

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

   648 val rls = verschoenere;

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

   650 *)

   652 (*@@@@@@@*)

   653 reset_states ();

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

   655 	    "normalform N"],

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

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

   658 moveActiveRoot 1;

   659 autoCalculate 1 CompleteCalc;

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

   662 UnparseC.term (get_obj g_res pt (fst p)) = "8 * a + 3 * a * 4 * a - 3 * a * 1 - 2";

   663 (** )//-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------\\( ** )

   664 if p = ([], Res) andalso

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

   666                                                "- 2 + 5 * a + 12 * a \<up> 2"

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

   668 ( ** )\\-----------TOODOO broken with merge after "eliminate ThmC.numerals_to_Free"--------//( **)

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

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

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

   673 reset_states ();

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

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

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

   677 moveActiveRoot 1;

   678 autoCalculate 1 CompleteCalc;

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

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

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

   683 "----------- Refine.refine Vereinfache ----------------------------------";

   684 "----------- Refine.refine Vereinfache ----------------------------------";

   685 "----------- Refine.refine Vereinfache ----------------------------------";

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

   687 (*default_print_depth 11;*)

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

   689 (*default_print_depth 3;*)

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

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

   693 val t = TermC.str2term

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

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

   696 case ma of

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   718 val t = TermC.str2term

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   738 (*show_types := true;

   739 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)"

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

   741 show_types := false;*)

   742 if UnparseC.term t =

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

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

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

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

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

author	wneuper <walther.neuper@jku.at>
	Tue, 27 Jul 2021 11:21:14 +0200
changeset 60340	0ee698b0a703
parent 60339	0d22a6bf1fc6
child 60351	d74e7e33db35
permissions	-rw-r--r--