wneuper/isa: test/Tools/isac/Knowledge/polyminus.sml@0c10aeff57d7

     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 "a ::real") = "a"       then () else error "identifier 2";

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

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

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

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

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

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

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

    50 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    51 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    52 "----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

    53 "a" < "b";

    54 "ba" < "ab";

    55 "123" < "a"; (*unused due to ---vvv*)

    56 "12" < "3"; (*true !!!*)

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

    59 TermC.str2term "aaa";

    60 TermC.str2term "222 * aaa";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    87            eval_kleiner "aaa" "bbb" t "ccc";

    88 "~~~~~ fun eval_kleiner , args:"; val (_, _, (p as (Const ("PolyMinus.kleiner",_) $ a $ b)), _) =

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

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

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

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

    94 (*+*)case a of

    95   Const ("Num.numeral_class.numeral", _) $ (Const ("Num.num.Bit0", _) $

    96     (Const ("Num.num.Bit0", _) $ (Const ("Num.num.Bit1", _) $ Const ("Num.num.One", _)))) => ()

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

   100 "----------- fun ist_monom ---------------------------------------------------------------------";

   101 "----------- fun ist_monom ---------------------------------------------------------------------";

   102 "----------- fun ist_monom ---------------------------------------------------------------------";

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

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

   106 val t = TermC.str2term "a";

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

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

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

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

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

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

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

   118 (*not covered before NEW numerals*)

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

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

   122 (*not covered before NEW numerals*)

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

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

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

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

   130 "----------- fun eval_ist_monom ----------------------------------";

   131 "----------- fun eval_ist_monom ----------------------------------";

   132 "----------- fun eval_ist_monom ----------------------------------";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   162 "----------- watch order_add_mult  -------------------------------";

   163 "----------- watch order_add_mult  -------------------------------";

   164 "----------- watch order_add_mult  -------------------------------";

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

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

   167 Rewrite.trace_on:=false;

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

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

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

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

   172 Rewrite.trace_on:=false;

   174 "----- the same stepwise...";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   218 "a" < "b";

   219 "ba" < "ab";

   220 "123" < "a"; (*unused due to ---vvv*)

   221 "12" < "3"; (*true !!!*)

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

   224 TermC.str2term "aaa";

   225 TermC.str2term "222 * aaa";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   255 "======= compare tausche_plus with real_num_collect";

   256 val od = dummy_ord;

   258 val erls = erls_ordne_alphabetisch;

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

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

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

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

   264 val erls = Atools_erls;

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

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

   268 "======= test rewrite_, rewrite_set_";

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

   270 val erls = erls_ordne_alphabetisch;

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

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

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

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

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

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

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

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

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

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

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

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

   286 "======= rewrite goes into subterms";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   305 "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

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

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

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

   311 "----------- build fasse_zusammen --------------------------------";

   312 "----------- build fasse_zusammen --------------------------------";

   313 "----------- build fasse_zusammen --------------------------------";

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

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

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

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

   319 "----------- build verschoenere ----------------------------------";

   320 "----------- build verschoenere ----------------------------------";

   321 "----------- build verschoenere ----------------------------------";

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

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

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

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

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

   328 Rewrite.trace_on:=false;

   330 "----------- met simplification for_polynomials with_minus -------";

   331 "----------- met simplification for_polynomials with_minus -------";

   332 "----------- met simplification for_polynomials with_minus -------";

   333 val str =

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

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

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

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

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

   339 TermC.atomty sc;

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

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

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

   344 val c = [];

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

   346       CalcTreeTEST

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

   348            "normalform N"],

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

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

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

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

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

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

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

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

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

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

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

   361    val                                 (*^^^*) Rewrite_Set "ordne_alphabetisch" = nxt;

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

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

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

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

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

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

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

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

   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;

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

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

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

   480 reset_states ();

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

   482 	    "normalform N"],

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

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

   485 moveActiveRoot 1;

   486 autoCalculate 1 CompleteCalc;

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

   488 if p = ([], Res) andalso

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

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

   491 Test_Tool.show_pt pt;

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

   494 reset_states ();

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

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

   497 	    "Geprueft b"],

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

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

   500 moveActiveRoot 1;

   501 autoCalculate 1 CompleteCalc;

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

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

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

   505 Test_Tool.show_pt pt;

   507 "----------- try fun applyTactics --------------------------------";

   508 "----------- try fun applyTactics --------------------------------";

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

   510 reset_states ();

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

   512 	    "normalform N"],

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

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

   515 moveActiveRoot 1;

   516 autoCalculate 1 CompleteCalcHead;

   517 autoCalculate 1 (Steps 1);

   518 autoCalculate 1 (Steps 1);

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

   520 "----- 1  \<up> ";

   521 fetchApplicableTactics 1 0 p;

   522 val appltacs = specific_from_prog pt p;

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

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

   525 "----- 2  \<up> ";

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

   527 val erls = erls_ordne_alphabetisch;

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

   529 val SOME (t',_) =

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

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

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

   534 val NONE =

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

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

   538 val SOME (t',_) =

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

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

   541 Rewrite.trace_on := false;

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

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

   546 "----- 3  \<up> ";

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

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

   549 "----- 4  \<up> ";

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

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

   552 "----- 5  \<up> ";

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

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

   555 "----- 6  \<up> ";

   557 (*<CALCMESSAGE> failure </CALCMESSAGE>

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

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

   560 "----- 7  \<up> ";

   561 *)

   562 autoCalculate 1 CompleteCalc;

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

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

   565 (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

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

   567 ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

   570 "#############################################################################";

   571 reset_states ();

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

   573 	    "normalform N"],

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

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

   576 moveActiveRoot 1;

   577 autoCalculate 1 CompleteCalc;

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

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

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

   583 "#############################################################################";

   584 reset_states ();

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

   586 	    "normalform N"],

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

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

   589 moveActiveRoot 1;

   590 autoCalculate 1 CompleteCalc;

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

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

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

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

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

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

   598 val rls = klammern_ausmultiplizieren;

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

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

   601 "3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

   602 val rls = discard_parentheses;

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

   604 "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

   605 val rls = ordne_monome;

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

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

   608 (*

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

   610 val rls = ordne_monome;

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

   612 *)

   613 val rls = klammern_aufloesen;

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

   615 "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

   616 val rls = ordne_alphabetisch;

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

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

   619 "3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

   620 (*STOPPED.WN080104

   621 val rls = fasse_zusammen;

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

   623 val rls = verschoenere;

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

   625 *)

   627 (*@@@@@@@*)

   628 reset_states ();

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

   630 	    "normalform N"],

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

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

   633 moveActiveRoot 1;

   634 autoCalculate 1 CompleteCalc;

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

   637 if p = ([], Res) andalso

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

   639                                                "- 2 + 5 * a + 12 * a \<up> 2"

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

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

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

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

   645 reset_states ();

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

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

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

   649 moveActiveRoot 1;

   650 autoCalculate 1 CompleteCalc;

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

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

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

   655 "----------- Refine.refine Vereinfache ----------------------------------";

   656 "----------- Refine.refine Vereinfache ----------------------------------";

   657 "----------- Refine.refine Vereinfache ----------------------------------";

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

   659 (*default_print_depth 11;*)

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

   661 (*default_print_depth 3;*)

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

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

   665 val t = TermC.str2term

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

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

   668 case ma of

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

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

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

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

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

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

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

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

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

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

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

   681 	      Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),

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

   683 	      Thm ("not_false",ThmC.numerals_to_Free @{thm not_false})

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

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

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

   687 Rewrite.trace_on := false;

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

   690 val t = TermC.str2term

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

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

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

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

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

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

   697 Rewrite.trace_on := false;

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

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

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

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

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

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

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

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

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

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

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

   710 (*show_types := true;

   711 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)"

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

   713 show_types := false;*)

   714 if UnparseC.term t =

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

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

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

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

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

author	wneuper <walther.neuper@jku.at>
	Sat, 17 Jul 2021 14:05:28 +0200
changeset 60329	0c10aeff57d7
parent 60325	a7c0e6ab4883
child 60330	e5e9a6c45597
permissions	-rw-r--r--