wneuper/isa: test/Tools/isac/Knowledge/polyminus.sml@06ec8abfd3bc

     1 (* title:  Knowledge/polyminus.sml

     2    author: Walther Neuper

     3    WN071207,

     4    (c) due to copyright terms

     5 *)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    34 val ctxt = Proof_Context.init_global thy;

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

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

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

    39 if identifier (TermC.parse_test @{context} "12 ::real") = "12"     then () else error "identifier 1";

    40 if identifier (TermC.parse_test @{context}

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

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

    44 if identifier (TermC.parse_test @{context} "a ::real") = "a"       then () else error "identifier 2";

    45 if identifier (TermC.parse_test @{context} "3 * a ::real") = "a"   then () else error "identifier 3";

    47 if identifier (TermC.parse_test @{context} "a \<up> 2 ::real") = "a"   then () else error "identifier 4";

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

    49 if identifier (TermC.parse_test @{context} "a * b ::real") = "b"   then () else error "identifier 5b";

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

    52 if identifier (TermC.parse_test @{context} "a*b ::real") = "b"     then () else error "identifier 6";

    53 if identifier (TermC.parse_test @{context} "(3*a*b) ::real") = "b" then () else error "identifier 7";

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

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

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

    59 "a" < "b";

    60 "ba" < "ab";

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

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

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

    65 TermC.parse_test @{context} "aaa";

    66 TermC.parse_test @{context} "222 * aaa";

    68 case eval_kleiner 0 0 (TermC.parse_test @{context} "123 kleiner 32") 0 of

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

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

    71 case eval_kleiner 0 0 (TermC.parse_test @{context} "a kleiner b") 0 of

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

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

    74 case eval_kleiner 0 0 (TermC.parse_test @{context} "(10*g) kleiner f") 0 of

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

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

    77 case eval_kleiner 0 0 (TermC.parse_test @{context} "(a \<up> 2) kleiner b") 0 of

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

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

    80 case eval_kleiner 0 0 (TermC.parse_test @{context} "(3*a \<up> 2) kleiner b") 0 of

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

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

    83 case eval_kleiner 0 0 (TermC.parse_test @{context} "(a*b) kleiner c") 0 of

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

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

    86 case eval_kleiner 0 0 (TermC.parse_test @{context} "(3*a*b) kleiner c") 0 of

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

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

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

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

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

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

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

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

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

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

   100 (*+*)case a of

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

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

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

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

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

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

   109 val t = TermC.parse_test @{context} "0 ::real";

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

   112 val t = TermC.parse_test @{context} "a";

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

   115 val t = TermC.parse_test @{context} "2 * a";

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

   118 val t = TermC.parse_test @{context} "2 * a * b";

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

   121 val t = TermC.parse_test @{context} "a * b";

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

   124 (*not covered before NEW numerals*)

   125 val t = TermC.parse_test @{context} "2 * a \<up> 2 * b";

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

   128 (*not covered before NEW numerals*)

   129 val t = TermC.parse_test @{context} "a \<up> 2 * b \<up> 3";

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

   132 val t = TermC.parse_test @{context} "a \<up> 2 * 4 * b \<up> 3 * 5";

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

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

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

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

   139 case eval_ist_monom 0 0 (TermC.parse_test @{context} "12 ist_monom") 0 of

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

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

   143 case eval_ist_monom 0 0 (TermC.parse_test @{context} "a ist_monom") 0 of

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

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

   147 case eval_ist_monom 0 0 (TermC.parse_test @{context} "(3*a) ist_monom") 0 of

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

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

   151 case eval_ist_monom 0 0 (TermC.parse_test @{context} "(a \<up> 2) ist_monom") 0 of

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

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

   155 case eval_ist_monom 0 0 (TermC.parse_test @{context} "(3*a \<up> 2) ist_monom") 0 of

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

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

   159 case eval_ist_monom 0 0 (TermC.parse_test @{context} "(a*b) ist_monom") 0 of

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

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

   163 case eval_ist_monom 0 0 (TermC.parse_test @{context} "(3*a*b) ist_monom") 0 of

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

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

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

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

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

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

   172 val ctxt = @{context};

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

   174 val SOME (t,_) = rewrite_set_ ctxt 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";

   178 "----- the same stepwise...";

   179 val od = ord_make_polynomial true

   180 val t = TermC.parse_test @{context} "((a + d) + c) + b";

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

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

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

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

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

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

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

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

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

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

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

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

   194 val t = TermC.parse_test @{context} "a + (d + (c + b))";

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

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

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

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

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

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

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

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

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

   205 val t = TermC.parse_test @{context} "((5*a + 4*d) + 3*c) + 2*b";

   206 val SOME (t,_) = rewrite_set_ ctxt false order_add_mult t; UnparseC.term t;

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

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

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

   211 val od = ord_make_polynomial false;

   212 val t = TermC.parse_test @{context} "b + a + c + d";

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

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

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

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

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

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

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

   222 "a" < "b";

   223 "ba" < "ab";

   224 "123" < "a"; (*unused due to ---vvv*)

   225 "12" < "3"; (*true !!!*)

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

   228 TermC.parse_test @{context} "aaa";

   229 TermC.parse_test @{context} "222 * aaa";

   231 case eval_kleiner 0 0 (TermC.parse_test @{context} "123 kleiner 32") 0 of

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

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

   235 case eval_kleiner 0 0 (TermC.parse_test @{context} "a kleiner b") 0 of

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

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

   239 case eval_kleiner 0 0 (TermC.parse_test @{context} "(10*g) kleiner f") 0 of

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

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

   243 case eval_kleiner 0 0 (TermC.parse_test @{context} "(a \<up> 2) kleiner b") 0 of

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

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

   247 case eval_kleiner 0 0 (TermC.parse_test @{context} "(3*a \<up> 2) kleiner b") 0 of

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

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

   251 case eval_kleiner 0 0 (TermC.parse_test @{context} "(a*b) kleiner c") 0 of

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

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

   255 case eval_kleiner 0 0 (TermC.parse_test @{context} "(3*a*b) kleiner c") 0 of

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

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

   259 "======= compare tausche_plus with real_num_collect";

   260 val od = Rewrite_Ord.function_empty;

   262 val asm_rls = erls_ordne_alphabetisch;

   263 val t = TermC.parse_test @{context} "b + a";

   264 val SOME (t,_) = rewrite_ ctxt od asm_rls false @{thm tausche_plus} t; UnparseC.term t;

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

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

   268 val asm_rls = Atools_erls;

   269 val t = TermC.parse_test @{context} "2*a + 3*a";

   270 val SOME (t,_) = rewrite_ ctxt od asm_rls false @{thm real_num_collect} t; UnparseC.term t;

   272 "======= test rewrite_, rewrite_set_";

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

   274 val asm_rls = erls_ordne_alphabetisch;

   275 val t = TermC.parse_test @{context} "b + a";

   276 val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

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

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

   280 val t = TermC.parse_test @{context} "2*b + a";

   281 val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

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

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

   285 val t = TermC.parse_test @{context} "a + c + b";

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

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

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

   290 "======= rewrite goes into subterms";

   291 val t = TermC.parse_test @{context} "a + c + b + d ::real";

   292 val SOME (t,_) = rewrite_ ctxt od asm_rls false @{thm tausche_plus_plus} t; UnparseC.term t;

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

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

   296 val t = TermC.parse_test @{context} "a + c + d + b";

   297 val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

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

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

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

   302 val t = TermC.parse_test @{context} "b + a + c + d";

   303 val SOME (t,_) = rewrite_ ctxt od asm_rls false @{thm tausche_plus} t; UnparseC.term t;

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

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

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

   308 val t = TermC.parse_test @{context} "5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12";

   309 "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

   310 val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t;

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

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

   316 "----------- build fasse_zusammen --------------------------------";

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

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

   319 val t = TermC.parse_test @{context} "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";

   320 val SOME (t,_) = rewrite_set_ ctxt false fasse_zusammen t;

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

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

   324 "----------- build verschoenere ----------------------------------";

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

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

   327 val t = TermC.parse_test @{context} "3 + - 2 * e + 2 * f + 2 * g";

   328 val SOME (t,_) = rewrite_set_ ctxt false verschoenere t;

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

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

   333 "----------- met simplification for_polynomials with_minus -------";

   334 "----------- met simplification for_polynomials with_minus -------";

   335 "----------- met simplification for_polynomials with_minus -------";

   336 val str =

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

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

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

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

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

   342 TermC.atom_trace_detail @{context} sc;

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

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

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

   347 val c = [];

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

   349       Test_Code.init_calc @{context}

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

   351            "normalform N"],

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

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

   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;

   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;

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

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

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

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

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

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

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

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

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

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

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

   373 "----------- 140 c ---";

   374 States.reset ();

   375 CalcTree @{context} [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

   376 	    "normalform N"],

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

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

   379 moveActiveRoot 1;

   380 autoCalculate 1 CompleteCalc;

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

   382 if p = ([], Res) andalso

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

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

   386 "======= 140 d ---";

   387 States.reset ();

   388 CalcTree @{context} [(["Term (-r - 2*s - 3*t + 5 + 4*r + 8*s - 5*t - 2)",

   389 	    "normalform N"],

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

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

   392 moveActiveRoot 1;

   393 autoCalculate 1 CompleteCalc;

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

   395 if p = ([], Res) andalso

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

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

   399 "======= 139 c ---";

   400 States.reset ();

   401 CalcTree @{context} [(["Term (3*e - 6*f - 8*e - 4*f + 5*e + 7*f)",

   402 	    "normalform N"],

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

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

   405 moveActiveRoot 1;

   406 autoCalculate 1 CompleteCalc;

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

   408 if p = ([], Res) andalso

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

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

   412 "======= 139 b ---";

   413 States.reset ();

   414 CalcTree @{context} [(["Term (8*u - 5*v - 5*u + 7*v - 6*u - 3*v)",

   415 	    "normalform N"],

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

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

   418 moveActiveRoot 1;

   419 autoCalculate 1 CompleteCalc;

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

   421 if p = ([], Res) andalso

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

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

   425 "======= 138 a ---";

   426 States.reset ();

   427 CalcTree @{context} [(["Term (2*u - 3*v - 6*u + 5*v)",

   428 	    "normalform N"],

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

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

   431 moveActiveRoot 1;

   432 autoCalculate 1 CompleteCalc;

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

   434 if p = ([], Res) andalso

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

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

   438 "----------- met probe fuer_polynom ------------------------------";

   439 "----------- met probe fuer_polynom ------------------------------";

   440 "----------- met probe fuer_polynom ------------------------------";

   441 val str =

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

   443 \ (let e_e = Take e_e;                             \

   444 \      e_e = Substitute w_s e_e                    \

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

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

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

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

   449 TermC.atom_trace_detail @{context} sc;

   451 "----------- pbl polynom probe -----------------------------------";

   452 "----------- pbl polynom probe -----------------------------------";

   453 "----------- pbl polynom probe -----------------------------------";

   454 States.reset ();

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

   456 	    \3 - 2 * e + 2 * f + 2 * (g::int))",

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

   458 	    "Geprueft b"],

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

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

   461 moveActiveRoot 1;

   462 autoCalculate 1 CompleteCalc;

   463 (* autoCalculate 1 CompleteCalcHead;

   464    autoCalculate 1 (Steps 1);

   465    autoCalculate 1 (Steps 1);

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

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

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

   469 val ((pt,p),_) = States.get_calc 1;

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

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

   472 Test_Tool.show_pt pt;

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

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

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

   478 States.reset ();

   479 CalcTree @{context} [(["Term (2*u - 5 - (3 - 4*u) + (8*u + 9))",

   480 	    "normalform N"],

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

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

   483 moveActiveRoot 1;

   484 autoCalculate 1 CompleteCalc;

   485 val ((pt,p),_) = States.get_calc 1;

   486 if p = ([], Res) andalso

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

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

   489 Test_Tool.show_pt pt;

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

   492 States.reset ();

   493 CalcTree @{context} [(["Pruefe (2*u - 5 - (3 - 4*u) + (8*u + 9) = 1 + 14 * (u::int))",

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

   495 	    "Geprueft b"],

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

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

   498 moveActiveRoot 1;

   499 autoCalculate 1 CompleteCalc;

   500 val ((pt,p),_) = States.get_calc 1;

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

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

   503 Test_Tool.show_pt pt;

   506 "----------- try fun applyTactics --------------------------------";

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

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

   509 States.reset ();

   510 CalcTree @{context} [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

   511 	    "normalform N"],

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

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

   514 moveActiveRoot 1;

   515 autoCalculate 1 CompleteCalcHead;

   516 autoCalculate 1 (Steps 1);

   517 autoCalculate 1 (Steps 1);

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

   519 "----- 1  \<up> ";

   520 fetchApplicableTactics 1 0 p;

   521 val appltacs = specific_from_prog pt p;

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

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

   524 "----- 2  \<up> ";

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

   526 val asm_rls = erls_ordne_alphabetisch;

   527 val t = TermC.parse_test @{context} "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

   528 val SOME (t',_) =

   529     rewrite_ ctxt Rewrite_Ord.function_empty asm_rls false @{thm tausche_minus} t;

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

   532 val t = TermC.parse_test @{context} "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

   533 val NONE =

   534     rewrite_ ctxt Rewrite_Ord.function_empty asm_rls false @{thm tausche_minus_plus} t;

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

   537 val SOME (t',_) =

   538     rewrite_set_ ctxt false ordne_alphabetisch t;

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

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

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

   544 "----- 3  \<up> ";

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

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

   547 "----- 4  \<up> ";

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

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

   550 "----- 5  \<up> ";

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

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

   553 "----- 6  \<up> ";

   555 (*<CALCMESSAGE> failure </CALCMESSAGE>

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

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

   558 "----- 7  \<up> ";

   559 *)

   560 autoCalculate 1 CompleteCalc;

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

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

   563 (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

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

   565 ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

   566 val ([], Res) = p;

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

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

   571 "#############################################################################";

   572 States.reset ();

   573 CalcTree @{context} [(["Term (- (8 * g) + 10 * g + h)",

   574 	    "normalform N"],

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

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

   577 moveActiveRoot 1;

   578 autoCalculate 1 CompleteCalc;

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

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

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

   584 "#############################################################################";

   585 States.reset ();

   586 CalcTree @{context} [(["Term (- (8 * g) + 10 * g + f)",

   587 	    "normalform N"],

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

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

   590 moveActiveRoot 1;

   591 autoCalculate 1 CompleteCalc;

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

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

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

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

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

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

   599 val thy = @{theory};

   600 val rls = klammern_ausmultiplizieren;

   601 val t = TermC.parse_test @{context} "(3 * a + 2) * (4 * a - 1::real)";

   602 val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

   603 "3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

   604 val rls = discard_parentheses;

   605 val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

   606 "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

   607 val rls = ordne_monome;

   608 val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

   609 "3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

   610 (*

   611 val t = TermC.parse_test @{context} "3 * a * 4 * a";

   612 val rls = ordne_monome;

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

   614 *)

   615 val rls = klammern_aufloesen;

   616 val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

   617 "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

   618 val rls = ordne_alphabetisch;

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

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

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

   622 (*STOPPED.WN080104

   623 val rls = fasse_zusammen;

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

   625 val rls = verschoenere;

   626 val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

   627 *)

   629 (*@@@@@@@*)

   630 States.reset ();

   631 CalcTree @{context} [(["Term ((3*a + 2) * (4*a - 1))",

   632 	    "normalform N"],

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

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

   635 moveActiveRoot 1;

   636 autoCalculate 1 CompleteCalc;

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

   639 if p = ([], Res) andalso

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

   641                                                "- 2 + 5 * a + 12 * a \<up> 2"

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

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

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

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

   647 States.reset ();

   648 CalcTree @{context} [(["Term (8*(a - q) + a - 2*q + 3*(a - 2*q))", "normalform N"],

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

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

   651 moveActiveRoot 1;

   652 autoCalculate 1 CompleteCalc;

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

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

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

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

   658 "----------- Refine.refine Vereinfache ----------------------------------";

   659 "----------- Refine.refine Vereinfache ----------------------------------";

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

   661 (*default_print_depth 11;*)

   662 val matches = Refine.xxxxx @{context} fmz ["vereinfachen"];

   663 (*default_print_depth 3;*)

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

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

   667 val t = TermC.parse_patt_test @{theory}

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

   669 val ma = eval_matchsub "" "Prog_Expr.matchsub" t ctxt;

   670 case ma of

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

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

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

   675 "--- does the respective where_rls rewrite ?";

   676 val where_rls = Rule_Set.append_rules "prls_pbl_vereinf_poly" Rule_Set.empty

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

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

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

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

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

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

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

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

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

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

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

   688 val SOME (t', _) = rewrite_set_ ctxt false where_rls t;

   690 "--- does the respective where_rls rewrite the whole predicate ?";

   691 val t = TermC.parse_patt_test @{theory}

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

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

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

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

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

   697 val SOME (t', _) = rewrite_set_ ctxt false where_rls t;

   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>
	Wed, 11 Jan 2023 11:38:01 +0100
changeset 60650	06ec8abfd3bc
parent 60594	439f7f3867ec
child 60660	c4b24621077e
permissions	-rw-r--r--