wneuper/isa: test/Tools/isac/Knowledge/polyminus.sml@96174a374a7a

     1 (* tests on PolyMinus

     2    author: Walther Neuper

     3    WN071207,

     4    (c) due to copyright terms

     6 use"../smltest/IsacKnowledge/polyminus.sml";

     7 use"polyminus.sml";

     8 *)

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

    10 "--------------------------------------------------------";

    11 "table of contents --------------------------------------";

    12 "--------------------------------------------------------";

    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 Vereinfache -------------------------";

    28 "----------- *** prep_pbt: syntax error in '#Where' of [v";

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

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

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

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

    35 "----------- fun eval_ist_monom ----------------------------------";

    36 "----------- fun eval_ist_monom ----------------------------------";

    37 "----------- fun eval_ist_monom ----------------------------------";

    38 ist_monom (str2term "12");

    39 case eval_ist_monom 0 0 (str2term "12 ist_monom") 0 of

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

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

    43 case eval_ist_monom 0 0 (str2term "a ist_monom") 0 of

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

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

    47 case eval_ist_monom 0 0 (str2term "(3*a) ist_monom") 0 of

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

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

    51 case eval_ist_monom 0 0 (str2term "(a^^^2) ist_monom") 0 of

    52    SOME ("a ^^^ 2 ist_monom = True", _) => ()

    53   | _ => error "polyminus.sml: a^^^2 ist_monom = True";

    55 case eval_ist_monom 0 0 (str2term "(3*a^^^2) ist_monom") 0 of

    56     SOME ("3 * a ^^^ 2 ist_monom = True", _) => ()

    57   | _ => error "polyminus.sml: 3*a^^^2 ist_monom = True";

    59 case eval_ist_monom 0 0 (str2term "(a*b) ist_monom") 0 of

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

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

    63 case eval_ist_monom 0 0 (str2term "(3*a*b) ist_monom") 0 of

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

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

    68 "----------- watch order_add_mult  -------------------------------";

    69 "----------- watch order_add_mult  -------------------------------";

    70 "----------- watch order_add_mult  -------------------------------";

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

    72 trace_rewrite:=true;

    73 trace_rewrite:=false;

    74 val t = str2term "((a + d) + c) + b";

    75 val SOME (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;

    76 if term2str t = "a + (b + (c + d))" then ()

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

    78 trace_rewrite:=false;

    80 "----- the same stepwise...";

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

    82 val t = str2term "((a + d) + c) + b";

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

    84 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_commute} t; term2str t;

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

    86 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_commute} t; term2str t;

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

    88 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_left_commute} t;term2str t;

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

    90 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_left_commute} t;term2str t;

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

    92 if term2str t = "a + (b + (c + d))" then ()

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

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

    96 val t = str2term "a + (d + (c + b))";

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

    98 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_left_commute} t;term2str t;

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

   100 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_commute} t;term2str t;

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

   102 val SOME (t,_) = rewrite_ thy od e_rls true @{thm add_left_commute} t;term2str t;

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

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

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

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

   108 val SOME (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;

   109 if term2str t = "2 * b + (3 * c + (4 * d + 5 * a))" then ()

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

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

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

   114 val t = str2term "b + a + c + d";

   115 val SOME (t,_) = rewrite_ thy od e_rls false @{thm add_commute} t; term2str t;

   116 val SOME (t,_) = rewrite_ thy od e_rls false @{thm add_commute} t; term2str t;

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

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

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

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

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

   124 "a" < "b";

   125 "ba" < "ab";

   126 "123" < "a"; (*unused due to ---vvv*)

   127 "12" < "3"; (*true !!!*)

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

   130 str2term "aaa";

   131 str2term "222 * aaa";

   133 case eval_kleiner 0 0 (str2term "123 kleiner 32") 0 of

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

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

   137 case eval_kleiner 0 0 (str2term "a kleiner b") 0 of

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

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

   141 case eval_kleiner 0 0 (str2term "(10*g) kleiner f") 0 of

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

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

   145 case eval_kleiner 0 0 (str2term "(a^^^2) kleiner b") 0 of

   146     SOME ("a ^^^ 2 kleiner b = True", _) => ()

   147   | _ => error "polyminus.sml: a ^^^ 2 kleiner b = True";

   149 case eval_kleiner 0 0 (str2term "(3*a^^^2) kleiner b") 0 of

   150     SOME ("3 * a ^^^ 2 kleiner b = True", _) => ()

   151   | _ => error "polyminus.sml: 3 * a ^^^ 2 kleiner b = True";

   153 case eval_kleiner 0 0 (str2term "(a*b) kleiner c") 0 of

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

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

   157 case eval_kleiner 0 0 (str2term "(3*a*b) kleiner c") 0 of

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

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

   161 "======= compare tausche_plus with real_num_collect";

   162 val od = dummy_ord;

   164 val erls = erls_ordne_alphabetisch;

   165 val t = str2term "b + a";

   166 val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; term2str t;

   167 if term2str t = "a + b" then ()

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

   170 val erls = Atools_erls;

   171 val t = str2term "2*a + 3*a";

   172 val SOME (t,_) = rewrite_ thy od erls false @{thm real_num_collect} t; term2str t;

   174 "======= test rewrite_, rewrite_set_";

   175 trace_rewrite:=true;

   176 val erls = erls_ordne_alphabetisch;

   177 val t = str2term "b + a";

   178 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

   179 if term2str t = "a + b" then ()

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

   182 val t = str2term "2*b + a";

   183 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

   184 if term2str t = "a + 2 * b" then ()

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

   187 val t = str2term "a + c + b";

   188 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

   189 if term2str t = "a + b + c" then ()

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

   192 "======= rewrite goes into subterms";

   193 val t = str2term "a + c + b + d";

   194 val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus_plus} t; term2str t;

   195 if term2str t = "a + b + c + d" then ()

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

   198 val t = str2term "a + c + d + b";

   199 val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

   200 if term2str t = "a + b + c + d" then ()

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

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

   204 val t = str2term "b + a + c + d";

   205 val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; term2str t;

   206 if term2str t = "a + b + c + d" then ()

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

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

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

   211 "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

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

   213 if term2str t = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g"

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

   217 "----------- build fasse_zusammen --------------------------------";

   218 "----------- build fasse_zusammen --------------------------------";

   219 "----------- build fasse_zusammen --------------------------------";

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

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

   222 if term2str t = "3 + -2 * e + 2 * f + 2 * g" then ()

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

   225 "----------- build verschoenere ----------------------------------";

   226 "----------- build verschoenere ----------------------------------";

   227 "----------- build verschoenere ----------------------------------";

   228 val t = str2term "3 + -2 * e + 2 * f + 2 * g";

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

   230 if term2str t = "3 - 2 * e + 2 * f + 2 * g" then ()

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

   233 trace_rewrite:=true;

   234 trace_rewrite:=false;

   236 "----------- met simplification for_polynomials with_minus -------";

   237 "----------- met simplification for_polynomials with_minus -------";

   238 "----------- met simplification for_polynomials with_minus -------";

   239 val str =

   240 "Script SimplifyScript (t_t::real) =                \

   241 \  (((Try (Rewrite_Set ordne_alphabetisch False)) @@     \

   242 \    (Try (Rewrite_Set fasse_zusammen False)) @@     \

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

   244 val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

   245 atomty sc;

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

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

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

   250 val c = [];

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

   252       CalcTreeTEST

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

   254            "normalform N"],

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

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

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

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

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

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

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

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

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

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

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

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

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

   269 if f2str f = "3 - 2 * e + 2 * f + 2 * g" andalso #1 nxt = "End_Proof'" then ()

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

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

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

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

   275 "----------- 140 c ---";

   276 states:=[];

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

   278 	    "normalform N"],

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

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

   281 moveActiveRoot 1;

   282 autoCalculate 1 CompleteCalc;

   283 val ((pt,p),_) = get_calc 1; show_pt pt;

   284 if p = ([], Res) andalso

   285    term2str (get_obj g_res pt (fst p)) = "3 - 2 * e + 2 * f + 2 * g"

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

   288 "======= 140 d ---";

   289 states:=[];

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

   291 	    "normalform N"],

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

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

   294 moveActiveRoot 1;

   295 autoCalculate 1 CompleteCalc;

   296 val ((pt,p),_) = get_calc 1; show_pt pt;

   297 if p = ([], Res) andalso

   298    term2str (get_obj g_res pt (fst p)) = "3 + 3 * r + 6 * s - 8 * t"

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

   301 "======= 139 c ---";

   302 states:=[];

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

   304 	    "normalform N"],

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

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

   307 moveActiveRoot 1;

   308 autoCalculate 1 CompleteCalc;

   309 val ((pt,p),_) = get_calc 1; show_pt pt;

   310 if p = ([], Res) andalso

   311    term2str (get_obj g_res pt (fst p)) = "- (3 * f)"

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

   314 "======= 139 b ---";

   315 states:=[];

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

   317 	    "normalform N"],

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

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

   320 moveActiveRoot 1;

   321 autoCalculate 1 CompleteCalc;

   322 val ((pt,p),_) = get_calc 1; show_pt pt;

   323 if p = ([], Res) andalso

   324    term2str (get_obj g_res pt (fst p)) = "-3 * u - v"

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

   327 "======= 138 a ---";

   328 states:=[];

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

   330 	    "normalform N"],

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

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

   333 moveActiveRoot 1;

   334 autoCalculate 1 CompleteCalc;

   335 val ((pt,p),_) = get_calc 1; show_pt pt;

   336 if p = ([], Res) andalso

   337    term2str (get_obj g_res pt (fst p)) = "-4 * u + 2 * v"

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

   340 "----------- met probe fuer_polynom ------------------------------";

   341 "----------- met probe fuer_polynom ------------------------------";

   342 "----------- met probe fuer_polynom ------------------------------";

   343 val str =

   344 "Script ProbeScript (e_e::bool) (w_s::bool list) =\

   345 \ (let e_e = Take e_e;                             \

   346 \      e_e = Substitute w_s e_e                    \

   347 \ in (Repeat((Try (Repeat (Calculate TIMES))) @@  \

   348 \            (Try (Repeat (Calculate PLUS ))) @@  \

   349 \            (Try (Repeat (Calculate MINUS))))) e_e)"

   350 val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

   351 atomty sc;

   353 "----------- pbl polynom probe -----------------------------------";

   354 "----------- pbl polynom probe -----------------------------------";

   355 "----------- pbl polynom probe -----------------------------------";

   356 states:=[];

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

   358 	    \3 - 2 * e + 2 * f + 2 * g)",

   359 	    "mitWert [e = 1, f = 2, g = 3]",

   360 	    "Geprueft b"],

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

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

   363 moveActiveRoot 1;

   364 autoCalculate 1 CompleteCalc;

   365 (* autoCalculate 1 CompleteCalcHead;

   366    autoCalculate 1 (Step 1);

   367    autoCalculate 1 (Step 1);

   368    val ((pt,p),_) = get_calc 1; term2str (get_obj g_res pt (fst p));

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

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

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

   372 if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "11 = 11"

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

   374 show_pt pt;

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

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

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

   379 states:=[];

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

   381 	    "normalform N"],

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

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

   384 moveActiveRoot 1;

   385 autoCalculate 1 CompleteCalc;

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

   387 if p = ([], Res) andalso

   388    term2str (get_obj g_res pt (fst p)) = "1 + 14 * u"

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

   390 show_pt pt;

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

   393 states:=[];

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

   395 	    "mitWert [u = 2]",

   396 	    "Geprueft b"],

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

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

   399 moveActiveRoot 1;

   400 autoCalculate 1 CompleteCalc;

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

   402 if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "29 = 29"

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

   404 show_pt pt;

   406 "----------- try fun applyTactics --------------------------------";

   407 "----------- try fun applyTactics --------------------------------";

   408 "----------- try fun applyTactics --------------------------------";

   409 states:=[];

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

   411 	    "normalform N"],

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

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

   414 moveActiveRoot 1;

   415 autoCalculate 1 CompleteCalcHead;

   416 autoCalculate 1 (Step 1);

   417 autoCalculate 1 (Step 1);

   418 val ((pt,p),_) = get_calc 1; show_pt pt;

   419 "----- 1 ^^^";

   420 fetchApplicableTactics 1 0 p;

   421 val appltacs = sel_appl_atomic_tacs pt p;

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

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

   424 "----- 2 ^^^";

   425 trace_rewrite := true;

   426 val erls = erls_ordne_alphabetisch;

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

   428 val SOME (t',_) =

   429     rewrite_ (@{theory "Isac"}) e_rew_ord erls false @{thm tausche_minus} t;

   430 term2str t';     "- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f - 8 * g + 10 * g";

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

   433 val NONE =

   434     rewrite_ (@{theory "Isac"}) e_rew_ord erls false @{thm tausche_minus_plus} t;

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

   437 val SOME (t',_) =

   438     rewrite_set_ (@{theory "Isac"}) false ordne_alphabetisch t;

   439 term2str t';     "- 9 + 12 + 5 * e - 7 * e - 8 * g + 10 * g + (- 4 + 6) * f";

   440 trace_rewrite := false;

   443 applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (*tausche_minus*);

   444 val ((pt,p),_) = get_calc 1; show_pt pt;

   445 "----- 3 ^^^";

   446 applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

   447 val ((pt,p),_) = get_calc 1; show_pt pt;

   448 "----- 4 ^^^";

   449 applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

   450 val ((pt,p),_) = get_calc 1; show_pt pt;

   451 "----- 5 ^^^";

   452 applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

   453 val ((pt,p),_) = get_calc 1; show_pt pt;

   454 "----- 6 ^^^";

   456 (*<CALCMESSAGE> failure </CALCMESSAGE>

   457 applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

   458 val ((pt,p),_) = get_calc 1; show_pt pt;

   459 "----- 7 ^^^";

   460 *)

   461 autoCalculate 1 CompleteCalc;

   462 val ((pt,p),_) = get_calc 1; show_pt pt;

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

   464 (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

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

   466 ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

   469 "#############################################################################";

   470 states:=[];

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

   472 	    "normalform N"],

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

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

   475 moveActiveRoot 1;

   476 autoCalculate 1 CompleteCalc;

   477 val ((pt,p),_) = get_calc 1; show_pt pt;

   478 if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "2 * g + h"

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

   482 "#############################################################################";

   483 states:=[];

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

   485 	    "normalform N"],

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

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

   488 moveActiveRoot 1;

   489 autoCalculate 1 CompleteCalc;

   490 val ((pt,p),_) = get_calc 1; show_pt pt;

   491 if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "f + 2 * g"

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

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

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

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

   497 val rls = klammern_ausmultiplizieren;

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

   499 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   500 "3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

   501 val rls = discard_parentheses;

   502 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   503 "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

   504 val rls = ordne_monome;

   505 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   506 "3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

   507 (*

   508 val t = str2term "3 * a * 4 * a";

   509 val rls = ordne_monome;

   510 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   511 *)

   512 val rls = klammern_aufloesen;

   513 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   514 "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

   515 val rls = ordne_alphabetisch;

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

   517 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   518 "3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

   519 (*STOPPED.WN080104

   520 val rls = fasse_zusammen;

   521 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   522 val rls = verschoenere;

   523 val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;

   524 *)

   526 (*@@@@@@@*)

   527 states:=[];

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

   529 	    "normalform N"],

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

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

   532 moveActiveRoot 1;

   533 autoCalculate 1 CompleteCalc;

   534 val ((pt,p),_) = get_calc 1; show_pt pt;

   535 if p = ([], Res) andalso

   536    term2str (get_obj g_res pt (fst p)) = "-2 + 12 * a ^^^ 2 + 5 * a"

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

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

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

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

   542 states:=[];

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

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

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

   546 moveActiveRoot 1;

   547 autoCalculate 1 CompleteCalc;

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

   549 if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "12 * a - 16 * q"

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

   552 "----------- refine Vereinfache ----------------------------------";

   553 "----------- refine Vereinfache ----------------------------------";

   554 "----------- refine Vereinfache ----------------------------------";

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

   556 print_depth 11;

   557 val matches = refine fmz ["vereinfachen"];

   558 print_depth 3;

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

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

   562 val t = str2term

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

   564 val ma = eval_matchsub "" "Tools.matchsub" t thy;

   565 case ma of

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

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

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

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

   571 val prls = append_rls "prls_pbl_vereinf_poly" e_rls

   572 	     [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),

   573 	      Calc ("Tools.matchsub", eval_matchsub ""),

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

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

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

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

   578 	      Thm ("not_true",num_str @{thm not_true}),

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

   580 	      Thm ("not_false",num_str @{thm not_false})

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

   582 trace_rewrite := true;

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

   584 trace_rewrite := false;

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

   587 val t = str2term

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

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

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

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

   592 trace_rewrite := true;

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

   594 trace_rewrite := false;

   595 if term2str t' = "False" then ()

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

   598 "----------- *** prep_pbt: syntax error in '#Where' of [v";

   599 "----------- *** prep_pbt: syntax error in '#Where' of [v";

   600 "----------- *** prep_pbt: syntax error in '#Where' of [v";

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

   602 val t = parse_patt thy "t_t is_polyexp";

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

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

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

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

   607 (*show_types := true;

   608 if term2str 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)"

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

   610 show_types := false;*)

   611 if term2str t = "~ (matchsub (?a + (?b + ?c)) t_t |\n   matchsub (?a + (?b - ?c)) t_t |\n" ^

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

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

author	Walther Neuper <neuper@ist.tugraz.at>
	Tue, 13 Mar 2012 15:04:09 +0100
changeset 42390	96174a374a7a
parent 42279	e2759e250604
child 52070	77138c64f4f6
permissions	-rw-r--r--