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(* title: Knowledge/polyminus.sml
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author: Walther Neuper
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WN071207,
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(c) due to copyright terms
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*)
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"--------------------------------------------------------";
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"--------------------------------------------------------";
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"table of contents --------------------------------------";
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"--------------------------------------------------------";
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"----------- fun eval_ist_monom -------------------------";
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"----------- watch order_add_mult ----------------------";
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"----------- build predicate for +- ordering ------------";
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"----------- build fasse_zusammen -----------------------";
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"----------- build verschoenere -------------------------";
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neuper@38037
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"----------- met simplification for_polynomials with_minu";
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"----------- me simplification.for_polynomials.with_minus";
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"----------- pbl polynom vereinfachen p.33 --------------";
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"----------- met probe fuer_polynom ---------------------";
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neuper@38037
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"----------- pbl polynom probe --------------------------";
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"----------- pbl klammer polynom vereinfachen p.34 ------";
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"----------- try fun applyTactics -----------------------";
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"----------- pbl binom polynom vereinfachen p.39 --------";
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"----------- pbl binom polynom vereinfachen: cube -------";
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"----------- refine Vereinfache -------------------------";
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"----------- *** prep_pbt: syntax error in '#Where' of [v";
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"--------------------------------------------------------";
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"--------------------------------------------------------";
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"--------------------------------------------------------";
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val thy = @{theory "PolyMinus"};
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"----------- fun eval_ist_monom ----------------------------------";
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"----------- fun eval_ist_monom ----------------------------------";
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"----------- fun eval_ist_monom ----------------------------------";
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ist_monom (str2term "12");
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case eval_ist_monom 0 0 (str2term "12 ist_monom") 0 of
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SOME ("12 ist_monom = True", _) => ()
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| _ => error "polyminus.sml: 12 ist_monom = True";
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case eval_ist_monom 0 0 (str2term "a ist_monom") 0 of
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SOME ("a ist_monom = True", _) => ()
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| _ => error "polyminus.sml: a ist_monom = True";
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case eval_ist_monom 0 0 (str2term "(3*a) ist_monom") 0 of
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SOME ("3 * a ist_monom = True", _) => ()
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| _ => error "polyminus.sml: 3 * a ist_monom = True";
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case eval_ist_monom 0 0 (str2term "(a^^^2) ist_monom") 0 of
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SOME ("a ^^^ 2 ist_monom = True", _) => ()
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| _ => error "polyminus.sml: a^^^2 ist_monom = True";
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case eval_ist_monom 0 0 (str2term "(3*a^^^2) ist_monom") 0 of
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SOME ("3 * a ^^^ 2 ist_monom = True", _) => ()
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| _ => error "polyminus.sml: 3*a^^^2 ist_monom = True";
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case eval_ist_monom 0 0 (str2term "(a*b) ist_monom") 0 of
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SOME ("a * b ist_monom = True", _) => ()
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| _ => error "polyminus.sml: a*b ist_monom = True";
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case eval_ist_monom 0 0 (str2term "(3*a*b) ist_monom") 0 of
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SOME ("3 * a * b ist_monom = True", _) => ()
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| _ => error "polyminus.sml: 3*a*b ist_monom = True";
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"----------- watch order_add_mult -------------------------------";
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"----------- watch order_add_mult -------------------------------";
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"----------- watch order_add_mult -------------------------------";
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"----- with these simple variables it works...";
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(*trace_rewrite := true; ..stopped Test_Isac.thy*)
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trace_rewrite:=false;
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val t = str2term "((a + d) + c) + b";
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val SOME (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;
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if term2str t = "a + (b + (c + d))" then ()
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else error "polyminus.sml 1 watch order_add_mult";
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trace_rewrite:=false;
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"----- the same stepwise...";
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val od = ord_make_polynomial true (@{theory "Poly"});
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val t = str2term "((a + d) + c) + b";
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"((a + d) + c) + b";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.commute} t; term2str t;
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"b + ((a + d) + c)";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.commute} t; term2str t;
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"b + (c + (a + d))";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
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"b + (a + (c + d))";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
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"a + (b + (c + d))";
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if term2str t = "a + (b + (c + d))" then ()
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else error "polyminus.sml 2 watch order_add_mult";
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"----- if parentheses are right, left_commute is (almost) sufficient...";
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val t = str2term "a + (d + (c + b))";
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"a + (d + (c + b))";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
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"a + (c + (d + b))";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.commute} t;term2str t;
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"a + (c + (b + d))";
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val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
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"a + (b + (c + d))";
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"----- but we do not want the parentheses at right; thus: cond.rew.";
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"WN0712707 complicated monomials do not yet work ...";
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val t = str2term "((5*a + 4*d) + 3*c) + 2*b";
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val SOME (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;
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if term2str t = "2 * b + (3 * c + (4 * d + 5 * a))" then ()
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else error "polyminus.sml: order_add_mult changed";
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"----- here we see rew_sub going into subterm with ord.rew....";
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val od = ord_make_polynomial false (@{theory "Poly"});
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val t = str2term "b + a + c + d";
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val SOME (t,_) = rewrite_ thy od e_rls false @{thm add.commute} t; term2str t;
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wneuper@59118
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val SOME (t,_) = rewrite_ thy od e_rls false @{thm add.commute} t; term2str t;
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(*@@@ rew_sub gosub: t = d + (b + a + c)
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@@@ rew_sub begin: t = b + a + c*)
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"----------- build predicate for +- ordering ---------------------";
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"----------- build predicate for +- ordering ---------------------";
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"----------- build predicate for +- ordering ---------------------";
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"a" < "b";
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"ba" < "ab";
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"123" < "a"; (*unused due to ---vvv*)
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"12" < "3"; (*true !!!*)
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" a kleiner b ==> (b + a) = (a + b)";
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str2term "aaa";
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str2term "222 * aaa";
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case eval_kleiner 0 0 (str2term "123 kleiner 32") 0 of
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SOME ("123 kleiner 32 = False", _) => ()
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| _ => error "polyminus.sml: 12 kleiner 9 = False";
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case eval_kleiner 0 0 (str2term "a kleiner b") 0 of
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SOME ("a kleiner b = True", _) => ()
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| _ => error "polyminus.sml: a kleiner b = True";
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case eval_kleiner 0 0 (str2term "(10*g) kleiner f") 0 of
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SOME ("10 * g kleiner f = False", _) => ()
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| _ => error "polyminus.sml: 10 * g kleiner f = False";
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case eval_kleiner 0 0 (str2term "(a^^^2) kleiner b") 0 of
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SOME ("a ^^^ 2 kleiner b = True", _) => ()
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| _ => error "polyminus.sml: a ^^^ 2 kleiner b = True";
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case eval_kleiner 0 0 (str2term "(3*a^^^2) kleiner b") 0 of
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SOME ("3 * a ^^^ 2 kleiner b = True", _) => ()
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| _ => error "polyminus.sml: 3 * a ^^^ 2 kleiner b = True";
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case eval_kleiner 0 0 (str2term "(a*b) kleiner c") 0 of
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SOME ("a * b kleiner c = True", _) => ()
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| _ => error "polyminus.sml: a * b kleiner b = True";
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case eval_kleiner 0 0 (str2term "(3*a*b) kleiner c") 0 of
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SOME ("3 * a * b kleiner c = True", _) => ()
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| _ => error "polyminus.sml: 3 * a * b kleiner b = True";
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"======= compare tausche_plus with real_num_collect";
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val od = dummy_ord;
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val erls = erls_ordne_alphabetisch;
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val t = str2term "b + a";
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val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; term2str t;
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if term2str t = "a + b" then ()
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else error "polyminus.sml: ordne_alphabetisch1 b + a";
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val erls = Atools_erls;
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val t = str2term "2*a + 3*a";
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val SOME (t,_) = rewrite_ thy od erls false @{thm real_num_collect} t; term2str t;
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"======= test rewrite_, rewrite_set_";
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(*trace_rewrite := true; ..stopped Test_Isac.thy*)
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val erls = erls_ordne_alphabetisch;
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val t = str2term "b + a";
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val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
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if term2str t = "a + b" then ()
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else error "polyminus.sml: ordne_alphabetisch a + b";
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val t = str2term "2*b + a";
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val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
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if term2str t = "a + 2 * b" then ()
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else error "polyminus.sml: ordne_alphabetisch a + 2 * b";
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val t = str2term "a + c + b";
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neuper@37926
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val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
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if term2str t = "a + b + c" then ()
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else error "polyminus.sml: ordne_alphabetisch a + b + c";
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"======= rewrite goes into subterms";
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val t = str2term "a + c + b + d";
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neuper@38080
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val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus_plus} t; term2str t;
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if term2str t = "a + b + c + d" then ()
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neuper@38031
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else error "polyminus.sml: ordne_alphabetisch1 a + b + c + d";
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val t = str2term "a + c + d + b";
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neuper@37926
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val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
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if term2str t = "a + b + c + d" then ()
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neuper@38031
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else error "polyminus.sml: ordne_alphabetisch2 a + b + c + d";
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neuper@42390
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"======= here we see rew_sub going into subterm with cond.rew....";
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neuper@37906
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val t = str2term "b + a + c + d";
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neuper@38080
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val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; term2str t;
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neuper@37906
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if term2str t = "a + b + c + d" then ()
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neuper@38031
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else error "polyminus.sml: ordne_alphabetisch3 a + b + c + d";
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neuper@42390
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"======= compile rls for the most complicated terms";
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neuper@37906
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val t = str2term "5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12";
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neuper@37906
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"5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";
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neuper@37926
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val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t;
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neuper@37906
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if term2str t = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g"
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neuper@38031
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then () else error "polyminus.sml: ordne_alphabetisch finished";
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neuper@37906
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neuper@37906
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neuper@37906
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"----------- build fasse_zusammen --------------------------------";
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neuper@37906
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"----------- build fasse_zusammen --------------------------------";
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neuper@37906
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"----------- build fasse_zusammen --------------------------------";
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neuper@37906
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val t = str2term "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";
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neuper@37926
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val SOME (t,_) = rewrite_set_ thy false fasse_zusammen t;
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neuper@37906
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if term2str t = "3 + -2 * e + 2 * f + 2 * g" then ()
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neuper@38031
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else error "polyminus.sml: fasse_zusammen finished";
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neuper@37906
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neuper@37906
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"----------- build verschoenere ----------------------------------";
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neuper@37906
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"----------- build verschoenere ----------------------------------";
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neuper@37906
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"----------- build verschoenere ----------------------------------";
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neuper@37906
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val t = str2term "3 + -2 * e + 2 * f + 2 * g";
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neuper@37926
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val SOME (t,_) = rewrite_set_ thy false verschoenere t;
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neuper@37906
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if term2str t = "3 - 2 * e + 2 * f + 2 * g" then ()
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neuper@38031
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else error "polyminus.sml: verschoenere 3 + -2 * e ...";
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neuper@37906
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neuper@52070
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(*trace_rewrite := true; ..stopped Test_Isac.thy*)
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neuper@37906
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trace_rewrite:=false;
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neuper@37906
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neuper@37906
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"----------- met simplification for_polynomials with_minus -------";
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neuper@37906
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"----------- met simplification for_polynomials with_minus -------";
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neuper@37906
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"----------- met simplification for_polynomials with_minus -------";
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neuper@37906
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val str =
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wneuper@59585
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"Program SimplifyScript (t_t::real) = \
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neuper@37906
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\ (((Try (Rewrite_Set ordne_alphabetisch False)) @@ \
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neuper@37906
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\ (Try (Rewrite_Set fasse_zusammen False)) @@ \
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neuper@38080
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\ (Try (Rewrite_Set verschoenere False))) t_t)"
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wneuper@59395
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val sc = (inst_abs o Thm.term_of o the o (parse thy)) str;
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neuper@37906
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atomty sc;
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neuper@37906
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neuper@38080
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"----------- me simplification.for_polynomials.with_minus";
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neuper@38080
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"----------- me simplification.for_polynomials.with_minus";
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neuper@38080
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"----------- me simplification.for_polynomials.with_minus";
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neuper@38080
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val c = [];
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neuper@38080
|
248 |
val (p,_,f,nxt,_,pt) =
|
neuper@38080
|
249 |
CalcTreeTEST
|
neuper@38083
|
250 |
[(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",
|
neuper@38080
|
251 |
"normalform N"],
|
neuper@38080
|
252 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@38080
|
253 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@38080
|
254 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
255 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
256 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
257 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
258 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
259 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
260 |
|
neuper@38085
|
261 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
262 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
263 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
264 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
265 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38085
|
266 |
if f2str f = "3 - 2 * e + 2 * f + 2 * g" andalso #1 nxt = "End_Proof'" then ()
|
neuper@38085
|
267 |
else error "polyminus.sml: me simplification.for_polynomials.with_minus";
|
neuper@38085
|
268 |
|
neuper@37906
|
269 |
"----------- pbl polynom vereinfachen p.33 -----------------------";
|
neuper@37906
|
270 |
"----------- pbl polynom vereinfachen p.33 -----------------------";
|
neuper@37906
|
271 |
"----------- pbl polynom vereinfachen p.33 -----------------------";
|
neuper@37906
|
272 |
"----------- 140 c ---";
|
s1210629013@55445
|
273 |
reset_states ();
|
neuper@38083
|
274 |
CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",
|
neuper@37906
|
275 |
"normalform N"],
|
neuper@37991
|
276 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
277 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
278 |
moveActiveRoot 1;
|
wneuper@59248
|
279 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
280 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
281 |
if p = ([], Res) andalso
|
neuper@37906
|
282 |
term2str (get_obj g_res pt (fst p)) = "3 - 2 * e + 2 * f + 2 * g"
|
neuper@38031
|
283 |
then () else error "polyminus.sml: Vereinfache (3 - 2 * e + 2 * f...";
|
neuper@37906
|
284 |
|
neuper@42390
|
285 |
"======= 140 d ---";
|
s1210629013@55445
|
286 |
reset_states ();
|
neuper@38083
|
287 |
CalcTree [(["Term (-r - 2*s - 3*t + 5 + 4*r + 8*s - 5*t - 2)",
|
neuper@37906
|
288 |
"normalform N"],
|
neuper@37991
|
289 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
290 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
291 |
moveActiveRoot 1;
|
wneuper@59248
|
292 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
293 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
294 |
if p = ([], Res) andalso
|
neuper@37906
|
295 |
term2str (get_obj g_res pt (fst p)) = "3 + 3 * r + 6 * s - 8 * t"
|
neuper@38031
|
296 |
then () else error "polyminus.sml: Vereinfache 140 d)";
|
neuper@37906
|
297 |
|
neuper@42390
|
298 |
"======= 139 c ---";
|
s1210629013@55445
|
299 |
reset_states ();
|
neuper@38083
|
300 |
CalcTree [(["Term (3*e - 6*f - 8*e - 4*f + 5*e + 7*f)",
|
neuper@37906
|
301 |
"normalform N"],
|
neuper@37991
|
302 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
303 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
304 |
moveActiveRoot 1;
|
wneuper@59248
|
305 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
306 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
307 |
if p = ([], Res) andalso
|
neuper@37906
|
308 |
term2str (get_obj g_res pt (fst p)) = "- (3 * f)"
|
neuper@38031
|
309 |
then () else error "polyminus.sml: Vereinfache 139 c)";
|
neuper@37906
|
310 |
|
neuper@42390
|
311 |
"======= 139 b ---";
|
s1210629013@55445
|
312 |
reset_states ();
|
neuper@38083
|
313 |
CalcTree [(["Term (8*u - 5*v - 5*u + 7*v - 6*u - 3*v)",
|
neuper@37906
|
314 |
"normalform N"],
|
neuper@37991
|
315 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
316 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
317 |
moveActiveRoot 1;
|
wneuper@59248
|
318 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
319 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
320 |
if p = ([], Res) andalso
|
neuper@37906
|
321 |
term2str (get_obj g_res pt (fst p)) = "-3 * u - v"
|
neuper@38031
|
322 |
then () else error "polyminus.sml: Vereinfache 139 b)";
|
neuper@37906
|
323 |
|
neuper@42390
|
324 |
"======= 138 a ---";
|
s1210629013@55445
|
325 |
reset_states ();
|
neuper@38083
|
326 |
CalcTree [(["Term (2*u - 3*v - 6*u + 5*v)",
|
neuper@37906
|
327 |
"normalform N"],
|
neuper@37991
|
328 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
329 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
330 |
moveActiveRoot 1;
|
wneuper@59248
|
331 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
332 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
333 |
if p = ([], Res) andalso
|
neuper@37906
|
334 |
term2str (get_obj g_res pt (fst p)) = "-4 * u + 2 * v"
|
neuper@38031
|
335 |
then () else error "polyminus.sml: Vereinfache 138 a)";
|
neuper@37906
|
336 |
|
neuper@37906
|
337 |
"----------- met probe fuer_polynom ------------------------------";
|
neuper@37906
|
338 |
"----------- met probe fuer_polynom ------------------------------";
|
neuper@37906
|
339 |
"----------- met probe fuer_polynom ------------------------------";
|
neuper@37906
|
340 |
val str =
|
wneuper@59585
|
341 |
"Program ProbeScript (e_e::bool) (w_s::bool list) =\
|
neuper@37991
|
342 |
\ (let e_e = Take e_e; \
|
neuper@38085
|
343 |
\ e_e = Substitute w_s e_e \
|
wneuper@59488
|
344 |
\ in (Repeat((Try (Repeat (Calculate ''TIMES''))) @@ \
|
wneuper@59488
|
345 |
\ (Try (Repeat (Calculate ''PLUS''))) @@ \
|
wneuper@59488
|
346 |
\ (Try (Repeat (Calculate ''MINUS''))))) e_e)"
|
wneuper@59395
|
347 |
val sc = (inst_abs o Thm.term_of o the o (parse thy)) str;
|
neuper@37906
|
348 |
atomty sc;
|
neuper@37906
|
349 |
|
neuper@37906
|
350 |
"----------- pbl polynom probe -----------------------------------";
|
neuper@37906
|
351 |
"----------- pbl polynom probe -----------------------------------";
|
neuper@37906
|
352 |
"----------- pbl polynom probe -----------------------------------";
|
s1210629013@55445
|
353 |
reset_states ();
|
bonzai@41949
|
354 |
CalcTree [(["Pruefe ((5::int)*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12 =\
|
wneuper@59582
|
355 |
\3 - 2 * e + 2 * f + 2 * (g::int))",
|
wneuper@59582
|
356 |
"mitWert [e = (1::int), f = (2::int), g = (3::int)]",
|
neuper@37906
|
357 |
"Geprueft b"],
|
neuper@37991
|
358 |
("PolyMinus",["polynom","probe"],
|
neuper@37906
|
359 |
["probe","fuer_polynom"]))];
|
neuper@37906
|
360 |
moveActiveRoot 1;
|
wneuper@59248
|
361 |
autoCalculate 1 CompleteCalc;
|
wneuper@59248
|
362 |
(* autoCalculate 1 CompleteCalcHead;
|
wneuper@59248
|
363 |
autoCalculate 1 (Step 1);
|
wneuper@59248
|
364 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
365 |
val ((pt,p),_) = get_calc 1; term2str (get_obj g_res pt (fst p));
|
neuper@37906
|
366 |
@@@@@WN081114 gives "??.empty", all "Pruefe" are the same,
|
neuper@37906
|
367 |
although analogies work in interface.sml: FIXME.WN081114 in "Pruefe"*)
|
neuper@37906
|
368 |
val ((pt,p),_) = get_calc 1;
|
neuper@37906
|
369 |
if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "11 = 11"
|
neuper@38031
|
370 |
then () else error "polyminus.sml: Probe 11 = 11";
|
neuper@37906
|
371 |
show_pt pt;
|
t@42115
|
372 |
|
neuper@37906
|
373 |
"----------- pbl klammer polynom vereinfachen p.34 ---------------";
|
neuper@37906
|
374 |
"----------- pbl klammer polynom vereinfachen p.34 ---------------";
|
neuper@37906
|
375 |
"----------- pbl klammer polynom vereinfachen p.34 ---------------";
|
s1210629013@55445
|
376 |
reset_states ();
|
neuper@38083
|
377 |
CalcTree [(["Term (2*u - 5 - (3 - 4*u) + (8*u + 9))",
|
neuper@37906
|
378 |
"normalform N"],
|
neuper@37991
|
379 |
("PolyMinus",["klammer","polynom","vereinfachen"],
|
neuper@37906
|
380 |
["simplification","for_polynomials","with_parentheses"]))];
|
neuper@37906
|
381 |
moveActiveRoot 1;
|
wneuper@59248
|
382 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
383 |
val ((pt,p),_) = get_calc 1;
|
neuper@37906
|
384 |
if p = ([], Res) andalso
|
neuper@37906
|
385 |
term2str (get_obj g_res pt (fst p)) = "1 + 14 * u"
|
neuper@38031
|
386 |
then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";
|
neuper@37906
|
387 |
show_pt pt;
|
neuper@37906
|
388 |
|
neuper@42390
|
389 |
"======= probe p.34 -----";
|
s1210629013@55445
|
390 |
reset_states ();
|
wneuper@59582
|
391 |
CalcTree [(["Pruefe (2*u - 5 - (3 - 4*u) + (8*u + 9) = 1 + 14 * (u::int))",
|
wneuper@59582
|
392 |
"mitWert [u = (2::int)]",
|
neuper@37906
|
393 |
"Geprueft b"],
|
neuper@37991
|
394 |
("PolyMinus",["polynom","probe"],
|
neuper@37906
|
395 |
["probe","fuer_polynom"]))];
|
neuper@37906
|
396 |
moveActiveRoot 1;
|
wneuper@59248
|
397 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
398 |
val ((pt,p),_) = get_calc 1;
|
neuper@37906
|
399 |
if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "29 = 29"
|
neuper@38031
|
400 |
then () else error "polyminus.sml: Probe 29 = 29";
|
neuper@37906
|
401 |
show_pt pt;
|
neuper@37906
|
402 |
|
neuper@37906
|
403 |
"----------- try fun applyTactics --------------------------------";
|
neuper@37906
|
404 |
"----------- try fun applyTactics --------------------------------";
|
neuper@37906
|
405 |
"----------- try fun applyTactics --------------------------------";
|
s1210629013@55445
|
406 |
reset_states ();
|
neuper@38083
|
407 |
CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",
|
neuper@37906
|
408 |
"normalform N"],
|
neuper@37991
|
409 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
410 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
411 |
moveActiveRoot 1;
|
wneuper@59248
|
412 |
autoCalculate 1 CompleteCalcHead;
|
wneuper@59248
|
413 |
autoCalculate 1 (Step 1);
|
wneuper@59248
|
414 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
415 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
416 |
"----- 1 ^^^";
|
neuper@37906
|
417 |
fetchApplicableTactics 1 0 p;
|
neuper@37906
|
418 |
val appltacs = sel_appl_atomic_tacs pt p;
|
neuper@37906
|
419 |
applyTactic 1 p (hd appltacs) (*addiere_x_plus_minus*);
|
neuper@37906
|
420 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
421 |
"----- 2 ^^^";
|
neuper@52070
|
422 |
(*trace_rewrite := true; ..stopped Test_Isac.thy*)
|
neuper@37906
|
423 |
val erls = erls_ordne_alphabetisch;
|
neuper@37906
|
424 |
val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";
|
neuper@37926
|
425 |
val SOME (t',_) =
|
wneuper@59592
|
426 |
rewrite_ (@{theory "Isac_Knowledge"}) e_rew_ord erls false @{thm tausche_minus} t;
|
neuper@37906
|
427 |
term2str t'; "- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f - 8 * g + 10 * g";
|
neuper@37906
|
428 |
|
neuper@37906
|
429 |
val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";
|
neuper@37926
|
430 |
val NONE =
|
wneuper@59592
|
431 |
rewrite_ (@{theory "Isac_Knowledge"}) e_rew_ord erls false @{thm tausche_minus_plus} t;
|
neuper@37906
|
432 |
|
neuper@37906
|
433 |
val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";
|
neuper@37926
|
434 |
val SOME (t',_) =
|
wneuper@59592
|
435 |
rewrite_set_ (@{theory "Isac_Knowledge"}) false ordne_alphabetisch t;
|
neuper@37906
|
436 |
term2str t'; "- 9 + 12 + 5 * e - 7 * e - 8 * g + 10 * g + (- 4 + 6) * f";
|
neuper@37906
|
437 |
trace_rewrite := false;
|
neuper@37906
|
438 |
|
neuper@37906
|
439 |
|
neuper@37906
|
440 |
applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (*tausche_minus*);
|
neuper@37906
|
441 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
442 |
"----- 3 ^^^";
|
neuper@37906
|
443 |
applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
|
neuper@37906
|
444 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
445 |
"----- 4 ^^^";
|
neuper@37906
|
446 |
applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
|
neuper@37906
|
447 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
448 |
"----- 5 ^^^";
|
neuper@37906
|
449 |
applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
|
neuper@37906
|
450 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
451 |
"----- 6 ^^^";
|
neuper@37906
|
452 |
|
neuper@37906
|
453 |
(*<CALCMESSAGE> failure </CALCMESSAGE>
|
neuper@37906
|
454 |
applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
|
neuper@37906
|
455 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
456 |
"----- 7 ^^^";
|
neuper@37906
|
457 |
*)
|
wneuper@59248
|
458 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
459 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
460 |
(*independent from failure above: met_simp_poly_minus not confluent:
|
neuper@37906
|
461 |
(([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),
|
neuper@37906
|
462 |
(([], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f))]
|
neuper@37906
|
463 |
~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
t@42115
|
464 |
|
neuper@37906
|
465 |
|
neuper@42107
|
466 |
"#############################################################################";
|
s1210629013@55445
|
467 |
reset_states ();
|
neuper@38083
|
468 |
CalcTree [(["Term (- (8 * g) + 10 * g + h)",
|
neuper@37906
|
469 |
"normalform N"],
|
neuper@37991
|
470 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
471 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
472 |
moveActiveRoot 1;
|
wneuper@59248
|
473 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
474 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
475 |
if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "2 * g + h"
|
neuper@38031
|
476 |
then () else error "polyminus.sml: addiere_vor_minus";
|
neuper@37906
|
477 |
|
neuper@37906
|
478 |
|
neuper@42107
|
479 |
"#############################################################################";
|
s1210629013@55445
|
480 |
reset_states ();
|
neuper@38083
|
481 |
CalcTree [(["Term (- (8 * g) + 10 * g + f)",
|
neuper@37906
|
482 |
"normalform N"],
|
neuper@37991
|
483 |
("PolyMinus",["plus_minus","polynom","vereinfachen"],
|
neuper@37906
|
484 |
["simplification","for_polynomials","with_minus"]))];
|
neuper@37906
|
485 |
moveActiveRoot 1;
|
wneuper@59248
|
486 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
487 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
488 |
if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "f + 2 * g"
|
neuper@38031
|
489 |
then () else error "polyminus.sml: tausche_vor_plus";
|
neuper@37906
|
490 |
|
neuper@37906
|
491 |
"----------- pbl binom polynom vereinfachen p.39 -----------------";
|
neuper@37906
|
492 |
"----------- pbl binom polynom vereinfachen p.39 -----------------";
|
neuper@37906
|
493 |
"----------- pbl binom polynom vereinfachen p.39 -----------------";
|
neuper@37906
|
494 |
val rls = klammern_ausmultiplizieren;
|
neuper@37906
|
495 |
val t = str2term "(3 * a + 2) * (4 * a - 1)";
|
neuper@37926
|
496 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
497 |
"3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";
|
neuper@37906
|
498 |
val rls = discard_parentheses;
|
neuper@37926
|
499 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
500 |
"3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";
|
neuper@37906
|
501 |
val rls = ordne_monome;
|
neuper@37926
|
502 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
503 |
"3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";
|
neuper@37906
|
504 |
(*
|
neuper@37906
|
505 |
val t = str2term "3 * a * 4 * a";
|
neuper@37906
|
506 |
val rls = ordne_monome;
|
neuper@37926
|
507 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
508 |
*)
|
neuper@37906
|
509 |
val rls = klammern_aufloesen;
|
neuper@37926
|
510 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
511 |
"3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";
|
neuper@37906
|
512 |
val rls = ordne_alphabetisch;
|
neuper@37906
|
513 |
(*TODO: make is_monom more general, a*a=a^2, ...*)
|
neuper@37926
|
514 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
515 |
"3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";
|
neuper@41977
|
516 |
(*STOPPED.WN080104
|
neuper@37906
|
517 |
val rls = fasse_zusammen;
|
neuper@37926
|
518 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
519 |
val rls = verschoenere;
|
neuper@37926
|
520 |
val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
|
neuper@37906
|
521 |
*)
|
neuper@37906
|
522 |
|
neuper@37906
|
523 |
(*@@@@@@@*)
|
s1210629013@55445
|
524 |
reset_states ();
|
neuper@38083
|
525 |
CalcTree [(["Term ((3*a + 2) * (4*a - 1))",
|
neuper@37906
|
526 |
"normalform N"],
|
neuper@37991
|
527 |
("PolyMinus",["binom_klammer","polynom","vereinfachen"],
|
neuper@37906
|
528 |
["simplification","for_polynomials","with_parentheses_mult"]))];
|
neuper@37906
|
529 |
moveActiveRoot 1;
|
wneuper@59248
|
530 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
531 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
532 |
if p = ([], Res) andalso
|
t@42111
|
533 |
term2str (get_obj g_res pt (fst p)) = "-2 + 12 * a ^^^ 2 + 5 * a"
|
neuper@38031
|
534 |
then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";
|
t@42111
|
535 |
|
neuper@37906
|
536 |
"----------- pbl binom polynom vereinfachen: cube ----------------";
|
neuper@37906
|
537 |
"----------- pbl binom polynom vereinfachen: cube ----------------";
|
neuper@37906
|
538 |
"----------- pbl binom polynom vereinfachen: cube ----------------";
|
s1210629013@55445
|
539 |
reset_states ();
|
neuper@38083
|
540 |
CalcTree [(["Term (8*(a - q) + a - 2*q + 3*(a - 2*q))", "normalform N"],
|
neuper@37991
|
541 |
("PolyMinus",["binom_klammer","polynom","vereinfachen"],
|
neuper@37906
|
542 |
["simplification","for_polynomials","with_parentheses_mult"]))];
|
neuper@37906
|
543 |
moveActiveRoot 1;
|
wneuper@59248
|
544 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
545 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@42107
|
546 |
if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "12 * a - 16 * q"
|
neuper@42107
|
547 |
then () else error "pbl binom polynom vereinfachen: cube";
|
neuper@37906
|
548 |
|
neuper@37906
|
549 |
"----------- refine Vereinfache ----------------------------------";
|
neuper@37906
|
550 |
"----------- refine Vereinfache ----------------------------------";
|
neuper@37906
|
551 |
"----------- refine Vereinfache ----------------------------------";
|
neuper@42390
|
552 |
val fmz = ["Term (8*(a - q) + a - 2*q + 3*(a - 2*(q::real)))", "normalform (N::real)"];
|
wneuper@59348
|
553 |
(*default_print_depth 11;*)
|
neuper@37906
|
554 |
val matches = refine fmz ["vereinfachen"];
|
wneuper@59348
|
555 |
(*default_print_depth 3;*)
|
neuper@37906
|
556 |
|
neuper@37906
|
557 |
"----- go into details, if it seems not to work -----";
|
neuper@37906
|
558 |
"--- does the predicate evaluate correctly ?";
|
neuper@37906
|
559 |
val t = str2term
|
neuper@42390
|
560 |
"matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q + 3 * (a - 2 * (q::real)))";
|
walther@59603
|
561 |
val ma = eval_matchsub "" "Prog_Expr.matchsub" t thy;
|
neuper@37906
|
562 |
case ma of
|
neuper@37926
|
563 |
SOME ("matchsub (?a * (?b - ?c)) (8 * (a - q) + \
|
neuper@37906
|
564 |
\a - 2 * q + 3 * (a - 2 * q)) = True", _) => ()
|
neuper@38031
|
565 |
| _ => error "polyminus.sml matchsub (?a * (?b - ?c)...A";
|
neuper@37906
|
566 |
|
neuper@37906
|
567 |
"--- does the respective prls rewrite ?";
|
neuper@37906
|
568 |
val prls = append_rls "prls_pbl_vereinf_poly" e_rls
|
neuper@37906
|
569 |
[Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
|
walther@59603
|
570 |
Calc ("Prog_Expr.matchsub", eval_matchsub ""),
|
neuper@38085
|
571 |
Thm ("or_true",@{thm or_true}),
|
neuper@37906
|
572 |
(*"(?a | True) = True"*)
|
neuper@38085
|
573 |
Thm ("or_false",@{thm or_false}),
|
neuper@37906
|
574 |
(*"(?a | False) = ?a"*)
|
neuper@37970
|
575 |
Thm ("not_true",num_str @{thm not_true}),
|
neuper@37906
|
576 |
(*"(~ True) = False"*)
|
neuper@37970
|
577 |
Thm ("not_false",num_str @{thm not_false})
|
neuper@37906
|
578 |
(*"(~ False) = True"*)];
|
neuper@52070
|
579 |
(*trace_rewrite := true; ..stopped Test_Isac.thy*)
|
neuper@37926
|
580 |
val SOME (t', _) = rewrite_set_ thy false prls t;
|
neuper@37906
|
581 |
trace_rewrite := false;
|
neuper@37906
|
582 |
|
neuper@37906
|
583 |
"--- does the respective prls rewrite the whole predicate ?";
|
neuper@37906
|
584 |
val t = str2term
|
neuper@37906
|
585 |
"Not (matchsub (?a * (?b + ?c)) (8 * (a - q) + a - 2 * q) | \
|
neuper@37906
|
586 |
\ matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q) | \
|
neuper@37906
|
587 |
\ matchsub ((?b + ?c) * ?a) (8 * (a - q) + a - 2 * q) | \
|
neuper@37906
|
588 |
\ matchsub ((?b - ?c) * ?a) (8 * (a - q) + a - 2 * q) )";
|
neuper@52070
|
589 |
(*trace_rewrite := true; ..stopped Test_Isac.thy*)
|
neuper@37926
|
590 |
val SOME (t', _) = rewrite_set_ thy false prls t;
|
neuper@37906
|
591 |
trace_rewrite := false;
|
neuper@42390
|
592 |
if term2str t' = "False" then ()
|
neuper@38031
|
593 |
else error "polyminus.sml Not (matchsub (?a * (?b + ?c)) (8 ...";
|
neuper@37906
|
594 |
|
neuper@38037
|
595 |
"----------- *** prep_pbt: syntax error in '#Where' of [v";
|
neuper@38037
|
596 |
"----------- *** prep_pbt: syntax error in '#Where' of [v";
|
neuper@38037
|
597 |
"----------- *** prep_pbt: syntax error in '#Where' of [v";
|
neuper@38037
|
598 |
(*see test/../termC.sml for details*)
|
neuper@38037
|
599 |
val t = parse_patt thy "t_t is_polyexp";
|
neuper@38037
|
600 |
val t = parse_patt thy ("Not (matchsub (?a + (?b + ?c)) t_t | " ^
|
neuper@38037
|
601 |
" matchsub (?a + (?b - ?c)) t_t | " ^
|
neuper@38037
|
602 |
" matchsub (?a - (?b + ?c)) t_t | " ^
|
neuper@38037
|
603 |
" matchsub (?a + (?b - ?c)) t_t )");
|
neuper@42390
|
604 |
(*show_types := true;
|
neuper@38037
|
605 |
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)"
|
neuper@38038
|
606 |
then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";
|
neuper@42390
|
607 |
show_types := false;*)
|
wneuper@59371
|
608 |
if term2str t =
|
wneuper@59371
|
609 |
"\<not> (matchsub (?a + (?b + ?c)) t_t \<or>\n " ^
|
wneuper@59371
|
610 |
"matchsub (?a + (?b - ?c)) t_t \<or>\n " ^
|
wneuper@59371
|
611 |
"matchsub (?a - (?b + ?c)) t_t \<or> " ^
|
wneuper@59371
|
612 |
"matchsub (?a + (?b - ?c)) t_t)"
|
neuper@42390
|
613 |
then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";
|
neuper@37906
|
614 |
|