wneuper@59582: (* title: Knowledge/polyminus.sml
neuper@37906: author: Walther Neuper
neuper@37906: WN071207,
neuper@37906: (c) due to copyright terms
neuper@37906: *)
neuper@38037: "--------------------------------------------------------";
neuper@38037: "--------------------------------------------------------";
neuper@38037: "table of contents --------------------------------------";
neuper@38037: "--------------------------------------------------------";
neuper@38037: "----------- fun eval_ist_monom -------------------------";
neuper@38037: "----------- watch order_add_mult ----------------------";
neuper@38037: "----------- build predicate for +- ordering ------------";
neuper@38037: "----------- build fasse_zusammen -----------------------";
neuper@38037: "----------- build verschoenere -------------------------";
neuper@38037: "----------- met simplification for_polynomials with_minu";
neuper@38080: "----------- me simplification.for_polynomials.with_minus";
neuper@38037: "----------- pbl polynom vereinfachen p.33 --------------";
neuper@38037: "----------- met probe fuer_polynom ---------------------";
neuper@38037: "----------- pbl polynom probe --------------------------";
neuper@38037: "----------- pbl klammer polynom vereinfachen p.34 ------";
neuper@38037: "----------- try fun applyTactics -----------------------";
neuper@38037: "----------- pbl binom polynom vereinfachen p.39 --------";
neuper@38037: "----------- pbl binom polynom vereinfachen: cube -------";
neuper@38037: "----------- refine Vereinfache -------------------------";
neuper@38037: "----------- *** prep_pbt: syntax error in '#Where' of [v";
neuper@38037: "--------------------------------------------------------";
neuper@38037: "--------------------------------------------------------";
neuper@38037: "--------------------------------------------------------";
neuper@38037:
neuper@41929: val thy = @{theory "PolyMinus"};
neuper@37906:
neuper@37906: "----------- fun eval_ist_monom ----------------------------------";
neuper@37906: "----------- fun eval_ist_monom ----------------------------------";
neuper@37906: "----------- fun eval_ist_monom ----------------------------------";
neuper@37906: ist_monom (str2term "12");
neuper@37906: case eval_ist_monom 0 0 (str2term "12 ist_monom") 0 of
neuper@37926: SOME ("12 ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: 12 ist_monom = True";
neuper@37906:
neuper@37906: case eval_ist_monom 0 0 (str2term "a ist_monom") 0 of
neuper@37926: SOME ("a ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: a ist_monom = True";
neuper@37906:
neuper@37906: case eval_ist_monom 0 0 (str2term "(3*a) ist_monom") 0 of
neuper@37926: SOME ("3 * a ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: 3 * a ist_monom = True";
neuper@37906:
neuper@37906: case eval_ist_monom 0 0 (str2term "(a^^^2) ist_monom") 0 of
neuper@37926: SOME ("a ^^^ 2 ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: a^^^2 ist_monom = True";
neuper@37906:
neuper@37906: case eval_ist_monom 0 0 (str2term "(3*a^^^2) ist_monom") 0 of
neuper@37926: SOME ("3 * a ^^^ 2 ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: 3*a^^^2 ist_monom = True";
neuper@37906:
neuper@37906: case eval_ist_monom 0 0 (str2term "(a*b) ist_monom") 0 of
neuper@37926: SOME ("a * b ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: a*b ist_monom = True";
neuper@37906:
neuper@37906: case eval_ist_monom 0 0 (str2term "(3*a*b) ist_monom") 0 of
neuper@37926: SOME ("3 * a * b ist_monom = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: 3*a*b ist_monom = True";
neuper@37906:
neuper@37906:
neuper@37906: "----------- watch order_add_mult -------------------------------";
neuper@37906: "----------- watch order_add_mult -------------------------------";
neuper@37906: "----------- watch order_add_mult -------------------------------";
neuper@37906: "----- with these simple variables it works...";
neuper@52070: (*trace_rewrite := true; ..stopped Test_Isac.thy*)
neuper@37906: trace_rewrite:=false;
neuper@37906: val t = str2term "((a + d) + c) + b";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;
neuper@37906: if term2str t = "a + (b + (c + d))" then ()
neuper@38031: else error "polyminus.sml 1 watch order_add_mult";
neuper@37906: trace_rewrite:=false;
neuper@37906:
neuper@37906: "----- the same stepwise...";
neuper@41929: val od = ord_make_polynomial true (@{theory "Poly"});
neuper@37906: val t = str2term "((a + d) + c) + b";
neuper@37906: "((a + d) + c) + b";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.commute} t; term2str t;
neuper@37906: "b + ((a + d) + c)";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.commute} t; term2str t;
neuper@37906: "b + (c + (a + d))";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
neuper@37906: "b + (a + (c + d))";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
neuper@37906: "a + (b + (c + d))";
neuper@37906: if term2str t = "a + (b + (c + d))" then ()
neuper@38031: else error "polyminus.sml 2 watch order_add_mult";
neuper@37906:
neuper@37906: "----- if parentheses are right, left_commute is (almost) sufficient...";
neuper@37906: val t = str2term "a + (d + (c + b))";
neuper@37906: "a + (d + (c + b))";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
neuper@37906: "a + (c + (d + b))";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.commute} t;term2str t;
neuper@37906: "a + (c + (b + d))";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls true @{thm add.left_commute} t;term2str t;
neuper@37906: "a + (b + (c + d))";
neuper@37906:
neuper@37906: "----- but we do not want the parentheses at right; thus: cond.rew.";
neuper@37906: "WN0712707 complicated monomials do not yet work ...";
neuper@37906: val t = str2term "((5*a + 4*d) + 3*c) + 2*b";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;
neuper@37906: if term2str t = "2 * b + (3 * c + (4 * d + 5 * a))" then ()
neuper@38031: else error "polyminus.sml: order_add_mult changed";
neuper@37906:
neuper@37906: "----- here we see rew_sub going into subterm with ord.rew....";
neuper@41929: val od = ord_make_polynomial false (@{theory "Poly"});
neuper@37906: val t = str2term "b + a + c + d";
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls false @{thm add.commute} t; term2str t;
wneuper@59118: val SOME (t,_) = rewrite_ thy od e_rls false @{thm add.commute} t; term2str t;
neuper@37906: (*@@@ rew_sub gosub: t = d + (b + a + c)
neuper@37906: @@@ rew_sub begin: t = b + a + c*)
neuper@37906:
neuper@37906:
neuper@37906: "----------- build predicate for +- ordering ---------------------";
neuper@37906: "----------- build predicate for +- ordering ---------------------";
neuper@37906: "----------- build predicate for +- ordering ---------------------";
neuper@37906: "a" < "b";
neuper@37906: "ba" < "ab";
neuper@37906: "123" < "a"; (*unused due to ---vvv*)
neuper@37906: "12" < "3"; (*true !!!*)
neuper@37906:
neuper@37906: " a kleiner b ==> (b + a) = (a + b)";
neuper@37906: str2term "aaa";
neuper@37906: str2term "222 * aaa";
neuper@42390:
neuper@37906: case eval_kleiner 0 0 (str2term "123 kleiner 32") 0 of
neuper@42390: SOME ("123 kleiner 32 = False", _) => ()
neuper@38031: | _ => error "polyminus.sml: 12 kleiner 9 = False";
neuper@42390:
neuper@37906: case eval_kleiner 0 0 (str2term "a kleiner b") 0 of
neuper@37926: SOME ("a kleiner b = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: a kleiner b = True";
neuper@37906:
neuper@37906: case eval_kleiner 0 0 (str2term "(10*g) kleiner f") 0 of
neuper@37926: SOME ("10 * g kleiner f = False", _) => ()
neuper@38031: | _ => error "polyminus.sml: 10 * g kleiner f = False";
neuper@37906:
neuper@37906: case eval_kleiner 0 0 (str2term "(a^^^2) kleiner b") 0 of
neuper@37926: SOME ("a ^^^ 2 kleiner b = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: a ^^^ 2 kleiner b = True";
neuper@37906:
neuper@37906: case eval_kleiner 0 0 (str2term "(3*a^^^2) kleiner b") 0 of
neuper@37926: SOME ("3 * a ^^^ 2 kleiner b = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: 3 * a ^^^ 2 kleiner b = True";
neuper@37906:
neuper@37906: case eval_kleiner 0 0 (str2term "(a*b) kleiner c") 0 of
neuper@37926: SOME ("a * b kleiner c = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: a * b kleiner b = True";
neuper@37906:
neuper@37906: case eval_kleiner 0 0 (str2term "(3*a*b) kleiner c") 0 of
neuper@37926: SOME ("3 * a * b kleiner c = True", _) => ()
neuper@38031: | _ => error "polyminus.sml: 3 * a * b kleiner b = True";
neuper@37906:
neuper@42390: "======= compare tausche_plus with real_num_collect";
neuper@37906: val od = dummy_ord;
neuper@37906:
neuper@37906: val erls = erls_ordne_alphabetisch;
neuper@37906: val t = str2term "b + a";
neuper@38080: val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; term2str t;
neuper@37906: if term2str t = "a + b" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch1 b + a";
neuper@37906:
neuper@37906: val erls = Atools_erls;
neuper@37906: val t = str2term "2*a + 3*a";
neuper@38080: val SOME (t,_) = rewrite_ thy od erls false @{thm real_num_collect} t; term2str t;
neuper@37906:
neuper@42390: "======= test rewrite_, rewrite_set_";
neuper@52070: (*trace_rewrite := true; ..stopped Test_Isac.thy*)
neuper@37906: val erls = erls_ordne_alphabetisch;
neuper@37906: val t = str2term "b + a";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
neuper@37906: if term2str t = "a + b" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch a + b";
neuper@37906:
neuper@37906: val t = str2term "2*b + a";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
neuper@37906: if term2str t = "a + 2 * b" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch a + 2 * b";
neuper@37906:
neuper@37906: val t = str2term "a + c + b";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
neuper@37906: if term2str t = "a + b + c" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch a + b + c";
neuper@37906:
neuper@42390: "======= rewrite goes into subterms";
neuper@37906: val t = str2term "a + c + b + d";
neuper@38080: val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus_plus} t; term2str t;
neuper@37906: if term2str t = "a + b + c + d" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch1 a + b + c + d";
neuper@37906:
neuper@37906: val t = str2term "a + c + d + b";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;
neuper@37906: if term2str t = "a + b + c + d" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch2 a + b + c + d";
neuper@37906:
neuper@42390: "======= here we see rew_sub going into subterm with cond.rew....";
neuper@37906: val t = str2term "b + a + c + d";
neuper@38080: val SOME (t,_) = rewrite_ thy od erls false @{thm tausche_plus} t; term2str t;
neuper@37906: if term2str t = "a + b + c + d" then ()
neuper@38031: else error "polyminus.sml: ordne_alphabetisch3 a + b + c + d";
neuper@37906:
neuper@42390: "======= compile rls for the most complicated terms";
neuper@37906: val t = str2term "5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12";
neuper@37906: "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false ordne_alphabetisch t;
neuper@37906: if term2str t = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g"
neuper@38031: then () else error "polyminus.sml: ordne_alphabetisch finished";
neuper@37906:
neuper@37906:
neuper@37906: "----------- build fasse_zusammen --------------------------------";
neuper@37906: "----------- build fasse_zusammen --------------------------------";
neuper@37906: "----------- build fasse_zusammen --------------------------------";
neuper@37906: val t = str2term "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false fasse_zusammen t;
neuper@37906: if term2str t = "3 + -2 * e + 2 * f + 2 * g" then ()
neuper@38031: else error "polyminus.sml: fasse_zusammen finished";
neuper@37906:
neuper@37906: "----------- build verschoenere ----------------------------------";
neuper@37906: "----------- build verschoenere ----------------------------------";
neuper@37906: "----------- build verschoenere ----------------------------------";
neuper@37906: val t = str2term "3 + -2 * e + 2 * f + 2 * g";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false verschoenere t;
neuper@37906: if term2str t = "3 - 2 * e + 2 * f + 2 * g" then ()
neuper@38031: else error "polyminus.sml: verschoenere 3 + -2 * e ...";
neuper@37906:
neuper@52070: (*trace_rewrite := true; ..stopped Test_Isac.thy*)
neuper@37906: trace_rewrite:=false;
neuper@37906:
neuper@37906: "----------- met simplification for_polynomials with_minus -------";
neuper@37906: "----------- met simplification for_polynomials with_minus -------";
neuper@37906: "----------- met simplification for_polynomials with_minus -------";
neuper@37906: val str =
wneuper@59585: "Program SimplifyScript (t_t::real) = \
neuper@37906: \ (((Try (Rewrite_Set ordne_alphabetisch False)) @@ \
neuper@37906: \ (Try (Rewrite_Set fasse_zusammen False)) @@ \
neuper@38080: \ (Try (Rewrite_Set verschoenere False))) t_t)"
wneuper@59395: val sc = (inst_abs o Thm.term_of o the o (parse thy)) str;
neuper@37906: atomty sc;
neuper@37906:
neuper@38080: "----------- me simplification.for_polynomials.with_minus";
neuper@38080: "----------- me simplification.for_polynomials.with_minus";
neuper@38080: "----------- me simplification.for_polynomials.with_minus";
neuper@38080: val c = [];
neuper@38080: val (p,_,f,nxt,_,pt) =
neuper@38080: CalcTreeTEST
neuper@38083: [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",
neuper@38080: "normalform N"],
neuper@38080: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@38080: ["simplification","for_polynomials","with_minus"]))];
neuper@38080: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906:
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@38085: if f2str f = "3 - 2 * e + 2 * f + 2 * g" andalso #1 nxt = "End_Proof'" then ()
neuper@38085: else error "polyminus.sml: me simplification.for_polynomials.with_minus";
neuper@38085:
neuper@37906: "----------- pbl polynom vereinfachen p.33 -----------------------";
neuper@37906: "----------- pbl polynom vereinfachen p.33 -----------------------";
neuper@37906: "----------- pbl polynom vereinfachen p.33 -----------------------";
neuper@37906: "----------- 140 c ---";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso
neuper@37906: term2str (get_obj g_res pt (fst p)) = "3 - 2 * e + 2 * f + 2 * g"
neuper@38031: then () else error "polyminus.sml: Vereinfache (3 - 2 * e + 2 * f...";
neuper@37906:
neuper@42390: "======= 140 d ---";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (-r - 2*s - 3*t + 5 + 4*r + 8*s - 5*t - 2)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso
neuper@37906: term2str (get_obj g_res pt (fst p)) = "3 + 3 * r + 6 * s - 8 * t"
neuper@38031: then () else error "polyminus.sml: Vereinfache 140 d)";
neuper@37906:
neuper@42390: "======= 139 c ---";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (3*e - 6*f - 8*e - 4*f + 5*e + 7*f)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso
neuper@37906: term2str (get_obj g_res pt (fst p)) = "- (3 * f)"
neuper@38031: then () else error "polyminus.sml: Vereinfache 139 c)";
neuper@37906:
neuper@42390: "======= 139 b ---";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (8*u - 5*v - 5*u + 7*v - 6*u - 3*v)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso
neuper@37906: term2str (get_obj g_res pt (fst p)) = "-3 * u - v"
neuper@38031: then () else error "polyminus.sml: Vereinfache 139 b)";
neuper@37906:
neuper@42390: "======= 138 a ---";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (2*u - 3*v - 6*u + 5*v)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso
neuper@37906: term2str (get_obj g_res pt (fst p)) = "-4 * u + 2 * v"
neuper@38031: then () else error "polyminus.sml: Vereinfache 138 a)";
neuper@37906:
neuper@37906: "----------- met probe fuer_polynom ------------------------------";
neuper@37906: "----------- met probe fuer_polynom ------------------------------";
neuper@37906: "----------- met probe fuer_polynom ------------------------------";
neuper@37906: val str =
wneuper@59585: "Program ProbeScript (e_e::bool) (w_s::bool list) =\
neuper@37991: \ (let e_e = Take e_e; \
neuper@38085: \ e_e = Substitute w_s e_e \
wneuper@59488: \ in (Repeat((Try (Repeat (Calculate ''TIMES''))) @@ \
wneuper@59488: \ (Try (Repeat (Calculate ''PLUS''))) @@ \
wneuper@59488: \ (Try (Repeat (Calculate ''MINUS''))))) e_e)"
wneuper@59395: val sc = (inst_abs o Thm.term_of o the o (parse thy)) str;
neuper@37906: atomty sc;
neuper@37906:
neuper@37906: "----------- pbl polynom probe -----------------------------------";
neuper@37906: "----------- pbl polynom probe -----------------------------------";
neuper@37906: "----------- pbl polynom probe -----------------------------------";
s1210629013@55445: reset_states ();
bonzai@41949: CalcTree [(["Pruefe ((5::int)*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12 =\
wneuper@59582: \3 - 2 * e + 2 * f + 2 * (g::int))",
wneuper@59582: "mitWert [e = (1::int), f = (2::int), g = (3::int)]",
neuper@37906: "Geprueft b"],
neuper@37991: ("PolyMinus",["polynom","probe"],
neuper@37906: ["probe","fuer_polynom"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
wneuper@59248: (* autoCalculate 1 CompleteCalcHead;
wneuper@59248: autoCalculate 1 (Step 1);
wneuper@59248: autoCalculate 1 (Step 1);
neuper@37906: val ((pt,p),_) = get_calc 1; term2str (get_obj g_res pt (fst p));
neuper@37906: @@@@@WN081114 gives "??.empty", all "Pruefe" are the same,
neuper@37906: although analogies work in interface.sml: FIXME.WN081114 in "Pruefe"*)
neuper@37906: val ((pt,p),_) = get_calc 1;
neuper@37906: if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "11 = 11"
neuper@38031: then () else error "polyminus.sml: Probe 11 = 11";
neuper@37906: show_pt pt;
t@42115:
neuper@37906: "----------- pbl klammer polynom vereinfachen p.34 ---------------";
neuper@37906: "----------- pbl klammer polynom vereinfachen p.34 ---------------";
neuper@37906: "----------- pbl klammer polynom vereinfachen p.34 ---------------";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (2*u - 5 - (3 - 4*u) + (8*u + 9))",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["klammer","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_parentheses"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1;
neuper@37906: if p = ([], Res) andalso
neuper@37906: term2str (get_obj g_res pt (fst p)) = "1 + 14 * u"
neuper@38031: then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";
neuper@37906: show_pt pt;
neuper@37906:
neuper@42390: "======= probe p.34 -----";
s1210629013@55445: reset_states ();
wneuper@59582: CalcTree [(["Pruefe (2*u - 5 - (3 - 4*u) + (8*u + 9) = 1 + 14 * (u::int))",
wneuper@59582: "mitWert [u = (2::int)]",
neuper@37906: "Geprueft b"],
neuper@37991: ("PolyMinus",["polynom","probe"],
neuper@37906: ["probe","fuer_polynom"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1;
neuper@37906: if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "29 = 29"
neuper@38031: then () else error "polyminus.sml: Probe 29 = 29";
neuper@37906: show_pt pt;
neuper@37906:
neuper@37906: "----------- try fun applyTactics --------------------------------";
neuper@37906: "----------- try fun applyTactics --------------------------------";
neuper@37906: "----------- try fun applyTactics --------------------------------";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalcHead;
wneuper@59248: autoCalculate 1 (Step 1);
wneuper@59248: autoCalculate 1 (Step 1);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 1 ^^^";
neuper@37906: fetchApplicableTactics 1 0 p;
neuper@37906: val appltacs = sel_appl_atomic_tacs pt p;
neuper@37906: applyTactic 1 p (hd appltacs) (*addiere_x_plus_minus*);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 2 ^^^";
neuper@52070: (*trace_rewrite := true; ..stopped Test_Isac.thy*)
neuper@37906: val erls = erls_ordne_alphabetisch;
neuper@37906: val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";
neuper@37926: val SOME (t',_) =
wneuper@59592: rewrite_ (@{theory "Isac_Knowledge"}) e_rew_ord erls false @{thm tausche_minus} t;
neuper@37906: term2str t'; "- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f - 8 * g + 10 * g";
neuper@37906:
neuper@37906: val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";
neuper@37926: val NONE =
wneuper@59592: rewrite_ (@{theory "Isac_Knowledge"}) e_rew_ord erls false @{thm tausche_minus_plus} t;
neuper@37906:
neuper@37906: val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";
neuper@37926: val SOME (t',_) =
wneuper@59592: rewrite_set_ (@{theory "Isac_Knowledge"}) false ordne_alphabetisch t;
neuper@37906: term2str t'; "- 9 + 12 + 5 * e - 7 * e - 8 * g + 10 * g + (- 4 + 6) * f";
neuper@37906: trace_rewrite := false;
neuper@37906:
neuper@37906:
neuper@37906: applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (*tausche_minus*);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 3 ^^^";
neuper@37906: applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 4 ^^^";
neuper@37906: applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 5 ^^^";
neuper@37906: applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 6 ^^^";
neuper@37906:
neuper@37906: (* failure
neuper@37906: applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: "----- 7 ^^^";
neuper@37906: *)
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: (*independent from failure above: met_simp_poly_minus not confluent:
neuper@37906: (([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),
neuper@37906: (([], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f))]
neuper@37906: ~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
t@42115:
neuper@37906:
neuper@42107: "#############################################################################";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (- (8 * g) + 10 * g + h)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "2 * g + h"
neuper@38031: then () else error "polyminus.sml: addiere_vor_minus";
neuper@37906:
neuper@37906:
neuper@42107: "#############################################################################";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (- (8 * g) + 10 * g + f)",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["plus_minus","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_minus"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "f + 2 * g"
neuper@38031: then () else error "polyminus.sml: tausche_vor_plus";
neuper@37906:
neuper@37906: "----------- pbl binom polynom vereinfachen p.39 -----------------";
neuper@37906: "----------- pbl binom polynom vereinfachen p.39 -----------------";
neuper@37906: "----------- pbl binom polynom vereinfachen p.39 -----------------";
neuper@37906: val rls = klammern_ausmultiplizieren;
neuper@37906: val t = str2term "(3 * a + 2) * (4 * a - 1)";
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: "3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";
neuper@37906: val rls = discard_parentheses;
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: "3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";
neuper@37906: val rls = ordne_monome;
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: "3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";
neuper@37906: (*
neuper@37906: val t = str2term "3 * a * 4 * a";
neuper@37906: val rls = ordne_monome;
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: *)
neuper@37906: val rls = klammern_aufloesen;
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: "3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";
neuper@37906: val rls = ordne_alphabetisch;
neuper@37906: (*TODO: make is_monom more general, a*a=a^2, ...*)
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: "3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";
neuper@41977: (*STOPPED.WN080104
neuper@37906: val rls = fasse_zusammen;
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: val rls = verschoenere;
neuper@37926: val SOME (t,_) = rewrite_set_ thy false rls t; term2str t;
neuper@37906: *)
neuper@37906:
neuper@37906: (*@@@@@@@*)
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term ((3*a + 2) * (4*a - 1))",
neuper@37906: "normalform N"],
neuper@37991: ("PolyMinus",["binom_klammer","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_parentheses_mult"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906: if p = ([], Res) andalso
t@42111: term2str (get_obj g_res pt (fst p)) = "-2 + 12 * a ^^^ 2 + 5 * a"
neuper@38031: then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";
t@42111:
neuper@37906: "----------- pbl binom polynom vereinfachen: cube ----------------";
neuper@37906: "----------- pbl binom polynom vereinfachen: cube ----------------";
neuper@37906: "----------- pbl binom polynom vereinfachen: cube ----------------";
s1210629013@55445: reset_states ();
neuper@38083: CalcTree [(["Term (8*(a - q) + a - 2*q + 3*(a - 2*q))", "normalform N"],
neuper@37991: ("PolyMinus",["binom_klammer","polynom","vereinfachen"],
neuper@37906: ["simplification","for_polynomials","with_parentheses_mult"]))];
neuper@37906: moveActiveRoot 1;
wneuper@59248: autoCalculate 1 CompleteCalc;
neuper@37906: val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@42107: if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "12 * a - 16 * q"
neuper@42107: then () else error "pbl binom polynom vereinfachen: cube";
neuper@37906:
neuper@37906: "----------- refine Vereinfache ----------------------------------";
neuper@37906: "----------- refine Vereinfache ----------------------------------";
neuper@37906: "----------- refine Vereinfache ----------------------------------";
neuper@42390: val fmz = ["Term (8*(a - q) + a - 2*q + 3*(a - 2*(q::real)))", "normalform (N::real)"];
wneuper@59348: (*default_print_depth 11;*)
neuper@37906: val matches = refine fmz ["vereinfachen"];
wneuper@59348: (*default_print_depth 3;*)
neuper@37906:
neuper@37906: "----- go into details, if it seems not to work -----";
neuper@37906: "--- does the predicate evaluate correctly ?";
neuper@37906: val t = str2term
neuper@42390: "matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q + 3 * (a - 2 * (q::real)))";
walther@59603: val ma = eval_matchsub "" "Prog_Expr.matchsub" t thy;
neuper@37906: case ma of
neuper@37926: SOME ("matchsub (?a * (?b - ?c)) (8 * (a - q) + \
neuper@37906: \a - 2 * q + 3 * (a - 2 * q)) = True", _) => ()
neuper@38031: | _ => error "polyminus.sml matchsub (?a * (?b - ?c)...A";
neuper@37906:
neuper@37906: "--- does the respective prls rewrite ?";
neuper@37906: val prls = append_rls "prls_pbl_vereinf_poly" e_rls
neuper@37906: [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
walther@59603: Calc ("Prog_Expr.matchsub", eval_matchsub ""),
neuper@38085: Thm ("or_true",@{thm or_true}),
neuper@37906: (*"(?a | True) = True"*)
neuper@38085: Thm ("or_false",@{thm or_false}),
neuper@37906: (*"(?a | False) = ?a"*)
neuper@37970: Thm ("not_true",num_str @{thm not_true}),
neuper@37906: (*"(~ True) = False"*)
neuper@37970: Thm ("not_false",num_str @{thm not_false})
neuper@37906: (*"(~ False) = True"*)];
neuper@52070: (*trace_rewrite := true; ..stopped Test_Isac.thy*)
neuper@37926: val SOME (t', _) = rewrite_set_ thy false prls t;
neuper@37906: trace_rewrite := false;
neuper@37906:
neuper@37906: "--- does the respective prls rewrite the whole predicate ?";
neuper@37906: val t = str2term
neuper@37906: "Not (matchsub (?a * (?b + ?c)) (8 * (a - q) + a - 2 * q) | \
neuper@37906: \ matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q) | \
neuper@37906: \ matchsub ((?b + ?c) * ?a) (8 * (a - q) + a - 2 * q) | \
neuper@37906: \ matchsub ((?b - ?c) * ?a) (8 * (a - q) + a - 2 * q) )";
neuper@52070: (*trace_rewrite := true; ..stopped Test_Isac.thy*)
neuper@37926: val SOME (t', _) = rewrite_set_ thy false prls t;
neuper@37906: trace_rewrite := false;
neuper@42390: if term2str t' = "False" then ()
neuper@38031: else error "polyminus.sml Not (matchsub (?a * (?b + ?c)) (8 ...";
neuper@37906:
neuper@38037: "----------- *** prep_pbt: syntax error in '#Where' of [v";
neuper@38037: "----------- *** prep_pbt: syntax error in '#Where' of [v";
neuper@38037: "----------- *** prep_pbt: syntax error in '#Where' of [v";
neuper@38037: (*see test/../termC.sml for details*)
neuper@38037: val t = parse_patt thy "t_t is_polyexp";
neuper@38037: val t = parse_patt thy ("Not (matchsub (?a + (?b + ?c)) t_t | " ^
neuper@38037: " matchsub (?a + (?b - ?c)) t_t | " ^
neuper@38037: " matchsub (?a - (?b + ?c)) t_t | " ^
neuper@38037: " matchsub (?a + (?b - ?c)) t_t )");
neuper@42390: (*show_types := true;
neuper@38037: 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: then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";
neuper@42390: show_types := false;*)
wneuper@59371: if term2str t =
wneuper@59371: "\ (matchsub (?a + (?b + ?c)) t_t \\n " ^
wneuper@59371: "matchsub (?a + (?b - ?c)) t_t \\n " ^
wneuper@59371: "matchsub (?a - (?b + ?c)) t_t \ " ^
wneuper@59371: "matchsub (?a + (?b - ?c)) t_t)"
neuper@42390: then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";
neuper@37906: