(* title:  Knowledge/polyminus.sml

    author: Walther Neuper

    WN071207,

    (c) due to copyright terms

 *)

 "--------------------------------------------------------";

 "--------------------------------------------------------";

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

 "--------------------------------------------------------";

 "----------- fun contains_mult_pot_only --------------------------------------------------------";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 "--------------------------------------------------------";

 "--------------------------------------------------------";

 "--------------------------------------------------------";

 val thy = @{theory "PolyMinus"};

 "----------- fun contains_mult_pot_only --------------------------------------------------------";

 "----------- fun contains_mult_pot_only --------------------------------------------------------";

 "----------- fun contains_mult_pot_only --------------------------------------------------------";

 val t = @{term 0};

  if contains_mult_pot_only t then () else error "contains_mult_pot_only 1";

 val t = @{term "a"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 2";

 val t = @{term "2 * a"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 3";

 val t = @{term "2 * a * b"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 4";

 val t = @{term "a * b"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 5";

 val t = @{term "2 * a \<up> 2 * b"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 6";

 val t = @{term "a \<up> 2 * b \<up> 3"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 7";

 (* but also ..*)

 val t = @{term "a \<up> 2 * 4 * b \<up> 3 * 5"};

 if contains_mult_pot_only t then () else error "contains_mult_pot_only 8";

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

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

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

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

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

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

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

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

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

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

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

 (*+*)case a of

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

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

 | _ => error "eval_kleiner CHANGED";

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

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

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

 ist_monom (TermC.str2term "12");

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 Rewrite.trace_on:=false;

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

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

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

 else error "polyminus.sml 1 watch order_add_mult";

 Rewrite.trace_on:=false;

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

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

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

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

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

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

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

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

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

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

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

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

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

 else error "polyminus.sml 2 watch order_add_mult";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 else error "polyminus.sml: order_add_mult changed";

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

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

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

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

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

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

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

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

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

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

 "a" < "b";

 "ba" < "ab";

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

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

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

 TermC.str2term "aaa";

 TermC.str2term "222 * aaa";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 val od = dummy_ord;

 val erls = erls_ordne_alphabetisch;

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

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

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

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

 val erls = Atools_erls;

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

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

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

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

 val erls = erls_ordne_alphabetisch;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 else error "polyminus.sml: fasse_zusammen finished";

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

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

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

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

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

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

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

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

 Rewrite.trace_on:=false;

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

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

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

 val str = 

 "Program SimplifyScript (t_t::real) =                \

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

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

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

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

 TermC.atomty sc;

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

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

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

 val c = [];

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

       CalcTreeTEST 

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

            "normalform N"],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

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

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

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

 val str = 

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

 \ (let e_e = Take e_e;                             \

 \      e_e = Substitute w_s e_e                    \

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

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

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

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

 TermC.atomty sc;

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

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

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

 reset_states ();

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

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

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

 	    "Geprueft b"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

 (* autoCalculate 1 CompleteCalcHead;

    autoCalculate 1 (Steps 1);

    autoCalculate 1 (Steps 1);

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

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

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

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

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

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

 Test_Tool.show_pt pt;

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

 Test_Tool.show_pt pt;

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

 reset_states ();

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

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

 	    "Geprueft b"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

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

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

 Test_Tool.show_pt pt;

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

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

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

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalcHead;

 autoCalculate 1 (Steps 1);

 autoCalculate 1 (Steps 1);

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

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

 fetchApplicableTactics 1 0 p;

 val appltacs = specific_from_prog pt p;

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

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

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

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

 val erls = erls_ordne_alphabetisch;

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

 val SOME (t',_) = 

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

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

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

 val NONE = 

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

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

 val SOME (t',_) = 

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

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

 Rewrite.trace_on := false;

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

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

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

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

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

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

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

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

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

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

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

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

 (*<CALCMESSAGE> failure </CALCMESSAGE>

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

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

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

 *)

 autoCalculate 1 CompleteCalc;

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

 (*independent from failure above: met_simp_poly_minus not confluent:

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

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

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

 "#############################################################################";

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

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

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

 "#############################################################################";

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

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

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

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

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

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

 val rls = klammern_ausmultiplizieren;

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

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

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

 val rls = discard_parentheses;

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

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

 val rls = ordne_monome;

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

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

 (*

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

 val rls = ordne_monome;

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

 *)

 val rls = klammern_aufloesen;

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

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

 val rls = ordne_alphabetisch;

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

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

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

 (*STOPPED.WN080104

 val rls = fasse_zusammen;

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

 val rls = verschoenere;

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

 *)

 (*@@@@@@@*)

 reset_states ();

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

 	    "normalform N"],

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

 if p = ([], Res) andalso 

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

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

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

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

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

 reset_states ();

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

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

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

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

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

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

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

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

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

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

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

 (*default_print_depth 11;*)

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

 (*default_print_depth 3;*)

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

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

 val t = TermC.str2term 

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

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

 case ma of

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 Rewrite.trace_on := false;

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

 val t = TermC.str2term 

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

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

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

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

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

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

 Rewrite.trace_on := false;

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

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

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

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

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

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

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

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

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

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

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

 (*show_types := true;

 if UnparseC.term t = "~ (matchsub ((?a::real) + ((?b::real) + (?c::real))) (t_t::real) |\n   matchsub (?a + (?b - ?c)) t_t |\n   matchsub (?a - (?b + ?c)) t_t | matchsub (?a + (?b - ?c)) t_t)"

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

 show_types := false;*)

 if UnparseC.term t =

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

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

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

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

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