(* questionable attempts to perserve binary minus as wanted by teachers

   WN071207

   (c) due to copyright terms

remove_thy"PolyMinus";

use_thy"IsacKnowledge/PolyMinus";

use_thy"IsacKnowledge/Isac";

use"IsacKnowledge/PolyMinus.ML";

*)

(** interface isabelle -- isac **)

theory' := overwritel (!theory', [("PolyMinus.thy",PolyMinus.thy)]);

(** eval functions **)

(*. get the identifier from specific monomials; see fun ist_monom .*)

(*HACK.WN080107*)

fun increase str = 

    let val s::ss = explode str

    in implode ((chr (ord s + 1))::ss) end;

fun identifier (Free (id,_)) = id                            (* 2,   a   *)

  | identifier (Const ("op *", _) $ Free (num, _) $ Free (id, _)) = 

    id                                                       (* 2*a, a*b *)

  | identifier (Const ("op *", _) $                          (* 3*a*b    *)

		     (Const ("op *", _) $

			    Free (num, _) $ Free _) $ Free (id, _)) = 

    if is_numeral num then id

    else "|||||||||||||"

  | identifier (Const ("Atools.pow", _) $ Free (base, _) $ Free (exp, _)) =

    if is_numeral base then "|||||||||||||"                  (* a^2      *)

    else (*increase*) base

  | identifier (Const ("op *", _) $ Free (num, _) $          (* 3*a^2    *)

		     (Const ("Atools.pow", _) $

			    Free (base, _) $ Free (exp, _))) = 

    if is_numeral num andalso not (is_numeral base) then (*increase*) base

    else "|||||||||||||"

  | identifier _ = "|||||||||||||"(*the "largest" string*);

(*("kleiner", ("PolyMinus.kleiner", eval_kleiner ""))*)

(* order "by alphabet" w.r.t. var: num < (var | num*var) > (var*var | ..) *)

fun eval_kleiner _ _ (p as (Const ("PolyMinus.kleiner",_) $ a $ b)) _  =

     if is_num b then

	 if is_num a then (*123 kleiner 32 = True !!!*)

	     if int_of_Free a < int_of_Free b then 

		 Some ((term2str p) ^ " = True",

		       Trueprop $ (mk_equality (p, HOLogic.true_const)))

	     else Some ((term2str p) ^ " = False",

			Trueprop $ (mk_equality (p, HOLogic.false_const)))

	 else (* -1 * -2 kleiner 0 *)

	     Some ((term2str p) ^ " = False",

		   Trueprop $ (mk_equality (p, HOLogic.false_const)))

    else

	if identifier a < identifier b then 

	     Some ((term2str p) ^ " = True",

		  Trueprop $ (mk_equality (p, HOLogic.true_const)))

	else Some ((term2str p) ^ " = False",

		   Trueprop $ (mk_equality (p, HOLogic.false_const)))

  | eval_kleiner _ _ _ _ =  None;

fun ist_monom (Free (id,_)) = true

  | ist_monom (Const ("op *", _) $ Free (num, _) $ Free (id, _)) = 

    if is_numeral num then true else false

  | ist_monom _ = false;

(*. this function only accepts the most simple monoms       vvvvvvvvvv .*)

fun ist_monom (Free (id,_)) = true                          (* 2,   a   *)

  | ist_monom (Const ("op *", _) $ Free _ $ Free (id, _)) = (* 2*a, a*b *)

    if is_numeral id then false else true

  | ist_monom (Const ("op *", _) $                          (* 3*a*b    *)

		     (Const ("op *", _) $

			    Free (num, _) $ Free _) $ Free (id, _)) =

    if is_numeral num andalso not (is_numeral id) then true else false

  | ist_monom (Const ("Atools.pow", _) $ Free (base, _) $ Free (exp, _)) = 

    true                                                    (* a^2      *)

  | ist_monom (Const ("op *", _) $ Free (num, _) $          (* 3*a^2    *)

		     (Const ("Atools.pow", _) $

			    Free (base, _) $ Free (exp, _))) = 

    if is_numeral num then true else false

  | ist_monom _ = false;

(* is this a univariate monomial ? *)

(*("ist_monom", ("PolyMinus.ist'_monom", eval_ist_monom ""))*)

fun eval_ist_monom _ _ (p as (Const ("PolyMinus.ist'_monom",_) $ a)) _  =

    if ist_monom a  then 

	Some ((term2str p) ^ " = True",

	      Trueprop $ (mk_equality (p, HOLogic.true_const)))

    else Some ((term2str p) ^ " = False",

	       Trueprop $ (mk_equality (p, HOLogic.false_const)))

  | eval_ist_monom _ _ _ _ =  None;

(** rewrite order **)

(** rulesets **)

val erls_ordne_alphabetisch =

    append_rls "erls_ordne_alphabetisch" e_rls

	       [Calc ("PolyMinus.kleiner", eval_kleiner ""),

		Calc ("PolyMinus.ist'_monom", eval_ist_monom "")

		];

val ordne_alphabetisch = 

  Rls{id = "ordne_alphabetisch", preconds = [], 

      rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],

      erls = erls_ordne_alphabetisch, 

      rules = [Thm ("tausche_plus",num_str tausche_plus),

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

	       Thm ("tausche_minus",num_str tausche_minus),

	       (*"b kleiner a ==> (b - a) = (-a + b)"*)

	       Thm ("tausche_vor_plus",num_str tausche_vor_plus),

	       (*"[| b ist_monom; a kleiner b  |] ==> (- b + a) = (a - b)"*)

	       Thm ("tausche_vor_minus",num_str tausche_vor_minus),

	       (*"[| b ist_monom; a kleiner b  |] ==> (- b - a) = (-a - b)"*)

	       Thm ("tausche_plus_plus",num_str tausche_plus_plus),

	       (*"c kleiner b ==> (a + c + b) = (a + b + c)"*)

	       Thm ("tausche_plus_minus",num_str tausche_plus_minus),

	       (*"c kleiner b ==> (a + c - b) = (a - b + c)"*)

	       Thm ("tausche_minus_plus",num_str tausche_minus_plus),

	       (*"c kleiner b ==> (a - c + b) = (a + b - c)"*)

	       Thm ("tausche_minus_minus",num_str tausche_minus_minus)

	       (*"c kleiner b ==> (a - c - b) = (a - b - c)"*)

	       ], scr = EmptyScr}:rls;

val fasse_zusammen = 

    Rls{id = "fasse_zusammen", preconds = [], 

	rew_ord = ("dummy_ord", dummy_ord),

	erls = append_rls "erls_fasse_zusammen" e_rls 

			  [Calc ("Atools.is'_const",eval_const "#is_const_")], 

	srls = Erls, calc = [],

	rules = 

	[Thm ("real_num_collect",num_str real_num_collect), 

	 (*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)

	 Thm ("real_num_collect_assoc_r",num_str real_num_collect_assoc_r),

	 (*"[| l is_const; m..|] ==>  (k + m * n) + l * n = k + (l + m)*n"*)

	 Thm ("real_one_collect",num_str real_one_collect),	

	 (*"m is_const ==> n + m * n = (1 + m) * n"*)

	 Thm ("real_one_collect_assoc_r",num_str real_one_collect_assoc_r), 

	 (*"m is_const ==> (k + n) + m * n = k + (m + 1) * n"*)

	 Thm ("subtrahiere",num_str subtrahiere),

	 (*"[| l is_const; m is_const |] ==> m * v - l * v = (m - l) * v"*)

	 Thm ("subtrahiere_von_1",num_str subtrahiere_von_1),

	 (*"[| l is_const |] ==> v - l * v = (1 - l) * v"*)

	 Thm ("subtrahiere_1",num_str subtrahiere_1),

	 (*"[| l is_const; m is_const |] ==> m * v - v = (m - 1) * v"*)

	 Thm ("subtrahiere_x_plus_minus",num_str subtrahiere_x_plus_minus), 

	 (*"[| l is_const; m..|] ==> (k + m * n) - l * n = k + ( m - l) * n"*)

	 Thm ("subtrahiere_x_plus1_minus",num_str subtrahiere_x_plus1_minus),

	 (*"[| l is_const |] ==> (x + v) - l * v = x + (1 - l) * v"*)

	 Thm ("subtrahiere_x_plus_minus1",num_str subtrahiere_x_plus_minus1),

	 (*"[| m is_const |] ==> (x + m * v) - v = x + (m - 1) * v"*)

	 Thm ("subtrahiere_x_minus_plus",num_str subtrahiere_x_minus_plus), 

	 (*"[| l is_const; m..|] ==> (k - m * n) + l * n = k + (-m + l) * n"*)

	 Thm ("subtrahiere_x_minus1_plus",num_str subtrahiere_x_minus1_plus),

	 (*"[| l is_const |] ==> (x - v) + l * v = x + (-1 + l) * v"*)

	 Thm ("subtrahiere_x_minus_plus1",num_str subtrahiere_x_minus_plus1),

	 (*"[| m is_const |] ==> (x - m * v) + v = x + (-m + 1) * v"*)

	 Thm ("subtrahiere_x_minus_minus",num_str subtrahiere_x_minus_minus), 

	 (*"[| l is_const; m..|] ==> (k - m * n) - l * n = k + (-m - l) * n"*)

	 Thm ("subtrahiere_x_minus1_minus",num_str subtrahiere_x_minus1_minus),

	 (*"[| l is_const |] ==> (x - v) - l * v = x + (-1 - l) * v"*)

	 Thm ("subtrahiere_x_minus_minus1",num_str subtrahiere_x_minus_minus1),

	 (*"[| m is_const |] ==> (x - m * v) - v = x + (-m - 1) * v"*)

	 Calc ("op +", eval_binop "#add_"),

	 Calc ("op -", eval_binop "#subtr_"),

	 (*MG: Reihenfolge der folgenden 2 Thm muss so bleiben, wegen

           (a+a)+a --> a + 2*a --> 3*a and not (a+a)+a --> 2*a + a *)

	 Thm ("real_mult_2_assoc_r",num_str real_mult_2_assoc_r),

	 (*"(k + z1) + z1 = k + 2 * z1"*)

	 Thm ("sym_real_mult_2",num_str (real_mult_2 RS sym)),

	 (*"z1 + z1 = 2 * z1"*)

	 Thm ("addiere_vor_minus",num_str addiere_vor_minus),

	 (*"[| l is_const; m is_const |] ==> -(l * v) +  m * v = (-l + m) *v"*)

	 Thm ("addiere_eins_vor_minus",num_str addiere_eins_vor_minus),

	 (*"[| m is_const |] ==> -  v +  m * v = (-1 + m) * v"*)

	 Thm ("subtrahiere_vor_minus",num_str subtrahiere_vor_minus),

	 (*"[| l is_const; m is_const |] ==> -(l * v) -  m * v = (-l - m) *v"*)

	 Thm ("subtrahiere_eins_vor_minus",num_str subtrahiere_eins_vor_minus)

	 (*"[| m is_const |] ==> -  v -  m * v = (-1 - m) * v"*)

	 ], scr = EmptyScr}:rls;

val verschoenere = 

  Rls{id = "verschoenere", preconds = [], 

      rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],

      erls = append_rls "erls_verschoenere" e_rls 

			[Calc ("PolyMinus.kleiner", eval_kleiner "")], 

      rules = [Thm ("vorzeichen_minus_weg1",num_str vorzeichen_minus_weg1),

	       (*"l kleiner 0 ==> a + l * b = a - -l * b"*)

	       Thm ("vorzeichen_minus_weg2",num_str vorzeichen_minus_weg2),

	       (*"l kleiner 0 ==> a - l * b = a + -l * b"*)

	       Thm ("vorzeichen_minus_weg3",num_str vorzeichen_minus_weg3),

	       (*"l kleiner 0 ==> k + a - l * b = k + a + -l * b"*)

	       Thm ("vorzeichen_minus_weg4",num_str vorzeichen_minus_weg4),

	       (*"l kleiner 0 ==> k - a - l * b = k - a + -l * b"*)

	       Calc ("op *", eval_binop "#mult_"),

	       Thm ("real_mult_0",num_str real_mult_0),    

	       (*"0 * z = 0"*)

	       Thm ("real_mult_1",num_str real_mult_1),     

	       (*"1 * z = z"*)

	       Thm ("real_add_zero_left",num_str real_add_zero_left),

	       (*"0 + z = z"*)

	       Thm ("null_minus",num_str null_minus),

	       (*"0 - a = -a"*)

	       Thm ("vor_minus_mal",num_str vor_minus_mal)

	       (*"- a * b = (-a) * b"*)

	       (*Thm ("",num_str ),*)

	       (**)

	       ], scr = EmptyScr}:rls (*end verschoenere*);

val klammern_aufloesen = 

  Rls{id = "klammern_aufloesen", preconds = [], 

      rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], erls = Erls, 

      rules = [Thm ("sym_real_add_assoc",num_str (real_add_assoc RS sym)),

	       (*"a + (b + c) = (a + b) + c"*)

	       Thm ("klammer_plus_minus",num_str klammer_plus_minus),

	       (*"a + (b - c) = (a + b) - c"*)

	       Thm ("klammer_minus_plus",num_str klammer_minus_plus),

	       (*"a - (b + c) = (a - b) - c"*)

	       Thm ("klammer_minus_minus",num_str klammer_minus_minus)

	       (*"a - (b - c) = (a - b) + c"*)

	       ], scr = EmptyScr}:rls;

val klammern_ausmultiplizieren = 

  Rls{id = "klammern_ausmultiplizieren", preconds = [], 

      rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], erls = Erls, 

      rules = [Thm ("real_add_mult_distrib" ,num_str real_add_mult_distrib),

	       (*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)

	       Thm ("real_add_mult_distrib2",num_str real_add_mult_distrib2),

	       (*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)

	       Thm ("klammer_mult_minus",num_str klammer_mult_minus),

	       (*"a * (b - c) = a * b - a * c"*)

	       Thm ("klammer_minus_mult",num_str klammer_minus_mult)

	       (*"(b - c) * a = b * a - c * a"*)

	       (*Thm ("",num_str ),

	       (*""*)*)

	       ], scr = EmptyScr}:rls;

val ordne_monome = 

  Rls{id = "ordne_monome", preconds = [], 

      rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], 

      erls = append_rls "erls_ordne_monome" e_rls

	       [Calc ("PolyMinus.kleiner", eval_kleiner ""),

		Calc ("Atools.is'_atom", eval_is_atom "")

		], 

      rules = [Thm ("tausche_mal",num_str tausche_mal),

	       (*"[| b is_atom; a kleiner b  |] ==> (b * a) = (a * b)"*)

	       Thm ("tausche_vor_mal",num_str tausche_vor_mal),

	       (*"[| b is_atom; a kleiner b  |] ==> (-b * a) = (-a * b)"*)

	       Thm ("tausche_mal_mal",num_str tausche_mal_mal),

	       (*"[| c is_atom; b kleiner c  |] ==> (a * c * b) = (a * b *c)"*)

	       Thm ("x_quadrat",num_str x_quadrat)

	       (*"(x * a) * a = x * a ^^^ 2"*)

	       (*Thm ("",num_str ),

	       (*""*)*)

	       ], scr = EmptyScr}:rls;

val rls_p_33 = 

    append_rls "rls_p_33" e_rls

	       [Rls_ ordne_alphabetisch,

		Rls_ fasse_zusammen,

		Rls_ verschoenere

		];

val rls_p_34 = 

    append_rls "rls_p_34" e_rls

	       [Rls_ klammern_aufloesen,

		Rls_ ordne_alphabetisch,

		Rls_ fasse_zusammen,

		Rls_ verschoenere

		];

val rechnen = 

    append_rls "rechnen" e_rls

	       [Calc ("op *", eval_binop "#mult_"),

		Calc ("op +", eval_binop "#add_"),

		Calc ("op -", eval_binop "#subtr_")

		];

ruleset' := 

overwritelthy thy (!ruleset',

		   [("ordne_alphabetisch", prep_rls ordne_alphabetisch),

		    ("fasse_zusammen", prep_rls fasse_zusammen),

		    ("verschoenere", prep_rls verschoenere),

		    ("ordne_monome", prep_rls ordne_monome),

		    ("klammern_aufloesen", prep_rls klammern_aufloesen),

		    ("klammern_ausmultiplizieren", 

		     prep_rls klammern_ausmultiplizieren)

		    ]);

(** problems **)

store_pbt

 (prep_pbt PolyMinus.thy "pbl_vereinf_poly" [] e_pblID

 (["polynom","vereinfachen"],

  [], Erls, None, []));

store_pbt

 (prep_pbt PolyMinus.thy "pbl_vereinf_poly_minus" [] e_pblID

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

  [("#Given" ,["term t_"]),

   ("#Where" ,["t_ is_polyexp",

	       "Not (matchsub (?a + (?b + ?c)) t_ | \

	       \     matchsub (?a + (?b - ?c)) t_ | \

	       \     matchsub (?a - (?b + ?c)) t_ | \

	       \     matchsub (?a + (?b - ?c)) t_ )",

	       "Not (matchsub (?a * (?b + ?c)) t_ | \

	       \     matchsub (?a * (?b - ?c)) t_ | \

	       \     matchsub ((?b + ?c) * ?a) t_ | \

	       \     matchsub ((?b - ?c) * ?a) t_ )"]),

   ("#Find"  ,["normalform n_"])

  ],

  append_rls "prls_pbl_vereinf_poly" e_rls 

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

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

	      Thm ("or_true",or_true),

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

	      Thm ("or_false",or_false),

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

	      Thm ("not_true",num_str not_true),

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

	      Thm ("not_false",num_str not_false)

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

  Some "Vereinfache t_", 

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

store_pbt

 (prep_pbt PolyMinus.thy "pbl_vereinf_poly_klammer" [] e_pblID

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

  [("#Given" ,["term t_"]),

   ("#Where" ,["t_ is_polyexp",

	       "Not (matchsub (?a * (?b + ?c)) t_ | \

	       \     matchsub (?a * (?b - ?c)) t_ | \

	       \     matchsub ((?b + ?c) * ?a) t_ | \

	       \     matchsub ((?b - ?c) * ?a) t_ )"]),

   ("#Find"  ,["normalform n_"])

  ],

  append_rls "prls_pbl_vereinf_poly_klammer" e_rls [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),

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

	      Thm ("or_true",or_true),

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

	      Thm ("or_false",or_false),

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

	      Thm ("not_true",num_str not_true),

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

	      Thm ("not_false",num_str not_false)

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

  Some "Vereinfache t_", 

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

store_pbt

 (prep_pbt PolyMinus.thy "pbl_vereinf_poly_klammer_mal" [] e_pblID

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

  [("#Given" ,["term t_"]),

   ("#Where" ,["t_ is_polyexp"]),

   ("#Find"  ,["normalform n_"])

  ],

  append_rls "e_rls" e_rls [(*for preds in where_*)

			    Calc ("Poly.is'_polyexp", eval_is_polyexp "")], 

  Some "Vereinfache t_", 

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

store_pbt

 (prep_pbt PolyMinus.thy "pbl_probe" [] e_pblID

 (["probe"],

  [], Erls, None, []));

store_pbt

 (prep_pbt PolyMinus.thy "pbl_probe_poly" [] e_pblID

 (["polynom","probe"],

  [("#Given" ,["Pruefe e_", "mitWert ws_"]),

   ("#Where" ,["e_ is_polyexp"]),

   ("#Find"  ,["Geprueft p_"])

  ],

  append_rls "prls_pbl_probe_poly" 

	     e_rls [(*for preds in where_*)

		    Calc ("Poly.is'_polyexp", eval_is_polyexp "")], 

  Some "Probe e_ ws_", 

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

store_pbt

 (prep_pbt PolyMinus.thy "pbl_probe_bruch" [] e_pblID

 (["bruch","probe"],

  [("#Given" ,["Pruefe e_", "mitWert ws_"]),

   ("#Where" ,["e_ is_ratpolyexp"]),

   ("#Find"  ,["Geprueft p_"])

  ],

  append_rls "prls_pbl_probe_bruch"

	     e_rls [(*for preds in where_*)

		    Calc ("Rational.is'_ratpolyexp", eval_is_ratpolyexp "")], 

  Some "Probe e_ ws_", 

  [["probe","fuer_bruch"]]));

(** methods **)

store_met

    (prep_met PolyMinus.thy "met_simp_poly_minus" [] e_metID

	      (["simplification","for_polynomials","with_minus"],

	       [("#Given" ,["term t_"]),

		("#Where" ,["t_ is_polyexp",

	       "Not (matchsub (?a + (?b + ?c)) t_ | \

	       \     matchsub (?a + (?b - ?c)) t_ | \

	       \     matchsub (?a - (?b + ?c)) t_ | \

	       \     matchsub (?a + (?b - ?c)) t_ )"]),

		("#Find"  ,["normalform n_"])

		],

	       {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, 

		prls = append_rls "prls_met_simp_poly_minus" e_rls 

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

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

	      Thm ("and_true",and_true),

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

	      Thm ("and_false",and_false),

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

	      Thm ("not_true",num_str not_true),

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

	      Thm ("not_false",num_str not_false)

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

		crls = e_rls, nrls = rls_p_33},

"Script SimplifyScript (t_::real) =                   \

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

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

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

	       ));

store_met

    (prep_met PolyMinus.thy "met_simp_poly_parenth" [] e_metID

	      (["simplification","for_polynomials","with_parentheses"],

	       [("#Given" ,["term t_"]),

		("#Where" ,["t_ is_polyexp"]),

		("#Find"  ,["normalform n_"])

		],

	       {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, 

		prls = append_rls "simplification_for_polynomials_prls" e_rls 

				  [(*for preds in where_*)

				   Calc("Poly.is'_polyexp",eval_is_polyexp"")],

		crls = e_rls, nrls = rls_p_34},

"Script SimplifyScript (t_::real) =                          \

\  ((Repeat((Try (Rewrite_Set klammern_aufloesen False)) @@  \

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

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

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

	       ));

store_met

    (prep_met PolyMinus.thy "met_simp_poly_parenth_mult" [] e_metID

	      (["simplification","for_polynomials","with_parentheses_mult"],

	       [("#Given" ,["term t_"]),

		("#Where" ,["t_ is_polyexp"]),

		("#Find"  ,["normalform n_"])

		],

	       {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, 

		prls = append_rls "simplification_for_polynomials_prls" e_rls 

				  [(*for preds in where_*)

				   Calc("Poly.is'_polyexp",eval_is_polyexp"")],

		crls = e_rls, nrls = rls_p_34},

"Script SimplifyScript (t_::real) =                          \

\  ((Repeat((Try (Rewrite_Set klammern_ausmultiplizieren False)) @@ \

\           (Try (Rewrite_Set discard_parentheses        False)) @@ \

\           (Try (Rewrite_Set ordne_monome               False)) @@ \

\           (Try (Rewrite_Set klammern_aufloesen         False)) @@ \

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

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

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

	       ));

store_met

    (prep_met PolyMinus.thy "met_probe" [] e_metID

	      (["probe"],

	       [],

	       {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, 

		prls = Erls, crls = e_rls, nrls = Erls}, 

	       "empty_script"));

store_met

    (prep_met PolyMinus.thy "met_probe_poly" [] e_metID

	      (["probe","fuer_polynom"],

	       [("#Given" ,["Pruefe e_", "mitWert ws_"]),

		("#Where" ,["e_ is_polyexp"]),

		("#Find"  ,["Geprueft p_"])

		],

	       {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, 

		prls = append_rls "prls_met_probe_bruch"

				  e_rls [(*for preds in where_*)

					 Calc ("Rational.is'_ratpolyexp", 

					       eval_is_ratpolyexp "")], 

		crls = e_rls, nrls = rechnen}, 

"Script ProbeScript (e_::bool) (ws_::bool list) = \

\ (let e_ = Take e_;                              \

\      e_ = Substitute ws_ e_                     \

\ in (Repeat((Try (Repeat (Calculate times))) @@  \

\            (Try (Repeat (Calculate plus ))) @@  \

\            (Try (Repeat (Calculate minus))))) e_)"

));

store_met

    (prep_met PolyMinus.thy "met_probe_bruch" [] e_metID

	      (["probe","fuer_bruch"],

	       [("#Given" ,["Pruefe e_", "mitWert ws_"]),

		("#Where" ,["e_ is_ratpolyexp"]),

		("#Find"  ,["Geprueft p_"])

		],

	       {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, 

		prls = append_rls "prls_met_probe_bruch"

				  e_rls [(*for preds in where_*)

					 Calc ("Rational.is'_ratpolyexp", 

					       eval_is_ratpolyexp "")], 

		crls = e_rls, nrls = Erls}, 

	       "empty_script"));