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(* attempts to perserve binary minus as wanted by Austrian teachers
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WN071207
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(c) due to copyright terms
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*)
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theory PolyMinus imports (*Poly// due to "is_ratpolyexp" in...*) Rational begin
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consts
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(*predicates for conditions in rewriting*)
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kleiner :: "['a, 'a] => bool" ("_ kleiner _")
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ist'_monom :: "'a => bool" ("_ ist'_monom")
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(*the CAS-command*)
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Probe :: "[bool, bool list] => bool"
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(*"Probe (3*a+2*b+a = 4*a+2*b) [a=1,b=2]"*)
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(*descriptions for the pbl and met*)
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Pruefe :: "bool => una"
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mitWert :: "bool list => tobooll"
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Geprueft :: "bool => una"
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(*Script-name*)
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ProbeScript :: "[bool, bool list, bool]
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=> bool"
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("((Script ProbeScript (_ _ =))// (_))" 9)
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rules
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null_minus "0 - a = -a"
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vor_minus_mal "- a * b = (-a) * b"
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(*commute with invariant (a.b).c -association*)
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tausche_plus "[| b ist_monom; a kleiner b |] ==>
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(b + a) = (a + b)"
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tausche_minus "[| b ist_monom; a kleiner b |] ==>
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(b - a) = (-a + b)"
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tausche_vor_plus "[| b ist_monom; a kleiner b |] ==>
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(- b + a) = (a - b)"
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tausche_vor_minus "[| b ist_monom; a kleiner b |] ==>
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(- b - a) = (-a - b)"
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tausche_plus_plus "b kleiner c ==> (a + c + b) = (a + b + c)"
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tausche_plus_minus "b kleiner c ==> (a + c - b) = (a - b + c)"
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tausche_minus_plus "b kleiner c ==> (a - c + b) = (a + b - c)"
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tausche_minus_minus "b kleiner c ==> (a - c - b) = (a - b - c)"
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(*commute with invariant (a.b).c -association*)
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tausche_mal "[| b is_atom; a kleiner b |] ==>
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(b * a) = (a * b)"
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tausche_vor_mal "[| b is_atom; a kleiner b |] ==>
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(-b * a) = (-a * b)"
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tausche_mal_mal "[| c is_atom; b kleiner c |] ==>
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(x * c * b) = (x * b * c)"
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x_quadrat "(x * a) * a = x * a ^^^ 2"
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subtrahiere "[| l is_const; m is_const |] ==>
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m * v - l * v = (m - l) * v"
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subtrahiere_von_1 "[| l is_const |] ==>
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v - l * v = (1 - l) * v"
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subtrahiere_1 "[| l is_const; m is_const |] ==>
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m * v - v = (m - 1) * v"
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subtrahiere_x_plus_minus "[| l is_const; m is_const |] ==>
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(x + m * v) - l * v = x + (m - l) * v"
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subtrahiere_x_plus1_minus "[| l is_const |] ==>
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(x + v) - l * v = x + (1 - l) * v"
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subtrahiere_x_plus_minus1 "[| m is_const |] ==>
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(x + m * v) - v = x + (m - 1) * v"
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subtrahiere_x_minus_plus "[| l is_const; m is_const |] ==>
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(x - m * v) + l * v = x + (-m + l) * v"
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subtrahiere_x_minus1_plus "[| l is_const |] ==>
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(x - v) + l * v = x + (-1 + l) * v"
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subtrahiere_x_minus_plus1 "[| m is_const |] ==>
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(x - m * v) + v = x + (-m + 1) * v"
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subtrahiere_x_minus_minus "[| l is_const; m is_const |] ==>
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(x - m * v) - l * v = x + (-m - l) * v"
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subtrahiere_x_minus1_minus"[| l is_const |] ==>
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(x - v) - l * v = x + (-1 - l) * v"
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subtrahiere_x_minus_minus1"[| m is_const |] ==>
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(x - m * v) - v = x + (-m - 1) * v"
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addiere_vor_minus "[| l is_const; m is_const |] ==>
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- (l * v) + m * v = (-l + m) * v"
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addiere_eins_vor_minus "[| m is_const |] ==>
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- v + m * v = (-1 + m) * v"
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subtrahiere_vor_minus "[| l is_const; m is_const |] ==>
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- (l * v) - m * v = (-l - m) * v"
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subtrahiere_eins_vor_minus"[| m is_const |] ==>
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- v - m * v = (-1 - m) * v"
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vorzeichen_minus_weg1 "l kleiner 0 ==> a + l * b = a - -1*l * b"
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vorzeichen_minus_weg2 "l kleiner 0 ==> a - l * b = a + -1*l * b"
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vorzeichen_minus_weg3 "l kleiner 0 ==> k + a - l * b = k + a + -1*l * b"
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vorzeichen_minus_weg4 "l kleiner 0 ==> k - a - l * b = k - a + -1*l * b"
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(*klammer_plus_plus = (real_add_assoc RS sym)*)
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klammer_plus_minus "a + (b - c) = (a + b) - c"
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klammer_minus_plus "a - (b + c) = (a - b) - c"
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klammer_minus_minus "a - (b - c) = (a - b) + c"
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klammer_mult_minus "a * (b - c) = a * b - a * c"
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klammer_minus_mult "(b - c) * a = b * a - c * a"
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ML {*
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(** eval functions **)
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(*. get the identifier from specific monomials; see fun ist_monom .*)
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(*HACK.WN080107*)
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fun increase str =
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let val s::ss = explode str
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in implode ((chr (ord s + 1))::ss) end;
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fun identifier (Free (id,_)) = id (* 2, a *)
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| identifier (Const ("op *", _) $ Free (num, _) $ Free (id, _)) =
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id (* 2*a, a*b *)
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| identifier (Const ("op *", _) $ (* 3*a*b *)
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(Const ("op *", _) $
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Free (num, _) $ Free _) $ Free (id, _)) =
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if is_numeral num then id
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else "|||||||||||||"
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| identifier (Const ("Atools.pow", _) $ Free (base, _) $ Free (exp, _)) =
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if is_numeral base then "|||||||||||||" (* a^2 *)
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else (*increase*) base
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| identifier (Const ("op *", _) $ Free (num, _) $ (* 3*a^2 *)
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(Const ("Atools.pow", _) $
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Free (base, _) $ Free (exp, _))) =
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if is_numeral num andalso not (is_numeral base) then (*increase*) base
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else "|||||||||||||"
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| identifier _ = "|||||||||||||"(*the "largest" string*);
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(*("kleiner", ("PolyMinus.kleiner", eval_kleiner ""))*)
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(* order "by alphabet" w.r.t. var: num < (var | num*var) > (var*var | ..) *)
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fun eval_kleiner _ _ (p as (Const ("PolyMinus.kleiner",_) $ a $ b)) _ =
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if is_num b then
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if is_num a then (*123 kleiner 32 = True !!!*)
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if int_of_Free a < int_of_Free b then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = False",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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else (* -1 * -2 kleiner 0 *)
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SOME ((term2str p) ^ " = False",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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else
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if identifier a < identifier b then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = False",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_kleiner _ _ _ _ = NONE;
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fun ist_monom (Free (id,_)) = true
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| ist_monom (Const ("op *", _) $ Free (num, _) $ Free (id, _)) =
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if is_numeral num then true else false
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| ist_monom _ = false;
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(*. this function only accepts the most simple monoms vvvvvvvvvv .*)
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fun ist_monom (Free (id,_)) = true (* 2, a *)
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| ist_monom (Const ("op *", _) $ Free _ $ Free (id, _)) = (* 2*a, a*b *)
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if is_numeral id then false else true
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| ist_monom (Const ("op *", _) $ (* 3*a*b *)
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(Const ("op *", _) $
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Free (num, _) $ Free _) $ Free (id, _)) =
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if is_numeral num andalso not (is_numeral id) then true else false
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| ist_monom (Const ("Atools.pow", _) $ Free (base, _) $ Free (exp, _)) =
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true (* a^2 *)
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| ist_monom (Const ("op *", _) $ Free (num, _) $ (* 3*a^2 *)
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(Const ("Atools.pow", _) $
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Free (base, _) $ Free (exp, _))) =
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if is_numeral num then true else false
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| ist_monom _ = false;
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(* is this a univariate monomial ? *)
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(*("ist_monom", ("PolyMinus.ist'_monom", eval_ist_monom ""))*)
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fun eval_ist_monom _ _ (p as (Const ("PolyMinus.ist'_monom",_) $ a)) _ =
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if ist_monom a then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = False",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_ist_monom _ _ _ _ = NONE;
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(** rewrite order **)
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(** rulesets **)
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val erls_ordne_alphabetisch =
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append_rls "erls_ordne_alphabetisch" e_rls
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[Calc ("PolyMinus.kleiner", eval_kleiner ""),
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Calc ("PolyMinus.ist'_monom", eval_ist_monom "")
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];
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val ordne_alphabetisch =
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Rls{id = "ordne_alphabetisch", preconds = [],
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rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],
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erls = erls_ordne_alphabetisch,
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rules = [Thm ("tausche_plus",num_str tausche_plus),
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(*"b kleiner a ==> (b + a) = (a + b)"*)
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Thm ("tausche_minus",num_str tausche_minus),
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(*"b kleiner a ==> (b - a) = (-a + b)"*)
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Thm ("tausche_vor_plus",num_str tausche_vor_plus),
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(*"[| b ist_monom; a kleiner b |] ==> (- b + a) = (a - b)"*)
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Thm ("tausche_vor_minus",num_str tausche_vor_minus),
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(*"[| b ist_monom; a kleiner b |] ==> (- b - a) = (-a - b)"*)
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Thm ("tausche_plus_plus",num_str tausche_plus_plus),
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(*"c kleiner b ==> (a + c + b) = (a + b + c)"*)
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Thm ("tausche_plus_minus",num_str tausche_plus_minus),
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(*"c kleiner b ==> (a + c - b) = (a - b + c)"*)
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Thm ("tausche_minus_plus",num_str tausche_minus_plus),
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(*"c kleiner b ==> (a - c + b) = (a + b - c)"*)
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Thm ("tausche_minus_minus",num_str tausche_minus_minus)
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(*"c kleiner b ==> (a - c - b) = (a - b - c)"*)
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], scr = EmptyScr}:rls;
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val fasse_zusammen =
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Rls{id = "fasse_zusammen", preconds = [],
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rew_ord = ("dummy_ord", dummy_ord),
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erls = append_rls "erls_fasse_zusammen" e_rls
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[Calc ("Atools.is'_const",eval_const "#is_const_")],
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srls = Erls, calc = [],
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rules =
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[Thm ("real_num_collect",num_str real_num_collect),
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(*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
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Thm ("real_num_collect_assoc_r",num_str real_num_collect_assoc_r),
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(*"[| l is_const; m..|] ==> (k + m * n) + l * n = k + (l + m)*n"*)
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Thm ("real_one_collect",num_str real_one_collect),
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(*"m is_const ==> n + m * n = (1 + m) * n"*)
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Thm ("real_one_collect_assoc_r",num_str real_one_collect_assoc_r),
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(*"m is_const ==> (k + n) + m * n = k + (m + 1) * n"*)
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Thm ("subtrahiere",num_str subtrahiere),
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(*"[| l is_const; m is_const |] ==> m * v - l * v = (m - l) * v"*)
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Thm ("subtrahiere_von_1",num_str subtrahiere_von_1),
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(*"[| l is_const |] ==> v - l * v = (1 - l) * v"*)
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Thm ("subtrahiere_1",num_str subtrahiere_1),
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(*"[| l is_const; m is_const |] ==> m * v - v = (m - 1) * v"*)
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241 |
|
neuper@37950
|
242 |
Thm ("subtrahiere_x_plus_minus",num_str subtrahiere_x_plus_minus),
|
neuper@37950
|
243 |
(*"[| l is_const; m..|] ==> (k + m * n) - l * n = k + ( m - l) * n"*)
|
neuper@37950
|
244 |
Thm ("subtrahiere_x_plus1_minus",num_str subtrahiere_x_plus1_minus),
|
neuper@37950
|
245 |
(*"[| l is_const |] ==> (x + v) - l * v = x + (1 - l) * v"*)
|
neuper@37950
|
246 |
Thm ("subtrahiere_x_plus_minus1",num_str subtrahiere_x_plus_minus1),
|
neuper@37950
|
247 |
(*"[| m is_const |] ==> (x + m * v) - v = x + (m - 1) * v"*)
|
neuper@37950
|
248 |
|
neuper@37950
|
249 |
Thm ("subtrahiere_x_minus_plus",num_str subtrahiere_x_minus_plus),
|
neuper@37950
|
250 |
(*"[| l is_const; m..|] ==> (k - m * n) + l * n = k + (-m + l) * n"*)
|
neuper@37950
|
251 |
Thm ("subtrahiere_x_minus1_plus",num_str subtrahiere_x_minus1_plus),
|
neuper@37950
|
252 |
(*"[| l is_const |] ==> (x - v) + l * v = x + (-1 + l) * v"*)
|
neuper@37950
|
253 |
Thm ("subtrahiere_x_minus_plus1",num_str subtrahiere_x_minus_plus1),
|
neuper@37950
|
254 |
(*"[| m is_const |] ==> (x - m * v) + v = x + (-m + 1) * v"*)
|
neuper@37950
|
255 |
|
neuper@37950
|
256 |
Thm ("subtrahiere_x_minus_minus",num_str subtrahiere_x_minus_minus),
|
neuper@37950
|
257 |
(*"[| l is_const; m..|] ==> (k - m * n) - l * n = k + (-m - l) * n"*)
|
neuper@37950
|
258 |
Thm ("subtrahiere_x_minus1_minus",num_str subtrahiere_x_minus1_minus),
|
neuper@37950
|
259 |
(*"[| l is_const |] ==> (x - v) - l * v = x + (-1 - l) * v"*)
|
neuper@37950
|
260 |
Thm ("subtrahiere_x_minus_minus1",num_str subtrahiere_x_minus_minus1),
|
neuper@37950
|
261 |
(*"[| m is_const |] ==> (x - m * v) - v = x + (-m - 1) * v"*)
|
neuper@37950
|
262 |
|
neuper@37950
|
263 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37950
|
264 |
Calc ("op -", eval_binop "#subtr_"),
|
neuper@37950
|
265 |
|
neuper@37950
|
266 |
(*MG: Reihenfolge der folgenden 2 Thm muss so bleiben, wegen
|
neuper@37950
|
267 |
(a+a)+a --> a + 2*a --> 3*a and not (a+a)+a --> 2*a + a *)
|
neuper@37950
|
268 |
Thm ("real_mult_2_assoc_r",num_str real_mult_2_assoc_r),
|
neuper@37950
|
269 |
(*"(k + z1) + z1 = k + 2 * z1"*)
|
neuper@37950
|
270 |
Thm ("sym_real_mult_2",num_str (real_mult_2 RS sym)),
|
neuper@37950
|
271 |
(*"z1 + z1 = 2 * z1"*)
|
neuper@37950
|
272 |
|
neuper@37950
|
273 |
Thm ("addiere_vor_minus",num_str addiere_vor_minus),
|
neuper@37950
|
274 |
(*"[| l is_const; m is_const |] ==> -(l * v) + m * v = (-l + m) *v"*)
|
neuper@37950
|
275 |
Thm ("addiere_eins_vor_minus",num_str addiere_eins_vor_minus),
|
neuper@37950
|
276 |
(*"[| m is_const |] ==> - v + m * v = (-1 + m) * v"*)
|
neuper@37950
|
277 |
Thm ("subtrahiere_vor_minus",num_str subtrahiere_vor_minus),
|
neuper@37950
|
278 |
(*"[| l is_const; m is_const |] ==> -(l * v) - m * v = (-l - m) *v"*)
|
neuper@37950
|
279 |
Thm ("subtrahiere_eins_vor_minus",num_str subtrahiere_eins_vor_minus)
|
neuper@37950
|
280 |
(*"[| m is_const |] ==> - v - m * v = (-1 - m) * v"*)
|
neuper@37950
|
281 |
|
neuper@37950
|
282 |
], scr = EmptyScr}:rls;
|
neuper@37950
|
283 |
|
neuper@37950
|
284 |
val verschoenere =
|
neuper@37950
|
285 |
Rls{id = "verschoenere", preconds = [],
|
neuper@37950
|
286 |
rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],
|
neuper@37950
|
287 |
erls = append_rls "erls_verschoenere" e_rls
|
neuper@37950
|
288 |
[Calc ("PolyMinus.kleiner", eval_kleiner "")],
|
neuper@37950
|
289 |
rules = [Thm ("vorzeichen_minus_weg1",num_str vorzeichen_minus_weg1),
|
neuper@37950
|
290 |
(*"l kleiner 0 ==> a + l * b = a - -l * b"*)
|
neuper@37950
|
291 |
Thm ("vorzeichen_minus_weg2",num_str vorzeichen_minus_weg2),
|
neuper@37950
|
292 |
(*"l kleiner 0 ==> a - l * b = a + -l * b"*)
|
neuper@37950
|
293 |
Thm ("vorzeichen_minus_weg3",num_str vorzeichen_minus_weg3),
|
neuper@37950
|
294 |
(*"l kleiner 0 ==> k + a - l * b = k + a + -l * b"*)
|
neuper@37950
|
295 |
Thm ("vorzeichen_minus_weg4",num_str vorzeichen_minus_weg4),
|
neuper@37950
|
296 |
(*"l kleiner 0 ==> k - a - l * b = k - a + -l * b"*)
|
neuper@37950
|
297 |
|
neuper@37950
|
298 |
Calc ("op *", eval_binop "#mult_"),
|
neuper@37950
|
299 |
|
neuper@37950
|
300 |
Thm ("real_mult_0",num_str real_mult_0),
|
neuper@37950
|
301 |
(*"0 * z = 0"*)
|
neuper@37950
|
302 |
Thm ("real_mult_1",num_str real_mult_1),
|
neuper@37950
|
303 |
(*"1 * z = z"*)
|
neuper@37950
|
304 |
Thm ("real_add_zero_left",num_str real_add_zero_left),
|
neuper@37950
|
305 |
(*"0 + z = z"*)
|
neuper@37950
|
306 |
Thm ("null_minus",num_str null_minus),
|
neuper@37950
|
307 |
(*"0 - a = -a"*)
|
neuper@37950
|
308 |
Thm ("vor_minus_mal",num_str vor_minus_mal)
|
neuper@37950
|
309 |
(*"- a * b = (-a) * b"*)
|
neuper@37950
|
310 |
|
neuper@37950
|
311 |
(*Thm ("",num_str ),*)
|
neuper@37950
|
312 |
(**)
|
neuper@37950
|
313 |
], scr = EmptyScr}:rls (*end verschoenere*);
|
neuper@37950
|
314 |
|
neuper@37950
|
315 |
val klammern_aufloesen =
|
neuper@37950
|
316 |
Rls{id = "klammern_aufloesen", preconds = [],
|
neuper@37950
|
317 |
rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], erls = Erls,
|
neuper@37950
|
318 |
rules = [Thm ("sym_real_add_assoc",num_str (real_add_assoc RS sym)),
|
neuper@37950
|
319 |
(*"a + (b + c) = (a + b) + c"*)
|
neuper@37950
|
320 |
Thm ("klammer_plus_minus",num_str klammer_plus_minus),
|
neuper@37950
|
321 |
(*"a + (b - c) = (a + b) - c"*)
|
neuper@37950
|
322 |
Thm ("klammer_minus_plus",num_str klammer_minus_plus),
|
neuper@37950
|
323 |
(*"a - (b + c) = (a - b) - c"*)
|
neuper@37950
|
324 |
Thm ("klammer_minus_minus",num_str klammer_minus_minus)
|
neuper@37950
|
325 |
(*"a - (b - c) = (a - b) + c"*)
|
neuper@37950
|
326 |
], scr = EmptyScr}:rls;
|
neuper@37950
|
327 |
|
neuper@37950
|
328 |
val klammern_ausmultiplizieren =
|
neuper@37950
|
329 |
Rls{id = "klammern_ausmultiplizieren", preconds = [],
|
neuper@37950
|
330 |
rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], erls = Erls,
|
neuper@37950
|
331 |
rules = [Thm ("real_add_mult_distrib" ,num_str real_add_mult_distrib),
|
neuper@37950
|
332 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
neuper@37950
|
333 |
Thm ("real_add_mult_distrib2",num_str real_add_mult_distrib2),
|
neuper@37950
|
334 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
neuper@37950
|
335 |
|
neuper@37950
|
336 |
Thm ("klammer_mult_minus",num_str klammer_mult_minus),
|
neuper@37950
|
337 |
(*"a * (b - c) = a * b - a * c"*)
|
neuper@37950
|
338 |
Thm ("klammer_minus_mult",num_str klammer_minus_mult)
|
neuper@37950
|
339 |
(*"(b - c) * a = b * a - c * a"*)
|
neuper@37950
|
340 |
|
neuper@37950
|
341 |
(*Thm ("",num_str ),
|
neuper@37950
|
342 |
(*""*)*)
|
neuper@37950
|
343 |
], scr = EmptyScr}:rls;
|
neuper@37950
|
344 |
|
neuper@37950
|
345 |
val ordne_monome =
|
neuper@37950
|
346 |
Rls{id = "ordne_monome", preconds = [],
|
neuper@37950
|
347 |
rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],
|
neuper@37950
|
348 |
erls = append_rls "erls_ordne_monome" e_rls
|
neuper@37950
|
349 |
[Calc ("PolyMinus.kleiner", eval_kleiner ""),
|
neuper@37950
|
350 |
Calc ("Atools.is'_atom", eval_is_atom "")
|
neuper@37950
|
351 |
],
|
neuper@37950
|
352 |
rules = [Thm ("tausche_mal",num_str tausche_mal),
|
neuper@37950
|
353 |
(*"[| b is_atom; a kleiner b |] ==> (b * a) = (a * b)"*)
|
neuper@37950
|
354 |
Thm ("tausche_vor_mal",num_str tausche_vor_mal),
|
neuper@37950
|
355 |
(*"[| b is_atom; a kleiner b |] ==> (-b * a) = (-a * b)"*)
|
neuper@37950
|
356 |
Thm ("tausche_mal_mal",num_str tausche_mal_mal),
|
neuper@37950
|
357 |
(*"[| c is_atom; b kleiner c |] ==> (a * c * b) = (a * b *c)"*)
|
neuper@37950
|
358 |
Thm ("x_quadrat",num_str x_quadrat)
|
neuper@37950
|
359 |
(*"(x * a) * a = x * a ^^^ 2"*)
|
neuper@37950
|
360 |
|
neuper@37950
|
361 |
(*Thm ("",num_str ),
|
neuper@37950
|
362 |
(*""*)*)
|
neuper@37950
|
363 |
], scr = EmptyScr}:rls;
|
neuper@37950
|
364 |
|
neuper@37950
|
365 |
|
neuper@37950
|
366 |
val rls_p_33 =
|
neuper@37950
|
367 |
append_rls "rls_p_33" e_rls
|
neuper@37950
|
368 |
[Rls_ ordne_alphabetisch,
|
neuper@37950
|
369 |
Rls_ fasse_zusammen,
|
neuper@37950
|
370 |
Rls_ verschoenere
|
neuper@37950
|
371 |
];
|
neuper@37950
|
372 |
val rls_p_34 =
|
neuper@37950
|
373 |
append_rls "rls_p_34" e_rls
|
neuper@37950
|
374 |
[Rls_ klammern_aufloesen,
|
neuper@37950
|
375 |
Rls_ ordne_alphabetisch,
|
neuper@37950
|
376 |
Rls_ fasse_zusammen,
|
neuper@37950
|
377 |
Rls_ verschoenere
|
neuper@37950
|
378 |
];
|
neuper@37950
|
379 |
val rechnen =
|
neuper@37950
|
380 |
append_rls "rechnen" e_rls
|
neuper@37950
|
381 |
[Calc ("op *", eval_binop "#mult_"),
|
neuper@37950
|
382 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37950
|
383 |
Calc ("op -", eval_binop "#subtr_")
|
neuper@37950
|
384 |
];
|
neuper@37950
|
385 |
|
neuper@37950
|
386 |
ruleset' :=
|
neuper@37950
|
387 |
overwritelthy thy (!ruleset',
|
neuper@37950
|
388 |
[("ordne_alphabetisch", prep_rls ordne_alphabetisch),
|
neuper@37950
|
389 |
("fasse_zusammen", prep_rls fasse_zusammen),
|
neuper@37950
|
390 |
("verschoenere", prep_rls verschoenere),
|
neuper@37950
|
391 |
("ordne_monome", prep_rls ordne_monome),
|
neuper@37950
|
392 |
("klammern_aufloesen", prep_rls klammern_aufloesen),
|
neuper@37950
|
393 |
("klammern_ausmultiplizieren",
|
neuper@37950
|
394 |
prep_rls klammern_ausmultiplizieren)
|
neuper@37950
|
395 |
]);
|
neuper@37950
|
396 |
|
neuper@37950
|
397 |
(** problems **)
|
neuper@37950
|
398 |
|
neuper@37950
|
399 |
store_pbt
|
neuper@37950
|
400 |
(prep_pbt PolyMinus.thy "pbl_vereinf_poly" [] e_pblID
|
neuper@37950
|
401 |
(["polynom","vereinfachen"],
|
neuper@37950
|
402 |
[], Erls, NONE, []));
|
neuper@37950
|
403 |
|
neuper@37950
|
404 |
store_pbt
|
neuper@37950
|
405 |
(prep_pbt PolyMinus.thy "pbl_vereinf_poly_minus" [] e_pblID
|
neuper@37950
|
406 |
(["plus_minus","polynom","vereinfachen"],
|
neuper@37950
|
407 |
[("#Given" ,["term t_"]),
|
neuper@37950
|
408 |
("#Where" ,["t_ is_polyexp",
|
neuper@37950
|
409 |
"Not (matchsub (?a + (?b + ?c)) t_ | " ^
|
neuper@37950
|
410 |
" matchsub (?a + (?b - ?c)) t_ | " ^
|
neuper@37950
|
411 |
" matchsub (?a - (?b + ?c)) t_ | " ^
|
neuper@37950
|
412 |
" matchsub (?a + (?b - ?c)) t_ )",
|
neuper@37950
|
413 |
"Not (matchsub (?a * (?b + ?c)) t_ | " ^
|
neuper@37950
|
414 |
" matchsub (?a * (?b - ?c)) t_ | " ^
|
neuper@37950
|
415 |
" matchsub ((?b + ?c) * ?a) t_ | " ^
|
neuper@37950
|
416 |
" matchsub ((?b - ?c) * ?a) t_ )"]),
|
neuper@37950
|
417 |
("#Find" ,["normalform n_"])
|
neuper@37950
|
418 |
],
|
neuper@37950
|
419 |
append_rls "prls_pbl_vereinf_poly" e_rls
|
neuper@37950
|
420 |
[Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
|
neuper@37950
|
421 |
Calc ("Tools.matchsub", eval_matchsub ""),
|
neuper@37950
|
422 |
Thm ("or_true",or_true),
|
neuper@37950
|
423 |
(*"(?a | True) = True"*)
|
neuper@37950
|
424 |
Thm ("or_false",or_false),
|
neuper@37950
|
425 |
(*"(?a | False) = ?a"*)
|
neuper@37950
|
426 |
Thm ("not_true",num_str not_true),
|
neuper@37950
|
427 |
(*"(~ True) = False"*)
|
neuper@37950
|
428 |
Thm ("not_false",num_str not_false)
|
neuper@37950
|
429 |
(*"(~ False) = True"*)],
|
neuper@37950
|
430 |
SOME "Vereinfache t_",
|
neuper@37950
|
431 |
[["simplification","for_polynomials","with_minus"]]));
|
neuper@37950
|
432 |
|
neuper@37950
|
433 |
store_pbt
|
neuper@37950
|
434 |
(prep_pbt PolyMinus.thy "pbl_vereinf_poly_klammer" [] e_pblID
|
neuper@37950
|
435 |
(["klammer","polynom","vereinfachen"],
|
neuper@37950
|
436 |
[("#Given" ,["term t_"]),
|
neuper@37950
|
437 |
("#Where" ,["t_ is_polyexp",
|
neuper@37950
|
438 |
"Not (matchsub (?a * (?b + ?c)) t_ | " ^
|
neuper@37950
|
439 |
" matchsub (?a * (?b - ?c)) t_ | " ^
|
neuper@37950
|
440 |
" matchsub ((?b + ?c) * ?a) t_ | " ^
|
neuper@37950
|
441 |
" matchsub ((?b - ?c) * ?a) t_ )"]),
|
neuper@37950
|
442 |
("#Find" ,["normalform n_"])
|
neuper@37950
|
443 |
],
|
neuper@37950
|
444 |
append_rls "prls_pbl_vereinf_poly_klammer" e_rls [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
|
neuper@37950
|
445 |
Calc ("Tools.matchsub", eval_matchsub ""),
|
neuper@37950
|
446 |
Thm ("or_true",or_true),
|
neuper@37950
|
447 |
(*"(?a | True) = True"*)
|
neuper@37950
|
448 |
Thm ("or_false",or_false),
|
neuper@37950
|
449 |
(*"(?a | False) = ?a"*)
|
neuper@37950
|
450 |
Thm ("not_true",num_str not_true),
|
neuper@37950
|
451 |
(*"(~ True) = False"*)
|
neuper@37950
|
452 |
Thm ("not_false",num_str not_false)
|
neuper@37950
|
453 |
(*"(~ False) = True"*)],
|
neuper@37950
|
454 |
SOME "Vereinfache t_",
|
neuper@37950
|
455 |
[["simplification","for_polynomials","with_parentheses"]]));
|
neuper@37950
|
456 |
|
neuper@37950
|
457 |
store_pbt
|
neuper@37950
|
458 |
(prep_pbt PolyMinus.thy "pbl_vereinf_poly_klammer_mal" [] e_pblID
|
neuper@37950
|
459 |
(["binom_klammer","polynom","vereinfachen"],
|
neuper@37950
|
460 |
[("#Given" ,["term t_"]),
|
neuper@37950
|
461 |
("#Where" ,["t_ is_polyexp"]),
|
neuper@37950
|
462 |
("#Find" ,["normalform n_"])
|
neuper@37950
|
463 |
],
|
neuper@37950
|
464 |
append_rls "e_rls" e_rls [(*for preds in where_*)
|
neuper@37950
|
465 |
Calc ("Poly.is'_polyexp", eval_is_polyexp "")],
|
neuper@37950
|
466 |
SOME "Vereinfache t_",
|
neuper@37950
|
467 |
[["simplification","for_polynomials","with_parentheses_mult"]]));
|
neuper@37950
|
468 |
|
neuper@37950
|
469 |
store_pbt
|
neuper@37950
|
470 |
(prep_pbt PolyMinus.thy "pbl_probe" [] e_pblID
|
neuper@37950
|
471 |
(["probe"],
|
neuper@37950
|
472 |
[], Erls, NONE, []));
|
neuper@37950
|
473 |
|
neuper@37950
|
474 |
store_pbt
|
neuper@37950
|
475 |
(prep_pbt PolyMinus.thy "pbl_probe_poly" [] e_pblID
|
neuper@37950
|
476 |
(["polynom","probe"],
|
neuper@37950
|
477 |
[("#Given" ,["Pruefe e_", "mitWert ws_"]),
|
neuper@37950
|
478 |
("#Where" ,["e_ is_polyexp"]),
|
neuper@37950
|
479 |
("#Find" ,["Geprueft p_"])
|
neuper@37950
|
480 |
],
|
neuper@37950
|
481 |
append_rls "prls_pbl_probe_poly"
|
neuper@37950
|
482 |
e_rls [(*for preds in where_*)
|
neuper@37950
|
483 |
Calc ("Poly.is'_polyexp", eval_is_polyexp "")],
|
neuper@37950
|
484 |
SOME "Probe e_ ws_",
|
neuper@37950
|
485 |
[["probe","fuer_polynom"]]));
|
neuper@37950
|
486 |
|
neuper@37950
|
487 |
store_pbt
|
neuper@37950
|
488 |
(prep_pbt PolyMinus.thy "pbl_probe_bruch" [] e_pblID
|
neuper@37950
|
489 |
(["bruch","probe"],
|
neuper@37950
|
490 |
[("#Given" ,["Pruefe e_", "mitWert ws_"]),
|
neuper@37950
|
491 |
("#Where" ,["e_ is_ratpolyexp"]),
|
neuper@37950
|
492 |
("#Find" ,["Geprueft p_"])
|
neuper@37950
|
493 |
],
|
neuper@37950
|
494 |
append_rls "prls_pbl_probe_bruch"
|
neuper@37950
|
495 |
e_rls [(*for preds in where_*)
|
neuper@37950
|
496 |
Calc ("Rational.is'_ratpolyexp", eval_is_ratpolyexp "")],
|
neuper@37950
|
497 |
SOME "Probe e_ ws_",
|
neuper@37950
|
498 |
[["probe","fuer_bruch"]]));
|
neuper@37950
|
499 |
|
neuper@37950
|
500 |
|
neuper@37950
|
501 |
(** methods **)
|
neuper@37950
|
502 |
|
neuper@37950
|
503 |
store_met
|
neuper@37950
|
504 |
(prep_met PolyMinus.thy "met_simp_poly_minus" [] e_metID
|
neuper@37950
|
505 |
(["simplification","for_polynomials","with_minus"],
|
neuper@37950
|
506 |
[("#Given" ,["term t_"]),
|
neuper@37950
|
507 |
("#Where" ,["t_ is_polyexp",
|
neuper@37950
|
508 |
"Not (matchsub (?a + (?b + ?c)) t_ | " ^
|
neuper@37950
|
509 |
" matchsub (?a + (?b - ?c)) t_ | " ^
|
neuper@37950
|
510 |
" matchsub (?a - (?b + ?c)) t_ | " ^
|
neuper@37950
|
511 |
" matchsub (?a + (?b - ?c)) t_ )"]),
|
neuper@37950
|
512 |
("#Find" ,["normalform n_"])
|
neuper@37950
|
513 |
],
|
neuper@37950
|
514 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
|
neuper@37950
|
515 |
prls = append_rls "prls_met_simp_poly_minus" e_rls
|
neuper@37950
|
516 |
[Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
|
neuper@37950
|
517 |
Calc ("Tools.matchsub", eval_matchsub ""),
|
neuper@37950
|
518 |
Thm ("and_true",and_true),
|
neuper@37950
|
519 |
(*"(?a & True) = ?a"*)
|
neuper@37950
|
520 |
Thm ("and_false",and_false),
|
neuper@37950
|
521 |
(*"(?a & False) = False"*)
|
neuper@37950
|
522 |
Thm ("not_true",num_str not_true),
|
neuper@37950
|
523 |
(*"(~ True) = False"*)
|
neuper@37950
|
524 |
Thm ("not_false",num_str not_false)
|
neuper@37950
|
525 |
(*"(~ False) = True"*)],
|
neuper@37950
|
526 |
crls = e_rls, nrls = rls_p_33},
|
neuper@37950
|
527 |
"Script SimplifyScript (t_::real) = " ^
|
neuper@37950
|
528 |
" ((Repeat((Try (Rewrite_Set ordne_alphabetisch False)) @@ " ^
|
neuper@37950
|
529 |
" (Try (Rewrite_Set fasse_zusammen False)) @@ " ^
|
neuper@37950
|
530 |
" (Try (Rewrite_Set verschoenere False)))) t_)"
|
neuper@37950
|
531 |
));
|
neuper@37950
|
532 |
|
neuper@37950
|
533 |
store_met
|
neuper@37950
|
534 |
(prep_met PolyMinus.thy "met_simp_poly_parenth" [] e_metID
|
neuper@37950
|
535 |
(["simplification","for_polynomials","with_parentheses"],
|
neuper@37950
|
536 |
[("#Given" ,["term t_"]),
|
neuper@37950
|
537 |
("#Where" ,["t_ is_polyexp"]),
|
neuper@37950
|
538 |
("#Find" ,["normalform n_"])
|
neuper@37950
|
539 |
],
|
neuper@37950
|
540 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
|
neuper@37950
|
541 |
prls = append_rls "simplification_for_polynomials_prls" e_rls
|
neuper@37950
|
542 |
[(*for preds in where_*)
|
neuper@37950
|
543 |
Calc("Poly.is'_polyexp",eval_is_polyexp"")],
|
neuper@37950
|
544 |
crls = e_rls, nrls = rls_p_34},
|
neuper@37950
|
545 |
"Script SimplifyScript (t_::real) = " ^
|
neuper@37950
|
546 |
" ((Repeat((Try (Rewrite_Set klammern_aufloesen False)) @@ " ^
|
neuper@37950
|
547 |
" (Try (Rewrite_Set ordne_alphabetisch False)) @@ " ^
|
neuper@37950
|
548 |
" (Try (Rewrite_Set fasse_zusammen False)) @@ " ^
|
neuper@37950
|
549 |
" (Try (Rewrite_Set verschoenere False)))) t_)"
|
neuper@37950
|
550 |
));
|
neuper@37950
|
551 |
|
neuper@37950
|
552 |
store_met
|
neuper@37950
|
553 |
(prep_met PolyMinus.thy "met_simp_poly_parenth_mult" [] e_metID
|
neuper@37950
|
554 |
(["simplification","for_polynomials","with_parentheses_mult"],
|
neuper@37950
|
555 |
[("#Given" ,["term t_"]),
|
neuper@37950
|
556 |
("#Where" ,["t_ is_polyexp"]),
|
neuper@37950
|
557 |
("#Find" ,["normalform n_"])
|
neuper@37950
|
558 |
],
|
neuper@37950
|
559 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
|
neuper@37950
|
560 |
prls = append_rls "simplification_for_polynomials_prls" e_rls
|
neuper@37950
|
561 |
[(*for preds in where_*)
|
neuper@37950
|
562 |
Calc("Poly.is'_polyexp",eval_is_polyexp"")],
|
neuper@37950
|
563 |
crls = e_rls, nrls = rls_p_34},
|
neuper@37950
|
564 |
"Script SimplifyScript (t_::real) = " ^
|
neuper@37950
|
565 |
" ((Repeat((Try (Rewrite_Set klammern_ausmultiplizieren False)) @@ " ^
|
neuper@37950
|
566 |
" (Try (Rewrite_Set discard_parentheses False)) @@ " ^
|
neuper@37950
|
567 |
" (Try (Rewrite_Set ordne_monome False)) @@ " ^
|
neuper@37950
|
568 |
" (Try (Rewrite_Set klammern_aufloesen False)) @@ " ^
|
neuper@37950
|
569 |
" (Try (Rewrite_Set ordne_alphabetisch False)) @@ " ^
|
neuper@37950
|
570 |
" (Try (Rewrite_Set fasse_zusammen False)) @@ " ^
|
neuper@37950
|
571 |
" (Try (Rewrite_Set verschoenere False)))) t_)"
|
neuper@37950
|
572 |
));
|
neuper@37950
|
573 |
|
neuper@37950
|
574 |
store_met
|
neuper@37950
|
575 |
(prep_met PolyMinus.thy "met_probe" [] e_metID
|
neuper@37950
|
576 |
(["probe"],
|
neuper@37950
|
577 |
[],
|
neuper@37950
|
578 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
|
neuper@37950
|
579 |
prls = Erls, crls = e_rls, nrls = Erls},
|
neuper@37950
|
580 |
"empty_script"));
|
neuper@37950
|
581 |
|
neuper@37950
|
582 |
store_met
|
neuper@37950
|
583 |
(prep_met PolyMinus.thy "met_probe_poly" [] e_metID
|
neuper@37950
|
584 |
(["probe","fuer_polynom"],
|
neuper@37950
|
585 |
[("#Given" ,["Pruefe e_", "mitWert ws_"]),
|
neuper@37950
|
586 |
("#Where" ,["e_ is_polyexp"]),
|
neuper@37950
|
587 |
("#Find" ,["Geprueft p_"])
|
neuper@37950
|
588 |
],
|
neuper@37950
|
589 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
|
neuper@37950
|
590 |
prls = append_rls "prls_met_probe_bruch"
|
neuper@37950
|
591 |
e_rls [(*for preds in where_*)
|
neuper@37950
|
592 |
Calc ("Rational.is'_ratpolyexp",
|
neuper@37950
|
593 |
eval_is_ratpolyexp "")],
|
neuper@37950
|
594 |
crls = e_rls, nrls = rechnen},
|
neuper@37950
|
595 |
"Script ProbeScript (e_::bool) (ws_::bool list) = " ^
|
neuper@37950
|
596 |
" (let e_ = Take e_; " ^
|
neuper@37950
|
597 |
" e_ = Substitute ws_ e_ " ^
|
neuper@37950
|
598 |
" in (Repeat((Try (Repeat (Calculate times))) @@ " ^
|
neuper@37950
|
599 |
" (Try (Repeat (Calculate plus ))) @@ " ^
|
neuper@37950
|
600 |
" (Try (Repeat (Calculate minus))))) e_)"
|
neuper@37950
|
601 |
));
|
neuper@37950
|
602 |
|
neuper@37950
|
603 |
store_met
|
neuper@37950
|
604 |
(prep_met PolyMinus.thy "met_probe_bruch" [] e_metID
|
neuper@37950
|
605 |
(["probe","fuer_bruch"],
|
neuper@37950
|
606 |
[("#Given" ,["Pruefe e_", "mitWert ws_"]),
|
neuper@37950
|
607 |
("#Where" ,["e_ is_ratpolyexp"]),
|
neuper@37950
|
608 |
("#Find" ,["Geprueft p_"])
|
neuper@37950
|
609 |
],
|
neuper@37950
|
610 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
|
neuper@37950
|
611 |
prls = append_rls "prls_met_probe_bruch"
|
neuper@37950
|
612 |
e_rls [(*for preds in where_*)
|
neuper@37950
|
613 |
Calc ("Rational.is'_ratpolyexp",
|
neuper@37950
|
614 |
eval_is_ratpolyexp "")],
|
neuper@37950
|
615 |
crls = e_rls, nrls = Erls},
|
neuper@37950
|
616 |
"empty_script"));
|
neuper@37950
|
617 |
*}
|
neuper@37906
|
618 |
|
neuper@37906
|
619 |
end
|
neuper@37906
|
620 |
|