1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/Tools/isac/Knowledge/PolyMinus.ML Wed Aug 25 16:20:07 2010 +0200
1.3 @@ -0,0 +1,521 @@
1.4 +(* questionable attempts to perserve binary minus as wanted by teachers
1.5 + WN071207
1.6 + (c) due to copyright terms
1.7 +remove_thy"PolyMinus";
1.8 +use_thy"Knowledge/PolyMinus";
1.9 +
1.10 +use_thy"Knowledge/Isac";
1.11 +use"Knowledge/PolyMinus.ML";
1.12 +*)
1.13 +
1.14 +(** interface isabelle -- isac **)
1.15 +theory' := overwritel (!theory', [("PolyMinus.thy",PolyMinus.thy)]);
1.16 +
1.17 +(** eval functions **)
1.18 +
1.19 +(*. get the identifier from specific monomials; see fun ist_monom .*)
1.20 +(*HACK.WN080107*)
1.21 +fun increase str =
1.22 + let val s::ss = explode str
1.23 + in implode ((chr (ord s + 1))::ss) end;
1.24 +fun identifier (Free (id,_)) = id (* 2, a *)
1.25 + | identifier (Const ("op *", _) $ Free (num, _) $ Free (id, _)) =
1.26 + id (* 2*a, a*b *)
1.27 + | identifier (Const ("op *", _) $ (* 3*a*b *)
1.28 + (Const ("op *", _) $
1.29 + Free (num, _) $ Free _) $ Free (id, _)) =
1.30 + if is_numeral num then id
1.31 + else "|||||||||||||"
1.32 + | identifier (Const ("Atools.pow", _) $ Free (base, _) $ Free (exp, _)) =
1.33 + if is_numeral base then "|||||||||||||" (* a^2 *)
1.34 + else (*increase*) base
1.35 + | identifier (Const ("op *", _) $ Free (num, _) $ (* 3*a^2 *)
1.36 + (Const ("Atools.pow", _) $
1.37 + Free (base, _) $ Free (exp, _))) =
1.38 + if is_numeral num andalso not (is_numeral base) then (*increase*) base
1.39 + else "|||||||||||||"
1.40 + | identifier _ = "|||||||||||||"(*the "largest" string*);
1.41 +
1.42 +(*("kleiner", ("PolyMinus.kleiner", eval_kleiner ""))*)
1.43 +(* order "by alphabet" w.r.t. var: num < (var | num*var) > (var*var | ..) *)
1.44 +fun eval_kleiner _ _ (p as (Const ("PolyMinus.kleiner",_) $ a $ b)) _ =
1.45 + if is_num b then
1.46 + if is_num a then (*123 kleiner 32 = True !!!*)
1.47 + if int_of_Free a < int_of_Free b then
1.48 + SOME ((term2str p) ^ " = True",
1.49 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.50 + else SOME ((term2str p) ^ " = False",
1.51 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.52 + else (* -1 * -2 kleiner 0 *)
1.53 + SOME ((term2str p) ^ " = False",
1.54 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.55 + else
1.56 + if identifier a < identifier b then
1.57 + SOME ((term2str p) ^ " = True",
1.58 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.59 + else SOME ((term2str p) ^ " = False",
1.60 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.61 + | eval_kleiner _ _ _ _ = NONE;
1.62 +
1.63 +fun ist_monom (Free (id,_)) = true
1.64 + | ist_monom (Const ("op *", _) $ Free (num, _) $ Free (id, _)) =
1.65 + if is_numeral num then true else false
1.66 + | ist_monom _ = false;
1.67 +(*. this function only accepts the most simple monoms vvvvvvvvvv .*)
1.68 +fun ist_monom (Free (id,_)) = true (* 2, a *)
1.69 + | ist_monom (Const ("op *", _) $ Free _ $ Free (id, _)) = (* 2*a, a*b *)
1.70 + if is_numeral id then false else true
1.71 + | ist_monom (Const ("op *", _) $ (* 3*a*b *)
1.72 + (Const ("op *", _) $
1.73 + Free (num, _) $ Free _) $ Free (id, _)) =
1.74 + if is_numeral num andalso not (is_numeral id) then true else false
1.75 + | ist_monom (Const ("Atools.pow", _) $ Free (base, _) $ Free (exp, _)) =
1.76 + true (* a^2 *)
1.77 + | ist_monom (Const ("op *", _) $ Free (num, _) $ (* 3*a^2 *)
1.78 + (Const ("Atools.pow", _) $
1.79 + Free (base, _) $ Free (exp, _))) =
1.80 + if is_numeral num then true else false
1.81 + | ist_monom _ = false;
1.82 +
1.83 +(* is this a univariate monomial ? *)
1.84 +(*("ist_monom", ("PolyMinus.ist'_monom", eval_ist_monom ""))*)
1.85 +fun eval_ist_monom _ _ (p as (Const ("PolyMinus.ist'_monom",_) $ a)) _ =
1.86 + if ist_monom a then
1.87 + SOME ((term2str p) ^ " = True",
1.88 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.89 + else SOME ((term2str p) ^ " = False",
1.90 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.91 + | eval_ist_monom _ _ _ _ = NONE;
1.92 +
1.93 +
1.94 +(** rewrite order **)
1.95 +
1.96 +(** rulesets **)
1.97 +
1.98 +val erls_ordne_alphabetisch =
1.99 + append_rls "erls_ordne_alphabetisch" e_rls
1.100 + [Calc ("PolyMinus.kleiner", eval_kleiner ""),
1.101 + Calc ("PolyMinus.ist'_monom", eval_ist_monom "")
1.102 + ];
1.103 +
1.104 +val ordne_alphabetisch =
1.105 + Rls{id = "ordne_alphabetisch", preconds = [],
1.106 + rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],
1.107 + erls = erls_ordne_alphabetisch,
1.108 + rules = [Thm ("tausche_plus",num_str tausche_plus),
1.109 + (*"b kleiner a ==> (b + a) = (a + b)"*)
1.110 + Thm ("tausche_minus",num_str tausche_minus),
1.111 + (*"b kleiner a ==> (b - a) = (-a + b)"*)
1.112 + Thm ("tausche_vor_plus",num_str tausche_vor_plus),
1.113 + (*"[| b ist_monom; a kleiner b |] ==> (- b + a) = (a - b)"*)
1.114 + Thm ("tausche_vor_minus",num_str tausche_vor_minus),
1.115 + (*"[| b ist_monom; a kleiner b |] ==> (- b - a) = (-a - b)"*)
1.116 + Thm ("tausche_plus_plus",num_str tausche_plus_plus),
1.117 + (*"c kleiner b ==> (a + c + b) = (a + b + c)"*)
1.118 + Thm ("tausche_plus_minus",num_str tausche_plus_minus),
1.119 + (*"c kleiner b ==> (a + c - b) = (a - b + c)"*)
1.120 + Thm ("tausche_minus_plus",num_str tausche_minus_plus),
1.121 + (*"c kleiner b ==> (a - c + b) = (a + b - c)"*)
1.122 + Thm ("tausche_minus_minus",num_str tausche_minus_minus)
1.123 + (*"c kleiner b ==> (a - c - b) = (a - b - c)"*)
1.124 + ], scr = EmptyScr}:rls;
1.125 +
1.126 +val fasse_zusammen =
1.127 + Rls{id = "fasse_zusammen", preconds = [],
1.128 + rew_ord = ("dummy_ord", dummy_ord),
1.129 + erls = append_rls "erls_fasse_zusammen" e_rls
1.130 + [Calc ("Atools.is'_const",eval_const "#is_const_")],
1.131 + srls = Erls, calc = [],
1.132 + rules =
1.133 + [Thm ("real_num_collect",num_str real_num_collect),
1.134 + (*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
1.135 + Thm ("real_num_collect_assoc_r",num_str real_num_collect_assoc_r),
1.136 + (*"[| l is_const; m..|] ==> (k + m * n) + l * n = k + (l + m)*n"*)
1.137 + Thm ("real_one_collect",num_str real_one_collect),
1.138 + (*"m is_const ==> n + m * n = (1 + m) * n"*)
1.139 + Thm ("real_one_collect_assoc_r",num_str real_one_collect_assoc_r),
1.140 + (*"m is_const ==> (k + n) + m * n = k + (m + 1) * n"*)
1.141 +
1.142 +
1.143 + Thm ("subtrahiere",num_str subtrahiere),
1.144 + (*"[| l is_const; m is_const |] ==> m * v - l * v = (m - l) * v"*)
1.145 + Thm ("subtrahiere_von_1",num_str subtrahiere_von_1),
1.146 + (*"[| l is_const |] ==> v - l * v = (1 - l) * v"*)
1.147 + Thm ("subtrahiere_1",num_str subtrahiere_1),
1.148 + (*"[| l is_const; m is_const |] ==> m * v - v = (m - 1) * v"*)
1.149 +
1.150 + Thm ("subtrahiere_x_plus_minus",num_str subtrahiere_x_plus_minus),
1.151 + (*"[| l is_const; m..|] ==> (k + m * n) - l * n = k + ( m - l) * n"*)
1.152 + Thm ("subtrahiere_x_plus1_minus",num_str subtrahiere_x_plus1_minus),
1.153 + (*"[| l is_const |] ==> (x + v) - l * v = x + (1 - l) * v"*)
1.154 + Thm ("subtrahiere_x_plus_minus1",num_str subtrahiere_x_plus_minus1),
1.155 + (*"[| m is_const |] ==> (x + m * v) - v = x + (m - 1) * v"*)
1.156 +
1.157 + Thm ("subtrahiere_x_minus_plus",num_str subtrahiere_x_minus_plus),
1.158 + (*"[| l is_const; m..|] ==> (k - m * n) + l * n = k + (-m + l) * n"*)
1.159 + Thm ("subtrahiere_x_minus1_plus",num_str subtrahiere_x_minus1_plus),
1.160 + (*"[| l is_const |] ==> (x - v) + l * v = x + (-1 + l) * v"*)
1.161 + Thm ("subtrahiere_x_minus_plus1",num_str subtrahiere_x_minus_plus1),
1.162 + (*"[| m is_const |] ==> (x - m * v) + v = x + (-m + 1) * v"*)
1.163 +
1.164 + Thm ("subtrahiere_x_minus_minus",num_str subtrahiere_x_minus_minus),
1.165 + (*"[| l is_const; m..|] ==> (k - m * n) - l * n = k + (-m - l) * n"*)
1.166 + Thm ("subtrahiere_x_minus1_minus",num_str subtrahiere_x_minus1_minus),
1.167 + (*"[| l is_const |] ==> (x - v) - l * v = x + (-1 - l) * v"*)
1.168 + Thm ("subtrahiere_x_minus_minus1",num_str subtrahiere_x_minus_minus1),
1.169 + (*"[| m is_const |] ==> (x - m * v) - v = x + (-m - 1) * v"*)
1.170 +
1.171 + Calc ("op +", eval_binop "#add_"),
1.172 + Calc ("op -", eval_binop "#subtr_"),
1.173 +
1.174 + (*MG: Reihenfolge der folgenden 2 Thm muss so bleiben, wegen
1.175 + (a+a)+a --> a + 2*a --> 3*a and not (a+a)+a --> 2*a + a *)
1.176 + Thm ("real_mult_2_assoc_r",num_str real_mult_2_assoc_r),
1.177 + (*"(k + z1) + z1 = k + 2 * z1"*)
1.178 + Thm ("sym_real_mult_2",num_str (real_mult_2 RS sym)),
1.179 + (*"z1 + z1 = 2 * z1"*)
1.180 +
1.181 + Thm ("addiere_vor_minus",num_str addiere_vor_minus),
1.182 + (*"[| l is_const; m is_const |] ==> -(l * v) + m * v = (-l + m) *v"*)
1.183 + Thm ("addiere_eins_vor_minus",num_str addiere_eins_vor_minus),
1.184 + (*"[| m is_const |] ==> - v + m * v = (-1 + m) * v"*)
1.185 + Thm ("subtrahiere_vor_minus",num_str subtrahiere_vor_minus),
1.186 + (*"[| l is_const; m is_const |] ==> -(l * v) - m * v = (-l - m) *v"*)
1.187 + Thm ("subtrahiere_eins_vor_minus",num_str subtrahiere_eins_vor_minus)
1.188 + (*"[| m is_const |] ==> - v - m * v = (-1 - m) * v"*)
1.189 +
1.190 + ], scr = EmptyScr}:rls;
1.191 +
1.192 +val verschoenere =
1.193 + Rls{id = "verschoenere", preconds = [],
1.194 + rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],
1.195 + erls = append_rls "erls_verschoenere" e_rls
1.196 + [Calc ("PolyMinus.kleiner", eval_kleiner "")],
1.197 + rules = [Thm ("vorzeichen_minus_weg1",num_str vorzeichen_minus_weg1),
1.198 + (*"l kleiner 0 ==> a + l * b = a - -l * b"*)
1.199 + Thm ("vorzeichen_minus_weg2",num_str vorzeichen_minus_weg2),
1.200 + (*"l kleiner 0 ==> a - l * b = a + -l * b"*)
1.201 + Thm ("vorzeichen_minus_weg3",num_str vorzeichen_minus_weg3),
1.202 + (*"l kleiner 0 ==> k + a - l * b = k + a + -l * b"*)
1.203 + Thm ("vorzeichen_minus_weg4",num_str vorzeichen_minus_weg4),
1.204 + (*"l kleiner 0 ==> k - a - l * b = k - a + -l * b"*)
1.205 +
1.206 + Calc ("op *", eval_binop "#mult_"),
1.207 +
1.208 + Thm ("real_mult_0",num_str real_mult_0),
1.209 + (*"0 * z = 0"*)
1.210 + Thm ("real_mult_1",num_str real_mult_1),
1.211 + (*"1 * z = z"*)
1.212 + Thm ("real_add_zero_left",num_str real_add_zero_left),
1.213 + (*"0 + z = z"*)
1.214 + Thm ("null_minus",num_str null_minus),
1.215 + (*"0 - a = -a"*)
1.216 + Thm ("vor_minus_mal",num_str vor_minus_mal)
1.217 + (*"- a * b = (-a) * b"*)
1.218 +
1.219 + (*Thm ("",num_str ),*)
1.220 + (**)
1.221 + ], scr = EmptyScr}:rls (*end verschoenere*);
1.222 +
1.223 +val klammern_aufloesen =
1.224 + Rls{id = "klammern_aufloesen", preconds = [],
1.225 + rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], erls = Erls,
1.226 + rules = [Thm ("sym_real_add_assoc",num_str (real_add_assoc RS sym)),
1.227 + (*"a + (b + c) = (a + b) + c"*)
1.228 + Thm ("klammer_plus_minus",num_str klammer_plus_minus),
1.229 + (*"a + (b - c) = (a + b) - c"*)
1.230 + Thm ("klammer_minus_plus",num_str klammer_minus_plus),
1.231 + (*"a - (b + c) = (a - b) - c"*)
1.232 + Thm ("klammer_minus_minus",num_str klammer_minus_minus)
1.233 + (*"a - (b - c) = (a - b) + c"*)
1.234 + ], scr = EmptyScr}:rls;
1.235 +
1.236 +val klammern_ausmultiplizieren =
1.237 + Rls{id = "klammern_ausmultiplizieren", preconds = [],
1.238 + rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [], erls = Erls,
1.239 + rules = [Thm ("real_add_mult_distrib" ,num_str real_add_mult_distrib),
1.240 + (*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
1.241 + Thm ("real_add_mult_distrib2",num_str real_add_mult_distrib2),
1.242 + (*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
1.243 +
1.244 + Thm ("klammer_mult_minus",num_str klammer_mult_minus),
1.245 + (*"a * (b - c) = a * b - a * c"*)
1.246 + Thm ("klammer_minus_mult",num_str klammer_minus_mult)
1.247 + (*"(b - c) * a = b * a - c * a"*)
1.248 +
1.249 + (*Thm ("",num_str ),
1.250 + (*""*)*)
1.251 + ], scr = EmptyScr}:rls;
1.252 +
1.253 +val ordne_monome =
1.254 + Rls{id = "ordne_monome", preconds = [],
1.255 + rew_ord = ("dummy_ord", dummy_ord), srls = Erls, calc = [],
1.256 + erls = append_rls "erls_ordne_monome" e_rls
1.257 + [Calc ("PolyMinus.kleiner", eval_kleiner ""),
1.258 + Calc ("Atools.is'_atom", eval_is_atom "")
1.259 + ],
1.260 + rules = [Thm ("tausche_mal",num_str tausche_mal),
1.261 + (*"[| b is_atom; a kleiner b |] ==> (b * a) = (a * b)"*)
1.262 + Thm ("tausche_vor_mal",num_str tausche_vor_mal),
1.263 + (*"[| b is_atom; a kleiner b |] ==> (-b * a) = (-a * b)"*)
1.264 + Thm ("tausche_mal_mal",num_str tausche_mal_mal),
1.265 + (*"[| c is_atom; b kleiner c |] ==> (a * c * b) = (a * b *c)"*)
1.266 + Thm ("x_quadrat",num_str x_quadrat)
1.267 + (*"(x * a) * a = x * a ^^^ 2"*)
1.268 +
1.269 + (*Thm ("",num_str ),
1.270 + (*""*)*)
1.271 + ], scr = EmptyScr}:rls;
1.272 +
1.273 +
1.274 +val rls_p_33 =
1.275 + append_rls "rls_p_33" e_rls
1.276 + [Rls_ ordne_alphabetisch,
1.277 + Rls_ fasse_zusammen,
1.278 + Rls_ verschoenere
1.279 + ];
1.280 +val rls_p_34 =
1.281 + append_rls "rls_p_34" e_rls
1.282 + [Rls_ klammern_aufloesen,
1.283 + Rls_ ordne_alphabetisch,
1.284 + Rls_ fasse_zusammen,
1.285 + Rls_ verschoenere
1.286 + ];
1.287 +val rechnen =
1.288 + append_rls "rechnen" e_rls
1.289 + [Calc ("op *", eval_binop "#mult_"),
1.290 + Calc ("op +", eval_binop "#add_"),
1.291 + Calc ("op -", eval_binop "#subtr_")
1.292 + ];
1.293 +
1.294 +ruleset' :=
1.295 +overwritelthy thy (!ruleset',
1.296 + [("ordne_alphabetisch", prep_rls ordne_alphabetisch),
1.297 + ("fasse_zusammen", prep_rls fasse_zusammen),
1.298 + ("verschoenere", prep_rls verschoenere),
1.299 + ("ordne_monome", prep_rls ordne_monome),
1.300 + ("klammern_aufloesen", prep_rls klammern_aufloesen),
1.301 + ("klammern_ausmultiplizieren",
1.302 + prep_rls klammern_ausmultiplizieren)
1.303 + ]);
1.304 +
1.305 +(** problems **)
1.306 +
1.307 +store_pbt
1.308 + (prep_pbt PolyMinus.thy "pbl_vereinf_poly" [] e_pblID
1.309 + (["polynom","vereinfachen"],
1.310 + [], Erls, NONE, []));
1.311 +
1.312 +store_pbt
1.313 + (prep_pbt PolyMinus.thy "pbl_vereinf_poly_minus" [] e_pblID
1.314 + (["plus_minus","polynom","vereinfachen"],
1.315 + [("#Given" ,["term t_"]),
1.316 + ("#Where" ,["t_ is_polyexp",
1.317 + "Not (matchsub (?a + (?b + ?c)) t_ | \
1.318 + \ matchsub (?a + (?b - ?c)) t_ | \
1.319 + \ matchsub (?a - (?b + ?c)) t_ | \
1.320 + \ matchsub (?a + (?b - ?c)) t_ )",
1.321 + "Not (matchsub (?a * (?b + ?c)) t_ | \
1.322 + \ matchsub (?a * (?b - ?c)) t_ | \
1.323 + \ matchsub ((?b + ?c) * ?a) t_ | \
1.324 + \ matchsub ((?b - ?c) * ?a) t_ )"]),
1.325 + ("#Find" ,["normalform n_"])
1.326 + ],
1.327 + append_rls "prls_pbl_vereinf_poly" e_rls
1.328 + [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
1.329 + Calc ("Tools.matchsub", eval_matchsub ""),
1.330 + Thm ("or_true",or_true),
1.331 + (*"(?a | True) = True"*)
1.332 + Thm ("or_false",or_false),
1.333 + (*"(?a | False) = ?a"*)
1.334 + Thm ("not_true",num_str not_true),
1.335 + (*"(~ True) = False"*)
1.336 + Thm ("not_false",num_str not_false)
1.337 + (*"(~ False) = True"*)],
1.338 + SOME "Vereinfache t_",
1.339 + [["simplification","for_polynomials","with_minus"]]));
1.340 +
1.341 +store_pbt
1.342 + (prep_pbt PolyMinus.thy "pbl_vereinf_poly_klammer" [] e_pblID
1.343 + (["klammer","polynom","vereinfachen"],
1.344 + [("#Given" ,["term t_"]),
1.345 + ("#Where" ,["t_ is_polyexp",
1.346 + "Not (matchsub (?a * (?b + ?c)) t_ | \
1.347 + \ matchsub (?a * (?b - ?c)) t_ | \
1.348 + \ matchsub ((?b + ?c) * ?a) t_ | \
1.349 + \ matchsub ((?b - ?c) * ?a) t_ )"]),
1.350 + ("#Find" ,["normalform n_"])
1.351 + ],
1.352 + append_rls "prls_pbl_vereinf_poly_klammer" e_rls [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
1.353 + Calc ("Tools.matchsub", eval_matchsub ""),
1.354 + Thm ("or_true",or_true),
1.355 + (*"(?a | True) = True"*)
1.356 + Thm ("or_false",or_false),
1.357 + (*"(?a | False) = ?a"*)
1.358 + Thm ("not_true",num_str not_true),
1.359 + (*"(~ True) = False"*)
1.360 + Thm ("not_false",num_str not_false)
1.361 + (*"(~ False) = True"*)],
1.362 + SOME "Vereinfache t_",
1.363 + [["simplification","for_polynomials","with_parentheses"]]));
1.364 +
1.365 +store_pbt
1.366 + (prep_pbt PolyMinus.thy "pbl_vereinf_poly_klammer_mal" [] e_pblID
1.367 + (["binom_klammer","polynom","vereinfachen"],
1.368 + [("#Given" ,["term t_"]),
1.369 + ("#Where" ,["t_ is_polyexp"]),
1.370 + ("#Find" ,["normalform n_"])
1.371 + ],
1.372 + append_rls "e_rls" e_rls [(*for preds in where_*)
1.373 + Calc ("Poly.is'_polyexp", eval_is_polyexp "")],
1.374 + SOME "Vereinfache t_",
1.375 + [["simplification","for_polynomials","with_parentheses_mult"]]));
1.376 +
1.377 +store_pbt
1.378 + (prep_pbt PolyMinus.thy "pbl_probe" [] e_pblID
1.379 + (["probe"],
1.380 + [], Erls, NONE, []));
1.381 +
1.382 +store_pbt
1.383 + (prep_pbt PolyMinus.thy "pbl_probe_poly" [] e_pblID
1.384 + (["polynom","probe"],
1.385 + [("#Given" ,["Pruefe e_", "mitWert ws_"]),
1.386 + ("#Where" ,["e_ is_polyexp"]),
1.387 + ("#Find" ,["Geprueft p_"])
1.388 + ],
1.389 + append_rls "prls_pbl_probe_poly"
1.390 + e_rls [(*for preds in where_*)
1.391 + Calc ("Poly.is'_polyexp", eval_is_polyexp "")],
1.392 + SOME "Probe e_ ws_",
1.393 + [["probe","fuer_polynom"]]));
1.394 +
1.395 +store_pbt
1.396 + (prep_pbt PolyMinus.thy "pbl_probe_bruch" [] e_pblID
1.397 + (["bruch","probe"],
1.398 + [("#Given" ,["Pruefe e_", "mitWert ws_"]),
1.399 + ("#Where" ,["e_ is_ratpolyexp"]),
1.400 + ("#Find" ,["Geprueft p_"])
1.401 + ],
1.402 + append_rls "prls_pbl_probe_bruch"
1.403 + e_rls [(*for preds in where_*)
1.404 + Calc ("Rational.is'_ratpolyexp", eval_is_ratpolyexp "")],
1.405 + SOME "Probe e_ ws_",
1.406 + [["probe","fuer_bruch"]]));
1.407 +
1.408 +
1.409 +(** methods **)
1.410 +
1.411 +store_met
1.412 + (prep_met PolyMinus.thy "met_simp_poly_minus" [] e_metID
1.413 + (["simplification","for_polynomials","with_minus"],
1.414 + [("#Given" ,["term t_"]),
1.415 + ("#Where" ,["t_ is_polyexp",
1.416 + "Not (matchsub (?a + (?b + ?c)) t_ | \
1.417 + \ matchsub (?a + (?b - ?c)) t_ | \
1.418 + \ matchsub (?a - (?b + ?c)) t_ | \
1.419 + \ matchsub (?a + (?b - ?c)) t_ )"]),
1.420 + ("#Find" ,["normalform n_"])
1.421 + ],
1.422 + {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
1.423 + prls = append_rls "prls_met_simp_poly_minus" e_rls
1.424 + [Calc ("Poly.is'_polyexp", eval_is_polyexp ""),
1.425 + Calc ("Tools.matchsub", eval_matchsub ""),
1.426 + Thm ("and_true",and_true),
1.427 + (*"(?a & True) = ?a"*)
1.428 + Thm ("and_false",and_false),
1.429 + (*"(?a & False) = False"*)
1.430 + Thm ("not_true",num_str not_true),
1.431 + (*"(~ True) = False"*)
1.432 + Thm ("not_false",num_str not_false)
1.433 + (*"(~ False) = True"*)],
1.434 + crls = e_rls, nrls = rls_p_33},
1.435 +"Script SimplifyScript (t_::real) = \
1.436 +\ ((Repeat((Try (Rewrite_Set ordne_alphabetisch False)) @@ \
1.437 +\ (Try (Rewrite_Set fasse_zusammen False)) @@ \
1.438 +\ (Try (Rewrite_Set verschoenere False)))) t_)"
1.439 + ));
1.440 +
1.441 +store_met
1.442 + (prep_met PolyMinus.thy "met_simp_poly_parenth" [] e_metID
1.443 + (["simplification","for_polynomials","with_parentheses"],
1.444 + [("#Given" ,["term t_"]),
1.445 + ("#Where" ,["t_ is_polyexp"]),
1.446 + ("#Find" ,["normalform n_"])
1.447 + ],
1.448 + {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
1.449 + prls = append_rls "simplification_for_polynomials_prls" e_rls
1.450 + [(*for preds in where_*)
1.451 + Calc("Poly.is'_polyexp",eval_is_polyexp"")],
1.452 + crls = e_rls, nrls = rls_p_34},
1.453 +"Script SimplifyScript (t_::real) = \
1.454 +\ ((Repeat((Try (Rewrite_Set klammern_aufloesen False)) @@ \
1.455 +\ (Try (Rewrite_Set ordne_alphabetisch False)) @@ \
1.456 +\ (Try (Rewrite_Set fasse_zusammen False)) @@ \
1.457 +\ (Try (Rewrite_Set verschoenere False)))) t_)"
1.458 + ));
1.459 +
1.460 +store_met
1.461 + (prep_met PolyMinus.thy "met_simp_poly_parenth_mult" [] e_metID
1.462 + (["simplification","for_polynomials","with_parentheses_mult"],
1.463 + [("#Given" ,["term t_"]),
1.464 + ("#Where" ,["t_ is_polyexp"]),
1.465 + ("#Find" ,["normalform n_"])
1.466 + ],
1.467 + {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
1.468 + prls = append_rls "simplification_for_polynomials_prls" e_rls
1.469 + [(*for preds in where_*)
1.470 + Calc("Poly.is'_polyexp",eval_is_polyexp"")],
1.471 + crls = e_rls, nrls = rls_p_34},
1.472 +"Script SimplifyScript (t_::real) = \
1.473 +\ ((Repeat((Try (Rewrite_Set klammern_ausmultiplizieren False)) @@ \
1.474 +\ (Try (Rewrite_Set discard_parentheses False)) @@ \
1.475 +\ (Try (Rewrite_Set ordne_monome False)) @@ \
1.476 +\ (Try (Rewrite_Set klammern_aufloesen False)) @@ \
1.477 +\ (Try (Rewrite_Set ordne_alphabetisch False)) @@ \
1.478 +\ (Try (Rewrite_Set fasse_zusammen False)) @@ \
1.479 +\ (Try (Rewrite_Set verschoenere False)))) t_)"
1.480 + ));
1.481 +
1.482 +store_met
1.483 + (prep_met PolyMinus.thy "met_probe" [] e_metID
1.484 + (["probe"],
1.485 + [],
1.486 + {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
1.487 + prls = Erls, crls = e_rls, nrls = Erls},
1.488 + "empty_script"));
1.489 +
1.490 +store_met
1.491 + (prep_met PolyMinus.thy "met_probe_poly" [] e_metID
1.492 + (["probe","fuer_polynom"],
1.493 + [("#Given" ,["Pruefe e_", "mitWert ws_"]),
1.494 + ("#Where" ,["e_ is_polyexp"]),
1.495 + ("#Find" ,["Geprueft p_"])
1.496 + ],
1.497 + {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
1.498 + prls = append_rls "prls_met_probe_bruch"
1.499 + e_rls [(*for preds in where_*)
1.500 + Calc ("Rational.is'_ratpolyexp",
1.501 + eval_is_ratpolyexp "")],
1.502 + crls = e_rls, nrls = rechnen},
1.503 +"Script ProbeScript (e_::bool) (ws_::bool list) = \
1.504 +\ (let e_ = Take e_; \
1.505 +\ e_ = Substitute ws_ e_ \
1.506 +\ in (Repeat((Try (Repeat (Calculate times))) @@ \
1.507 +\ (Try (Repeat (Calculate plus ))) @@ \
1.508 +\ (Try (Repeat (Calculate minus))))) e_)"
1.509 +));
1.510 +
1.511 +store_met
1.512 + (prep_met PolyMinus.thy "met_probe_bruch" [] e_metID
1.513 + (["probe","fuer_bruch"],
1.514 + [("#Given" ,["Pruefe e_", "mitWert ws_"]),
1.515 + ("#Where" ,["e_ is_ratpolyexp"]),
1.516 + ("#Find" ,["Geprueft p_"])
1.517 + ],
1.518 + {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
1.519 + prls = append_rls "prls_met_probe_bruch"
1.520 + e_rls [(*for preds in where_*)
1.521 + Calc ("Rational.is'_ratpolyexp",
1.522 + eval_is_ratpolyexp "")],
1.523 + crls = e_rls, nrls = Erls},
1.524 + "empty_script"));