1 (* attempts to perserve binary minus as wanted by Austrian teachers
3 (c) due to copyright terms
6 theory PolyMinus imports (*Poly// due to "is_ratpolyexp" in...*) Rational begin
10 (*predicates for conditions in rewriting*)
11 kleiner :: "['a, 'a] => bool" ("_ kleiner _")
12 ist_monom :: "'a => bool" ("_ ist'_monom")
15 Probe :: "[bool, bool list] => bool"
16 (*"Probe (3*a+2*b+a = 4*a+2*b) [a=1,b=2]"*)
18 (*descriptions for the pbl and met*)
19 Pruefe :: "bool => una"
20 mitWert :: "bool list => tobooll"
21 Geprueft :: "bool => una"
25 null_minus: "0 - a = -a" and
26 vor_minus_mal: "- a * b = (-a) * b" and
28 (*commute with invariant (a.b).c -association*)
29 tausche_plus: "[| b ist_monom; a kleiner b |] ==>
30 (b + a) = (a + b)" and
31 tausche_minus: "[| b ist_monom; a kleiner b |] ==>
32 (b - a) = (-a + b)" and
33 tausche_vor_plus: "[| b ist_monom; a kleiner b |] ==>
34 (- b + a) = (a - b)" and
35 tausche_vor_minus: "[| b ist_monom; a kleiner b |] ==>
36 (- b - a) = (-a - b)" and
37 (*Ambiguous input\<^here> produces 3 parse trees -----------------------------\\*)
38 tausche_plus_plus: "b kleiner c ==> (a + c + b) = (a + b + c)" and
39 tausche_plus_minus: "b kleiner c ==> (a + c - b) = (a - b + c)" and
40 tausche_minus_plus: "b kleiner c ==> (a - c + b) = (a + b - c)" and
41 tausche_minus_minus: "b kleiner c ==> (a - c - b) = (a - b - c)" and
42 (*Ambiguous input\<^here> produces 3 parse trees -----------------------------//*)
44 (*commute with invariant (a.b).c -association*)
45 tausche_mal: "[| b is_atom; a kleiner b |] ==>
46 (b * a) = (a * b)" and
47 tausche_vor_mal: "[| b is_atom; a kleiner b |] ==>
48 (-b * a) = (-a * b)" and
49 tausche_mal_mal: "[| c is_atom; b kleiner c |] ==>
50 (x * c * b) = (x * b * c)" and
51 x_quadrat: "(x * a) * a = x * a \<up> 2" and
54 subtrahiere: "[| l is_const; m is_const |] ==>
55 m * v - l * v = (m - l) * v" and
56 subtrahiere_von_1: "[| l is_const |] ==>
57 v - l * v = (1 - l) * v" and
58 subtrahiere_1: "[| l is_const; m is_const |] ==>
59 m * v - v = (m - 1) * v" and
61 subtrahiere_x_plus_minus: "[| l is_const; m is_const |] ==>
62 (x + m * v) - l * v = x + (m - l) * v" and
63 subtrahiere_x_plus1_minus: "[| l is_const |] ==>
64 (x + v) - l * v = x + (1 - l) * v" and
65 subtrahiere_x_plus_minus1: "[| m is_const |] ==>
66 (x + m * v) - v = x + (m - 1) * v" and
68 subtrahiere_x_minus_plus: "[| l is_const; m is_const |] ==>
69 (x - m * v) + l * v = x + (-m + l) * v" and
70 subtrahiere_x_minus1_plus: "[| l is_const |] ==>
71 (x - v) + l * v = x + (-1 + l) * v" and
72 subtrahiere_x_minus_plus1: "[| m is_const |] ==>
73 (x - m * v) + v = x + (-m + 1) * v" and
75 subtrahiere_x_minus_minus: "[| l is_const; m is_const |] ==>
76 (x - m * v) - l * v = x + (-m - l) * v" and
77 subtrahiere_x_minus1_minus:"[| l is_const |] ==>
78 (x - v) - l * v = x + (-1 - l) * v" and
79 subtrahiere_x_minus_minus1:"[| m is_const |] ==>
80 (x - m * v) - v = x + (-m - 1) * v" and
83 addiere_vor_minus: "[| l is_const; m is_const |] ==>
84 - (l * v) + m * v = (-l + m) * v" and
85 addiere_eins_vor_minus: "[| m is_const |] ==>
86 - v + m * v = (-1 + m) * v" and
87 subtrahiere_vor_minus: "[| l is_const; m is_const |] ==>
88 - (l * v) - m * v = (-l - m) * v" and
89 subtrahiere_eins_vor_minus:"[| m is_const |] ==>
90 - v - m * v = (-1 - m) * v" and
92 (*Ambiguous input\<^here> produces 3 parse trees -----------------------------\\*)
93 vorzeichen_minus_weg1: "l kleiner 0 ==> a + l * b = a - -1*l * b" and
94 vorzeichen_minus_weg2: "l kleiner 0 ==> a - l * b = a + -1*l * b" and
95 vorzeichen_minus_weg3: "l kleiner 0 ==> k + a - l * b = k + a + -1*l * b" and
96 vorzeichen_minus_weg4: "l kleiner 0 ==> k - a - l * b = k - a + -1*l * b" and
97 (*Ambiguous input\<^here> produces 3 parse trees -----------------------------//*)
99 (*klammer_plus_plus = (add.assoc RS sym)*)
100 klammer_plus_minus: "a + (b - c) = (a + b) - c" and
101 klammer_minus_plus: "a - (b + c) = (a - b) - c" and
102 klammer_minus_minus: "a - (b - c) = (a - b) + c" and
104 klammer_mult_minus: "a * (b - c) = a * b - a * c" and
105 klammer_minus_mult: "(b - c) * a = b * a - c * a"
110 (** eval functions **)
112 (*. get the identifier from specific monomials; see fun ist_monom .*)
117 case Symbol.explode str of
119 | _ => raise ERROR "PolyMinus.increase: uncovered case"
120 in implode ((chr (ord s + 1))::ss) end;
121 fun identifier (Free (id,_)) = id (* 2 , a *)
122 | identifier (Const ("Groups.times_class.times", _) $ Free (_(*num*), _) $ Free (id, _)) =
124 | identifier (Const ("Groups.times_class.times", _) $ (* 3*a*b *)
125 (Const ("Groups.times_class.times", _) $
126 Free (num, _) $ Free _) $ Free (id, _)) =
127 if TermC.is_num' num then id
129 | identifier (Const ("Transcendental.powr", _) $ Free (base, _) $ Free (_(*exp*), _)) =
130 if TermC.is_num' base then "|||||||||||||" (* a^2 *)
131 else (*increase*) base
132 | identifier (Const ("Groups.times_class.times", _) $ Free (num, _) $ (* 3*a^2 *)
133 (Const ("Transcendental.powr", _) $
134 Free (base, _) $ Free (_(*exp*), _))) =
135 if TermC.is_num' num andalso not (TermC.is_num' base) then (*increase*) base
137 | identifier _ = "|||||||||||||"(*the "largest" string*);
139 (*("kleiner", ("PolyMinus.kleiner", eval_kleiner ""))*)
140 (* order "by alphabet" w.r.t. var: num < (var | num*var) > (var*var | ..) *)
141 fun eval_kleiner _ _ (p as (Const ("PolyMinus.kleiner",_) $ a $ b)) _ =
142 if TermC.is_num b then
143 if TermC.is_num a then (*123 kleiner 32 = True !!!*)
144 if TermC.num_of_term a < TermC.num_of_term b then
145 SOME ((UnparseC.term p) ^ " = True",
146 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
147 else SOME ((UnparseC.term p) ^ " = False",
148 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
149 else (* -1 * -2 kleiner 0 *)
150 SOME ((UnparseC.term p) ^ " = False",
151 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
153 if identifier a < identifier b then
154 SOME ((UnparseC.term p) ^ " = True",
155 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
156 else SOME ((UnparseC.term p) ^ " = False",
157 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
158 | eval_kleiner _ _ _ _ = NONE;
160 fun ist_monom (Free _) = true (* 2, a *)
161 | ist_monom (Const ("Groups.times_class.times", _) $
162 (Const ("Num.numeral_class.numeral", _) $ _) $ Free _) = true
163 | ist_monom (Const ("Groups.times_class.times", _) $ (* 2*a, a*b *)
164 Free _ $ (Const ("Num.numeral_class.numeral", _) $ _)) = false
165 | ist_monom (Const ("Groups.times_class.times", _) $ (* 3*a*b *)
166 (Const ("Groups.times_class.times", _) $
167 (Const ("Num.numeral_class.numeral", _) $ _) $ Free _) $ Free _) = true
168 | ist_monom (Const ("Transcendental.powr", _) $ (* a^2 *)
169 Free _ $ (Const ("Num.numeral_class.numeral", _) $ _)) = true
170 | ist_monom (Const ("Groups.times_class.times", _) $ (* 3*a^2 *)
171 (Const ("Num.numeral_class.numeral", _) $ _) $
172 (Const ("Transcendental.powr", _) $ Free _ $ Free _)) = true
173 | ist_monom _ = false;
175 (* is this a univariate monomial ? *)
176 (*("ist_monom", ("PolyMinus.ist_monom", eval_ist_monom ""))*)
177 fun eval_ist_monom _ _ (p as (Const ("PolyMinus.ist_monom",_) $ a)) _ =
179 SOME ((UnparseC.term p) ^ " = True",
180 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
181 else SOME ((UnparseC.term p) ^ " = False",
182 HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
183 | eval_ist_monom _ _ _ _ = NONE;
186 (** rewrite order **)
190 val erls_ordne_alphabetisch =
191 Rule_Set.append_rules "erls_ordne_alphabetisch" Rule_Set.empty
192 [Rule.Eval ("PolyMinus.kleiner", eval_kleiner ""),
193 Rule.Eval ("PolyMinus.ist_monom", eval_ist_monom "")
196 val ordne_alphabetisch =
197 Rule_Def.Repeat{id = "ordne_alphabetisch", preconds = [],
198 rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), srls = Rule_Set.Empty, calc = [], errpatts = [],
199 erls = erls_ordne_alphabetisch,
200 rules = [Rule.Thm ("tausche_plus",ThmC.numerals_to_Free @{thm tausche_plus}),
201 (*"b kleiner a ==> (b + a) = (a + b)"*)
202 Rule.Thm ("tausche_minus",ThmC.numerals_to_Free @{thm tausche_minus}),
203 (*"b kleiner a ==> (b - a) = (-a + b)"*)
204 Rule.Thm ("tausche_vor_plus",ThmC.numerals_to_Free @{thm tausche_vor_plus}),
205 (*"[| b ist_monom; a kleiner b |] ==> (- b + a) = (a - b)"*)
206 Rule.Thm ("tausche_vor_minus",ThmC.numerals_to_Free @{thm tausche_vor_minus}),
207 (*"[| b ist_monom; a kleiner b |] ==> (- b - a) = (-a - b)"*)
208 Rule.Thm ("tausche_plus_plus",ThmC.numerals_to_Free @{thm tausche_plus_plus}),
209 (*"c kleiner b ==> (a + c + b) = (a + b + c)"*)
210 Rule.Thm ("tausche_plus_minus",ThmC.numerals_to_Free @{thm tausche_plus_minus}),
211 (*"c kleiner b ==> (a + c - b) = (a - b + c)"*)
212 Rule.Thm ("tausche_minus_plus",ThmC.numerals_to_Free @{thm tausche_minus_plus}),
213 (*"c kleiner b ==> (a - c + b) = (a + b - c)"*)
214 Rule.Thm ("tausche_minus_minus",ThmC.numerals_to_Free @{thm tausche_minus_minus})
215 (*"c kleiner b ==> (a - c - b) = (a - b - c)"*)
216 ], scr = Rule.Empty_Prog};
219 Rule_Def.Repeat{id = "fasse_zusammen", preconds = [],
220 rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
221 erls = Rule_Set.append_rules "erls_fasse_zusammen" Rule_Set.empty
222 [Rule.Eval ("Prog_Expr.is_const", Prog_Expr.eval_const "#is_const_")],
223 srls = Rule_Set.Empty, calc = [], errpatts = [],
225 [Rule.Thm ("real_num_collect",ThmC.numerals_to_Free @{thm real_num_collect}),
226 (*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
227 Rule.Thm ("real_num_collect_assoc_r",ThmC.numerals_to_Free @{thm real_num_collect_assoc_r}),
228 (*"[| l is_const; m..|] ==> (k + m * n) + l * n = k + (l + m)*n"*)
229 Rule.Thm ("real_one_collect",ThmC.numerals_to_Free @{thm real_one_collect}),
230 (*"m is_const ==> n + m * n = (1 + m) * n"*)
231 Rule.Thm ("real_one_collect_assoc_r",ThmC.numerals_to_Free @{thm real_one_collect_assoc_r}),
232 (*"m is_const ==> (k + n) + m * n = k + (m + 1) * n"*)
235 Rule.Thm ("subtrahiere",ThmC.numerals_to_Free @{thm subtrahiere}),
236 (*"[| l is_const; m is_const |] ==> m * v - l * v = (m - l) * v"*)
237 Rule.Thm ("subtrahiere_von_1",ThmC.numerals_to_Free @{thm subtrahiere_von_1}),
238 (*"[| l is_const |] ==> v - l * v = (1 - l) * v"*)
239 Rule.Thm ("subtrahiere_1",ThmC.numerals_to_Free @{thm subtrahiere_1}),
240 (*"[| l is_const; m is_const |] ==> m * v - v = (m - 1) * v"*)
242 Rule.Thm ("subtrahiere_x_plus_minus",ThmC.numerals_to_Free @{thm subtrahiere_x_plus_minus}),
243 (*"[| l is_const; m..|] ==> (k + m * n) - l * n = k + ( m - l) * n"*)
244 Rule.Thm ("subtrahiere_x_plus1_minus",ThmC.numerals_to_Free @{thm subtrahiere_x_plus1_minus}),
245 (*"[| l is_const |] ==> (x + v) - l * v = x + (1 - l) * v"*)
246 Rule.Thm ("subtrahiere_x_plus_minus1",ThmC.numerals_to_Free @{thm subtrahiere_x_plus_minus1}),
247 (*"[| m is_const |] ==> (x + m * v) - v = x + (m - 1) * v"*)
249 Rule.Thm ("subtrahiere_x_minus_plus",ThmC.numerals_to_Free @{thm subtrahiere_x_minus_plus}),
250 (*"[| l is_const; m..|] ==> (k - m * n) + l * n = k + (-m + l) * n"*)
251 Rule.Thm ("subtrahiere_x_minus1_plus",ThmC.numerals_to_Free @{thm subtrahiere_x_minus1_plus}),
252 (*"[| l is_const |] ==> (x - v) + l * v = x + (-1 + l) * v"*)
253 Rule.Thm ("subtrahiere_x_minus_plus1",ThmC.numerals_to_Free @{thm subtrahiere_x_minus_plus1}),
254 (*"[| m is_const |] ==> (x - m * v) + v = x + (-m + 1) * v"*)
256 Rule.Thm ("subtrahiere_x_minus_minus",ThmC.numerals_to_Free @{thm subtrahiere_x_minus_minus}),
257 (*"[| l is_const; m..|] ==> (k - m * n) - l * n = k + (-m - l) * n"*)
258 Rule.Thm ("subtrahiere_x_minus1_minus",ThmC.numerals_to_Free @{thm subtrahiere_x_minus1_minus}),
259 (*"[| l is_const |] ==> (x - v) - l * v = x + (-1 - l) * v"*)
260 Rule.Thm ("subtrahiere_x_minus_minus1",ThmC.numerals_to_Free @{thm subtrahiere_x_minus_minus1}),
261 (*"[| m is_const |] ==> (x - m * v) - v = x + (-m - 1) * v"*)
263 Rule.Eval ("Groups.plus_class.plus", (**)eval_binop "#add_"),
264 Rule.Eval ("Groups.minus_class.minus", (**)eval_binop "#subtr_"),
266 (*MG: Reihenfolge der folgenden 2 Rule.Thm muss so bleiben, wegen
267 (a+a)+a --> a + 2*a --> 3*a and not (a+a)+a --> 2*a + a *)
268 Rule.Thm ("real_mult_2_assoc_r",ThmC.numerals_to_Free @{thm real_mult_2_assoc_r}),
269 (*"(k + z1) + z1 = k + 2 * z1"*)
270 Rule.Thm ("sym_real_mult_2",ThmC.numerals_to_Free (@{thm real_mult_2} RS @{thm sym})),
271 (*"z1 + z1 = 2 * z1"*)
273 Rule.Thm ("addiere_vor_minus",ThmC.numerals_to_Free @{thm addiere_vor_minus}),
274 (*"[| l is_const; m is_const |] ==> -(l * v) + m * v = (-l + m) *v"*)
275 Rule.Thm ("addiere_eins_vor_minus",ThmC.numerals_to_Free @{thm addiere_eins_vor_minus}),
276 (*"[| m is_const |] ==> - v + m * v = (-1 + m) * v"*)
277 Rule.Thm ("subtrahiere_vor_minus",ThmC.numerals_to_Free @{thm subtrahiere_vor_minus}),
278 (*"[| l is_const; m is_const |] ==> -(l * v) - m * v = (-l - m) *v"*)
279 Rule.Thm ("subtrahiere_eins_vor_minus",ThmC.numerals_to_Free @{thm subtrahiere_eins_vor_minus})
280 (*"[| m is_const |] ==> - v - m * v = (-1 - m) * v"*)
282 ], scr = Rule.Empty_Prog};
285 Rule_Def.Repeat{id = "verschoenere", preconds = [],
286 rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), srls = Rule_Set.Empty, calc = [], errpatts = [],
287 erls = Rule_Set.append_rules "erls_verschoenere" Rule_Set.empty
288 [Rule.Eval ("PolyMinus.kleiner", eval_kleiner "")],
289 rules = [Rule.Thm ("vorzeichen_minus_weg1",ThmC.numerals_to_Free @{thm vorzeichen_minus_weg1}),
290 (*"l kleiner 0 ==> a + l * b = a - -l * b"*)
291 Rule.Thm ("vorzeichen_minus_weg2",ThmC.numerals_to_Free @{thm vorzeichen_minus_weg2}),
292 (*"l kleiner 0 ==> a - l * b = a + -l * b"*)
293 Rule.Thm ("vorzeichen_minus_weg3",ThmC.numerals_to_Free @{thm vorzeichen_minus_weg3}),
294 (*"l kleiner 0 ==> k + a - l * b = k + a + -l * b"*)
295 Rule.Thm ("vorzeichen_minus_weg4",ThmC.numerals_to_Free @{thm vorzeichen_minus_weg4}),
296 (*"l kleiner 0 ==> k - a - l * b = k - a + -l * b"*)
298 Rule.Eval ("Groups.times_class.times", (**)eval_binop "#mult_"),
300 Rule.Thm ("mult_zero_left",ThmC.numerals_to_Free @{thm mult_zero_left}),
302 Rule.Thm ("mult_1_left",ThmC.numerals_to_Free @{thm mult_1_left}),
304 Rule.Thm ("add_0_left",ThmC.numerals_to_Free @{thm add_0_left}),
306 Rule.Thm ("null_minus",ThmC.numerals_to_Free @{thm null_minus}),
308 Rule.Thm ("vor_minus_mal",ThmC.numerals_to_Free @{thm vor_minus_mal})
309 (*"- a * b = (-a) * b"*)
311 (*Rule.Thm ("",ThmC.numerals_to_Free @{}),*)
313 ], scr = Rule.Empty_Prog} (*end verschoenere*);
315 val klammern_aufloesen =
316 Rule_Def.Repeat{id = "klammern_aufloesen", preconds = [],
317 rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), srls = Rule_Set.Empty, calc = [], errpatts = [], erls = Rule_Set.Empty,
318 rules = [Rule.Thm ("sym_add.assoc",
319 ThmC.numerals_to_Free (@{thm add.assoc} RS @{thm sym})),
320 (*"a + (b + c) = (a + b) + c"*)
321 Rule.Thm ("klammer_plus_minus",ThmC.numerals_to_Free @{thm klammer_plus_minus}),
322 (*"a + (b - c) = (a + b) - c"*)
323 Rule.Thm ("klammer_minus_plus",ThmC.numerals_to_Free @{thm klammer_minus_plus}),
324 (*"a - (b + c) = (a - b) - c"*)
325 Rule.Thm ("klammer_minus_minus",ThmC.numerals_to_Free @{thm klammer_minus_minus})
326 (*"a - (b - c) = (a - b) + c"*)
327 ], scr = Rule.Empty_Prog};
329 val klammern_ausmultiplizieren =
330 Rule_Def.Repeat{id = "klammern_ausmultiplizieren", preconds = [],
331 rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), srls = Rule_Set.Empty, calc = [], errpatts = [], erls = Rule_Set.Empty,
332 rules = [Rule.Thm ("distrib_right" ,ThmC.numerals_to_Free @{thm distrib_right}),
333 (*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
334 Rule.Thm ("distrib_left",ThmC.numerals_to_Free @{thm distrib_left}),
335 (*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
337 Rule.Thm ("klammer_mult_minus",ThmC.numerals_to_Free @{thm klammer_mult_minus}),
338 (*"a * (b - c) = a * b - a * c"*)
339 Rule.Thm ("klammer_minus_mult",ThmC.numerals_to_Free @{thm klammer_minus_mult})
340 (*"(b - c) * a = b * a - c * a"*)
342 (*Rule.Thm ("",ThmC.numerals_to_Free @{}),
344 ], scr = Rule.Empty_Prog};
347 Rule_Def.Repeat{id = "ordne_monome", preconds = [],
348 rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), srls = Rule_Set.Empty, calc = [], errpatts = [],
349 erls = Rule_Set.append_rules "erls_ordne_monome" Rule_Set.empty
350 [Rule.Eval ("PolyMinus.kleiner", eval_kleiner ""),
351 Rule.Eval ("Prog_Expr.is_atom", Prog_Expr.eval_is_atom "")
353 rules = [Rule.Thm ("tausche_mal",ThmC.numerals_to_Free @{thm tausche_mal}),
354 (*"[| b is_atom; a kleiner b |] ==> (b * a) = (a * b)"*)
355 Rule.Thm ("tausche_vor_mal",ThmC.numerals_to_Free @{thm tausche_vor_mal}),
356 (*"[| b is_atom; a kleiner b |] ==> (-b * a) = (-a * b)"*)
357 Rule.Thm ("tausche_mal_mal",ThmC.numerals_to_Free @{thm tausche_mal_mal}),
358 (*"[| c is_atom; b kleiner c |] ==> (a * c * b) = (a * b *c)"*)
359 Rule.Thm ("x_quadrat",ThmC.numerals_to_Free @{thm x_quadrat})
360 (*"(x * a) * a = x * a \<up> 2"*)
362 (*Rule.Thm ("",ThmC.numerals_to_Free @{}),
364 ], scr = Rule.Empty_Prog};
368 Rule_Set.append_rules "rls_p_33" Rule_Set.empty
369 [Rule.Rls_ ordne_alphabetisch,
370 Rule.Rls_ fasse_zusammen,
371 Rule.Rls_ verschoenere
374 Rule_Set.append_rules "rls_p_34" Rule_Set.empty
375 [Rule.Rls_ klammern_aufloesen,
376 Rule.Rls_ ordne_alphabetisch,
377 Rule.Rls_ fasse_zusammen,
378 Rule.Rls_ verschoenere
381 Rule_Set.append_rules "rechnen" Rule_Set.empty
382 [Rule.Eval ("Groups.times_class.times", (**)eval_binop "#mult_"),
383 Rule.Eval ("Groups.plus_class.plus", (**)eval_binop "#add_"),
384 Rule.Eval ("Groups.minus_class.minus", (**)eval_binop "#subtr_")
387 setup \<open>KEStore_Elems.add_rlss
388 [("ordne_alphabetisch", (Context.theory_name @{theory}, prep_rls' ordne_alphabetisch)),
389 ("fasse_zusammen", (Context.theory_name @{theory}, prep_rls' fasse_zusammen)),
390 ("verschoenere", (Context.theory_name @{theory}, prep_rls' verschoenere)),
391 ("ordne_monome", (Context.theory_name @{theory}, prep_rls' ordne_monome)),
392 ("klammern_aufloesen", (Context.theory_name @{theory}, prep_rls' klammern_aufloesen)),
393 ("klammern_ausmultiplizieren",
394 (Context.theory_name @{theory}, prep_rls' klammern_ausmultiplizieren))]\<close>
397 setup \<open>KEStore_Elems.add_pbts
398 [(Problem.prep_input thy "pbl_vereinf_poly" [] Problem.id_empty
399 (["polynom", "vereinfachen"], [], Rule_Set.Empty, NONE, [])),
400 (Problem.prep_input thy "pbl_vereinf_poly_minus" [] Problem.id_empty
401 (["plus_minus", "polynom", "vereinfachen"],
402 [("#Given", ["Term t_t"]),
403 ("#Where", ["t_t is_polyexp",
404 "Not (matchsub (?a + (?b + ?c)) t_t | " ^
405 " matchsub (?a + (?b - ?c)) t_t | " ^
406 " matchsub (?a - (?b + ?c)) t_t | " ^
407 " matchsub (?a + (?b - ?c)) t_t )",
408 "Not (matchsub (?a * (?b + ?c)) t_t | " ^
409 " matchsub (?a * (?b - ?c)) t_t | " ^
410 " matchsub ((?b + ?c) * ?a) t_t | " ^
411 " matchsub ((?b - ?c) * ?a) t_t )"]),
412 ("#Find", ["normalform n_n"])],
413 Rule_Set.append_rules "prls_pbl_vereinf_poly" Rule_Set.empty
414 [Rule.Eval ("Poly.is_polyexp", eval_is_polyexp ""),
415 Rule.Eval ("Prog_Expr.matchsub", Prog_Expr.eval_matchsub ""),
416 Rule.Thm ("or_true", ThmC.numerals_to_Free @{thm or_true}),
417 (*"(?a | True) = True"*)
418 Rule.Thm ("or_false", ThmC.numerals_to_Free @{thm or_false}),
419 (*"(?a | False) = ?a"*)
420 Rule.Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),
421 (*"(~ True) = False"*)
422 Rule.Thm ("not_false",ThmC.numerals_to_Free @{thm not_false})
423 (*"(~ False) = True"*)],
424 SOME "Vereinfache t_t", [["simplification", "for_polynomials", "with_minus"]])),
425 (Problem.prep_input thy "pbl_vereinf_poly_klammer" [] Problem.id_empty
426 (["klammer", "polynom", "vereinfachen"],
427 [("#Given" ,["Term t_t"]),
428 ("#Where" ,["t_t is_polyexp",
429 "Not (matchsub (?a * (?b + ?c)) t_t | " ^
430 " matchsub (?a * (?b - ?c)) t_t | " ^
431 " matchsub ((?b + ?c) * ?a) t_t | " ^
432 " matchsub ((?b - ?c) * ?a) t_t )"]),
433 ("#Find" ,["normalform n_n"])],
434 Rule_Set.append_rules "prls_pbl_vereinf_poly_klammer" Rule_Set.empty
435 [Rule.Eval ("Poly.is_polyexp", eval_is_polyexp ""),
436 Rule.Eval ("Prog_Expr.matchsub", Prog_Expr.eval_matchsub ""),
437 Rule.Thm ("or_true", ThmC.numerals_to_Free @{thm or_true}),
438 (*"(?a | True) = True"*)
439 Rule.Thm ("or_false", ThmC.numerals_to_Free @{thm or_false}),
440 (*"(?a | False) = ?a"*)
441 Rule.Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),
442 (*"(~ True) = False"*)
443 Rule.Thm ("not_false",ThmC.numerals_to_Free @{thm not_false})
444 (*"(~ False) = True"*)],
445 SOME "Vereinfache t_t",
446 [["simplification", "for_polynomials", "with_parentheses"]])),
447 (Problem.prep_input thy "pbl_vereinf_poly_klammer_mal" [] Problem.id_empty
448 (["binom_klammer", "polynom", "vereinfachen"],
449 [("#Given", ["Term t_t"]),
450 ("#Where", ["t_t is_polyexp"]),
451 ("#Find", ["normalform n_n"])],
452 Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)
453 Rule.Eval ("Poly.is_polyexp", eval_is_polyexp "")],
454 SOME "Vereinfache t_t",
455 [["simplification", "for_polynomials", "with_parentheses_mult"]])),
456 (Problem.prep_input thy "pbl_probe" [] Problem.id_empty (["probe"], [], Rule_Set.Empty, NONE, [])),
457 (Problem.prep_input thy "pbl_probe_poly" [] Problem.id_empty
458 (["polynom", "probe"],
459 [("#Given", ["Pruefe e_e", "mitWert w_w"]),
460 ("#Where", ["e_e is_polyexp"]),
461 ("#Find", ["Geprueft p_p"])],
462 Rule_Set.append_rules "prls_pbl_probe_poly" Rule_Set.empty [(*for preds in where_*)
463 Rule.Eval ("Poly.is_polyexp", eval_is_polyexp "")],
464 SOME "Probe e_e w_w",
465 [["probe", "fuer_polynom"]])),
466 (Problem.prep_input thy "pbl_probe_bruch" [] Problem.id_empty
468 [("#Given" ,["Pruefe e_e", "mitWert w_w"]),
469 ("#Where" ,["e_e is_ratpolyexp"]),
470 ("#Find" ,["Geprueft p_p"])],
471 Rule_Set.append_rules "prls_pbl_probe_bruch" Rule_Set.empty [(*for preds in where_*)
472 Rule.Eval ("Rational.is_ratpolyexp", eval_is_ratpolyexp "")],
473 SOME "Probe e_e w_w", [["probe", "fuer_bruch"]]))]\<close>
477 partial_function (tailrec) simplify :: "real \<Rightarrow> real"
481 (Try (Rewrite_Set ''ordne_alphabetisch'')) #>
482 (Try (Rewrite_Set ''fasse_zusammen'')) #>
483 (Try (Rewrite_Set ''verschoenere'')))
485 setup \<open>KEStore_Elems.add_mets
486 [MethodC.prep_input thy "met_simp_poly_minus" [] MethodC.id_empty
487 (["simplification", "for_polynomials", "with_minus"],
488 [("#Given" ,["Term t_t"]),
489 ("#Where" ,["t_t is_polyexp",
490 "Not (matchsub (?a + (?b + ?c)) t_t | " ^
491 " matchsub (?a + (?b - ?c)) t_t | " ^
492 " matchsub (?a - (?b + ?c)) t_t | " ^
493 " matchsub (?a + (?b - ?c)) t_t )"]),
494 ("#Find" ,["normalform n_n"])],
495 {rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty,
496 prls = Rule_Set.append_rules "prls_met_simp_poly_minus" Rule_Set.empty
497 [Rule.Eval ("Poly.is_polyexp", eval_is_polyexp ""),
498 Rule.Eval ("Prog_Expr.matchsub", Prog_Expr.eval_matchsub ""),
499 Rule.Thm ("and_true",ThmC.numerals_to_Free @{thm and_true}),
500 (*"(?a & True) = ?a"*)
501 Rule.Thm ("and_false",ThmC.numerals_to_Free @{thm and_false}),
502 (*"(?a & False) = False"*)
503 Rule.Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),
504 (*"(~ True) = False"*)
505 Rule.Thm ("not_false",ThmC.numerals_to_Free @{thm not_false})
506 (*"(~ False) = True"*)],
507 crls = Rule_Set.empty, errpats = [], nrls = rls_p_33},
508 @{thm simplify.simps})]
511 partial_function (tailrec) simplify2 :: "real \<Rightarrow> real"
515 (Try (Rewrite_Set ''klammern_aufloesen'')) #>
516 (Try (Rewrite_Set ''ordne_alphabetisch'')) #>
517 (Try (Rewrite_Set ''fasse_zusammen'')) #>
518 (Try (Rewrite_Set ''verschoenere'')))
520 setup \<open>KEStore_Elems.add_mets
521 [MethodC.prep_input thy "met_simp_poly_parenth" [] MethodC.id_empty
522 (["simplification", "for_polynomials", "with_parentheses"],
523 [("#Given" ,["Term t_t"]),
524 ("#Where" ,["t_t is_polyexp"]),
525 ("#Find" ,["normalform n_n"])],
526 {rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty,
527 prls = Rule_Set.append_rules "simplification_for_polynomials_prls" Rule_Set.empty
528 [(*for preds in where_*) Rule.Eval("Poly.is_polyexp", eval_is_polyexp"")],
529 crls = Rule_Set.empty, errpats = [], nrls = rls_p_34},
530 @{thm simplify2.simps})]
533 partial_function (tailrec) simplify3 :: "real \<Rightarrow> real"
537 (Try (Rewrite_Set ''klammern_ausmultiplizieren'')) #>
538 (Try (Rewrite_Set ''discard_parentheses'')) #>
539 (Try (Rewrite_Set ''ordne_monome'')) #>
540 (Try (Rewrite_Set ''klammern_aufloesen'')) #>
541 (Try (Rewrite_Set ''ordne_alphabetisch'')) #>
542 (Try (Rewrite_Set ''fasse_zusammen'')) #>
543 (Try (Rewrite_Set ''verschoenere'')))
545 setup \<open>KEStore_Elems.add_mets
546 [MethodC.prep_input thy "met_simp_poly_parenth_mult" [] MethodC.id_empty
547 (["simplification", "for_polynomials", "with_parentheses_mult"],
548 [("#Given" ,["Term t_t"]), ("#Where" ,["t_t is_polyexp"]), ("#Find" ,["normalform n_n"])],
549 {rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty,
550 prls = Rule_Set.append_rules "simplification_for_polynomials_prls" Rule_Set.empty
551 [(*for preds in where_*) Rule.Eval("Poly.is_polyexp", eval_is_polyexp"")],
552 crls = Rule_Set.empty, errpats = [], nrls = rls_p_34},
553 @{thm simplify3.simps})]
555 setup \<open>KEStore_Elems.add_mets
556 [MethodC.prep_input thy "met_probe" [] MethodC.id_empty
558 {rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty, prls = Rule_Set.Empty, crls = Rule_Set.empty,
559 errpats = [], nrls = Rule_Set.Empty},
563 partial_function (tailrec) mache_probe :: "bool \<Rightarrow> bool list \<Rightarrow> bool"
565 "mache_probe e_e w_w = (
568 e_e = Substitute w_w e_e
571 (Try (Repeat (Calculate ''TIMES''))) #>
572 (Try (Repeat (Calculate ''PLUS'' ))) #>
573 (Try (Repeat (Calculate ''MINUS''))))
575 setup \<open>KEStore_Elems.add_mets
576 [MethodC.prep_input thy "met_probe_poly" [] MethodC.id_empty
577 (["probe", "fuer_polynom"],
578 [("#Given" ,["Pruefe e_e", "mitWert w_w"]),
579 ("#Where" ,["e_e is_polyexp"]),
580 ("#Find" ,["Geprueft p_p"])],
581 {rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty,
582 prls = Rule_Set.append_rules "prls_met_probe_bruch" Rule_Set.empty
583 [(*for preds in where_*) Rule.Eval ("Rational.is_ratpolyexp", eval_is_ratpolyexp "")],
584 crls = Rule_Set.empty, errpats = [], nrls = rechnen},
585 @{thm mache_probe.simps})]
587 setup \<open>KEStore_Elems.add_mets
588 [MethodC.prep_input thy "met_probe_bruch" [] MethodC.id_empty
589 (["probe", "fuer_bruch"],
590 [("#Given" ,["Pruefe e_e", "mitWert w_w"]),
591 ("#Where" ,["e_e is_ratpolyexp"]),
592 ("#Find" ,["Geprueft p_p"])],
593 {rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty,
594 prls = Rule_Set.append_rules "prls_met_probe_bruch" Rule_Set.empty
595 [(*for preds in where_*) Rule.Eval ("Rational.is_ratpolyexp", eval_is_ratpolyexp "")],
596 crls = Rule_Set.empty, errpats = [], nrls = Rule_Set.Empty},