1 (* Title: tests for ProgLang/rewrite.sml
2 TODO.WN0509 collect typical tests from systest here !!!!!
3 Author: Walther Neuper 050908
4 (c) copyright due to lincense terms.
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10 "--------------------------------------------------------";
11 "table of contents --------------------------------------";
12 "--------------------------------------------------------";
13 "----------- assemble rewrite ---------------------------";
14 "----------- test rewriting without Isac's thys ---------";
15 "----------- conditional rewriting without Isac's thys --";
16 "----------- step through 'and rew_sub': ----------------";
17 "----------- step through 'fun rewrite_terms_' ---------";
18 "----------- rewrite_inst_ bdvs -------------------------";
19 "----------- check diff 2002--2009-3 --------------------";
20 "----------- compare all prepat's existing 2010 ---------";
21 "----------- fun app_rev, Rrls, -------------------------";
22 "----------- 2011 thms with axclasses -------------------";
23 "----------- repair NO asms from rls RatEq_eliminate ----";
24 "----------- fun assoc_thm' -----------------------------";
25 "----------- fun rewrite_ down to Pattern.match ------------------------------------------------";
26 "--------------------------------------------------------";
27 "--------------------------------------------------------";
28 "--------------------------------------------------------";
31 "----------- assemble rewrite ---------------------------";
32 "----------- assemble rewrite ---------------------------";
33 "----------- assemble rewrite ---------------------------";
34 "===== rewriting by thm with 'a";
35 (*show_types := true;*)
37 val thy = @{theory Complex_Main};
38 val ctxt = @{context};
39 val thm = @{thm add.commute};
40 val t = (Thm.term_of o the) (parse thy "((r + u) + t) + s");
41 "----- from old: fun rewrite__";
43 val r = (((inst_bdv bdv) o norm o #prop o Thm.rep_thm) thm);
44 "----- from old: and rew_sub";
45 val (LHS,RHS) = (dest_equals' o strip_trueprop
46 o Logic.strip_imp_concl) r;
48 val insts = Pattern.match thy (LHS,t) (Vartab.empty, Vartab.empty);*)
49 "----- fun match_rew in Pure/pattern.ML";
50 val rtm = the_default RHS (Term.rename_abs LHS t RHS);
52 writeln(Syntax.string_of_term ctxt rtm);
53 writeln(Syntax.string_of_term ctxt LHS);
54 writeln(Syntax.string_of_term ctxt t);
56 (Pattern.match thy (LHS, t) (Vartab.empty, Vartab.empty));
57 val (rew, RHS) = (Envir.subst_term
58 (Pattern.match thy (LHS, t) (Vartab.empty, Vartab.empty)) rtm, rtm);
59 (*lookup in isabelle?trace?response...*)
60 writeln(Syntax.string_of_term ctxt rew);
61 writeln(Syntax.string_of_term ctxt RHS);
62 "===== rewriting: prep insertion into rew_sub";
63 val thy = @{theory Complex_Main};
64 val ctxt = @{context};
65 val thm = @{thm nonzero_divide_mult_cancel_right};
66 val r = Thm.prop_of thm;
67 val tm = @{term "x / (2 * x)::real"};
69 val (LHS, RHS) = (HOLogic.dest_eq o HOLogic.dest_Trueprop
70 o Logic.strip_imp_concl) r;
71 val r' = Envir.subst_term (Pattern.match thy (LHS, tm)
72 (Vartab.empty, Vartab.empty)) r;
73 val p' = (fst o Logic.strip_prems) (Logic.count_prems r', [], r');
74 val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop
75 o Logic.strip_imp_concl) r';
77 (*is displayed on top of <response> buffer...*)
78 Pretty.writeln (Proof_Context.pretty_term_abbrev @{context} r');
79 Pretty.writeln (Proof_Context.pretty_term_abbrev @{context} t');
82 "----------- test rewriting without Isac's thys ---------";
83 "----------- test rewriting without Isac's thys ---------";
84 "----------- test rewriting without Isac's thys ---------";
86 "===== rewriting with Isabelle2009-1 only, i.e without isac-hacks";
87 val thy = @{theory Complex_Main};
88 val ctxt = @{context};
89 val thm = @{thm add.commute};
90 val tm = @{term "x + y*z::real"};
92 val SOME (r,_) = (rewrite_ thy dummy_ord e_rls false thm tm)
93 handle _ => error "rewrite.sml diff.behav. in rewriting";
94 (*is displayed on _TOP_ of <response> buffer...*)
95 Pretty.writeln (Proof_Context.pretty_term_abbrev @{context} r);
96 if r = @{term "y*z + x::real"}
97 then () else error "rewrite.sml diff.result in rewriting";
99 "----- rewriting a subterm";
100 val tm = @{term "w*(x + y*z)::real"};
102 val SOME (r,_) = (rewrite_ thy dummy_ord e_rls false thm tm)
103 handle _ => error "rewrite.sml diff.behav. in rew_sub";
105 "----- ordered rewriting";
106 fun tord (_:subst) pp = Term_Ord.termless pp;
107 if tord [] (@{term "x + y*z::real"}, @{term "y*z + x::real"}) then ()
108 else error "rewrite.sml diff.behav. in ord.rewr.";
110 val NONE = (rewrite_ thy tord e_rls false thm tm)
111 handle _ => error "rewrite.sml diff.behav. in rewriting";
112 (*is displayed on _TOP_ of <response> buffer...*)
113 Pretty.writeln (Proof_Context.pretty_term_abbrev @{context} r);
115 val tm = @{term "x*y + z::real"};
116 val SOME (r,_) = (rewrite_ thy tord e_rls false thm tm)
117 handle _ => error "rewrite.sml diff.behav. in rewriting";
120 "----------- conditional rewriting without Isac's thys --";
121 "----------- conditional rewriting without Isac's thys --";
122 "----------- conditional rewriting without Isac's thys --";
124 "===== prepr cond.rew. with Pattern.match";
125 val thy = @{theory Complex_Main};
126 val ctxt = @{context};
127 val thm = @{thm nonzero_divide_mult_cancel_right};
128 val rule = Thm.prop_of thm;
129 val tm = @{term "x / (2 * x)::real"};
131 val prem = Logic.strip_imp_prems rule;
132 val nps = Logic.count_prems rule;
133 val prems = Logic.strip_prems (nps, [], rule);
135 val eq = Logic.strip_imp_concl rule;
136 val (LHS, RHS) = (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;
138 val mtcs = Pattern.match thy (LHS, tm) (Vartab.empty, Vartab.empty);
139 val rule' = Envir.subst_term mtcs rule;
141 val prems' = (fst o Logic.strip_prems)
142 (Logic.count_prems rule', [], rule');
143 val RHS' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop
144 o Logic.strip_imp_concl) rule';
146 "----- conditional rewriting creating an assumption";
147 "----- conditional rewriting creating an assumption";
148 val thm = @{thm nonzero_divide_mult_cancel_right};
149 val tm = @{term "x / (2 * x)::real"};
150 val SOME (rew, asm) = (rewrite_ thy dummy_ord e_rls false thm tm)
151 handle _ => error "rewrite.sml diff.behav. in cond.rew.";
153 if rew = @{term "1 / 2::real"} then () (* the rewrite is _NO_ Trueprop *)
154 else error "rewrite.sml diff.result in cond.rew.";
156 if hd asm = @{term "x \<noteq> (0::real)"} (* dropped Trueprop $ ...*)
157 then () else error "rewrite.sml diff.asm in cond.rew.";
158 "----- conditional rewriting immediately: can only be done with ";
159 "------Isabelle numerals, because erls cannot handle them yet.";
162 "----------- step through 'and rew_sub': ----------------";
163 "----------- step through 'and rew_sub': ----------------";
164 "----------- step through 'and rew_sub': ----------------";
165 (*and make asms without Trueprop, beginning with the result:*)
166 val tm = @{term "x / (2 * x)::real"};
167 val (t', asm, _, _) = rew_sub thy 0 [] dummy_ord e_rls true [] (Thm.prop_of thm) tm;
168 (*show_types := false;*)
169 "----- evaluate arguments";
170 val (thy, i, bdv, tless, rls, put_asm, lrd, r, t) =
171 (thy, 0, [], dummy_ord, e_rls, true, [], (Thm.prop_of thm), tm);
172 "----- step 1: LHS, RHS of rule";
173 val (LHS, RHS) = (HOLogic.dest_eq o HOLogic.dest_Trueprop
174 o Logic.strip_imp_concl) r;
175 term2str r = "?b \<noteq> (0::?'a) \<Longrightarrow> ?b / (?a * ?b) = (1::?'a) / ?a";
176 term2str LHS = "?b / (?a * ?b)"; term2str RHS = "(1::?'a) / ?a";
177 "----- step 2: the rule instantiated";
178 val r' = Envir.subst_term
179 (Pattern.match thy (LHS, t) (Vartab.empty, Vartab.empty)) r;
180 term2str r' = "x \<noteq> 0 \<Longrightarrow> x / (2 * x) = 1 / 2";
181 "----- step 3: get the (instantiated) assumption(s)";
182 val p' = (fst o Logic.strip_prems) (Logic.count_prems r', [], r');
183 term2str (hd p') = "x \<noteq> 0";
184 "=====vvv make asms without Trueprop ---vvv";
185 val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems)
186 (Logic.count_prems r', [], r'));
188 [Const ("HOL.Not", _) $ (Const ("HOL.eq", _)
189 $ Free ("x", _) $ Const ("Groups.zero_class.zero", _))] => ()
190 | _ => error "rewrite.sml assumption changed";
191 "=====^^^ make asms without Trueprop ---^^^";
192 "----- step 4: get the (instantiated) RHS";
193 val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop
194 o Logic.strip_imp_concl) r';
195 term2str t' = "1 / 2";
197 "----------- step through 'fun rewrite_terms_' ---------";
198 "----------- step through 'fun rewrite_terms_' ---------";
199 "----------- step through 'fun rewrite_terms_' ---------";
200 "----- step 0: args for rewrite_terms_, local fun";
201 val (thy, ord, erls, equs, t) =
202 (@{theory "Biegelinie"}, dummy_ord, Erls, [str2term "x = 0"],
203 str2term "M_b x = -1 * q_0 * x ^^^ 2 / 2 + x * c + c_2");
204 "----- step 1: args for rew_";
205 val ((t', asm'), (rules as r::rs), t) = ((e_term, []), equs, t);
206 "----- step 2: rew_sub";
207 rew_sub thy 1 [] ord erls false [] (Trueprop $ r) t;
208 "----- step 3: step through rew_sub -- inefficient: goes into subterms";
211 val SOME (t', _) = rewrite_terms_ thy dummy_ord Erls equs t;
212 writeln "----------- rewrite_terms_ 1---------------------------";
213 if term2str t' = "M_b 0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2" then ()
214 else error "rewrite.sml rewrite_terms_ [x = 0]";
216 val equs = [str2term "M_b 0 = 0"];
217 val t = str2term "M_b 0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2";
218 val SOME (t', _) = rewrite_terms_ thy dummy_ord Erls equs t;
219 writeln "----------- rewrite_terms_ 2---------------------------";
220 if term2str t' = "0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2" then ()
221 else error "rewrite.sml rewrite_terms_ [M_b 0 = 0]";
223 val equs = [str2term "x = 0", str2term"M_b 0 = 0"];
224 val t = str2term "M_b x = -1 * q_0 * x ^^^ 2 / 2 + x * c + c_2";
225 val SOME (t', _) = rewrite_terms_ thy dummy_ord Erls equs t;
226 writeln "----------- rewrite_terms_ 3---------------------------";
227 if term2str t' = "0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2" then ()
228 else error "rewrite.sml rewrite_terms_ [x = 0, M_b 0 = 0]";
231 "----------- rewrite_inst_ bdvs -------------------------";
232 "----------- rewrite_inst_ bdvs -------------------------";
233 "----------- rewrite_inst_ bdvs -------------------------";
234 (*see smltest/Scripts/term_G.sml: inst_bdv 2*)
235 val t = str2term"-1 * (q_0 * L ^^^ 2) / 2 + (L * c_3 + c_4) = 0";
236 val bdvs = [(str2term"bdv_1",str2term"c"),
237 (str2term"bdv_2",str2term"c_2"),
238 (str2term"bdv_3",str2term"c_3"),
239 (str2term"bdv_4",str2term"c_4")];
240 (*------------ outcommented WN071210, after inclusion into ROOT.ML
242 rewrite_inst_ thy e_rew_ord
243 (append_rls "erls_isolate_bdvs" e_rls
244 [(Calc ("EqSystem.occur'_exactly'_in",
245 eval_occur_exactly_in
246 "#eval_occur_exactly_in_"))
248 false bdvs (num_str @{separate_bdvs_add) t;
249 (writeln o term2str) t;
250 if term2str t = "L * c_3 + c_4 = 0 + -1 * (-1 * (q_0 * L ^^^ 2) / 2)"
251 then () else error "rewrite.sml rewrite_inst_ bdvs";
253 trace_rewrite:=false;--------------------------------------------*)
256 "----------- check diff 2002--2009-3 --------------------";
257 "----------- check diff 2002--2009-3 --------------------";
258 "----------- check diff 2002--2009-3 --------------------";
259 (*----- 2002 -------------------------------------------------------------------
260 # rls: norm_Rational_noadd_fractions on: 1 / EI * (L * q_0 * x / 2 + -1 *
262 ## rls: discard_minus_ on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2
264 ### try thm: real_diff_minus
265 ### try thm: sym_real_mult_minus1
266 ## rls: rat_mult_poly on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2
268 ### try thm: rat_mult_poly_l
269 ### try thm: rat_mult_poly_r
270 #### eval asms: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp
271 ==> 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) =
272 1 * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) / EI
273 ##### rls: e_rls-is_polyexp on: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2
275 ###### try calc: Poly.is'_polyexp'
276 ====== calc. to: False
277 ###### try calc: Poly.is'_polyexp'
278 ###### try calc: Poly.is'_polyexp'
279 #### asms false: ["L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp"]
280 ----- 2002 NONE rewrite --------------------------------------------------------
281 ----- 2009 should maintain this behaviour, but: --------------------------------
282 # rls: norm_Rational_noadd_fractions on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)
283 ## rls: discard_minus on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)
284 ### try thm: real_diff_minus
285 ### try thm: sym_real_mult_minus1
286 ## rls: rat_mult_poly on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)
287 ### try thm: rat_mult_poly_l
288 ### try thm: rat_mult_poly_r
289 #### eval asms: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp
290 ==> 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) =
291 1 * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) / EI
292 ##### rls: e_rls-is_polyexp on: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp
293 ###### try calc: Poly.is'_polyexp'
294 ====== calc. to: False
295 ###### try calc: Poly.is'_polyexp'
296 ###### try calc: Poly.is'_polyexp'
297 #### asms accepted: ["L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp"] stored: ["False"]
298 === rewrites to: 1 * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) / EI
299 ----- 2009 -------------------------------------------------------------------*)
301 (*the situation as was before repair (asm without Trueprop) is outcommented*)
302 val thy = @{theory "Isac"};
303 "===== example which raised the problem =================";
304 val t = @{term "1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)"};
305 "----- rewrite_set_inst_ norm_Rational_noadd_fractions--";
306 val subs = [(str2term "bdv", str2term "x")];
307 val rls = norm_Rational_noadd_fractions;
308 val SOME (t', asms) = rewrite_set_inst_ thy true subs rls t;
309 if term2str t' = "1 / EI * (L * q_0 * x / 2 + -1 * 1 * q_0 * x ^^^ 2 / 2)" andalso
310 terms2str asms = "[]" then {}
311 else error "this was NONE with Isabelle2013-2 ?!?"
312 "----- rewrite_ rat_mult_poly_r--------------------------";
313 val thm = @{thm rat_mult_poly_r};
314 "?c::real is_polyexp ==> (?a::real) / (?b::real) * ?c = ?a * ?c / ?b";
315 val erls = append_rls "e_rls-is_polyexp" e_rls
316 [Calc ("Poly.is'_polyexp", eval_is_polyexp "")];
317 val NONE (*SOME (t'', _)*) = rewrite_ thy dummy_ord erls true thm t;
318 (*t' = t''; (*false because of further rewrites in t'*)*)
319 "----- rew_sub --------------------------------";
320 val (t''', _, _, _) = rew_sub thy 0 [] dummy_ord erls true [] (Thm.prop_of thm) t;
321 (*t'' = t'''; (*true*)*)
322 "----- rewrite_set_ erls --------------------------------";
323 val cond = @{term "(L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)"};
324 val NONE = rewrite_set_ thy true erls cond;
325 (* ^^^^^ goes with '====== calc. to: False' above from beginning*)
327 writeln "===== maximally simplified example =====================";
328 val t = @{term "a / b * (x / x ^^^ 2)"};
329 "?c::real is_polyexp ==> (?a::real) / (?b::real) * ?c = ?a * ?c / ?b";
330 writeln "----- rewrite_set_inst_ norm_Rational_noadd_fractions--";
331 val (*NONE*) SOME (t', asm) = rewrite_set_inst_ thy true subs rls t;
332 term2str t' = "a * x / (b * x ^^^ 2)"; (*rew. by thm outside test case*)
333 (*checked visually: trace_rewrite looks like above for 2009*)
335 writeln "----- rewrite_ rat_mult_poly_r--------------------------";
336 val NONE (*SOME (t'', _)*) = rewrite_ thy dummy_ord erls true thm t;
337 (*t' = t''; (*false because of further rewrites in t'*)*)
338 writeln "----- rew_sub --------------------------------";
339 val (t''', _, _, _) = rew_sub thy 0 [] dummy_ord erls true [] (Thm.prop_of thm) t;
340 (*t'' = t'''; (*true*)*)
341 writeln "----- rewrite_set_ erls --------------------------------";
342 val cond = @{term "(x / x ^^^ 2)"};
343 val NONE = rewrite_set_ thy true erls cond;
344 (* ^^^^^ goes with '====== calc. to: False' above from beginning*)
347 "----------- compare all prepat's existing 2010 ---------";
348 "----------- compare all prepat's existing 2010 ---------";
349 "----------- compare all prepat's existing 2010 ---------";
350 val thy = @{theory "Isac"};
351 val t = @{term "a + b * x = (0 ::real)"};
352 val pat = parse_patt thy "?l = (?r ::real)";
353 val precond = parse_patt thy "is_polynomial (?l::real)";(*no infix def*)
354 val precond = parse_patt thy "(?l::real) is_expanded";
356 val inst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);
357 val preinst = Envir.subst_term inst precond;
360 "===== Rational.thy: cancel ===";
361 (* pat matched with the current term gives an environment
362 (or not: hen the Rrls not applied);
363 if pre1 and pre2 evaluate to @{term True} in this environment,
364 then the Rrls is applied. *)
365 val t = str2term "(a + b) / c ::real";
366 val pat = parse_patt thy "?r / ?s ::real";
367 val pres = [parse_patt thy "?r is_expanded", parse_patt thy "?s is_expanded"];
368 val prepat = [(pres, pat)];
369 val erls = rational_erls;
370 (* erls got from Rrls {erls, prepat, scr = Rfuns {normal_form, ...}, ...} *)
372 val subst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);
373 val asms = map (Envir.subst_term subst) pres;
374 if terms2str asms = "[\"a + b is_expanded\",\"c is_expanded\"]"
375 then () else error "rewrite.sml: prepat cancel subst";
376 if ([], true) = eval__true thy 0 asms [] erls
377 then () else error "rewrite.sml: prepat cancel eval__true";
379 "===== Rational.thy: add_fractions_p ===";
380 (* if each pat* matches with the current term, the Rrls is applied
381 (there are no preconditions to be checked, they are @{term True}) *)
382 val t = str2term "a / b + 1 / 2";
383 val pat = parse_patt thy "?r / ?s + ?u / ?v";
384 val pres = [@{term True}];
385 val prepat = [(pres, pat)];
386 val erls = rational_erls;
387 (* erls got from Rrls {erls, prepat, scr = Rfuns {normal_form, ...}, ...} *)
389 val subst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);
390 if ([], true) = eval__true thy 0 (map (Envir.subst_term subst) pres) [] erls
391 then () else error "rewrite.sml: prepat add_fractions_p";
393 "===== Poly.thy: order_mult_ ===";
394 (* ?p matched with the current term gives an environment,
395 which evaluates (the instantiated) "p is_multUnordered" to true*)
396 val t = str2term "x^^^2 * x";
397 val pat = parse_patt thy "?p :: real"
398 val pres = [parse_patt thy "?p is_multUnordered"];
399 val prepat = [(pres, pat)];
400 val erls = append_rls "e_rls-is_multUnordered" e_rls
401 [Calc ("Poly.is'_multUnordered",
402 eval_is_multUnordered "")];
404 val subst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);
405 val asms = map (Envir.subst_term subst) pres;
406 if terms2str asms = "[\"x ^^^ 2 * x is_multUnordered\"]"
407 then () else error "rewrite.sml: prepat order_mult_ subst";
408 if ([], true) = eval__true thy 0 asms [] erls
409 then () else error "rewrite.sml: prepat order_mult_ eval__true";
412 "----------- fun app_rev, Rrls, -------------------------";
413 "----------- fun app_rev, Rrls, -------------------------";
414 "----------- fun app_rev, Rrls, -------------------------";
415 val t = str2term "x^^^2 * x";
417 if is_multUnordered t then () else error "rewrite.sml diff. is_multUnordered 2";
418 val tm = str2term "(x^^^2 * x) is_multUnordered";
419 eval_is_multUnordered "testid" "" tm thy;
421 case eval_is_multUnordered "testid" "" tm thy of
422 SOME (_, Const ("HOL.Trueprop", _) $
423 (Const ("HOL.eq", _) $
424 (Const ("Poly.is'_multUnordered", _) $ _) $
425 Const ("HOL.True", _))) => ()
426 | _ => error "rewrite.sml diff. eval_is_multUnordered 2b";
428 tracing "----- begin rewrite x^^^2 * x ---"; trace_rewrite := true;
429 val SOME (t', _) = rewrite_set_ thy true order_mult_ t;
430 tracing "----- end rewrite x^^^2 * x ---"; trace_rewrite := false;
431 if term2str t' = "x * x ^^^ 2" then ()
432 else error "rewrite.sml Poly.is'_multUnordered doesn't work";
434 (* for achieving the previous result, the following code was taken apart *)
435 "----- rewrite__set_ ---";
436 val (thy, i, _, _, (rrls as Rrls _), t) = (thy, 0, true, [], order_mult_, tm);
437 val (t', asm, rew) = app_rev thy (i+1) rrls t;
439 val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
440 fun chk_prepat thy erls [] t = true
441 | chk_prepat thy erls prepat t =
442 let fun chk (pres, pat) =
443 (let val subst: Type.tyenv * Envir.tenv =
444 Pattern.match thy (pat, t)
445 (Vartab.empty, Vartab.empty)
446 in snd (eval__true thy (i+1)
447 (map (Envir.subst_term subst) pres)
451 fun scan_ f [] = false (*scan_ NEVER called by []*)
452 | scan_ f (pp::pps) = if f pp then true
454 in scan_ chk prepat end;
456 (*.apply the normal_form of a rev-set.*)
457 fun app_rev' thy (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}) t =
458 if chk_prepat thy erls prepat t
459 then ((*tracing("### app_rev': t = "^(term2str t));*)
462 (*fixme val NONE = app_rev' thy rrls t;*)
463 "----- app_rev' ---";
464 val (thy, Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}, t) = (thy, rrls, t);
465 (*fixme false*) chk_prepat thy erls prepat t;
466 "----- chk_prepat ---";
467 val (thy, erls, prepat, t) = (thy, erls, prepat, t);
468 fun chk (pres, pat) =
469 (let val subst: Type.tyenv * Envir.tenv =
470 Pattern.match thy (pat, t)
471 (Vartab.empty, Vartab.empty)
472 in snd (eval__true thy (i+1)
473 (map (Envir.subst_term subst) pres)
477 fun scan_ f [] = false (*scan_ NEVER called by []*)
478 | scan_ f (pp::pps) = if f pp then true
480 tracing "=== poly.sml: scan_ chk prepat begin";
482 tracing "=== poly.sml: scan_ chk prepat end";
485 (*reestablish...*) val t = str2term "x ^^^ 2 * x";
486 val [(pres, pat)] = prepat;
487 val subst: Type.tyenv * Envir.tenv =
488 Pattern.match thy (pat, t)
489 (Vartab.empty, Vartab.empty);
491 (*fixme: asms = ["p is_multUnordered"]...instantiate*)
492 "----- eval__true ---";
493 val asms = (map (Envir.subst_term subst) pres);
494 if terms2str asms = "[\"x ^^^ 2 * x is_multUnordered\"]" then ()
495 else error "rewrite.sml: diff. is_multUnordered, asms";
496 val (thy, i, asms, bdv, rls) =
497 (thy, (i+1), [str2term "(x^^^2 * x) is_multUnordered"],
498 [] : (term * term) list, erls);
499 case eval__true thy i asms bdv rls of
501 | _ => error "rewrite.sml: diff. is_multUnordered, eval__true";
503 "----------- 2011 thms with axclasses -------------------";
504 "----------- 2011 thms with axclasses -------------------";
505 "----------- 2011 thms with axclasses -------------------";
506 val thm = num_str @{thm div_by_1};
507 val prop = Thm.prop_of thm;
508 atomty prop; (*Type 'a*)
509 val t = str2term "(2*x)/1"; (*Type real*)
511 val (thy, ro, er, inst) =
512 (@{theory "Isac"}, tless_true, eval_rls, [(@{term "bdv::real"}, @{term "x::real"})]);
513 val SOME (t, _) = rewrite_ thy ro er true thm t; (*real matches 'a ?via ring? etc*)
515 "----------- repair NO asms from rls RatEq_eliminate ----";
516 "----------- repair NO asms from rls RatEq_eliminate ----";
517 "----------- repair NO asms from rls RatEq_eliminate ----";
518 val t = str2term "1 / x = 5";
519 trace_rewrite := true;
520 val SOME (t', asm) = rewrite_ thy e_rew_ord e_rls true @{thm rat_mult_denominator_right} t;
521 term2str t' = "1 = 5 * x";
522 terms2str asm = "[\"x ~= 0\"]";
524 ## eval asms: x ~= 0 ==> (1 / x = 5) = (1 = 5 * x)
525 ### rls: e_rls on: x ~= 0
526 ## asms accepted: ["x ~= 0"] stored: ["x ~= 0"]
528 trace_rewrite := false;
530 trace_rewrite := false;
531 val SOME (t', []) = rewrite_set_ thy true RatEq_eliminate t; (*= [] must be = "x ~= 0"*)
532 term2str t' = "1 = 5 * x";
535 #### rls: rateq_erls on: x ~= 0
537 ##### try calc: HOL.eq' <<<------------------------------- here the error comes from
538 ===== calc. to: ~ False
539 ##### try calc: HOL.eq'
540 ##### try thm: not_true
541 ##### try thm: not_false
542 ===== rewrites to: True
544 ### asms accepted: ["x ~= 0"] stored: []
547 trace_rewrite := false;
548 (* WN120317.TODO dropped rateq: the above error is the same in 2002 *)
550 "----------- fun assoc_thm' -----------------------------";
551 "----------- fun assoc_thm' -----------------------------";
552 "----------- fun assoc_thm' -----------------------------";
553 val thy = @{theory ProgLang}
555 val tth = assoc_thm' thy ("sym_#mult_2_3","6 = 2 * 3");
556 if string_of_thm' thy tth = "6 = 2 * 3" then ()
557 else error "assoc_thm' (sym_#mult_2_3, 6 = 2 * 3) changed";
559 val tth = assoc_thm' thy ("add_0_left","");
560 if string_of_thm' thy tth = "0 + ?a = ?a" then ()
561 else error "assoc_thm' (add_0_left,\"\") changed";
563 val tth = assoc_thm' thy ("sym_add_0_left","");
564 if string_of_thm' thy tth = "?t = 0 + ?t" then ()
565 else error "assoc_thm' (sym_add_0_left,\"\") changed";
567 val tth = assoc_thm' thy ("add_commute","");
568 if string_of_thm' thy tth = "?a + ?b = ?b + ?a" then ()
569 else error "assoc_thm' (add_commute,\"\") changed"
571 "----------- fun rewrite_ down to Pattern.match ------------------------------------------------";
572 "----------- fun rewrite_ down to Pattern.match ------------------------------------------------";
573 "----------- fun rewrite_ down to Pattern.match ------------------------------------------------";
574 "~~~~~ fun rewrite_ , args:"; val (thy, rew_ord, erls, bool, thm, term) =
575 (@{theory}, dummy_ord, e_rls, false, @{thm distrib_left}, @{term "x * (y + z) :: int"});
576 "~~~~~ fun rewrite__ , args:"; val (thy, i, bdv, tless, rls, put_asm, thm, ct) =
577 (thy, 1, [], rew_ord, erls, bool, thm, term);
578 "~~~~~ and rew_sub , args:"; val (thy, i, bdv, tless, rls, put_asm, lrd, r, t) =
579 (thy, i, bdv, tless, rls, put_asm, [], (((inst_bdv bdv) o norm o #prop o Thm.rep_thm) thm), ct)
580 val (lhss, rhss) = (HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r
581 val r' = Envir.subst_term (Pattern.match thy (lhss, t) (Vartab.empty, Vartab.empty)) r
582 val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems) (Logic.count_prems r', [], r'))
583 val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r'
585 if term2str lhss = "?a * (?b + ?c)" andalso term2str t = "x * (y + z)" then ()
586 else error "ARGS FOR Pattern.match CHANGED";
587 val match = Pattern.match thy (lhss, t) (Vartab.empty, Vartab.empty);
588 if (Envir.subst_term match r |> term2str) = "x * (y + z) = x * y + x * z" then ()
589 else error "Pattern.match CHANGED";