1 (* Title: Knowledge/eqsystem-1.sml
2 author: Walther Neuper 050826,
3 (c) due to copyright terms
6 "-----------------------------------------------------------------";
7 "table of contents -----------------------------------------------";
8 "-----------------------------------------------------------------";
9 "----------- occur_exactly_in ------------------------------------";
10 "----------- problems --------------------------------------------";
11 "----------- rewrite-order ord_simplify_System -------------------";
12 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
13 "----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
14 "----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
15 "----------- rewrite in [EqSystem,normalise,4x4] -----------------";
16 "----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";
17 "----------- refine [linear,system]-------------------------------";
18 "----------- refine [2x2,linear,system] search error--------------";
19 "----------- me [EqSystem,normalise,2x2] -------------------------";
20 (*^^^--- eqsystem-1.sml #####################################################################
21 vvv--- eqsystem-2.sml #####################################################################*)
22 "----------- me [linear,system] ..normalise..top_down_sub..-------";
23 "----------- all systems from Biegelinie -------------------------";
24 "----------- 4x4 systems from Biegelinie -------------------------";
25 "-----------------------------------------------------------------";
26 "-----------------------------------------------------------------";
27 "-----------------------------------------------------------------";
29 val thy = @{theory "EqSystem"};
30 val ctxt = Proof_Context.init_global thy;
32 "----------- occur_exactly_in ------------------------------------";
33 "----------- occur_exactly_in ------------------------------------";
34 "----------- occur_exactly_in ------------------------------------";
35 val all = [TermC.str2term"c", TermC.str2term"c_2", TermC.str2term"c_3"];
36 val t = TermC.str2term"0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
38 if occur_exactly_in [TermC.str2term"c", TermC.str2term"c_2"] all t
39 then () else error "eqsystem.sml occur_exactly_in 1";
41 if not (occur_exactly_in [TermC.str2term"c", TermC.str2term"c_2", TermC.str2term"c_3"] all t)
42 then () else error "eqsystem.sml occur_exactly_in 2";
44 if not (occur_exactly_in [TermC.str2term"c_2"] all t)
45 then () else error "eqsystem.sml occur_exactly_in 3";
47 val t = TermC.str2term"[c,c_2] from [c,c_2,c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
48 eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
49 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
50 if str = "[c, c_2] from [c, c_2,\n" ^
51 " c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = True"
52 then () else error "eval_occur_exactly_in [c, c_2]";
54 val t = TermC.str2term ("[c,c_2,c_3] from [c,c_2,c_3] occur_exactly_in " ^
55 "- 1 * q_0 * L \<up> 2 / 2 + L * c + c_2");
56 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
57 if str = "[c, c_2,\n c_3] from [c, c_2,\n" ^
58 " c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = False"
59 then () else error "eval_occur_exactly_in [c, c_2, c_3]";
61 val t = TermC.str2term"[c_2] from [c,c_2,c_3] occur_exactly_in \
62 \- 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
63 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
64 if str = "[c_2] from [c, c_2,\n" ^
65 " c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = False"
66 then () else error "eval_occur_exactly_in [c, c_2, c_3]";
68 val t = TermC.str2term"[] from [c,c_2,c_3] occur_exactly_in 0";
69 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
70 if str = "[] from [c, c_2, c_3] occur_exactly_in 0 = True" then ()
71 else error "eval_occur_exactly_in [c, c_2, c_3]";
75 "[] from [c, c_2, c_3, c_4] occur_exactly_in - 1 * (q_0 * L \<up> 2) /2";
76 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
77 if str = "[] from [c, c_2, c_3, c_4] occur_exactly_in \
78 \- 1 * (q_0 * L \<up> 2) / 2 = True" then ()
79 else error "eval_occur_exactly_in [c, c_2, c_3, c_4]";
81 "----------- problems --------------------------------------------";
82 "----------- problems --------------------------------------------";
83 "----------- problems --------------------------------------------";
84 val t = TermC.str2term "Length [x+y=1,y=2] = 2";
86 val testrls = Rule_Set.append_rules "testrls" Rule_Set.empty
87 [(Thm ("LENGTH_NIL", @{thm LENGTH_NIL})),
88 (Thm ("LENGTH_CONS", @{thm LENGTH_CONS})),
89 Eval (\<^const_name>\<open>plus\<close>, eval_binop "#add_"),
90 Eval (\<^const_name>\<open>HOL.eq\<close>,eval_equal "#equal_")
92 val SOME (t',_) = rewrite_set_ ctxt false testrls t;
93 if UnparseC.term t' = "True" then ()
94 else error "eqsystem.sml: length_ [x+y=1,y=2] = 2";
96 val SOME t = TermC.parseNEW ctxt "solution LL";
98 val SOME t = TermC.parseNEW ctxt "solution LL";
101 val t = TermC.str2term
102 "(tl (tl (tl v_s))) from v_s occur_exactly_in (NTH 1 (e_s::bool list))";
104 val t = TermC.str2term ("(tl (tl (tl [c, c_2, c_3, c_4]))) from [c, c_2, c_3, c_4] occur_exactly_in " ^
105 "(NTH 1 [c_4 = 1, 2 = 2, 3 = 3, 4 = 4])");
106 (*----- broken in child of.1790e1073acc : eliminate "handle _ => ..." from Rewrite.rewrite -----\\
107 assume flawed test setup hidden by "handle _ => ..."
108 ERROR rewrite__set_ called with 'Erls' for '1 < 1'
110 rewrite_set_ ctxt true
111 (Rule_Set.append_rules "prls_" Rule_Set.empty
112 [Thm ("NTH_CONS",ThmC.numerals_to_Free @{thm NTH_CONS}),
113 Thm ("NTH_NIL",ThmC.numerals_to_Free @{thm NTH_NIL}),
114 Thm ("TL_CONS",ThmC.numerals_to_Free @{thm tl_Cons}),
115 Thm ("TL_NIL",ThmC.numerals_to_Free @{thm tl_Nil}),
116 Eval ("EqSystem.occur_exactly_in", eval_occur_exactly_in "#eval_occur_exactly_in_")
118 if t = @{term True} then ()
119 else error "eqsystem.sml ..occur_exactly_in (nth_ 1 [c_4..";
120 broken in child of.1790e1073acc : eliminate "handle _ => ..." from Rewrite.rewrite ---//*)
123 "----------- rewrite-order ord_simplify_System -------------------";
124 "----------- rewrite-order ord_simplify_System -------------------";
125 "----------- rewrite-order ord_simplify_System -------------------";
126 "M_b x = c * x + - 1 * q_0 * (x \<up> 2 / 2) + c_2";
127 "--- add.commute ---"; (* ... add.commute cf. b42e334c97ee *)
128 if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2)",
129 TermC.str2term"c * x") then ()
130 else error "integrate.sml, (- 1 * q_0 * (x \<up> 2 / 2)) < (c * x) not#1";
132 if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2)",
133 TermC.str2term"c_2") then ()
134 else error "integrate.sml, (- 1 * q_0 * (x \<up> 2 / 2)) < (c_2) not#2";
136 if ord_simplify_System false thy [] (TermC.str2term"c * x",
137 TermC.str2term"c_2") then ()
138 else error "integrate.sml, (c * x) < (c_2) not#3";
140 "--- mult.commute ---";
141 if ord_simplify_System false thy [] (TermC.str2term"x * c",
142 TermC.str2term"c * x") then ()
143 else error "integrate.sml, (x * c) < (c * x) not#4";
145 if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2) * c",
146 TermC.str2term"- 1 * q_0 * c * (x \<up> 2 / 2)")
147 then () else error "integrate.sml, (. * .) < (. * .) not#5";
149 if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2) * c",
150 TermC.str2term"c * - 1 * q_0 * (x \<up> 2 / 2)")
151 then () else error "integrate.sml, (. * .) < (. * .) not#6";
154 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
155 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
156 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
157 val t = TermC.str2term"[0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2,\
158 \0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2]";
159 val bdvs = [(TermC.str2term"bdv_1",TermC.str2term"c"),
160 (TermC.str2term"bdv_2",TermC.str2term"c_2")];
161 val SOME(t,_)= rewrite_set_inst_ ctxt true bdvs simplify_System_parenthesized t;
162 if UnparseC.term t = "[0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2), 0 = c_2]"
163 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1";
165 val SOME (t,_) = rewrite_set_inst_ ctxt true bdvs isolate_bdvs t;
166 if UnparseC.term t = "[L * c + c_2 = 0 + - 1 * (- 1 * q_0 * L \<up> 2 / 2), c_2 = 0]"
167 then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs";
169 val SOME(t,_)= rewrite_set_inst_ ctxt true bdvs simplify_System t;
170 if UnparseC.term t = "[L * c + c_2 = q_0 * L \<up> 2 / 2, c_2 = 0]"
171 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.2";
173 "--- 3--- see EqSystem.thy (*..if replaced by 'and' ...*)";
174 val SOME (t,_) = rewrite_set_ ctxt true order_system t;
175 if UnparseC.term t = "[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"
176 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.3";
178 "----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
179 "----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
180 "----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
181 val thy = @{theory "Isac_Knowledge"} (*because of Undeclared constant "Biegelinie.EI*);
182 val ctxt = Proof_Context.init_global thy;
184 TermC.str2term"[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 \<up> 3 + \
185 \ - 1 * q_0 / 24 * 0 \<up> 4),\
186 \ 0 = c_2 + c * L + 1 / EI * (L * q_0 / 12 * L \<up> 3 + \
187 \ - 1 * q_0 / 24 * L \<up> 4)]";
188 val SOME (t, _) = rewrite_set_ ctxt true norm_Rational t;
189 if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
190 "[c_2 = 0, 0 = q_0 * L \<up> 4 / (24 * EI) + (L * c + c_2)]"*)
191 "[0 = c_2, 0 = (24 * c_2 + 24 * L * c + L \<up> 4 * q_0) / 24]"
192 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.0b";
194 val SOME(t, _)= rewrite_set_inst_ ctxt true bdvs simplify_System_parenthesized t;
195 if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
196 "[c_2 = 0, 0 = q_0 * L \<up> 4 / (24 * EI) + (L * c + c_2)]"*)
197 "[0 = c_2, 0 = q_0 * L \<up> 4 / 24 + (L * c + c_2)]"
198 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1b";
200 val SOME (t,_) = rewrite_set_inst_ ctxt true bdvs isolate_bdvs t;
201 if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
202 "[c_2 = 0, L * c + c_2 = 0 + - 1 * (q_0 * L \<up> 4 / (24 * EI))]"*)
203 "[c_2 = 0, L * c + c_2 = 0 + - 1 * (q_0 * L \<up> 4 / 24)]"
204 then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs b";
206 val SOME(t,_)= rewrite_set_inst_ ctxt true bdvs simplify_System t;
207 if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
208 "[c_2 = 0, L * c + c_2 = - 1 * q_0 * L \<up> 4 / (24 * EI)]"*)
209 "[c_2 = 0, L * c + c_2 = - 1 * q_0 * L \<up> 4 / 24]"
210 then () else error "eqsystem.sml rewrite in 2x2 simplify_System.2b";
212 val xxx = rewrite_set_ ctxt true order_system t;
214 then () else error "eqsystem.sml rewrite in 2x2 simplify_System.3b";
217 "----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
218 "----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
219 "----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
220 val e1__ = TermC.str2term "c_2 = 77";
221 val e2__ = TermC.str2term "L * c + c_2 = q_0 * L \<up> 2 / 2";
222 val bdvs = [(TermC.str2term"bdv_1",TermC.str2term"c"),
223 (TermC.str2term"bdv_2",TermC.str2term"c_2")];
224 val SOME (e2__,_) = rewrite_terms_ ctxt Rewrite_Ord.function_empty Rule_Set.Empty [e1__] e2__;
225 if UnparseC.term e2__ = "L * c + 77 = q_0 * L \<up> 2 / 2" then ()
226 else error "eqsystem.sml top_down_substitution,2x2] subst";
229 rewrite_set_inst_ ctxt true bdvs simplify_System_parenthesized e2__;
230 if UnparseC.term e2__ = "77 + L * c = q_0 * L \<up> 2 / 2" then ()
231 else error "eqsystem.sml top_down_substitution,2x2] simpl_par";
233 val SOME (e2__,_) = rewrite_set_inst_ ctxt true bdvs isolate_bdvs e2__;
234 if UnparseC.term e2__ = "c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L" then ()
235 else error "eqsystem.sml top_down_substitution,2x2] isolate";
237 val t = TermC.str2term "[c_2 = 77, c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L]";
238 val SOME (t,_) = rewrite_set_ ctxt true order_system t;
239 if UnparseC.term t = "[c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L, c_2 = 77]" then ()
240 else error "eqsystem.sml top_down_substitution,2x2] order_system";
242 if not (ord_simplify_System
244 (TermC.str2term"[c_2 = 77, c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L]",
245 TermC.str2term"[c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L, c_2 = 77]"))
246 then () else error "eqsystem.sml, order_result rew_ord";
249 "----------- rewrite in [EqSystem,normalise,4x4] -----------------";
250 "----------- rewrite in [EqSystem,normalise,4x4] -----------------";
251 "----------- rewrite in [EqSystem,normalise,4x4] -----------------";
252 (*STOPPED.WN06?: revise rewrite in [EqSystem,normalise,4x4] from before 0609*)
253 val t = TermC.str2term (
254 "[(0::real) = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c_3 + c_4, " ^
255 "(0::real) = - 1 * q_0 * L \<up> 2 / 2 + L * c_3 + c_4, " ^
256 "c + c_2 + c_3 + c_4 = 0, " ^
257 "c_2 + c_3 + c_4 = 0]");
258 val bdvs = [(TermC.str2term"bdv_1::real",TermC.str2term"c::real"),
259 (TermC.str2term"bdv_2::real",TermC.str2term"c_2::real"),
260 (TermC.str2term"bdv_3::real",TermC.str2term"c_3::real"),
261 (TermC.str2term"bdv_4::real",TermC.str2term"c_4::real")];
263 rewrite_set_inst_ ctxt true bdvs simplify_System_parenthesized t;
264 if UnparseC.term t = "[0 = c_4, 0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c_3 + c_4),\n c + (c_2 + (c_3 + c_4)) = 0, c_2 + (c_3 + c_4) = 0]"
265 then () else error "eqsystem.sml rewrite in 4x4 simplify_System_paren";
267 val SOME (t, _) = rewrite_set_inst_ ctxt true bdvs isolate_bdvs t;
268 if UnparseC.term t = "[c_4 = 0, \
269 \L * c_3 + c_4 = 0 + - 1 * (- 1 * q_0 * L \<up> 2 / 2),\n \
270 \c + (c_2 + (c_3 + c_4)) = 0, c_2 + (c_3 + c_4) = 0]"
271 then () else error "eqsystem.sml rewrite in 4x4 isolate_bdvs";
273 val SOME(t, _)= rewrite_set_inst_ ctxt true bdvs simplify_System_parenthesized t;
274 if UnparseC.term t = "[c_4 = 0,\
275 \ L * c_3 + c_4 = q_0 * L \<up> 2 / 2,\
276 \ c + (c_2 + (c_3 + c_4)) = 0,\n\
277 \ c_2 + (c_3 + c_4) = 0]"
278 then () else error "eqsystem.sml rewrite in 4x4 simplify_System_p..2";
280 val SOME (t, _) = rewrite_set_ ctxt true order_system t;
281 if UnparseC.term t = "[c_4 = 0,\
282 \ L * c_3 + c_4 = q_0 * L \<up> 2 / 2,\
283 \ c_2 + (c_3 + c_4) = 0,\n\
284 \ c + (c_2 + (c_3 + c_4)) = 0]"
285 then () else error "eqsystem.sml rewrite in 4x4 order_system";
287 "----------- refine [linear,system]-------------------------------";
288 "----------- refine [linear,system]-------------------------------";
289 "----------- refine [linear,system]-------------------------------";
291 ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2," ^
292 "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + (c_2::real)]",
293 "solveForVars [c, c_2]", "solution LL"];
295 (*WN120313 in "solution L" above "Refine.refine fmz ["LINEAR", "system"]" caused an error...*)
296 "~~~~~ fun Refine.refine, args:"; val ((fmz: Formalise.model), (pblID:Problem.id)) = (fmz, ["LINEAR", "system"]);
297 "~~~~~ fun refin', args:"; val ((pblRD: Problem.id_reverse), fmz, pbls, ((Store.Node (pI, [py], [])): Problem.T Store.node)) =
298 ((rev o tl) pblID, fmz, [(*match list*)],
299 ((Store.Node ("LINEAR", [Problem.from_store ["LINEAR", "system"]], [])): Problem.T Store.node));
300 val {thy, ppc, where_, prls, ...} = py ;
301 "~~~~~ fun O_Model.init, args:"; val (thy, fmz, pbt) = (thy, fmz, ppc);
302 val ctxt = Proof_Context.init_global thy;
303 "~~~~~ fun declare_constraints, args:"; val (t, ctxt) = (nth 1 fmz, ctxt);
304 fun get_vars ((v,T)::vs) = (case raw_explode v |> Library.read_int of
305 (_, _::_) => (Free (v,T)::get_vars vs)
306 | (_, [] ) => get_vars vs) (*filter out nums as long as
307 we have Free ("123",_)*)
309 t = "equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,"^
310 "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + (c_2::real)]";
311 val ts = Term.add_frees (Syntax.read_term ctxt t) [] |> get_vars;
312 val ctxt = Variable.declare_constraints (nth 1 ts) ctxt;
313 val ctxt = Variable.declare_constraints (nth 2 ts) ctxt;
314 val ctxt = Variable.declare_constraints (nth 3 ts) ctxt;
315 val ctxt = Variable.declare_constraints (nth 4 ts) ctxt;
316 val t = nth 2 fmz; t = "solveForVars [c, c_2]";
317 val ts = Term.add_frees (Syntax.read_term ctxt t) [] |> get_vars;
318 val ctxt = Variable.declare_constraints (nth 1 ts) ctxt;
319 val t = nth 3 fmz; t = "solution LL";
320 (*(Syntax.read_term ctxt t);
321 Type unification failed: Clash of types "real" and "_ list"
322 Type error in application: incompatible operand type
324 Operator: solution :: bool list \<Rightarrow> toreall
325 Operand: L :: real ========== L was already present in equalities ========== *)
327 "===== case 1 =====";
328 val matches = Refine.refine fmz ["LINEAR", "system"];
330 [M_Match.Matches (["LINEAR", "system"], _),
331 M_Match.Matches (["2x2", "LINEAR", "system"], _),
332 M_Match.NoMatch (["triangular", "2x2", "LINEAR", "system"], _),
333 M_Match.Matches (["normalise", "2x2", "LINEAR", "system"],
334 {Find = [Correct "solution LL"],
338 "equalities\n [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,\n 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]",
339 Correct "solveForVars [c, c_2]"],
342 | _ => error "eqsystem.sml Refine.refine ['normalise','2x2'...]";
344 "===== case 2 =====";
345 val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
346 "solveForVars [c, c_2]", "solution LL"];
347 val matches = Refine.refine fmz ["LINEAR", "system"];
348 case matches of [_,_,
350 (["triangular", "2x2", "LINEAR", "system"],
351 {Find = [Correct "solution LL"],
354 [Correct "equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
355 Correct "solveForVars [c, c_2]"],
357 "tl [c, c_2] from [c, c_2] occur_exactly_in NTH 1\n [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
359 "[c, c_2] from [c, c_2] occur_exactly_in NTH 2\n [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"],
361 | _ => error "eqsystem.sml Refine.refine ['triangular','2x2'...]";
363 (*WN051014-----------------------------------------------------------------------------------\\
364 the above 'val matches = Refine.refine fmz ["LINEAR", "system"]'
365 didn't work anymore; we investigated in these steps:*)
366 val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
367 "solveForVars [c, c_2]", "solution LL"];
368 val matches = Refine.refine fmz ["triangular", "2x2", "LINEAR", "system"];
370 False "[c, c_2] from_ [c, c_2] occur_exactly_in nth_ 2\n
371 [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"]*)
372 val t = TermC.str2term ("[c, c_2] from [c, c_2] occur_exactly_in NTH 2" ^
373 "[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]");
375 val SOME (t', _) = rewrite_set_ ctxt false prls_triangular t;
378 ### eval asms: 1 < 2 + - 1
379 ==> nth_ (2 + - 1) [L * c + c_2 = q_0 * L \<up> 2 / 2] =
380 nth_ (2 + - 1 + - 1) []
381 #### rls: erls_prls_triangular on: 1 < 2 + - 1
382 ##### try calc: op <'
383 ### asms accepted: ["1 < 2 + - 1"] stored: ["1 < 2 + - 1"]
385 ... i.e Eval ("Groups.plus_class.plus", eval_binop "#add_") was missing in erls_prls_triangular*)
386 (*--------------------------------------------------------------------------------------------//*)
389 "===== case 3: relaxed preconditions for triangular system =====";
390 val fmz = ["equalities [L * q_0 = c, \
391 \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2,\
394 "solveForVars [c, c_2, c_3, c_4]", "solution LL"];
395 (*============ inhibit exn WN120314 TODO: investigate type error (same) in these 2 cases:
396 probably exn thrown by fun declare_constraints
397 /-------------------------------------------------------\
398 Type unification failed
399 Type error in application: incompatible operand type
401 Operator: op # c_3 :: 'a list \<Rightarrow> 'a list
402 Operand: [c_4] :: 'b list
403 \-------------------------------------------------------/
404 val TermC.matches = Refine.refine fmz ["LINEAR", "system"];
405 case TermC.matches of
406 [M_Match.Matches (["LINEAR", "system"], _),
407 M_Match.NoMatch (["2x2", "LINEAR", "system"], _),
408 M_Match.NoMatch (["3x3", "LINEAR", "system"], _),
409 M_Match.Matches (["4x4", "LINEAR", "system"], _),
410 M_Match.NoMatch (["triangular", "4x4", "LINEAR", "system"], _),
411 M_Match.Matches (["normalise", "4x4", "LINEAR", "system"], _)] => ()
412 | _ => error "eqsystem.sml: Refine.refine relaxed triangular sys M_Match.NoMatch";
413 (*WN060914 does NOT match, because 3rd and 4th equ are not ordered*)
415 "===== case 4 =====";
416 val fmz = ["equalities [L * q_0 = c, \
417 \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2,\
420 "solveForVars [c, c_2, c_3, c_4]", "solution LL"];
421 val TermC.matches = Refine.refine fmz ["triangular", "4x4", "LINEAR", "system"];
422 case TermC.matches of
423 [M_Match.Matches (["triangular", "4x4", "LINEAR", "system"], _)] => ()
424 | _ => error "eqsystem.sml: Refine.refine relaxed triangular sys M_Match.NoMatch";
425 val TermC.matches = Refine.refine fmz ["LINEAR", "system"];
426 ============ inhibit exn WN120314 ==============================================*)
428 "----------- Refine.refine [2x2,linear,system] search error--------------";
429 "----------- Refine.refine [2x2,linear,system] search error--------------";
430 "----------- Refine.refine [2x2,linear,system] search error--------------";
431 (*didn't go into ["2x2", "LINEAR", "system"];
432 we investigated in these steps:*)
433 val fmz = ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,\
434 \0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]",
435 "solveForVars [c, c_2]", "solution LL"];
436 val matches = Refine.refine fmz ["2x2", "LINEAR", "system"];
437 (*default_print_depth 11;*) TermC.matches; (*default_print_depth 3;*)
438 (*brought: 'False "length_ es_ = 2"'*)
440 (*-----fun refin' (pblRD:Problem.id_reverse) fmz pbls ((Store.Node (pI,[py],[])):pbt Store.store) =
441 (* val ((pblRD:Problem.id_reverse), fmz, pbls, ((Store.Node (pI,[py],[])):pbt Store.store)) =
442 (rev ["LINEAR", "system"], fmz, [(*match list*)],
443 ((Store.Node ("2x2",[Problem.from_store ["2x2", "LINEAR", "system"]],[])):pbt Store.store));
445 > show_types:=true; UnparseC.term (hd where_); show_types:=false;
446 val it = "length_ (es_::real list) = (2::real)" : string
448 =========================================================================\
449 -------fun Problem.prep_input
450 (* val (thy, (pblID, dsc_dats: (string * (string list)) list,
451 ev:rls, ca: string option, metIDs:metID list)) =
452 (EqSystem.thy, (["system"],
453 [("#Given" ,["equalities es_", "solveForVars v_s"]),
454 ("#Find" ,["solution ss___"](*___ is copy-named*))
456 Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)],
457 SOME "solveSystem es_ v_s",
460 > val [("#Given", [equalities_es_, "solveForVars v_s"])] = gi;
461 val equalities_es_ = "equalities es_" : string
462 > val (dd, ii) = (split_did o Thm.term_of o the o (TermC.parse thy)) equalities_es_;
463 > show_types:=true; UnparseC.term ii; show_types:=false;
464 val it = "es_::bool list" : string
465 ~~~~~~~~~~~~~~~ \<up> \<up> \<up> OK~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
467 > val {where_,...} = Problem.from_store ["2x2", "LINEAR", "system"];
468 > show_types:=true; UnparseC.term (hd where_); show_types:=false;
470 =========================================================================/
473 > (writeln o (I_Model.to_string (Proof_Context.init_global @{theory Isac_Knowledge}))) itms;
475 (1 ,[1] ,true ,#Given ,Cor equalities
476 [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
477 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2] ,(es_, [[0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
478 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]])),
479 (2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
480 (3 ,[1] ,true ,#Find ,Cor solution L ,(ss___, [L]))]
482 > (writeln o pres2str) pre';
484 (false, length_ es_ = 2),
485 (true, length_ [c, c_2] = 2)]
487 ----- fun match_oris':
488 > (writeln o (I_Model.to_string (Proof_Context.init_global @{theory Isac_Knowledge}))) itms;
489 > (writeln o pres2str) pre';
492 ----- fun check in Pre_Conds.
493 > (writeln o env2str) env;
495 (es_, [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
496 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2])", "
500 > val es_ = (fst o hd) env;
501 val es_ = Free ("es_", "bool List.list") : Term.term
503 > val pre1 = hd pres;
506 *** Const (op =, [real, real] => bool)
507 *** . Const (ListG.length_, real list => real)
508 *** . . Free (es_, real list)
509 ~~~~~~~~~~~~~~~~~~~ \<up> \<up> \<up> should be bool list~~~~~~~~~~~~~~~~~~~
513 THE REASON WAS A non-type-constrained variable IN #WHERE OF PROBLEM
514 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
517 "----------- me [EqSystem,normalise,2x2] -------------------------";
518 "----------- me [EqSystem,normalise,2x2] -------------------------";
519 "----------- me [EqSystem,normalise,2x2] -------------------------";
520 val fmz = ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,\
521 \0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]",
522 "solveForVars [c, c_2]", "solution LL"];
524 ("Biegelinie",["normalise", "2x2", "LINEAR", "system"],
525 ["EqSystem", "normalise", "2x2"]);
526 val p = e_pos'; val c = [];
527 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
528 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
529 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
530 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
531 val (p,_,f,nxt,_,pt) = me nxt p c pt;
532 case nxt of Specify_Method ["EqSystem", "normalise", "2x2"] => ()
533 | _ => error "eqsystem.sml [EqSystem,normalise,2x2] specify";
535 val (p,_,f,nxt,_,pt) = me nxt p c pt;
536 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
537 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f(*["(bdv_1, c)", "(bdv_2, hd (tl [c, c_2] ... corrected srls; ran only AFTER use"RCODE-root.sml", store_met was NOT SUFFICIENT*);
538 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
539 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
540 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
542 (Subproblem ("Biegelinie", ["triangular", "2x2", "LINEAR",_])) => ()
543 | _ => error "eqsystem.sml me [EqSystem,normalise,2x2] SubProblem";
545 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
546 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
547 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
548 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
550 (Specify_Method ["EqSystem", "top_down_substitution", "2x2"]) => ()
551 | _ => error "eqsystem.sml me [EqSys...2x2] top_down_substitution";
553 val (p,_,f,nxt,_,pt) = me nxt p c pt;
554 val PblObj {probl,...} = get_obj I pt [5];
555 (writeln o (I_Model.to_string (Proof_Context.init_global @{theory Isac_Knowledge}))) probl;
557 (1 ,[1] ,true ,#Given ,Cor equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2] ,(es_, [[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]])),
558 (2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
559 (3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]
561 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
562 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
563 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
564 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
565 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
566 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
567 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
568 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
570 (Check_Postcond ["triangular", "2x2", "LINEAR", "system"]) => ()
571 | _ => error "eqsystem.sml me Subpbl .[EqSys...2x2] finished";
572 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
573 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
574 if f2str f = "[c = L * q_0 / 2, c_2 = 0]" then ()
575 else error "eqsystem.sml me [EqSys...2x2] finished f2str f";
578 | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'";