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 ---------------------------------------------------equsystem-1.sml";
10 "----------- problems -----------------------------------------------------------equsystem-1.sml";
11 "----------- rewrite-order ord_simplify_System ----------------------------------equsystem-1.sml";
12 "----------- rewrite in [EqSystem,normalise,2x2] --------------------------------equsystem-1.sml";
13 "----------- rewrite example from 2nd [EqSystem,normalise,2x2] ------------------equsystem-1.sml";
14 "----------- rewrite in [EqSystem,top_down_substitution,2x2] --------------------equsystem-1.sml";
15 "----------- rewrite in [EqSystem,normalise,4x4] --------------------------------equsystem-1.sml";
16 "----------- script [EqSystem,top_down_substitution,2x2] Vers.1 -----------------equsystem-1.sml";
17 "----------- refine [linear,system]----------------------------------------------equsystem-1.sml";
18 "----------- refine [2x2,linear,system] search error-----------------------------equsystem-1.sml";
19 "----------- me [EqSystem,normalise,2x2], refine Subproblem ---------------------equsystem-1.sml";
20 "----------- me [EqSystem,normalise,2x2], refine Subproblem, step into istate---equsystem-1a.sml";
21 "----------- me [linear,system] ..normalise..top_down_sub..----------------------equsystem-2.sml";
22 "----------- all systems from Biegelinie ----------------------------------------equsystem-2.sml";
23 "----------- 4x4 systems from Biegelinie ----------------------------------------equsystem-2.sml";
24 "-----------------------------------------------------------------------------------------------";
25 "-----------------------------------------------------------------------------------------------";
26 "-----------------------------------------------------------------------------------------------";
28 val thy = @{theory "EqSystem"};
29 val ctxt = Proof_Context.init_global thy;
31 "----------- occur_exactly_in ------------------------------------";
32 "----------- occur_exactly_in ------------------------------------";
33 "----------- occur_exactly_in ------------------------------------";
34 val all = [TermC.parse_test @{context}"c", TermC.parse_test @{context}"c_2", TermC.parse_test @{context}"c_3"];
35 val t = TermC.parse_test @{context}"0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
37 if occur_exactly_in [TermC.parse_test @{context}"c", TermC.parse_test @{context}"c_2"] all t
38 then () else error "eqsystem.sml occur_exactly_in 1";
40 if not (occur_exactly_in [TermC.parse_test @{context}"c", TermC.parse_test @{context}"c_2", TermC.parse_test @{context}"c_3"] all t)
41 then () else error "eqsystem.sml occur_exactly_in 2";
43 if not (occur_exactly_in [TermC.parse_test @{context}"c_2"] all t)
44 then () else error "eqsystem.sml occur_exactly_in 3";
46 val t = TermC.parse_test @{context}"[c,c_2] from [c,c_2,c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
47 eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
48 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
49 if str = "[c, c_2] from [c, c_2,\n" ^
50 " c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = True"
51 then () else error "eval_occur_exactly_in [c, c_2]";
53 val t = TermC.parse_test @{context} ("[c,c_2,c_3] from [c,c_2,c_3] occur_exactly_in " ^
54 "- 1 * q_0 * L \<up> 2 / 2 + L * c + c_2");
55 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
56 if str = "[c, c_2,\n c_3] from [c, c_2,\n" ^
57 " c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = False"
58 then () else error "eval_occur_exactly_in [c, c_2, c_3]";
60 val t = TermC.parse_test @{context}"[c_2] from [c,c_2,c_3] occur_exactly_in \
61 \- 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
62 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
63 if str = "[c_2] from [c, c_2,\n" ^
64 " c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = False"
65 then () else error "eval_occur_exactly_in [c, c_2, c_3]";
67 val t = TermC.parse_test @{context}"[] from [c,c_2,c_3] occur_exactly_in 0";
68 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
69 if str = "[] from [c, c_2, c_3] occur_exactly_in 0 = True" then ()
70 else error "eval_occur_exactly_in [c, c_2, c_3]";
73 TermC.parse_test @{context}
74 "[] from [c, c_2, c_3, c_4] occur_exactly_in - 1 * (q_0 * L \<up> 2) /2";
75 val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
76 if str = "[] from [c, c_2, c_3, c_4] occur_exactly_in \
77 \- 1 * (q_0 * L \<up> 2) / 2 = True" then ()
78 else error "eval_occur_exactly_in [c, c_2, c_3, c_4]";
80 "----------- problems --------------------------------------------";
81 "----------- problems --------------------------------------------";
82 "----------- problems --------------------------------------------";
83 val t = TermC.parse_test @{context} "Length [x+y=1,y=2] = 2";
84 TermC.atom_trace_detail @{context} t;
85 val testrls = Rule_Set.append_rules "testrls" Rule_Set.empty
86 [(Thm ("LENGTH_NIL", @{thm LENGTH_NIL})),
87 (Thm ("LENGTH_CONS", @{thm LENGTH_CONS})),
88 Eval (\<^const_name>\<open>plus\<close>, Calc_Binop.numeric "#add_"),
89 Eval (\<^const_name>\<open>HOL.eq\<close>,eval_equal "#equal_")
91 val SOME (t',_) = rewrite_set_ ctxt false testrls t;
92 if UnparseC.term t' = "True" then ()
93 else error "eqsystem.sml: length_ [x+y=1,y=2] = 2";
95 val SOME t = TermC.parseNEW ctxt "solution LL";
96 TermC.atom_trace_detail @{context} t;
97 val SOME t = TermC.parseNEW ctxt "solution LL";
98 TermC.atom_trace_detail @{context} t;
100 val t = TermC.parse_test @{context}
101 "(tl (tl (tl v_s))) from v_s occur_exactly_in (NTH 1 (e_s::bool list))";
102 TermC.atom_trace_detail @{context} t;
103 val t = TermC.parse_test @{context} ("(tl (tl (tl [c, c_2, c_3, c_4]))) from [c, c_2, c_3, c_4] occur_exactly_in " ^
104 "(NTH 1 [c_4 = 1, 2 = 2, 3 = 3, 4 = 4])");
105 (*----- broken in child of.1790e1073acc : eliminate "handle _ => ..." from Rewrite.rewrite -----\\
106 assume flawed test setup hidden by "handle _ => ..."
107 ERROR rewrite__set_ called with 'Erls' for '1 < 1'
109 rewrite_set_ ctxt true
110 (Rule_Set.append_rules "prls_" Rule_Set.empty
111 [Thm ("NTH_CONS",ThmC.numerals_to_Free @{thm NTH_CONS}),
112 Thm ("NTH_NIL",ThmC.numerals_to_Free @{thm NTH_NIL}),
113 Thm ("TL_CONS",ThmC.numerals_to_Free @{thm tl_Cons}),
114 Thm ("TL_NIL",ThmC.numerals_to_Free @{thm tl_Nil}),
115 Eval ("EqSystem.occur_exactly_in", eval_occur_exactly_in "#eval_occur_exactly_in_")
117 if t = @{term True} then ()
118 else error "eqsystem.sml ..occur_exactly_in (nth_ 1 [c_4..";
119 broken in child of.1790e1073acc : eliminate "handle _ => ..." from Rewrite.rewrite ---//*)
122 "----------- rewrite-order ord_simplify_System -------------------";
123 "----------- rewrite-order ord_simplify_System -------------------";
124 "----------- rewrite-order ord_simplify_System -------------------";
125 "M_b x = c * x + - 1 * q_0 * (x \<up> 2 / 2) + c_2";
126 "--- add.commute ---"; (* ... add.commute cf. b42e334c97ee *)
127 if ord_simplify_System false ctxt [] (TermC.parse_test @{context}"- 1 * q_0 * (x \<up> 2 / 2)",
128 TermC.parse_test @{context}"c * x") then ()
129 else error "integrate.sml, (- 1 * q_0 * (x \<up> 2 / 2)) < (c * x) not#1";
131 if ord_simplify_System false ctxt [] (TermC.parse_test @{context}"- 1 * q_0 * (x \<up> 2 / 2)",
132 TermC.parse_test @{context}"c_2") then ()
133 else error "integrate.sml, (- 1 * q_0 * (x \<up> 2 / 2)) < (c_2) not#2";
135 if ord_simplify_System false ctxt [] (TermC.parse_test @{context}"c * x",
136 TermC.parse_test @{context}"c_2") then ()
137 else error "integrate.sml, (c * x) < (c_2) not#3";
139 "--- mult.commute ---";
140 if ord_simplify_System false ctxt [] (TermC.parse_test @{context}"x * c",
141 TermC.parse_test @{context}"c * x") then ()
142 else error "integrate.sml, (x * c) < (c * x) not#4";
144 if ord_simplify_System false ctxt [] (TermC.parse_test @{context}"- 1 * q_0 * (x \<up> 2 / 2) * c",
145 TermC.parse_test @{context}"- 1 * q_0 * c * (x \<up> 2 / 2)")
146 then () else error "integrate.sml, (. * .) < (. * .) not#5";
148 if ord_simplify_System false ctxt [] (TermC.parse_test @{context}"- 1 * q_0 * (x \<up> 2 / 2) * c",
149 TermC.parse_test @{context}"c * - 1 * q_0 * (x \<up> 2 / 2)")
150 then () else error "integrate.sml, (. * .) < (. * .) not#6";
153 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
154 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
155 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";
156 val t = TermC.parse_test @{context}"[0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2,\
157 \0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2]";
158 val bdvs = [(TermC.parse_test @{context}"bdv_1",TermC.parse_test @{context}"c"),
159 (TermC.parse_test @{context}"bdv_2",TermC.parse_test @{context}"c_2")];
160 val SOME (t,_) = rewrite_set_inst_ ctxt true bdvs simplify_System_parenthesized t;
161 if UnparseC.term t = "[0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2), 0 = c_2]"
162 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1";
164 val SOME (t,_) = rewrite_set_inst_ ctxt true bdvs isolate_bdvs t;
165 if UnparseC.term t = "[L * c + c_2 = 0 + - 1 * (- 1 * q_0 * L \<up> 2 / 2), c_2 = 0]"
166 then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs";
168 val SOME (t,_)= rewrite_set_inst_ ctxt true bdvs simplify_System t;
169 if UnparseC.term t = "[L * c + c_2 = q_0 * L \<up> 2 / 2, c_2 = 0]"
170 then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.2";
172 "--- 3--- see EqSystem.thy (*..if replaced by 'and' ...*)";
173 val SOME (t,_) = rewrite_set_ ctxt true order_system t;
174 if UnparseC.term t = "[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"
175 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.parse_test @{context}"[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.parse_test @{context} "c_2 = 77";
221 val e2__ = TermC.parse_test @{context} "L * c + c_2 = q_0 * L \<up> 2 / 2";
222 val bdvs = [(TermC.parse_test @{context}"bdv_1",TermC.parse_test @{context}"c"),
223 (TermC.parse_test @{context}"bdv_2",TermC.parse_test @{context}"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.parse_test @{context} "[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.parse_test @{context}"[c_2 = 77, c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L]",
245 TermC.parse_test @{context}"[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.parse_test @{context} (
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.parse_test @{context}"bdv_1::real",TermC.parse_test @{context}"c::real"),
259 (TermC.parse_test @{context}"bdv_2::real",TermC.parse_test @{context}"c_2::real"),
260 (TermC.parse_test @{context}"bdv_3::real",TermC.parse_test @{context}"c_3::real"),
261 (TermC.parse_test @{context}"bdv_4::real",TermC.parse_test @{context}"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";
289 "----------- refine [linear,system]-------------------------------";
290 "----------- refine [linear,system]-------------------------------";
291 "----------- refine [linear,system]-------------------------------";
293 ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2," ^
294 "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + (c_2::real)]",
295 "solveForVars [c, c_2]", "solution LL"];
297 (*WN120313 in "solution L" above "Refine.xxxxx @{context} fmz ["LINEAR", "system"]" caused an error...*)
298 "~~~~~ fun Refine.refine , args:"; val ((fmz: Formalise.model), (pblID:Problem.id)) = (fmz, ["LINEAR", "system"]);
299 "~~~~~ fun refin' , args:"; val ((pblRD: Problem.id_reverse), fmz, pbls, ((Store.Node (pI, [py], [])): Problem.T Store.node)) =
300 ((rev o tl) pblID, fmz, [(*match list*)],
301 ((Store.Node ("LINEAR", [Problem.from_store ctxt ["LINEAR", "system"]], [])): Problem.T Store.node));
302 val {thy, model, where_, where_rls, ...} = py ;
303 "~~~~~ fun O_Model.init, args:"; val (thy, fmz, pbt) = (thy, fmz, model);
304 val ctxt = Proof_Context.init_global thy;
305 "~~~~~ fun declare_constraints, args:"; val (t, ctxt) = (nth 1 fmz, ctxt);
306 fun get_vars ((v,T)::vs) = (case raw_explode v |> Library.read_int of
307 (_, _::_) => (Free (v,T)::get_vars vs)
308 | (_, [] ) => get_vars vs) (*filter out nums as long as
309 we have Free ("123",_)*)
311 t = "equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,"^
312 "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + (c_2::real)]";
313 val ts = Term.add_frees (Syntax.read_term ctxt t) [] |> get_vars;
314 val ctxt = Variable.declare_constraints (nth 1 ts) ctxt;
315 val ctxt = Variable.declare_constraints (nth 2 ts) ctxt;
316 val ctxt = Variable.declare_constraints (nth 3 ts) ctxt;
317 val ctxt = Variable.declare_constraints (nth 4 ts) ctxt;
318 val t = nth 2 fmz; t = "solveForVars [c, c_2]";
319 val ts = Term.add_frees (Syntax.read_term ctxt t) [] |> get_vars;
320 val ctxt = Variable.declare_constraints (nth 1 ts) ctxt;
321 val t = nth 3 fmz; t = "solution LL";
322 (*(Syntax.read_term ctxt t);
323 Type unification failed: Clash of types "real" and "_ list"
324 Type error in application: incompatible operand type
326 Operator: solution :: bool list \<Rightarrow> toreall
327 Operand: L :: real ========== L was already present in equalities ========== *)
329 "===== case 1 =====";
330 val matches = Refine.xxxxx @{context} fmz ["LINEAR", "system"];
332 [M_Match.Matches (["LINEAR", "system"], _), (*Matches*)
333 M_Match.Matches (["2x2", "LINEAR", "system"], _), (*NoMatch ! GOON !*)
334 M_Match.NoMatch (["triangular", "2x2", "LINEAR", "system"], _), (**)
335 M_Match.Matches (["normalise", "2x2", "LINEAR", "system"], (**)
336 {Find = [Correct "solution LL"], With = [], (**)
337 Given = [Correct "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]",
338 Correct "solveForVars [c, c_2]"],
341 | _ => error "eqsystem.sml Refine.refine ['normalise','2x2'...]";
343 "===== case 2 =====";
344 val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
345 "solveForVars [c, c_2]", "solution LL"];
346 val matches = Refine.xxxxx @{context} fmz ["LINEAR", "system"];
347 case matches of [_,_,
349 (["triangular", "2x2", "LINEAR", "system"],
350 {Find = [Correct "solution LL"],
353 [Correct "equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
354 Correct "solveForVars [c, c_2]"],
356 "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]",
358 "[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]"],
360 | _ => error "eqsystem.sml Refine.refine ['triangular','2x2'...]";
362 (*WN051014-----------------------------------------------------------------------------------\\
363 the above 'val matches = Refine.xxxxx @{context} fmz ["LINEAR", "system"]'
364 didn't work anymore; we investigated in these steps:*)
365 val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
366 "solveForVars [c, c_2]", "solution LL"];
367 val matches = Refine.xxxxx @{context} fmz ["triangular", "2x2", "LINEAR", "system"];
369 False "[c, c_2] from_ [c, c_2] occur_exactly_in nth_ 2\n
370 [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"]*)
371 val t = TermC.parse_test @{context} ("[c, c_2] from [c, c_2] occur_exactly_in NTH 2" ^
372 "[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]");
374 val SOME (t', _) = rewrite_set_ ctxt false prls_triangular t;
377 ### eval asms: 1 < 2 + - 1
378 ==> nth_ (2 + - 1) [L * c + c_2 = q_0 * L \<up> 2 / 2] =
379 nth_ (2 + - 1 + - 1) []
380 #### rls: erls_prls_triangular on: 1 < 2 + - 1
381 ##### try calc: op <'
382 ### asms accepted: ["1 < 2 + - 1"] stored: ["1 < 2 + - 1"]
384 ... i.e Eval ("Groups.plus_class.plus", Calc_Binop.numeric "#add_") was missing in erls_prls_triangular*)
385 (*--------------------------------------------------------------------------------------------//*)
388 "===== case 3: relaxed preconditions for triangular system =====";
389 val fmz = ["equalities [L * q_0 = c, \
390 \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2,\
393 "solveForVars [c, c_2, c_3, c_4]", "solution LL"];
394 (*============ inhibit exn WN120314 TODO: investigate type error (same) in these 2 cases:
395 probably exn thrown by fun declare_constraints
396 /-------------------------------------------------------\
397 Type unification failed
398 Type error in application: incompatible operand type
400 Operator: op # c_3 :: 'a list \<Rightarrow> 'a list
401 Operand: [c_4] :: 'b list
402 \-------------------------------------------------------/
403 val TermC.matches = Refine.refine fmz ["LINEAR", "system"];
404 case TermC.matches of
405 [M_Match.Matches (["LINEAR", "system"], _),
406 M_Match.NoMatch (["2x2", "LINEAR", "system"], _),
407 M_Match.NoMatch (["3x3", "LINEAR", "system"], _),
408 M_Match.Matches (["4x4", "LINEAR", "system"], _),
409 M_Match.NoMatch (["triangular", "4x4", "LINEAR", "system"], _),
410 M_Match.Matches (["normalise", "4x4", "LINEAR", "system"], _)] => ()
411 | _ => error "eqsystem.sml: Refine.refine relaxed triangular sys M_Match.NoMatch";
412 (*WN060914 does NOT match, because 3rd and 4th equ are not ordered*)
414 "===== case 4 =====";
415 val fmz = ["equalities [L * q_0 = c, \
416 \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2,\
419 "solveForVars [c, c_2, c_3, c_4]", "solution LL"];
420 val TermC.matches = Refine.refine fmz ["triangular", "4x4", "LINEAR", "system"];
421 case TermC.matches of
422 [M_Match.Matches (["triangular", "4x4", "LINEAR", "system"], _)] => ()
423 | _ => error "eqsystem.sml: Refine.refine relaxed triangular sys M_Match.NoMatch";
424 val TermC.matches = Refine.refine fmz ["LINEAR", "system"];
425 ============ inhibit exn WN120314 ==============================================*)
429 "----------- Refine.refine [2x2,linear,system] search error--------------";
430 "----------- Refine.refine [2x2,linear,system] search error--------------";
431 "----------- Refine.refine [2x2,linear,system] search error--------------";
432 (*didn't go into ["2x2", "LINEAR", "system"];
433 we investigated in these steps:*)
434 val fmz = ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,\
435 \0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]",
436 "solveForVars [c, c_2]", "solution LL"];
437 val matches = Refine.xxxxx @{context} fmz ["2x2", "LINEAR", "system"];
438 (*default_print_depth 11;*) TermC.matches; (*default_print_depth 3;*)
439 (*brought: 'False "length_ es_ = 2"'*)
441 (*-----fun refin' (pblRD:Problem.id_reverse) fmz pbls ((Store.Node (pI,[py],[])):pbt Store.store) =
442 (* val ((pblRD:Problem.id_reverse), fmz, pbls, ((Store.Node (pI,[py],[])):pbt Store.store)) =
443 (rev ["LINEAR", "system"], fmz, [(*match list*)],
444 ((Store.Node ("2x2",[Problem.from_store ["2x2", "LINEAR", "system"]],[])):pbt Store.store));
446 > show_types:=true; UnparseC.term (hd where_); show_types:=false;
447 val it = "length_ (es_::real list) = (2::real)" : string
449 =========================================================================\
450 -------fun Problem.prep_input
451 (* val (thy, (pblID, dsc_dats: (string * (string list)) list,
452 ev:rls, ca: string option, metIDs:metID list)) =
453 (EqSystem.thy, (["system"],
454 [("#Given" ,["equalities es_", "solveForVars v_s"]),
455 ("#Find" ,["solution ss___"](*___ is copy-named*))
457 Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)],
458 SOME "solveSystem es_ v_s",
461 > val [("#Given", [equalities_es_, "solveForVars v_s"])] = gi;
462 val equalities_es_ = "equalities es_" : string
463 > val (dd, ii) = ((Model_Pattern.split_descriptor ctxt) o Thm.term_of o the o (TermC.parse thy)) equalities_es_;
464 > show_types:=true; UnparseC.term ii; show_types:=false;
465 val it = "es_::bool list" : string
466 ~~~~~~~~~~~~~~~ \<up> \<up> \<up> OK~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
468 > val {where_,...} = Problem.from_store ["2x2", "LINEAR", "system"];
469 > show_types:=true; UnparseC.term (hd where_); show_types:=false;
471 =========================================================================/
474 > (writeln o (I_Model.to_string (Proof_Context.init_global @{theory Isac_Knowledge}))) itms;
476 (1 ,[1] ,true ,#Given ,Cor equalities
477 [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] ,(es_, [[0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
479 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]])),
480 (2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
481 (3 ,[1] ,true ,#Find ,Cor solution L ,(ss___, [L]))]
483 > (writeln o pres2str) pre';
485 (false, length_ es_ = 2),
486 (true, length_ [c, c_2] = 2)]
488 ----- fun match_oris':
489 > (writeln o (I_Model.to_string (Proof_Context.init_global @{theory Isac_Knowledge}))) itms;
490 > (writeln o pres2str) pre';
493 ----- fun check in Pre_Conds.
494 > (writeln o env2str) env;
496 (es_, [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
497 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2])", "
501 > val es_ = (fst o hd) env;
502 val es_ = Free ("es_", "bool List.list") : Term.term
504 > val pre1 = hd pres;
505 TermC.atom_trace_detail @{context} pre1;
507 *** Const (op =, [real, real] => bool)
508 *** . Const (ListG.length_, real list => real)
509 *** . . Free (es_, real list)
510 ~~~~~~~~~~~~~~~~~~~ \<up> \<up> \<up> should be bool list~~~~~~~~~~~~~~~~~~~
514 THE REASON WAS A non-type-constrained variable IN #WHERE OF PROBLEM
515 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
519 "----------- me [EqSystem,normalise,2x2], refine Subproblem ------------------------------------";
520 "----------- me [EqSystem,normalise,2x2], refine Subproblem ------------------------------------";
521 "----------- me [EqSystem,normalise,2x2], refine Subproblem ------------------------------------";
522 val fmz = ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2," ^
523 "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]",
524 "solveForVars [c, c_2]", "solution LL"];
526 ("Biegelinie",["normalise", "2x2", "LINEAR", "system"],
527 ["EqSystem", "normalise", "2x2"]);
528 val p = e_pos'; val c = [];
529 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
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;val (p,_,f,nxt,_,pt) = me nxt p c pt;
532 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
533 val (p,_,f,nxt,_,pt) = me nxt p c pt;
534 case nxt of Specify_Method ["EqSystem", "normalise", "2x2"] => ()
535 | _ => error "eqsystem.sml [EqSystem,normalise,2x2] specify";
537 val (p,_,f,nxt,_,pt) = me nxt p c pt;
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;
541 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
542 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
544 (Subproblem ("Biegelinie", ["triangular", "2x2", "LINEAR",_])) => ()
545 | _ => error "eqsystem.sml me [EqSystem,normalise,2x2] SubProblem";
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;
549 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
550 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
552 (Specify_Method ["EqSystem", "top_down_substitution", "2x2"]) => ()
553 | _ => error "eqsystem.sml me [EqSys...2x2] top_down_substitution";
555 val (p,_,f,nxt,_,pt) = me nxt p c pt;
556 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
557 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
558 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
559 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
560 val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
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;
565 (Check_Postcond ["triangular", "2x2", "LINEAR", "system"]) => ()
566 | _ => error "eqsystem.sml me Subpbl .[EqSys...2x2] finished";
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;
569 (* final test ... ----------------------------------------------------------------------------*)
570 if f2str f = "[c = L * q_0 / 2, c_2 = 0]" then ()
571 else error "eqsystem.sml me [EqSys...2x2] finished f2str f";
575 | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'";
577 Test_Tool.show_pt pt (*[
578 (([], Frm), solveSystem
579 [[0 = - 1 * q_0 * 0 \<up> 2 div 2 + 0 * c + c_2],
580 [0 = - 1 * q_0 * L \<up> 2 div 2 + L * c + c_2]]
582 (([1], Frm), [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
583 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]),
584 (([1], Res), [0 = c_2, 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2]),
585 (([2], Res), [0 = c_2, 0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2)]),
586 (([3], Res), [c_2 = 0, L * c + c_2 = 0 + - 1 * (- 1 * q_0 * L \<up> 2 / 2)]),
587 (([4], Res), [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]),
588 (([5], Pbl), solveSystem [L * c + c_2 = q_0 * L \<up> 2 / 2] [c_2]),
589 (([5, 1], Frm), L * c + c_2 = q_0 * L \<up> 2 / 2),
590 (([5, 1], Res), L * c + 0 = q_0 * L \<up> 2 / 2),
591 (([5, 2], Res), L * c = q_0 * L \<up> 2 / 2),
592 (([5, 3], Res), c = q_0 * L \<up> 2 / 2 / L),
593 (([5, 4], Res), c = L * q_0 / 2),
594 (([5, 5], Frm), [c_2 = 0, c = L * q_0 / 2]),
595 (([5, 5], Res), [c = L * q_0 / 2, c_2 = 0]),
596 (([5], Res), [c = L * q_0 / 2, c_2 = 0]),
597 (([], Res), [c = L * q_0 / 2, c_2 = 0])]