test/Tools/isac/Knowledge/eqsystem-1.sml
changeset 60347 301b4bf4655e
child 60360 49680d595342
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/test/Tools/isac/Knowledge/eqsystem-1.sml	Tue Aug 03 19:16:27 2021 +0200
     1.3 @@ -0,0 +1,580 @@
     1.4 +(* Title: Knowledge/eqsystem-1.sml
     1.5 +   author: Walther Neuper 050826,
     1.6 +   (c) due to copyright terms
     1.7 +*)
     1.8 +
     1.9 +Rewrite.trace_on := false; (*true false*)
    1.10 +"-----------------------------------------------------------------";
    1.11 +"table of contents -----------------------------------------------";
    1.12 +"-----------------------------------------------------------------";
    1.13 +"----------- occur_exactly_in ------------------------------------";
    1.14 +"----------- problems --------------------------------------------";
    1.15 +"----------- rewrite-order ord_simplify_System -------------------";
    1.16 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
    1.17 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
    1.18 +"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
    1.19 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
    1.20 +"----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";
    1.21 +"----------- refine [linear,system]-------------------------------";
    1.22 +"----------- refine [2x2,linear,system] search error--------------";
    1.23 +"----------- me [EqSystem,normalise,2x2] -------------------------";
    1.24 +(*^^^--- eqsystem-1.sml #####################################################################
    1.25 +  vvv--- eqsystem-2.sml #####################################################################*)
    1.26 +"----------- me [linear,system] ..normalise..top_down_sub..-------";
    1.27 +"----------- all systems from Biegelinie -------------------------";
    1.28 +"----------- 4x4 systems from Biegelinie -------------------------";
    1.29 +"-----------------------------------------------------------------";
    1.30 +"-----------------------------------------------------------------";
    1.31 +"-----------------------------------------------------------------";
    1.32 +
    1.33 +val thy = @{theory "EqSystem"};
    1.34 +val ctxt = Proof_Context.init_global thy;
    1.35 +
    1.36 +"----------- occur_exactly_in ------------------------------------";
    1.37 +"----------- occur_exactly_in ------------------------------------";
    1.38 +"----------- occur_exactly_in ------------------------------------";
    1.39 +val all = [TermC.str2term"c", TermC.str2term"c_2", TermC.str2term"c_3"];
    1.40 +val t = TermC.str2term"0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
    1.41 +
    1.42 +if occur_exactly_in [TermC.str2term"c", TermC.str2term"c_2"] all t
    1.43 +then () else error "eqsystem.sml occur_exactly_in 1";
    1.44 +
    1.45 +if not (occur_exactly_in [TermC.str2term"c", TermC.str2term"c_2", TermC.str2term"c_3"] all t)
    1.46 +then () else error "eqsystem.sml occur_exactly_in 2";
    1.47 +
    1.48 +if not (occur_exactly_in [TermC.str2term"c_2"] all t)
    1.49 +then () else error "eqsystem.sml occur_exactly_in 3";
    1.50 +
    1.51 +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";
    1.52 +eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
    1.53 +val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
    1.54 +if str = "[c, c_2] from [c, c_2,\n" ^
    1.55 +  "               c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = True"
    1.56 +then () else error "eval_occur_exactly_in [c, c_2]";
    1.57 +
    1.58 +val t = TermC.str2term ("[c,c_2,c_3] from [c,c_2,c_3] occur_exactly_in " ^
    1.59 +		  "- 1 * q_0 * L \<up> 2 / 2 + L * c + c_2");
    1.60 +val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
    1.61 +if str = "[c, c_2,\n c_3] from [c, c_2,\n" ^
    1.62 +"            c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = False"
    1.63 +then () else error "eval_occur_exactly_in [c, c_2, c_3]";
    1.64 +
    1.65 +val t = TermC.str2term"[c_2] from [c,c_2,c_3] occur_exactly_in \
    1.66 +		\- 1 * q_0 * L \<up> 2 / 2 + L * c + c_2";
    1.67 +val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
    1.68 +if str = "[c_2] from [c, c_2,\n" ^
    1.69 +  "            c_3] occur_exactly_in - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2 = False"
    1.70 +then () else error "eval_occur_exactly_in [c, c_2, c_3]";
    1.71 +
    1.72 +val t = TermC.str2term"[] from [c,c_2,c_3] occur_exactly_in 0";
    1.73 +val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
    1.74 +if str = "[] from [c, c_2, c_3] occur_exactly_in 0 = True" then ()
    1.75 +else error "eval_occur_exactly_in [c, c_2, c_3]";
    1.76 +
    1.77 +val t = 
    1.78 +    TermC.str2term
    1.79 +	"[] from [c, c_2, c_3, c_4] occur_exactly_in - 1 * (q_0 * L \<up> 2) /2";
    1.80 +val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur_exactly_in" t 0;
    1.81 +if str = "[] from [c, c_2, c_3, c_4] occur_exactly_in \
    1.82 +	 \- 1 * (q_0 * L \<up> 2) / 2 = True" then ()
    1.83 +else error "eval_occur_exactly_in [c, c_2, c_3, c_4]";
    1.84 +
    1.85 +"----------- problems --------------------------------------------";
    1.86 +"----------- problems --------------------------------------------";
    1.87 +"----------- problems --------------------------------------------";
    1.88 +val t = TermC.str2term "Length [x+y=1,y=2] = 2";
    1.89 +TermC.atomty t;
    1.90 +val testrls = Rule_Set.append_rules "testrls" Rule_Set.empty 
    1.91 +			 [(Thm ("LENGTH_NIL", @{thm LENGTH_NIL})),
    1.92 +			  (Thm ("LENGTH_CONS", @{thm LENGTH_CONS})),
    1.93 +			  Eval (\<^const_name>\<open>plus\<close>, eval_binop "#add_"),
    1.94 +			  Eval (\<^const_name>\<open>HOL.eq\<close>,eval_equal "#equal_")
    1.95 +			  ];
    1.96 +val SOME (t',_) = rewrite_set_ thy false testrls t;
    1.97 +if UnparseC.term t' = "True" then () 
    1.98 +else error "eqsystem.sml: length_ [x+y=1,y=2] = 2";
    1.99 +
   1.100 +val SOME t = TermC.parse thy "solution LL";
   1.101 +TermC.atomty (Thm.term_of t);
   1.102 +val SOME t = TermC.parse thy "solution LL";
   1.103 +TermC.atomty (Thm.term_of t);
   1.104 +
   1.105 +val t = TermC.str2term 
   1.106 +"(tl (tl (tl v_s))) from v_s occur_exactly_in (NTH 1 (e_s::bool list))";
   1.107 +TermC.atomty t;
   1.108 +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 " ^
   1.109 +  "(NTH 1 [c_4 = 1, 2 = 2, 3 = 3, 4 = 4])");
   1.110 +(*----- broken in child of.1790e1073acc : eliminate "handle _ => ..." from Rewrite.rewrite -----\\
   1.111 +        assume flawed test setup hidden by "handle _ => ..."
   1.112 +        ERROR rewrite__set_ called with 'Erls' for '1 < 1'
   1.113 +val SOME (t,_) = 
   1.114 +    rewrite_set_ thy true 
   1.115 +		 (Rule_Set.append_rules "prls_" Rule_Set.empty 
   1.116 +			     [Thm ("NTH_CONS",ThmC.numerals_to_Free @{thm NTH_CONS}),
   1.117 +			      Thm ("NTH_NIL",ThmC.numerals_to_Free @{thm NTH_NIL}),
   1.118 +			      Thm ("TL_CONS",ThmC.numerals_to_Free @{thm tl_Cons}),
   1.119 +			      Thm ("TL_NIL",ThmC.numerals_to_Free @{thm tl_Nil}),
   1.120 +			      Eval ("EqSystem.occur_exactly_in", eval_occur_exactly_in "#eval_occur_exactly_in_")
   1.121 +			      ]) t;
   1.122 +if t = @{term True} then () 
   1.123 +else error "eqsystem.sml ..occur_exactly_in (nth_ 1 [c_4..";
   1.124 +        broken in child of.1790e1073acc : eliminate "handle _ => ..." from Rewrite.rewrite ---//*)
   1.125 +
   1.126 +
   1.127 +"----------- rewrite-order ord_simplify_System -------------------";
   1.128 +"----------- rewrite-order ord_simplify_System -------------------";
   1.129 +"----------- rewrite-order ord_simplify_System -------------------";
   1.130 +"M_b x = c * x + - 1 * q_0 * (x \<up> 2 / 2) + c_2";
   1.131 +"--- add.commute ---"; (* ... add.commute cf. b42e334c97ee *)
   1.132 +if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2)", 
   1.133 +				       TermC.str2term"c * x") then ()
   1.134 +else error "integrate.sml, (- 1 * q_0 * (x \<up> 2 / 2)) < (c * x) not#1";
   1.135 +
   1.136 +if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2)", 
   1.137 +				       TermC.str2term"c_2") then ()
   1.138 +else error "integrate.sml, (- 1 * q_0 * (x \<up> 2 / 2)) < (c_2) not#2";
   1.139 +
   1.140 +if ord_simplify_System false thy [] (TermC.str2term"c * x", 
   1.141 +				       TermC.str2term"c_2") then ()
   1.142 +else error "integrate.sml, (c * x) < (c_2) not#3";
   1.143 +
   1.144 +"--- mult.commute ---";
   1.145 +if ord_simplify_System false thy [] (TermC.str2term"x * c", 
   1.146 +				       TermC.str2term"c * x") then ()
   1.147 +else error "integrate.sml, (x * c) < (c * x) not#4";
   1.148 +
   1.149 +if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2) * c", 
   1.150 +				       TermC.str2term"- 1 * q_0 * c * (x \<up> 2 / 2)") 
   1.151 +then () else error "integrate.sml, (. * .) < (. * .) not#5";
   1.152 +
   1.153 +if ord_simplify_System false thy [] (TermC.str2term"- 1 * q_0 * (x \<up> 2 / 2) * c", 
   1.154 +				       TermC.str2term"c * - 1 * q_0 * (x \<up> 2 / 2)") 
   1.155 +then () else error "integrate.sml, (. * .) < (. * .) not#6";
   1.156 +
   1.157 +
   1.158 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   1.159 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   1.160 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   1.161 +val t = TermC.str2term"[0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2,\
   1.162 +	        \0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2]";
   1.163 +val bdvs = [(TermC.str2term"bdv_1",TermC.str2term"c"),
   1.164 +	    (TermC.str2term"bdv_2",TermC.str2term"c_2")];
   1.165 +val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;
   1.166 +if UnparseC.term t = "[0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2), 0 = c_2]"
   1.167 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1";
   1.168 +
   1.169 +val SOME (t,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs t;
   1.170 +if UnparseC.term t = "[L * c + c_2 = 0 + - 1 * (- 1 * q_0 * L \<up> 2 / 2), c_2 = 0]"
   1.171 +then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs";
   1.172 +
   1.173 +val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System t;
   1.174 +if UnparseC.term t = "[L * c + c_2 = q_0 * L \<up> 2 / 2, c_2 = 0]"
   1.175 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.2";
   1.176 +
   1.177 +"--- 3--- see EqSystem.thy (*..if replaced by 'and' ...*)";
   1.178 +val SOME (t,_) = rewrite_set_ thy true order_system t;
   1.179 +if UnparseC.term t = "[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"
   1.180 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.3";
   1.181 +
   1.182 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   1.183 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   1.184 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   1.185 +val thy = @{theory "Isac_Knowledge"} (*because of Undeclared constant "Biegelinie.EI*);
   1.186 +val t = 
   1.187 +    TermC.str2term"[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 \<up> 3 +         \
   1.188 +	    \                                     - 1 * q_0 / 24 * 0 \<up> 4),\
   1.189 +	    \ 0 = c_2 + c * L + 1 / EI * (L * q_0 / 12 * L \<up> 3 +         \
   1.190 +	    \                                     - 1 * q_0 / 24 * L \<up> 4)]";
   1.191 +val SOME (t, _) = rewrite_set_ thy true norm_Rational t;
   1.192 +if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
   1.193 +                      "[c_2 = 0, 0 = q_0 * L \<up> 4 / (24 * EI) + (L * c + c_2)]"*)
   1.194 +                      "[0 = c_2, 0 = (24 * c_2 + 24 * L * c + L \<up> 4 * q_0) / 24]"
   1.195 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.0b";
   1.196 +
   1.197 +val SOME(t, _)= rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;
   1.198 +if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
   1.199 +                       "[c_2 = 0, 0 = q_0 * L \<up> 4 / (24 * EI) + (L * c + c_2)]"*)
   1.200 +                       "[0 = c_2, 0 = q_0 * L \<up> 4 / 24 + (L * c + c_2)]"
   1.201 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1b";
   1.202 +
   1.203 +val SOME (t,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs t;
   1.204 +if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
   1.205 +                       "[c_2 = 0, L * c + c_2 = 0 + - 1 * (q_0 * L \<up> 4 / (24 * EI))]"*)
   1.206 +                       "[c_2 = 0, L * c + c_2 = 0 + - 1 * (q_0 * L \<up> 4 / 24)]"
   1.207 +then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs b";
   1.208 +
   1.209 +val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System t;
   1.210 +if UnparseC.term t = (*BEFORE "eliminate ThmC.numerals_to_Free"..
   1.211 +                       "[c_2 = 0, L * c + c_2 = - 1 * q_0 * L \<up> 4 / (24 * EI)]"*)
   1.212 +                       "[c_2 = 0, L * c + c_2 = - 1 * q_0 * L \<up> 4 / 24]"
   1.213 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System.2b";
   1.214 +
   1.215 +val xxx = rewrite_set_ thy true order_system t;
   1.216 +if is_none xxx
   1.217 +then () else error "eqsystem.sml rewrite in 2x2 simplify_System.3b";
   1.218 +
   1.219 +
   1.220 +"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
   1.221 +"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
   1.222 +"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
   1.223 +val e1__ = TermC.str2term "c_2 = 77";
   1.224 +val e2__ = TermC.str2term "L * c + c_2 = q_0 * L \<up> 2 / 2";
   1.225 +val bdvs = [(TermC.str2term"bdv_1",TermC.str2term"c"),
   1.226 +	    (TermC.str2term"bdv_2",TermC.str2term"c_2")];
   1.227 +val SOME (e2__,_) = rewrite_terms_ thy dummy_ord Rule_Set.Empty [e1__] e2__;
   1.228 +if UnparseC.term e2__ = "L * c + 77 = q_0 * L \<up> 2 / 2" then ()
   1.229 +else error "eqsystem.sml top_down_substitution,2x2] subst";
   1.230 +
   1.231 +val SOME (e2__,_) = 
   1.232 +    rewrite_set_inst_ thy true bdvs simplify_System_parenthesized e2__;
   1.233 +if UnparseC.term e2__ = "77 + L * c = q_0 * L \<up> 2 / 2" then ()
   1.234 +else error "eqsystem.sml top_down_substitution,2x2] simpl_par";
   1.235 +
   1.236 +val SOME (e2__,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs e2__;
   1.237 +if UnparseC.term e2__ = "c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L" then ()
   1.238 +else error "eqsystem.sml top_down_substitution,2x2] isolate";
   1.239 +
   1.240 +val t = TermC.str2term "[c_2 = 77, c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L]";
   1.241 +val SOME (t,_) = rewrite_set_ thy true order_system t;
   1.242 +if UnparseC.term t = "[c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L, c_2 = 77]" then ()
   1.243 +else error "eqsystem.sml top_down_substitution,2x2] order_system";
   1.244 +
   1.245 +if not (ord_simplify_System
   1.246 +	    false thy [] 
   1.247 +	    (TermC.str2term"[c_2 = 77, c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L]", 
   1.248 +	     TermC.str2term"[c = (q_0 * L \<up> 2 / 2 + - 1 * 77) / L, c_2 = 77]")) 
   1.249 +then () else error "eqsystem.sml, order_result rew_ord";
   1.250 +
   1.251 +
   1.252 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   1.253 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   1.254 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   1.255 +(*STOPPED.WN06?: revise rewrite in [EqSystem,normalise,4x4] from before 0609*)
   1.256 +val t = TermC.str2term (
   1.257 +  "[(0::real) = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c_3 + c_4, " ^ 
   1.258 +  "(0::real) = - 1 * q_0 * L \<up> 2 / 2 + L * c_3 + c_4, " ^ 
   1.259 +  "c + c_2 + c_3 + c_4 = 0, " ^ 
   1.260 +  "c_2 + c_3 + c_4 = 0]");
   1.261 +val bdvs = [(TermC.str2term"bdv_1::real",TermC.str2term"c::real"),
   1.262 +	    (TermC.str2term"bdv_2::real",TermC.str2term"c_2::real"),
   1.263 +	    (TermC.str2term"bdv_3::real",TermC.str2term"c_3::real"),
   1.264 +	    (TermC.str2term"bdv_4::real",TermC.str2term"c_4::real")];
   1.265 +val SOME (t, _) = 
   1.266 +    rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;
   1.267 +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]"
   1.268 +then () else error "eqsystem.sml rewrite in 4x4 simplify_System_paren";
   1.269 +
   1.270 +val SOME (t, _) = rewrite_set_inst_ thy true bdvs isolate_bdvs t;
   1.271 +if UnparseC.term t = "[c_4 = 0, \
   1.272 +	        \L * c_3 + c_4 = 0 + - 1 * (- 1 * q_0 * L \<up> 2 / 2),\n \
   1.273 +		\c + (c_2 + (c_3 + c_4)) = 0, c_2 + (c_3 + c_4) = 0]"
   1.274 +then () else error "eqsystem.sml rewrite in 4x4 isolate_bdvs";
   1.275 +
   1.276 +val SOME(t, _)= rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;
   1.277 +if UnparseC.term t = "[c_4 = 0,\
   1.278 +		\ L * c_3 + c_4 = q_0 * L \<up> 2 / 2,\
   1.279 +		\ c + (c_2 + (c_3 + c_4)) = 0,\n\
   1.280 +		\ c_2 + (c_3 + c_4) = 0]"
   1.281 +then () else error "eqsystem.sml rewrite in 4x4 simplify_System_p..2";
   1.282 +
   1.283 +val SOME (t, _) = rewrite_set_ thy true order_system t;
   1.284 +if UnparseC.term t = "[c_4 = 0,\
   1.285 +		\ L * c_3 + c_4 = q_0 * L \<up> 2 / 2,\
   1.286 +		\ c_2 + (c_3 + c_4) = 0,\n\
   1.287 +		\ c + (c_2 + (c_3 + c_4)) = 0]"
   1.288 +then () else error "eqsystem.sml rewrite in 4x4 order_system";
   1.289 +
   1.290 +"----------- refine [linear,system]-------------------------------";
   1.291 +"----------- refine [linear,system]-------------------------------";
   1.292 +"----------- refine [linear,system]-------------------------------";
   1.293 +val fmz =
   1.294 +  ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2," ^
   1.295 +               "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + (c_2::real)]", 
   1.296 +	   "solveForVars [c, c_2]", "solution LL"];
   1.297 +
   1.298 +(*WN120313 in "solution L" above "Refine.refine fmz ["LINEAR", "system"]" caused an error...*)
   1.299 +"~~~~~ fun Refine.refine, args:"; val ((fmz: Formalise.model), (pblID:Problem.id)) = (fmz, ["LINEAR", "system"]);
   1.300 +"~~~~~ fun refin', args:"; val ((pblRD: Problem.id_reverse), fmz, pbls, ((Store.Node (pI, [py], [])): Problem.T Store.node)) =
   1.301 +   ((rev o tl) pblID, fmz, [(*match list*)],
   1.302 +     ((Store.Node ("LINEAR", [Problem.from_store ["LINEAR", "system"]], [])): Problem.T Store.node));
   1.303 +      val {thy, ppc, where_, prls, ...} = py ;
   1.304 +"~~~~~ fun O_Model.init, args:"; val (fmz, thy, pbt) = (fmz, thy, ppc);
   1.305 +        val ctxt = Proof_Context.init_global thy;
   1.306 +"~~~~~ fun declare_constraints, args:"; val (t, ctxt) = (nth 1 fmz, ctxt);
   1.307 +      fun get_vars ((v,T)::vs) = (case raw_explode v |> Library.read_int of
   1.308 +              (_, _::_) => (Free (v,T)::get_vars vs)
   1.309 +            | (_, []  ) => get_vars vs) (*filter out nums as long as 
   1.310 +                                          we have Free ("123",_)*)
   1.311 +        | get_vars [] = [];
   1.312 +                                        t = "equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,"^
   1.313 +                                            "0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + (c_2::real)]";
   1.314 +      val ts = Term.add_frees (Syntax.read_term ctxt t) [] |> get_vars;
   1.315 +val ctxt = Variable.declare_constraints (nth 1 ts) ctxt;
   1.316 +val ctxt = Variable.declare_constraints (nth 2 ts) ctxt;
   1.317 +val ctxt = Variable.declare_constraints (nth 3 ts) ctxt;
   1.318 +val ctxt = Variable.declare_constraints (nth 4 ts) ctxt;
   1.319 +                                        val t = nth 2 fmz; t = "solveForVars [c, c_2]";
   1.320 +      val ts = Term.add_frees (Syntax.read_term ctxt t) [] |> get_vars;
   1.321 +val ctxt = Variable.declare_constraints (nth 1 ts) ctxt;
   1.322 +                                        val t = nth 3 fmz; t = "solution LL";
   1.323 +      (*(Syntax.read_term ctxt t); 
   1.324 +Type unification failed: Clash of types "real" and "_ list"
   1.325 +Type error in application: incompatible operand type
   1.326 +
   1.327 +Operator:  solution :: bool list \<Rightarrow> toreall
   1.328 +Operand:   L :: real                 ========== L was already present in equalities ========== *)
   1.329 +
   1.330 +"===== case 1 =====";
   1.331 +val matches = Refine.refine fmz ["LINEAR", "system"];
   1.332 +case matches of 
   1.333 + [M_Match.Matches (["LINEAR", "system"], _),
   1.334 +  M_Match.Matches (["2x2", "LINEAR", "system"], _),
   1.335 +  M_Match.NoMatch (["triangular", "2x2", "LINEAR", "system"], _),
   1.336 +		  M_Match.Matches (["normalise", "2x2", "LINEAR", "system"],
   1.337 +			    {Find = [Correct "solution LL"],
   1.338 +			     With = [],
   1.339 +			     Given =
   1.340 +			       [Correct
   1.341 +				"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]",
   1.342 +				        Correct "solveForVars [c, c_2]"],
   1.343 +				     Where = [],
   1.344 +				     Relate = []})] => ()
   1.345 +| _ => error "eqsystem.sml Refine.refine ['normalise','2x2'...]";
   1.346 +
   1.347 +"===== case 2 =====";
   1.348 +val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]", 
   1.349 +	   "solveForVars [c, c_2]", "solution LL"];
   1.350 +val matches = Refine.refine fmz ["LINEAR", "system"];
   1.351 +case matches of [_,_,
   1.352 +		  M_Match.Matches
   1.353 +		    (["triangular", "2x2", "LINEAR", "system"],
   1.354 +		      {Find = [Correct "solution LL"],
   1.355 +		       With = [],
   1.356 +		       Given =
   1.357 +		        [Correct "equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]",
   1.358 +		         Correct "solveForVars [c, c_2]"],
   1.359 +		       Where = [Correct
   1.360 +			"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]",
   1.361 +			                Correct
   1.362 +				"[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]"],
   1.363 +		       Relate = []})] => ()
   1.364 +| _ => error "eqsystem.sml Refine.refine ['triangular','2x2'...]";
   1.365 +
   1.366 +(*WN051014-----------------------------------------------------------------------------------\\
   1.367 +  the above 'val matches = Refine.refine fmz ["LINEAR", "system"]'
   1.368 +  didn't work anymore; we investigated in these steps:*)
   1.369 +val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]", 
   1.370 +	  "solveForVars [c, c_2]", "solution LL"];
   1.371 +val matches = Refine.refine fmz ["triangular", "2x2", "LINEAR", "system"];
   1.372 +(*... resulted in 
   1.373 +   False "[c, c_2] from_ [c, c_2] occur_exactly_in nth_ 2\n    
   1.374 +          [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]"]*)
   1.375 +val t = TermC.str2term ("[c, c_2] from [c, c_2] occur_exactly_in NTH 2" ^   
   1.376 +		  "[c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2]");
   1.377 +Rewrite.trace_on := false; (*true false*)
   1.378 +val SOME (t', _) = rewrite_set_ thy false prls_triangular t;
   1.379 +(*found:...
   1.380 +##  try thm: NTH_CONS
   1.381 +###  eval asms: 1 < 2 + - 1
   1.382 +==> nth_ (2 + - 1) [L * c + c_2 = q_0 * L \<up> 2 / 2] =
   1.383 +    nth_ (2 + - 1 + - 1) []
   1.384 +####  rls: erls_prls_triangular on: 1 < 2 + - 1
   1.385 +#####  try calc: op <'
   1.386 +###  asms accepted: ["1 < 2 + - 1"]   stored: ["1 < 2 + - 1"]
   1.387 +
   1.388 +... i.e Eval ("Groups.plus_class.plus", eval_binop "#add_") was missing in erls_prls_triangular*)
   1.389 +(*--------------------------------------------------------------------------------------------//*)
   1.390 +
   1.391 +
   1.392 +"===== case 3: relaxed preconditions for triangular system =====";
   1.393 +val fmz = ["equalities [L * q_0 = c,                               \
   1.394 +	   \            0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2,\
   1.395 +	   \            0 = c_4,                                           \
   1.396 +	   \            0 = c_3]", 
   1.397 +	   "solveForVars [c, c_2, c_3, c_4]", "solution LL"];
   1.398 +(*============ inhibit exn WN120314 TODO: investigate type error (same) in these 2 cases:
   1.399 +probably exn thrown by fun declare_constraints
   1.400 +/-------------------------------------------------------\
   1.401 +Type unification failed
   1.402 +Type error in application: incompatible operand type
   1.403 +
   1.404 +Operator:  op # c_3 :: 'a list \<Rightarrow> 'a list
   1.405 +Operand:   [c_4] :: 'b list
   1.406 +\-------------------------------------------------------/
   1.407 +val TermC.matches = Refine.refine fmz ["LINEAR", "system"];
   1.408 +case TermC.matches of 
   1.409 +    [M_Match.Matches (["LINEAR", "system"], _),
   1.410 +     M_Match.NoMatch (["2x2", "LINEAR", "system"], _),
   1.411 +     M_Match.NoMatch (["3x3", "LINEAR", "system"], _),
   1.412 +     M_Match.Matches (["4x4", "LINEAR", "system"], _),
   1.413 +     M_Match.NoMatch (["triangular", "4x4", "LINEAR", "system"], _),
   1.414 +     M_Match.Matches (["normalise", "4x4", "LINEAR", "system"], _)] => ()
   1.415 +  | _ => error "eqsystem.sml: Refine.refine relaxed triangular sys M_Match.NoMatch";
   1.416 +(*WN060914 does NOT match, because 3rd and 4th equ are not ordered*)
   1.417 +
   1.418 +"===== case 4 =====";
   1.419 +val fmz = ["equalities [L * q_0 = c,                                       \
   1.420 +	   \            0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2,\
   1.421 +	   \            0 = c_3,                           \
   1.422 +	   \            0 = c_4]", 
   1.423 +	   "solveForVars [c, c_2, c_3, c_4]", "solution LL"];
   1.424 +val TermC.matches = Refine.refine fmz ["triangular", "4x4", "LINEAR", "system"];
   1.425 +case TermC.matches of 
   1.426 +    [M_Match.Matches (["triangular", "4x4", "LINEAR", "system"], _)] => ()
   1.427 +  | _ => error "eqsystem.sml: Refine.refine relaxed triangular sys M_Match.NoMatch";
   1.428 +val TermC.matches = Refine.refine fmz ["LINEAR", "system"];
   1.429 +============ inhibit exn WN120314 ==============================================*)
   1.430 +
   1.431 +"----------- Refine.refine [2x2,linear,system] search error--------------";
   1.432 +"----------- Refine.refine [2x2,linear,system] search error--------------";
   1.433 +"----------- Refine.refine [2x2,linear,system] search error--------------";
   1.434 +(*didn't go into ["2x2", "LINEAR", "system"]; 
   1.435 +  we investigated in these steps:*)
   1.436 +val fmz = ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,\
   1.437 +	               \0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]", 
   1.438 +	   "solveForVars [c, c_2]", "solution LL"];
   1.439 +Rewrite.trace_on := false; (*true false*)
   1.440 +val matches = Refine.refine fmz ["2x2", "LINEAR", "system"];
   1.441 +Rewrite.trace_on := false; (*true false*)
   1.442 +(*default_print_depth 11;*) TermC.matches; (*default_print_depth 3;*)
   1.443 +(*brought: 'False "length_ es_ = 2"'*)
   1.444 +
   1.445 +(*-----fun refin' (pblRD:Problem.id_reverse) fmz pbls ((Store.Node (pI,[py],[])):pbt Store.store) =
   1.446 +(* val ((pblRD:Problem.id_reverse), fmz, pbls, ((Store.Node (pI,[py],[])):pbt Store.store)) =
   1.447 +       (rev ["LINEAR", "system"], fmz, [(*match list*)],
   1.448 +	((Store.Node ("2x2",[Problem.from_store ["2x2", "LINEAR", "system"]],[])):pbt Store.store));
   1.449 +   *)
   1.450 +> show_types:=true; UnparseC.term (hd where_); show_types:=false;
   1.451 +val it = "length_ (es_::real list) = (2::real)" : string
   1.452 +
   1.453 +=========================================================================\
   1.454 +-------fun Problem.prep_input
   1.455 +(* val (thy, (pblID, dsc_dats: (string * (string list)) list, 
   1.456 +		  ev:rls, ca: string option, metIDs:metID list)) =
   1.457 +       (EqSystem.thy, (["system"],
   1.458 +		       [("#Given" ,["equalities es_", "solveForVars v_s"]),
   1.459 +			("#Find"  ,["solution ss___"](*___ is copy-named*))
   1.460 +			],
   1.461 +		       Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)], 
   1.462 +		       SOME "solveSystem es_ v_s", 
   1.463 +		       []));
   1.464 +   *)
   1.465 +> val [("#Given", [equalities_es_, "solveForVars v_s"])] = gi;
   1.466 +val equalities_es_ = "equalities es_" : string
   1.467 +> val (dd, ii) = (split_did o Thm.term_of o the o (TermC.parse thy)) equalities_es_;
   1.468 +> show_types:=true; UnparseC.term ii; show_types:=false;
   1.469 +val it = "es_::bool list" : string
   1.470 +~~~~~~~~~~~~~~~ \<up> \<up> \<up>  OK~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   1.471 +
   1.472 +> val {where_,...} = Problem.from_store ["2x2", "LINEAR", "system"];
   1.473 +> show_types:=true; UnparseC.term (hd where_); show_types:=false;
   1.474 +
   1.475 +=========================================================================/
   1.476 +
   1.477 +-----fun refin' ff:
   1.478 +> (writeln o (I_Model.to_string (ThyC.to_ctxt @{theory Isac_Knowledge}))) itms;
   1.479 +[
   1.480 +(1 ,[1] ,true ,#Given ,Cor equalities
   1.481 + [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
   1.482 +  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,
   1.483 + 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]])),
   1.484 +(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
   1.485 +(3 ,[1] ,true ,#Find ,Cor solution L ,(ss___, [L]))]
   1.486 +
   1.487 +> (writeln o pres2str) pre';
   1.488 +[
   1.489 +(false, length_ es_ = 2),
   1.490 +(true, length_ [c, c_2] = 2)]
   1.491 +
   1.492 +----- fun match_oris':
   1.493 +> (writeln o (I_Model.to_string (ThyC.to_ctxt @{theory Isac_Knowledge}))) itms;
   1.494 +> (writeln o pres2str) pre';
   1.495 +..as in refin'
   1.496 +
   1.497 +----- fun check in Pre_Conds.
   1.498 +> (writeln o env2str) env;
   1.499 +["
   1.500 +(es_, [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,
   1.501 + 0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2])", "
   1.502 +(v_s, [c, c_2])", "
   1.503 +(ss___, L)"]
   1.504 +
   1.505 +> val es_ = (fst o hd) env;
   1.506 +val es_ = Free ("es_", "bool List.list") : Term.term
   1.507 +
   1.508 +> val pre1 = hd pres;
   1.509 +TermC.atomty pre1;
   1.510 +***
   1.511 +*** Const (op =, [real, real] => bool)
   1.512 +*** . Const (ListG.length_, real list => real)
   1.513 +*** . . Free (es_, real list)
   1.514 +~~~~~~~~~~~~~~~~~~~ \<up> \<up> \<up>  should be bool list~~~~~~~~~~~~~~~~~~~
   1.515 +*** . Free (2, real)
   1.516 +***
   1.517 +
   1.518 +THE REASON WAS A non-type-constrained variable IN #WHERE OF PROBLEM
   1.519 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   1.520 +*)
   1.521 +
   1.522 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   1.523 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   1.524 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   1.525 +val fmz = ["equalities [0 = - 1 * q_0 * 0 \<up> 2 / 2 + 0 * c + c_2,\
   1.526 +	               \0 = - 1 * q_0 * L \<up> 2 / 2 + L * c + c_2]", 
   1.527 +	   "solveForVars [c, c_2]", "solution LL"];
   1.528 +val (dI',pI',mI') =
   1.529 +  ("Biegelinie",["normalise", "2x2", "LINEAR", "system"],
   1.530 +   ["EqSystem", "normalise", "2x2"]);
   1.531 +val p = e_pos'; val c = []; 
   1.532 +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.533 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.534 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.535 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.536 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.537 +case nxt of Specify_Method ["EqSystem", "normalise", "2x2"] => ()
   1.538 +	  | _ => error "eqsystem.sml [EqSystem,normalise,2x2] specify";
   1.539 +
   1.540 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.541 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.542 +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*);
   1.543 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.544 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.545 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.546 +case nxt of
   1.547 +    (Subproblem ("Biegelinie", ["triangular", "2x2", "LINEAR",_])) => ()
   1.548 +  | _ => error "eqsystem.sml me [EqSystem,normalise,2x2] SubProblem";
   1.549 +
   1.550 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.551 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.552 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.553 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.554 +case nxt of
   1.555 +    (Specify_Method ["EqSystem", "top_down_substitution", "2x2"]) => ()
   1.556 +  | _ => error "eqsystem.sml me [EqSys...2x2] top_down_substitution";
   1.557 +
   1.558 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
   1.559 +val PblObj {probl,...} = get_obj I pt [5];
   1.560 +    (writeln o (I_Model.to_string (ThyC.to_ctxt @{theory Isac_Knowledge}))) probl;
   1.561 +(*[
   1.562 +(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]])),
   1.563 +(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
   1.564 +(3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]
   1.565 +*)
   1.566 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.567 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.568 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.569 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.570 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.571 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.572 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.573 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.574 +case nxt of
   1.575 +    (Check_Postcond ["triangular", "2x2", "LINEAR", "system"]) => ()
   1.576 +  | _ => error "eqsystem.sml me Subpbl .[EqSys...2x2] finished";
   1.577 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.578 +val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   1.579 +if f2str f = "[c = L * q_0 / 2, c_2 = 0]" then ()
   1.580 +else error "eqsystem.sml me [EqSys...2x2] finished f2str f";
   1.581 +case nxt of
   1.582 +    (End_Proof') => ()
   1.583 +  | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'";