1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/test/Tools/isac/IsacKnowledge/diffapp.sml Thu Aug 12 11:02:32 2010 +0200
1.3 @@ -0,0 +1,752 @@
1.4 +(* tests for IsacKnowledge/DiffApp
1.5 + author Walther Neuper 000301
1.6 + (c) due to copyright terms
1.7 +
1.8 + use"../smltest/IsacKnowledge/diffapp.sml";
1.9 + use"diffapp.sml";
1.10 +*)
1.11 +
1.12 +"Contents----------------------------------------------";
1.13 +" Specify_Problem (match_itms_oris) ";
1.14 +" test specify, fmz <> [] ";
1.15 +" test specify, fmz = [] ";
1.16 +" problemtypes + formalizations ";
1.17 +"-------------------- ptree of {(a,b). is-max ... ----------------";
1.18 +"--------- me .. scripts for maximum-example ---------------------";
1.19 +"--------- autoCalc .. scripts for maximum-example ---------------";
1.20 +
1.21 +"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
1.22 +"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
1.23 +"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
1.24 +
1.25 +
1.26 +
1.27 +
1.28 +
1.29 +" #################################################### ";
1.30 +" problemtypes + formalizations ";
1.31 +" #################################################### ";
1.32 +" -------------- [maximum_of,function] --------------- ";
1.33 +val pbt =
1.34 + ["fixedValues fix_","maximum m_","valuesFor vs_","relations rs_"];
1.35 +map (the o (parseold thy)) pbt;
1.36 +val fmz =
1.37 + ["fixedValues [r=Arbfix]","maximum A",
1.38 + "valuesFor [a,b]",
1.39 + "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.40 + "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.41 + "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
1.42 +
1.43 + "boundVariable a","boundVariable b","boundVariable alpha",
1.44 + "interval {x::real. 0 <= x & x <= 2*r}",
1.45 + "interval {x::real. 0 <= x & x <= 2*r}",
1.46 + "interval {x::real. 0 <= x & x <= pi}",
1.47 + "errorBound (eps=(0::real))"];
1.48 +map (the o (parseold thy)) fmz;
1.49 +" -------------- [make,function] -------------- ";
1.50 +val pbt =
1.51 + ["functionOf f_","boundVariable v_","equalities eqs_",
1.52 + "functionTerm f_0_"];
1.53 +map (the o (parseold thy)) pbt;
1.54 +val fmz12 =
1.55 + ["functionOf A","boundVariable a","boundVariable b",
1.56 + "equalities [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.57 + (*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];
1.58 +map (the o (parseold thy)) fmz12;
1.59 +val fmz3 =
1.60 + ["functionOf A","boundVariable a","boundVariable b",
1.61 + "equalities [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
1.62 + (*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];
1.63 +map (the o (parseold thy)) fmz3;
1.64 +" --------- [univar,equation] --------- ";
1.65 +val pbt =
1.66 + ["equality e_","solveFor v_","solutions v_i_"];
1.67 +map (the o (parseold thy)) pbt;
1.68 +val fmz =
1.69 + ["equality ((a/2)^^^2 + (b/2)^^^2 = r^^^2)",
1.70 + "solveFor b","solutions b_i"];
1.71 +map (the o (parseold thy)) fmz;
1.72 +" ---- [on_interval,maximum_of,function] ---- ";
1.73 +val pbt =
1.74 + ["functionTerm t_","boundVariable v_","interval itv_",
1.75 + "errorBound err_","maxArgument v_0_"];
1.76 +map (the o (parseold thy)) pbt;
1.77 +val fmz12 =
1.78 + [(*28.11.00: "functionTerm (A_0 = a*sqrt(#4*r^^^#2 - a^^^#2))",*)
1.79 + "functionTerm (a*sqrt(4*r^^^2 - a^^^2))",
1.80 + (*28.11.00: "functionTerm (A_0 = b*sqrt(#4*r^^^#2 - b^^^#2))",*)
1.81 + "functionTerm (b*sqrt(4*r^^^2 - b^^^2))",
1.82 + "boundVariable a","boundVariable b",
1.83 + "interval {x::real. 0 <= x & x <= 2*r}",
1.84 + "errorBound (eps=0)","maxArgument (a_0=Undef)"];
1.85 +map (the o (parseold thy)) fmz12;
1.86 +val fmz3 =
1.87 + [(*28.11.00: "functionTerm (A_0 = (#2*r*sin alpha)*(#2*r*cos alpha))",*)
1.88 + "functionTerm ((2*r*sin alpha)*(2*r*cos alpha))",
1.89 + "boundVariable alpha",
1.90 + "interval {x::real. 0 <= x & x <= pi}",
1.91 + "errorBound (eps=0)","maxArgument (a_0=Undef)"];
1.92 +map (the o (parseold thy)) fmz3;
1.93 +" --------- [derivative_of,function] --------- ";
1.94 +val pbt =
1.95 + ["functionTerm f_","boundVariable v_","derivative f_'_"];
1.96 +map (the o (parseold thy)) pbt;
1.97 +val fmz =
1.98 + [(*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)
1.99 + "functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",
1.100 + "boundVariable a",
1.101 + (*28.11.00: "derivative (A_0'=Undef)"*)"derivative (Undef)"];
1.102 +map (the o (parseold thy)) fmz;
1.103 +" --------- [find_values,tool] --------- ";
1.104 +val pbt =
1.105 + ["maxArgument ma_","functionTerm f_","boundVariable v_",
1.106 + "valuesFor vls_","additionalRels rs_"];
1.107 +map (the o (parseold thy)) pbt;
1.108 +val fmz1 =
1.109 + ["maxArgument (a_0=(srqt 2)*r)",
1.110 + (*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)
1.111 + "functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",
1.112 + "boundVariable a",
1.113 + "valuesFor [a,b]","maximum A",
1.114 + "additionalRels [(a/2)^^^2 + (b/2)^^^2 = r^^^2]"];
1.115 +map (the o (parseold thy)) fmz1;
1.116 +
1.117 +
1.118 +
1.119 +"-------------------- ptree of {(a,b). is-max ... --------------------------";
1.120 +"-------------------- ptree of {(a,b). is-max ... --------------------------";
1.121 +"-------------------- ptree of {(a,b). is-max ... --------------------------";
1.122 +
1.123 +(* Teil von max-on-surface.sml,
1.124 + der nach Init_Proof -> prep_ori wieder l"auft
1.125 + (f"ur tests mit neuer pos')
1.126 + use"test-max-surf1.sml";
1.127 +
1.128 + Compiler.Control.Print.printDepth:=7; (*4 is default*)
1.129 + Compiler.Control.Print.printDepth:=4; (*4 is default*)
1.130 + *)
1.131 +
1.132 +(* --vvv-- ausgeliehen von test-root-equ/sml *)
1.133 +val loc = e_istate;
1.134 +val (dI',pI',mI') =
1.135 + ("Script.thy",["sqroot-test","univariate","equation"],
1.136 + ["Script","squ-equ-test2"]);
1.137 +val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
1.138 + "solveFor x","errorBound (eps=0)",
1.139 + "solutions L"];
1.140 +(*
1.141 +val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
1.142 +val ((p,p_),_,_,_,_,(_,pt,_)) = do_ (mI,m) e_pos'[1](e_scr,EmptyPtree,[]);
1.143 + --^^^-- ausgeliehen von test-root-equ/sml *)
1.144 +(*-------------- 9.6.03 --- cappend_ ... term -------irreparabler test
1.145 +val (pt,_) =
1.146 + cappend_problem EmptyPtree [] loc ([],(dI',pI',mI'));
1.147 +val pos = (lev_on o lev_dn) [];
1.148 +(* val pos = ([1]) *)
1.149 +val (pt,_) = cappend_parent pt pos loc "{(a,b). is-max ..."
1.150 + Empty_Tac TransitiveB;
1.151 +val pos = (lev_on o lev_dn) pos;
1.152 +(*val pos = ([1,1])*)
1.153 +val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-max ..."
1.154 + Empty_Tac ("[1,1]:{(a,b). is-extremum ...",[]) Complete;
1.155 +val pos = lev_on pos;
1.156 +(*val pos = ([1,2])*)
1.157 +val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-extremum ..."
1.158 + Empty_Tac ("[1,2]:{(a,b). f_x(a,b) ...",[]) Complete;
1.159 +val pos = lev_up pos;
1.160 +(*val pos = ([1])*)
1.161 +val (pt,_) = append_result pt pos e_istate ("[1#]:{(a,b). f_x(a,b) ...",[])
1.162 + Complete;
1.163 +
1.164 +val pos = lev_on pos;
1.165 +(*val pos = ([2]) *)
1.166 +val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x(a,b) ..."
1.167 + Empty_Tac ("[2]:{(a,b). f_x & f_xx &...",[]) Complete;
1.168 +val pos = lev_on pos;
1.169 +(*al pos = [3] : pos*)
1.170 +val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x & f_xx &..."
1.171 + Empty_Tac TransitiveB;
1.172 +val pos = (lev_on o lev_dn) pos;
1.173 +(*pos = ([3,1]) *)
1.174 +val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx & ..."
1.175 + Empty_Tac ("[3,1]:{(a,b). f_x & f_xx } cup ...",[]) Complete;
1.176 +val pos = lev_on pos;
1.177 +(*pos = ([3,2]) *)
1.178 +val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx } cup.."
1.179 + Empty_Tac ("[3,2]:{(a,b). f_x ..} cup ...",[]) Complete;
1.180 +
1.181 +val pos = lev_up pos;
1.182 +(*pos = ([3]) *)
1.183 +val (pt,_) = append_result pt pos e_istate ("[3#]:{(a,b). f_x ..} cup..",[])
1.184 + Complete;
1.185 +val pos = lev_on pos;
1.186 +(*val pos = [4] : pos *)
1.187 +val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x ..} cup ..."
1.188 + Empty_Tac IntersectB;
1.189 +val pos = (lev_on o lev_dn) pos;
1.190 +(*val pos = ([4,1]) *)
1.191 +val (pt,_) = cappend_parent pt pos loc "set_1 = ..."
1.192 + Empty_Tac SequenceB;
1.193 +
1.194 +
1.195 +val pos = (lev_on o lev_dn) pos;
1.196 +(*val pos = ([4,1,1]) *)
1.197 +val (pt,_) = cappend_parent(*pbl*) pt pos loc"f_x = d/dx x^3 ..."
1.198 + Empty_Tac TransitiveB;
1.199 +val pos = (lev_on o lev_dn) pos;
1.200 +(*val pos = ([4,1,1,1]) *)
1.201 +val (pt,_) = cappend_parent pt pos loc "d/dx x^3 ..."
1.202 + Empty_Tac TransitiveB;
1.203 +val pos = (lev_on o lev_dn) pos;
1.204 +(*val pos = ([4,1,1,1,1]) *)
1.205 +val (pt,_) = cappend_atomic pt pos loc "d/dx x^3 ..."
1.206 + Empty_Tac ("[4,1,1,1,1]:3x^2 + d/dx ...",[]) Complete;
1.207 +val pos = lev_on pos;
1.208 +(*val pos = ([4,1,1,1,2]) *)
1.209 +val (pt,_) = cappend_atomic pt pos loc "3x^2 + d/dx ..."
1.210 + Empty_Tac ("[4,1,1,1,2]:3x^2 + 0 + d/dx ...",[]) Complete;
1.211 +val pos = lev_on pos;
1.212 +(*pos = ([4,1,1,1,3]) *)
1.213 +val (pt,_) = cappend_atomic pt pos loc "3x^2 + 0 + d/dx ..."
1.214 + Empty_Tac ("[4,1,1,1,3]:3x^2 + 0 -3 ...",[]) Complete;
1.215 +"--- 1 ---";
1.216 +val pos = lev_up pos;
1.217 +(*pos = ([4,1,1,1]) *)
1.218 +val (pt,_) = append_result pt pos e_istate ("[4,1,1,1#]:3x^2 -3.",[])Complete;
1.219 +"--- 2 ---";
1.220 +val pos = lev_up pos;
1.221 +(*val pos = ([4,1,1]) *)
1.222 +val (pt,_) = append_result pt pos e_istate ("[4,1,1#]:found 3x^2 -3 ...",[])
1.223 + Complete;
1.224 +"--- 3 ---";
1.225 +val pos = lev_on pos;
1.226 +(*val pos = ([4,1,2]+) *)
1.227 +val (pt,_) = cappend_parent(*pbl*) pt pos loc "f_y = d/dy x^3 ..."
1.228 + Empty_Tac TransitiveB;
1.229 +"--- 4 ---";
1.230 +writeln (pr_ptree pr_short pt);
1.231 +
1.232 +(*
1.233 +. ----- pblobj -----
1.234 +1. {(a,b). is-max ...
1.235 +1.1. {(a,b). is-max ...
1.236 +1.2. {(a,b). is-extremum ...
1.237 +2. {(a,b). f_x(a,b) ...
1.238 +3. {(a,b). f_x & f_xx &...
1.239 +3.1. {(a,b). f_x & f_xx & ...
1.240 +3.2. {(a,b). f_x & f_xx } cup..
1.241 +4. {(a,b). f_x ..} cup ...
1.242 +4.1. set_1 = ...
1.243 +4.1.1. f_x = d/dx x^3 ...
1.244 +4.1.1.1. d/dx x^3 ...
1.245 +4.1.1.1.1. d/dx x^3 ...
1.246 +4.1.1.1.2. 3x^2 + d/dx ...
1.247 +4.1.1.1.3. 3x^2 + 0 + d/dx ...
1.248 +4.1.2. f_y = d/dy x^3 ...
1.249 +
1.250 + use"test-max-surf1.sml";
1.251 + *)
1.252 +-------------- 9.6.03 --- cappend_ ... term -------irreparabler test---*)
1.253 +
1.254 +
1.255 +"--------- me .. scripts for maximum-example ---------------------";
1.256 +"--------- me .. scripts for maximum-example ---------------------";
1.257 +"--------- me .. scripts for maximum-example ---------------------";
1.258 +
1.259 +val fmz =
1.260 + ["fixedValues [r=Arbfix]","maximum A",
1.261 + "valuesFor [a,b]",
1.262 + "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.263 + "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
1.264 + "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
1.265 +
1.266 + "boundVariable a","boundVariable b","boundVariable alpha",
1.267 + "interval {x::real. 0 <= x & x <= 2*r}",
1.268 + "interval {x::real. 0 <= x & x <= 2*r}",
1.269 + "interval {x::real. 0 <= x & x <= pi}",
1.270 + "errorBound (eps=(0::real))"];
1.271 +val (dI',pI',mI') =
1.272 + ("DiffApp.thy",["maximum_of","function"],
1.273 + ["DiffApp","max_by_calculus"]);
1.274 +
1.275 +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1.276 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.277 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.278 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.279 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.280 +val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn e;
1.281 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.282 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.283 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.284 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.285 +case nxt of (_, Specify_Method ["DiffApp","max_by_calculus"]) => ()
1.286 + | _ => raise error "diffapp.sml: max-exp me, nxt = Specify_Method";
1.287 +
1.288 +val oris = fst3 (get_obj g_origin pt (fst p)); writeln(oris2str oris);
1.289 +val pits = get_obj g_pbl pt (fst p); writeln(itms2str thy pits);
1.290 +
1.291 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.292 +val mits = get_obj g_met pt (fst p); writeln(itms2str thy mits);
1.293 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.294 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.295 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.296 +case nxt of (_,Apply_Method ["DiffApp","max_by_calculus"] ) => ()
1.297 + | _ => raise error "diffapp.sml: max-exp me, nxt = Apply_Method";
1.298 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.299 +
1.300 +(*since 0508 Apply_Method does the 1st step, if None init_form -------------
1.301 +(*val nxt = ("Subproblem",Subproblem ("DiffApp.thy",["make","function"]))*)
1.302 +val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn_G e;
1.303 +(*val nxt = ("Refine_Tacitly",Refine_Tacitly ["make","function"])*)
1.304 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.305 +(*val nxt = ("Model_Problem",Model_Problem ["by_explicit","make","function"])*)
1.306 +----------------------------------------------------------------------------*)
1.307 +case nxt of (_, Model_Problem(*["by_explicit", "make", "function"]*)) => ()
1.308 + | _ => raise error "diffapp.sml: max-exp me, nxt = Model_Problem";
1.309 +
1.310 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.311 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.312 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.313 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.314 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.315 +
1.316 +val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
1.317 +val pits = get_obj g_pbl pt (fst p);writeln(itms2str thy pits);
1.318 +
1.319 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.320 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.321 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.322 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.323 +case nxt of (_, Apply_Method ["DiffApp", "make_fun_by_explicit"]) => ()
1.324 + | _ => raise error "diffapp.sml: max-exp Apply_Method ([1], Met) ";
1.325 +
1.326 +(*----since WN050901 (ie. corr. mathengine#nxt_specify_ ..nxt_spec Pbl->p_
1.327 +we get at ...
1.328 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.329 +...
1.330 +### assod: NotAss m= Subproblem' ,
1.331 + stac= Substitute
1.332 + [(b, (rhs o hd)
1.333 + (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
1.334 + (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
1.335 +*** stac2tac_ TODO: no match for Substitute
1.336 +*** [(b, (rhs o hd)
1.337 +*** (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
1.338 +*** (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
1.339 +Exception- ERROR raised
1.340 +
1.341 +############################################################################
1.342 +# presumerably didnt work before either, but not detected due to Emtpy_Tac #
1.343 +############################################################################
1.344 +
1.345 +(*val nxt = Subproblem ("DiffApp.thy",["univariate","equation"])) *)
1.346 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.347 +(*val nxt = Refine_Tacitly ["univariate","equation"])*)
1.348 +
1.349 +val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
1.350 +val pits = get_obj g_pbl pt (fst p);writeln(itms2str thy pits);
1.351 +
1.352 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.353 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.354 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.355 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.356 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.357 +(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)
1.358 +
1.359 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.360 +(*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"A = a * b"))*)
1.361 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.362 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.363 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.364 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.365 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.366 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.367 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.368 +val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.369 +(*val f = Form' (FormKF (~1,EdUndef,4,Nundef,"[b = A / a]"))*)
1.370 +
1.371 +------------------------------------------------------------------------*)
1.372 +
1.373 +(*val f =
1.374 +Error' (Error_ "Refine_Tacitly [\"univariate\",\"equation\"] not applicable")*)
1.375 +
1.376 +
1.377 +(*----postponed.15.5.03 run scripts for maximum-example: univariate equation
1.378 +
1.379 +val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn e;
1.380 +
1.381 +val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
1.382 +
1.383 +val pits = get_obj g_pbl pt (fst p);writeln(itms2str thy pits);
1.384 +val pits = get_obj g_pbl pt [];writeln(itms2str thy pits);
1.385 +
1.386 +val mits = get_obj g_met pt (fst p);writeln(itms2str thy mits);
1.387 +val mits = get_obj g_met pt [];writeln(itms2str thy mits);
1.388 +
1.389 +itms2args thy ["DiffApp","max_by_calculus"] mits;
1.390 +
1.391 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.392 +
1.393 +---*)
1.394 +
1.395 +"--------- autoCalc .. scripts for maximum-example ---------------";
1.396 +"--------- autoCalc .. scripts for maximum-example ---------------";
1.397 +"--------- autoCalc .. scripts for maximum-example ---------------";
1.398 +(*++++++++ see systest/inform.sml 'complete_metitms' ++++++++*)
1.399 + states:=[];
1.400 +val fmz =
1.401 + ["fixedValues [r=Arbfix]","maximum A",
1.402 + "valuesFor [a,b]",
1.403 + "relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",
1.404 + "relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",
1.405 + "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
1.406 +
1.407 + "boundVariable a","boundVariable b","boundVariable alpha",
1.408 + "interval {x::real. 0 <= x & x <= 2*r}",
1.409 + "interval {x::real. 0 <= x & x <= 2*r}",
1.410 + "interval {x::real. 0 <= x & x <= pi}",
1.411 + "errorBound (eps=(0::real))"];
1.412 +val (dI',pI',mI') =
1.413 + ("DiffApp.thy",["maximum_of","function"],
1.414 + ["DiffApp","max_by_calculus"]);
1.415 +
1.416 + CalcTree [(fmz, (dI',pI',mI'))];
1.417 + Iterator 1; moveActiveRoot 1;
1.418 + autoCalculate 1 CompleteCalcHead;
1.419 + refFormula 1 (get_pos 1 1);
1.420 +
1.421 + fetchProposedTactic 1;
1.422 + autoCalculate 1 (Step 1);
1.423 +
1.424 + fetchProposedTactic 1;
1.425 + autoCalculate 1 (Step 1);
1.426 + (*Subproblem on_interval maximum_of function*)
1.427 + autoCalculate 1 CompleteCalcHead;
1.428 +
1.429 + fetchProposedTactic 1;
1.430 + val ((pt,p),_) = get_calc 1;
1.431 + val mits = get_obj g_met pt (fst p);
1.432 + writeln (itms2str thy mits);
1.433 +(*
1.434 + if itms2str thy mits = "[\n(1 ,[1] ,true ,#Given ,Cor functionEq (hd rs_) ,(t_, [hd rs_])),\n(2 ,[1] ,true ,#Given ,Cor boundVariable v_ ,(v_, [v_])),\n(3 ,[1] ,true ,#Given ,Cor interval itv_ ,(itv_, [itv_])),\n(4 ,[1] ,true ,#Find ,Cor maxArgument v__0 ,(v_0_, [v__0]))]" then ()
1.435 + else raise error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
1.436 +*)
1.437 + (*FIXME: the environments contain identifers, and NOT values ?!?!?*)
1.438 +(* WN051209 while extending 'fun step' for initac, this became better ...
1.439 + if itms2str thy mits = "[\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),\n(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),\n(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(vs_, [[a],[b]])),\n(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2] ,(rs_, [[A = a * b],[(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]])),\n(6 ,[1] ,true ,#undef ,Cor boundVariable a ,(v_, [a])),\n(9 ,[1,2] ,true ,#undef ,Cor interval {x. 0 <= x & x <= 2 * r} ,(itv_, [{x. 0 <= x & x <= 2 * r}])),\n(11 ,[1,2,3] ,true ,#undef ,Cor errorBound (eps = 0) ,(err_, [eps = 0]))]" then ()
1.440 + else raise error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
1.441 +*)
1.442 +
1.443 +
1.444 +
1.445 +"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
1.446 +"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
1.447 +"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
1.448 +str2term
1.449 + "Script Maximum_value(fix_::bool list)(m_::real) (rs_::bool list)\
1.450 + \ (v_::real) (itv_::real set) (err_::bool) = \
1.451 + \ (let e_ = (hd o (filterVar m_)) rs_; \
1.452 + \ t_ = (if 1 < length_ rs_ \
1.453 + \ then (SubProblem (Reals_,[make,function],[no_met])\
1.454 + \ [real_ m_, real_ v_, bool_list_ rs_])\
1.455 + \ else (hd rs_)); \
1.456 + \ (mx_::real) = SubProblem (Reals_,[on_interval,max_of,function], \
1.457 + \ [Isac,maximum_on_interval])\
1.458 + \ [bool_ t_, real_ v_, real_set_ itv_]\
1.459 + \ in ((SubProblem (Reals_,[find_values,tool],[Isac,find_values]) \
1.460 + \ [real_ mx_, real_ (Rhs t_), real_ v_, real_ m_, \
1.461 + \ bool_list_ (dropWhile (ident e_) rs_)])::bool list))";
1.462 +
1.463 +val fix_ = (str2term "fix_::bool list",
1.464 + str2term "[r=Arbfix]");
1.465 +val m_ = (str2term "m_::real",
1.466 + str2term "A");
1.467 +val rs_ = (str2term "rs_::bool list",
1.468 + str2term "[A = a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]");
1.469 +val v_ = (str2term "v_::real",
1.470 + str2term "b");
1.471 +val itv_ = (str2term "itv_::real set",
1.472 + str2term "{x::real. 0 <= x & x <= 2*r}");
1.473 +val err_ = (str2term "err_::bool",
1.474 + str2term "eps=0");
1.475 +val env = [fix_, m_, rs_ ,v_, itv_, err_];
1.476 +
1.477 +(*--- 1.line in script ---*)
1.478 +val t = str2term "(hd o (filterVar m_)) (rs_::bool list)";
1.479 +val s = subst_atomic env t;
1.480 +term2str s;
1.481 +"(hd o filterVar A) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
1.482 +val Some (s',_) = rewrite_set_ thy false list_rls s;
1.483 +val s'' = term2str s';
1.484 +if s''="A = a * b" then () else raise error "new behaviour with list_rls 1.1.";
1.485 +val env = env @ [(str2term "e_::bool",str2term "A = a * b")];
1.486 +
1.487 +(*--- 2.line: condition alone ---*)
1.488 +val t = str2term "1 < length_ (rs_::bool list)";
1.489 +val s = subst_atomic env t;
1.490 +term2str s;
1.491 +"1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
1.492 +val Some (s',_) = rewrite_set_ thy false list_rls s;
1.493 +val s'' = term2str s';
1.494 +if s''="True" then () else raise error "new behaviour with list_rls 1.2.";
1.495 +
1.496 +(*--- 2.line in script ---*)
1.497 +val t = str2term
1.498 + "(if 1 < length_ rs_ \
1.499 + \ then (SubProblem (Reals_,[make,function],[no_met])\
1.500 + \ [real_ m_, real_ v_, bool_list_ rs_])\
1.501 + \ else (hd rs_))";
1.502 +val s = subst_atomic env t;
1.503 +term2str s;
1.504 +"if 1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]\
1.505 +\then SubProblem (Reals_, [make, function], [no_met])\
1.506 +\ [real_ A, real_ b,\
1.507 +\ bool_list_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]\
1.508 +\else hd [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
1.509 +val Some (s',_) = rewrite_set_ thy false list_rls s;
1.510 +val s'' = term2str s';
1.511 +if s'' =
1.512 +"SubProblem (Reals_, [make, function], [no_met])\n\
1.513 +\ [real_ A, real_ b,\n\
1.514 +\ bool_list_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]" then ()
1.515 +else raise error "new behaviour with list_rls 1.3.";
1.516 +val env = env @ [(str2term "t_::bool",
1.517 + str2term "A = (2*sqrt(r^^^2-(b/2)^^^2)) * b")];
1.518 +
1.519 +
1.520 +
1.521 +"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
1.522 +"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
1.523 +"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
1.524 +str2term
1.525 + "Script Make_fun_by_explicit (f_::real) (v_::real) \
1.526 + \ (eqs_::bool list) = \
1.527 + \ (let h_ = (hd o (filterVar f_)) eqs_; \
1.528 + \ e_1 = hd (dropWhile (ident h_) eqs_); \
1.529 + \ vs_ = dropWhile (ident f_) (Vars h_); \
1.530 + \ v_1 = hd (dropWhile (ident v_) vs_); \
1.531 + \ (s_1::bool list)=(SubProblem(Reals_,[univar,equation],[no_met])\
1.532 + \ [bool_ e_1, real_ v_1])\
1.533 + \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
1.534 +val f_ = (str2term "f_::real",
1.535 + str2term "A");
1.536 +val v_ = (str2term "v_::real",
1.537 + str2term "b");
1.538 +val eqs_=(str2term "eqs_::bool list",
1.539 + str2term "[A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]");
1.540 +val env = [f_, v_, eqs_];
1.541 +
1.542 +(*--- 1.line in script ---*)
1.543 +val t = str2term "(hd o (filterVar v_)) (eqs_::bool list)";
1.544 +val s = subst_atomic env t;
1.545 +term2str s;
1.546 +val t = str2term
1.547 + "(hd o filterVar b) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
1.548 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.549 +val s' = term2str t';
1.550 +if s' = "A = a * b" then () else raise error "new behaviour with list_rls 2.1";
1.551 +val env = env @ [(str2term "h_::bool", str2term s')];
1.552 +
1.553 +(*--- 2.line in script ---*)
1.554 +val t = str2term "hd (dropWhile (ident h_) (eqs_::bool list))";
1.555 +val s = subst_atomic env t;
1.556 +term2str s;
1.557 +val t = str2term
1.558 + "hd (dropWhile (ident (A = a * b))\
1.559 + \ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2])";
1.560 +mem_rls "dropWhile_Cons" list_rls;
1.561 +mem_rls "Atools.ident" list_rls;
1.562 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.563 +val s' = term2str t';
1.564 +if s' = "(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2" then ()
1.565 +else raise error "new behaviour with list_rls 2.2";
1.566 +val env = env @ [(str2term "e_1::bool", str2term s')];
1.567 +
1.568 +(*--- 3.line in script ---*)
1.569 +val t = str2term "dropWhile (ident f_) (Vars (h_::bool))";
1.570 +val s = subst_atomic env t;
1.571 +term2str s;
1.572 +val t = str2term "dropWhile (ident A) (Vars (A = a * b))";
1.573 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.574 +val s' = term2str t';
1.575 +if s' = "[a, b]" then () else raise error "new behaviour with list_rls 2.3";
1.576 +val env = env @ [(str2term "vs_::real list", str2term s')];
1.577 +
1.578 +(*--- 4.line in script ---*)
1.579 +val t = str2term "hd (dropWhile (ident v_) vs_)";
1.580 +val s = subst_atomic env t;
1.581 +term2str s;
1.582 +val t = str2term "hd (dropWhile (ident b) [a, b])";
1.583 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.584 +val s' = term2str t';
1.585 +if s' = "a" then () else raise error "new behaviour with list_rls 2.4.";
1.586 +val env = env @ [(str2term "v_1::real", str2term s')];
1.587 +
1.588 +(*--- 5.line in script ---*)
1.589 +val t = str2term "(SubProblem(Reals_,[univar,equation],[no_met])\
1.590 + \ [bool_ e_1, real_ v_1])";
1.591 +val s = subst_atomic env t;
1.592 +term2str s;
1.593 +"SubProblem (Reals_, [univar, equation], [no_met])\n\
1.594 +\ [bool_ ((a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2), real_ a]";
1.595 +val env = env @ [(str2term "s_1::bool list",
1.596 + str2term "[a = 2 * sqrt (r^^^2 - (b/2)^^^2)]")];
1.597 +
1.598 +(*--- 6.line in script ---*)
1.599 +val t = str2term "Substitute [(v_1 = (rhs o hd) (s_1::bool list))] (h_::bool)";
1.600 +val s = subst_atomic env t;
1.601 +term2str s;
1.602 +val t = str2term
1.603 +"Substitute [(a = (rhs o hd) [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)])]\n\
1.604 +\ (A = a * b)";
1.605 +mem_rls "Tools.rhs" list_rls;
1.606 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.607 +val s' = term2str t';
1.608 +if s' = "Substitute [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)] (A = a * b)"
1.609 +then () else raise error "new behaviour with list_rls 2.6.";
1.610 +
1.611 +
1.612 +"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
1.613 +"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
1.614 +"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
1.615 +str2term
1.616 + "Script Make_fun_by_new_variable (f_::real) (v_::real) \
1.617 + \ (eqs_::bool list) = \
1.618 + \(let h_ = (hd o (filterVar f_)) eqs_; \
1.619 + \ es_ = dropWhile (ident h_) eqs_; \
1.620 + \ vs_ = dropWhile (ident f_) (Vars h_); \
1.621 + \ v_1 = nth_ 1 vs_; \
1.622 + \ v_2 = nth_ 2 vs_; \
1.623 + \ e_1 = (hd o (filterVar v_1)) es_; \
1.624 + \ e_2 = (hd o (filterVar v_2)) es_; \
1.625 + \ (s_1::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
1.626 + \ [bool_ e_1, real_ v_1]);\
1.627 + \ (s_2::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
1.628 + \ [bool_ e_2, real_ v_2])\
1.629 + \in Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] h_)";
1.630 +val f_ = (str2term "f_::real",
1.631 + str2term "A");
1.632 +val v_ = (str2term "v_::real",
1.633 + str2term "alpha");
1.634 +val eqs_=(str2term "eqs_::bool list",
1.635 + str2term "[A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]");
1.636 +val env = [f_, v_, eqs_];
1.637 +
1.638 +(*--- 1.line in script ---*)
1.639 +val t = str2term "(hd o (filterVar (f_::real))) (eqs_::bool list)";
1.640 +val s = subst_atomic env t;
1.641 +term2str s;
1.642 +val t = str2term
1.643 +"(hd o filterVar A) [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
1.644 +trace_rewrite:=true;
1.645 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.646 +trace_rewrite:=false;
1.647 +val s' = term2str t';
1.648 +if s' = "A = a * b" then() else raise error "new behaviour with list_rls 3.1.";
1.649 +val env = env @ [(str2term "h_::bool", str2term s')];
1.650 +
1.651 +(*--- 2.line in script ---*)
1.652 +val t = str2term "dropWhile (ident (h_::bool)) (eqs_::bool list)";
1.653 +val s = subst_atomic env t;
1.654 +term2str s;
1.655 +val t = str2term
1.656 +"dropWhile (ident (A = a * b))\
1.657 +\ [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
1.658 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.659 +val s' = term2str t';
1.660 +if s' = "[a / 2 = r * sin alpha, b / 2 = r * cos alpha]"
1.661 +then () else raise error "new behaviour with list_rls 3.2.";
1.662 +val env = env @ [(str2term "es_::bool list", str2term s')];
1.663 +
1.664 +(*--- 3.line in script ---*)
1.665 +val t = str2term "dropWhile (ident (f_::real)) (Vars (h_::bool))";
1.666 +val s = subst_atomic env t;
1.667 +term2str s;
1.668 +val t = str2term "dropWhile (ident A) (Vars (A = a * b))";
1.669 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.670 +val s' = term2str t';
1.671 +if s' = "[a, b]" then () else raise error "new behaviour with list_rls 3.3.";
1.672 +val env = env @ [(str2term "vs_::real list", str2term s')];
1.673 +
1.674 +(*--- 4.line in script ---*)
1.675 +val t = str2term "nth_ 1 vs_";
1.676 +val s = subst_atomic env t;
1.677 +term2str s;
1.678 +val t = str2term "nth_ 1 [a, b]";
1.679 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.680 +val s' = term2str t';
1.681 +if s' = "a" then () else raise error "new behaviour with list_rls 3.4.";
1.682 +val env = env @ [(str2term "v_1", str2term s')];
1.683 +
1.684 +(*--- 5.line in script ---*)
1.685 +val t = str2term "nth_ 2 vs_";
1.686 +val s = subst_atomic env t;
1.687 +term2str s;
1.688 +val t = str2term "nth_ 2 [a, b]";
1.689 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.690 +val s' = term2str t';
1.691 +if s' = "b" then () else raise error "new behaviour with list_rls 3.5.";
1.692 +val env = env @ [(str2term "v_2", str2term s')];
1.693 +
1.694 +(*--- 6.line in script ---*)
1.695 +val t = str2term "(hd o (filterVar v_1)) (es_::bool list)";
1.696 +val s = subst_atomic env t;
1.697 +term2str s;
1.698 +val t = str2term
1.699 + "(hd o filterVar a) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
1.700 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.701 +val s' = term2str t';
1.702 +if s' = "a / 2 = r * sin alpha" then ()
1.703 +else raise error "new behaviour with list_rls 3.6.";
1.704 +val e_1 = str2term "e_1::bool";
1.705 +val env = env @ [(e_1, str2term s')];
1.706 +
1.707 +(*--- 7.line in script ---*)
1.708 +val t = str2term "(hd o (filterVar v_2)) (es_::bool list)";
1.709 +val s = subst_atomic env t;
1.710 +term2str s;
1.711 +val t = str2term
1.712 + "(hd o filterVar b) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
1.713 +val Some (t',_) = rewrite_set_ thy false list_rls t;
1.714 +val s' = term2str t';
1.715 +if s' = "b / 2 = r * cos alpha" then ()
1.716 +else raise error "new behaviour with list_rls 3.7.";
1.717 +val env = env @ [(str2term "e_2::bool", str2term s')];
1.718 +
1.719 +(*--- 8.line in script ---*)
1.720 +val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\
1.721 + \ [bool_ e_1, real_ v_1])";
1.722 +val s = subst_atomic env t;
1.723 +term2str s;
1.724 +"SubProblem (Reals_, [univar, equation], [no_met])\
1.725 + \ [bool_ (a / 2 = r * sin alpha), real_ a]";
1.726 +val s_1 = str2term "[a = 2*r*sin alpha]";
1.727 +val env = env @ [(str2term "s_1::bool list", s_1)];
1.728 +
1.729 +(*--- 9.line in script ---*)
1.730 +val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\
1.731 + \ [bool_ e_2, real_ v_2])";
1.732 +val s = subst_atomic env t;
1.733 +term2str s;
1.734 +"SubProblem (Reals_, [univar, equation], [no_met])\
1.735 + \ [bool_ (b / 2 = r * cos alpha), real_ b]";
1.736 +val s_2 = str2term "[b = 2*r*cos alpha]";
1.737 +val env = env @ [(str2term "s_2::bool list", s_2)];
1.738 +
1.739 +(*--- 10.line in script ---*)
1.740 +val t = str2term
1.741 +"Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] (h_::bool)";
1.742 +val s = subst_atomic env t;
1.743 +term2str s;
1.744 +"Substitute\n [(a = (rhs o hd) [a = 2 * r * sin alpha]),\
1.745 +\ (b = (rhs o hd) [b = 2 * r * cos alpha])] (A = a * b)";
1.746 +val Some (s',_) = rewrite_set_ thy false list_rls s;
1.747 +val s'' = term2str s';
1.748 +if s'' =
1.749 +"Substitute [a = 2 * r * sin alpha, b = 2 * r * cos alpha] (A = a * b)"
1.750 +then () else raise error "new behaviour with list_rls 3.10.";
1.751 +
1.752 +
1.753 +
1.754 +
1.755 +