neuper@37906: (* tests for IsacKnowledge/DiffApp
neuper@37906:    author Walther Neuper 000301
neuper@37906:    (c) due to copyright terms
neuper@37906: 
neuper@37906:    use"../smltest/IsacKnowledge/diffapp.sml";
neuper@37906:    use"diffapp.sml";
neuper@37906: *)
neuper@37906: 
neuper@37906: "Contents----------------------------------------------";
neuper@37906: "              Specify_Problem (match_itms_oris)       ";
neuper@37906: "              test specify, fmz <> []                  ";
neuper@37906: "              test specify, fmz = []                  ";
neuper@37906: "          problemtypes + formalizations               ";
neuper@37906: "-------------------- ptree of {(a,b). is-max ... ----------------";
neuper@37906: "--------- me .. scripts for maximum-example ---------------------";
neuper@37906: "--------- autoCalc .. scripts for maximum-example ---------------";
neuper@37906: 
neuper@37906: "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
neuper@37906: "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
neuper@37906: "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: " #################################################### ";
neuper@37906: "          problemtypes + formalizations               ";
neuper@37906: " #################################################### ";
neuper@37906: " -------------- [maximum_of,function] --------------- ";
neuper@37906: val pbt = 
neuper@37906:     ["fixedValues fix_","maximum m_","valuesFor vs_","relations rs_"];
neuper@37906: map (the o (parseold thy)) pbt;
neuper@37906: val fmz =
neuper@37906:     ["fixedValues [r=Arbfix]","maximum A",
neuper@37906:      "valuesFor [a,b]",
neuper@37906:      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
neuper@37906:      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
neuper@37906:      "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
neuper@37906: 
neuper@37906:      "boundVariable a","boundVariable b","boundVariable alpha",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "interval {x::real. 0 <= x & x <= pi}",
neuper@37906:      "errorBound (eps=(0::real))"];
neuper@37906: map (the o (parseold thy)) fmz;
neuper@37906: " -------------- [make,function] -------------- ";
neuper@37906: val pbt = 
neuper@37906:     ["functionOf f_","boundVariable v_","equalities eqs_",
neuper@37906:      "functionTerm f_0_"];
neuper@37906: map (the o (parseold thy)) pbt;
neuper@37906: val fmz12 =
neuper@37906:     ["functionOf A","boundVariable a","boundVariable b",
neuper@37906:      "equalities [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
neuper@37906:      (*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];
neuper@37906: map (the o (parseold thy)) fmz12;
neuper@37906: val fmz3 =
neuper@37906:     ["functionOf A","boundVariable a","boundVariable b",
neuper@37906:      "equalities [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
neuper@37906:      (*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];
neuper@37906: map (the o (parseold thy)) fmz3;
neuper@37906: " --------- [univar,equation] --------- ";
neuper@37906: val pbt = 
neuper@37906:     ["equality e_","solveFor v_","solutions v_i_"];
neuper@37906: map (the o (parseold thy)) pbt;
neuper@37906: val fmz =
neuper@37906:     ["equality ((a/2)^^^2 + (b/2)^^^2 = r^^^2)",
neuper@37906:      "solveFor b","solutions b_i"];
neuper@37906: map (the o (parseold thy)) fmz;
neuper@37906: " ---- [on_interval,maximum_of,function] ---- ";
neuper@37906: val pbt = 
neuper@37906:     ["functionTerm t_","boundVariable v_","interval itv_",
neuper@37906:      "errorBound err_","maxArgument v_0_"];
neuper@37906: map (the o (parseold thy)) pbt;
neuper@37906: val fmz12 =
neuper@37906:     [(*28.11.00: "functionTerm (A_0 = a*sqrt(#4*r^^^#2 - a^^^#2))",*)
neuper@37906:      "functionTerm (a*sqrt(4*r^^^2 - a^^^2))",
neuper@37906:      (*28.11.00: "functionTerm (A_0 = b*sqrt(#4*r^^^#2 - b^^^#2))",*)
neuper@37906:      "functionTerm (b*sqrt(4*r^^^2 - b^^^2))",
neuper@37906:      "boundVariable a","boundVariable b",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "errorBound (eps=0)","maxArgument (a_0=Undef)"];
neuper@37906: map (the o (parseold thy)) fmz12;
neuper@37906: val fmz3 =
neuper@37906:     [(*28.11.00: "functionTerm (A_0 = (#2*r*sin alpha)*(#2*r*cos alpha))",*)
neuper@37906:      "functionTerm ((2*r*sin alpha)*(2*r*cos alpha))",
neuper@37906:      "boundVariable alpha",
neuper@37906:      "interval {x::real. 0 <= x & x <= pi}",
neuper@37906:      "errorBound (eps=0)","maxArgument (a_0=Undef)"];
neuper@37906: map (the o (parseold thy)) fmz3;
neuper@37906: " --------- [derivative_of,function] --------- ";
neuper@37906: val pbt = 
neuper@37906:     ["functionTerm f_","boundVariable v_","derivative f_'_"];
neuper@37906: map (the o (parseold thy)) pbt;
neuper@37906: val fmz =
neuper@37906:     [(*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)
neuper@37906:      "functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",
neuper@37906:      "boundVariable a",
neuper@37906:      (*28.11.00: "derivative (A_0'=Undef)"*)"derivative (Undef)"];
neuper@37906: map (the o (parseold thy)) fmz;
neuper@37906: " --------- [find_values,tool] --------- ";
neuper@37906: val pbt = 
neuper@37906:     ["maxArgument ma_","functionTerm f_","boundVariable v_",
neuper@37906:      "valuesFor vls_","additionalRels rs_"];
neuper@37906: map (the o (parseold thy)) pbt;
neuper@37906: val fmz1 =
neuper@37906:     ["maxArgument (a_0=(srqt 2)*r)",
neuper@37906:      (*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)
neuper@37906:      "functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",
neuper@37906:      "boundVariable a",
neuper@37906:      "valuesFor [a,b]","maximum A",
neuper@37906:      "additionalRels [(a/2)^^^2 + (b/2)^^^2 = r^^^2]"];
neuper@37906: map (the o (parseold thy)) fmz1;
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: "-------------------- ptree of {(a,b). is-max ... --------------------------";
neuper@37906: "-------------------- ptree of {(a,b). is-max ... --------------------------";
neuper@37906: "-------------------- ptree of {(a,b). is-max ... --------------------------";
neuper@37906: 
neuper@37906: (* Teil von max-on-surface.sml,
neuper@37906:    der nach Init_Proof -> prep_ori wieder l"auft
neuper@37906:    (f"ur tests mit neuer pos')
neuper@37906:    use"test-max-surf1.sml";
neuper@37906: 
neuper@37906:    Compiler.Control.Print.printDepth:=7; (*4 is default*)
neuper@37906:    Compiler.Control.Print.printDepth:=4; (*4 is default*)
neuper@37906:    *)
neuper@37906: 
neuper@37906: (* --vvv-- ausgeliehen von test-root-equ/sml *)
neuper@37906: val loc = e_istate;
neuper@37906: val (dI',pI',mI') =
neuper@37906:   ("Script.thy",["sqroot-test","univariate","equation"],
neuper@37906:    ["Script","squ-equ-test2"]);
neuper@37906: val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
neuper@37906: 	   "solveFor x","errorBound (eps=0)",
neuper@37906: 	   "solutions L"];
neuper@37906: (*
neuper@37906: val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906: val ((p,p_),_,_,_,_,(_,pt,_)) = do_ (mI,m) e_pos'[1](e_scr,EmptyPtree,[]);
neuper@37906:  --^^^-- ausgeliehen von test-root-equ/sml *)
neuper@37906: (*-------------- 9.6.03 --- cappend_ ... term -------irreparabler test
neuper@37906: val (pt,_) = 
neuper@37906:   cappend_problem EmptyPtree [] loc ([],(dI',pI',mI'));
neuper@37906: val pos = (lev_on o lev_dn) [];
neuper@37906: (* val pos = ([1]) *)
neuper@37906: val (pt,_) = cappend_parent pt pos loc "{(a,b). is-max ..." 
neuper@37906:     Empty_Tac TransitiveB;
neuper@37906: val pos = (lev_on o lev_dn) pos;
neuper@37906: (*val pos = ([1,1])*)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-max ..." 
neuper@37906:     Empty_Tac ("[1,1]:{(a,b). is-extremum ...",[]) Complete;
neuper@37906: val pos = lev_on pos;
neuper@37906: (*val pos = ([1,2])*)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-extremum ..." 
neuper@37906:     Empty_Tac ("[1,2]:{(a,b). f_x(a,b) ...",[]) Complete;
neuper@37906: val pos = lev_up pos;
neuper@37906: (*val pos = ([1])*)
neuper@37906: val (pt,_) = append_result pt pos e_istate ("[1#]:{(a,b). f_x(a,b) ...",[])
neuper@37906:     Complete;
neuper@37906: 
neuper@37906: val pos = lev_on pos;
neuper@37906: (*val pos = ([2]) *)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x(a,b) ..." 
neuper@37906:     Empty_Tac ("[2]:{(a,b). f_x & f_xx &...",[]) Complete;
neuper@37906: val pos = lev_on pos;
neuper@37906: (*al pos = [3] : pos*)
neuper@37906: val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x & f_xx &..." 
neuper@37906:     Empty_Tac TransitiveB;
neuper@37906: val pos = (lev_on o lev_dn) pos;
neuper@37906: (*pos = ([3,1]) *)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx & ..." 
neuper@37906:     Empty_Tac ("[3,1]:{(a,b). f_x & f_xx } cup ...",[]) Complete;
neuper@37906: val pos = lev_on pos;
neuper@37906: (*pos = ([3,2]) *)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx } cup.."
neuper@37906:     Empty_Tac ("[3,2]:{(a,b). f_x ..} cup ...",[]) Complete;
neuper@37906: 
neuper@37906: val pos = lev_up pos;
neuper@37906: (*pos = ([3]) *)
neuper@37906: val (pt,_) = append_result pt pos e_istate ("[3#]:{(a,b). f_x ..} cup..",[])
neuper@37906:     Complete;
neuper@37906: val pos = lev_on pos;
neuper@37906: (*val pos = [4] : pos *)
neuper@37906: val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x ..} cup ..." 
neuper@37906:     Empty_Tac IntersectB;
neuper@37906: val pos = (lev_on o lev_dn) pos;
neuper@37906: (*val pos = ([4,1]) *)
neuper@37906: val (pt,_) = cappend_parent pt pos loc "set_1 = ..." 
neuper@37906:     Empty_Tac SequenceB;
neuper@37906: 
neuper@37906: 
neuper@37906: val pos = (lev_on o lev_dn) pos;
neuper@37906: (*val pos = ([4,1,1]) *)
neuper@37906: val (pt,_) = cappend_parent(*pbl*) pt pos loc"f_x = d/dx x^3 ..."
neuper@37906:     Empty_Tac TransitiveB;
neuper@37906: val pos = (lev_on o lev_dn) pos;
neuper@37906: (*val pos = ([4,1,1,1]) *)
neuper@37906: val (pt,_) = cappend_parent pt pos loc "d/dx x^3 ..." 
neuper@37906:     Empty_Tac TransitiveB;
neuper@37906: val pos = (lev_on o lev_dn) pos;
neuper@37906: (*val pos = ([4,1,1,1,1]) *)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "d/dx x^3 ..." 
neuper@37906:     Empty_Tac ("[4,1,1,1,1]:3x^2 + d/dx ...",[]) Complete;
neuper@37906: val pos = lev_on pos;
neuper@37906: (*val pos = ([4,1,1,1,2]) *)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "3x^2 + d/dx ..." 
neuper@37906:     Empty_Tac ("[4,1,1,1,2]:3x^2 + 0 + d/dx ...",[]) Complete;
neuper@37906: val pos = lev_on pos;
neuper@37906: (*pos = ([4,1,1,1,3]) *)
neuper@37906: val (pt,_) = cappend_atomic pt pos loc "3x^2 + 0 + d/dx ..." 
neuper@37906:     Empty_Tac ("[4,1,1,1,3]:3x^2 + 0 -3 ...",[]) Complete;
neuper@37906: "--- 1 ---";
neuper@37906: val pos = lev_up pos;
neuper@37906: (*pos = ([4,1,1,1]) *)
neuper@37906: val (pt,_) = append_result pt pos e_istate ("[4,1,1,1#]:3x^2 -3.",[])Complete;
neuper@37906: "--- 2 ---";
neuper@37906: val pos = lev_up pos;
neuper@37906: (*val pos = ([4,1,1]) *)
neuper@37906: val (pt,_) = append_result pt pos e_istate ("[4,1,1#]:found 3x^2 -3 ...",[])
neuper@37906:     Complete;
neuper@37906: "--- 3 ---";
neuper@37906: val pos = lev_on pos;
neuper@37906: (*val pos = ([4,1,2]+) *)
neuper@37906: val (pt,_) = cappend_parent(*pbl*) pt pos loc "f_y = d/dy x^3 ..."
neuper@37906:     Empty_Tac TransitiveB;
neuper@37906: "--- 4 ---";
neuper@37906: writeln (pr_ptree pr_short pt);
neuper@37906: 
neuper@37906: (*
neuper@37906: .    ----- pblobj -----
neuper@37906: 1.   {(a,b). is-max ...
neuper@37906: 1.1.   {(a,b). is-max ...
neuper@37906: 1.2.   {(a,b). is-extremum ...
neuper@37906: 2.   {(a,b). f_x(a,b) ...
neuper@37906: 3.   {(a,b). f_x & f_xx &...
neuper@37906: 3.1.   {(a,b). f_x & f_xx & ...
neuper@37906: 3.2.   {(a,b). f_x & f_xx } cup..
neuper@37906: 4.   {(a,b). f_x ..} cup ...
neuper@37906: 4.1.   set_1 = ...
neuper@37906: 4.1.1.   f_x = d/dx x^3 ...
neuper@37906: 4.1.1.1.   d/dx x^3 ...
neuper@37906: 4.1.1.1.1.   d/dx x^3 ...
neuper@37906: 4.1.1.1.2.   3x^2 + d/dx ...
neuper@37906: 4.1.1.1.3.   3x^2 + 0 + d/dx ...
neuper@37906: 4.1.2.   f_y = d/dy x^3 ...
neuper@37906:   
neuper@37906:  use"test-max-surf1.sml";
neuper@37906:    *)
neuper@37906: -------------- 9.6.03 --- cappend_ ... term -------irreparabler test---*)
neuper@37906: 
neuper@37906: 
neuper@37906: "--------- me .. scripts for maximum-example ---------------------";
neuper@37906: "--------- me .. scripts for maximum-example ---------------------";
neuper@37906: "--------- me .. scripts for maximum-example ---------------------";
neuper@37906: 
neuper@37906: val fmz =
neuper@37906:     ["fixedValues [r=Arbfix]","maximum A",
neuper@37906:      "valuesFor [a,b]",
neuper@37906:      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
neuper@37906:      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
neuper@37906:      "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
neuper@37906: 
neuper@37906:      "boundVariable a","boundVariable b","boundVariable alpha",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "interval {x::real. 0 <= x & x <= pi}",
neuper@37906:      "errorBound (eps=(0::real))"];
neuper@37906: val (dI',pI',mI') =
neuper@37906:   ("DiffApp.thy",["maximum_of","function"],
neuper@37906:    ["DiffApp","max_by_calculus"]);
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn e;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: case nxt of (_, Specify_Method ["DiffApp","max_by_calculus"]) => ()
neuper@37906: 	  | _ => raise error "diffapp.sml: max-exp me, nxt = Specify_Method";
neuper@37906: 
neuper@37906: val oris = fst3 (get_obj g_origin pt (fst p)); writeln(oris2str oris);
neuper@37924: val pits = get_obj g_pbl pt (fst p); writeln(itms2str_ ctxt pits);
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37924: val mits = get_obj g_met pt (fst p); writeln(itms2str_ ctxt mits);
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: case nxt of (_,Apply_Method ["DiffApp","max_by_calculus"] ) => ()
neuper@37906: 	  | _ => raise error "diffapp.sml: max-exp me, nxt = Apply_Method";
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: 
neuper@37906: (*since 0508 Apply_Method does the 1st step, if None init_form -------------
neuper@37906: (*val nxt = ("Subproblem",Subproblem ("DiffApp.thy",["make","function"]))*)
neuper@37906: val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn_G e;
neuper@37906: (*val nxt = ("Refine_Tacitly",Refine_Tacitly ["make","function"])*)
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: (*val nxt = ("Model_Problem",Model_Problem ["by_explicit","make","function"])*)
neuper@37906: ----------------------------------------------------------------------------*)
neuper@37906: case nxt of (_, Model_Problem(*["by_explicit", "make", "function"]*)) => ()
neuper@37906: 	  | _ => raise error "diffapp.sml: max-exp me, nxt = Model_Problem";
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: 
neuper@37906: val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
neuper@37924: val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: case nxt of (_, Apply_Method ["DiffApp", "make_fun_by_explicit"]) => ()
neuper@37906: 	  | _ => raise error "diffapp.sml: max-exp Apply_Method ([1], Met) ";
neuper@37906: 
neuper@37906: (*----since WN050901 (ie. corr. mathengine#nxt_specify_ ..nxt_spec Pbl->p_
neuper@37906: we get at ...
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: ...
neuper@37906: ### assod: NotAss m= Subproblem'  ,
neuper@37906:  stac= Substitute
neuper@37906:  [(b, (rhs o hd)
neuper@37906:        (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
neuper@37906:  (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
neuper@37906: *** stac2tac_ TODO: no match for Substitute
neuper@37906: ***  [(b, (rhs o hd)
neuper@37906: ***        (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
neuper@37906: ***  (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
neuper@37906: Exception- ERROR raised
neuper@37906: 
neuper@37906: ############################################################################
neuper@37906: # presumerably didnt work before either, but not detected due to Emtpy_Tac #
neuper@37906: ############################################################################
neuper@37906: 
neuper@37906: (*val nxt = Subproblem ("DiffApp.thy",["univariate","equation"]))   *)
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: (*val nxt = Refine_Tacitly ["univariate","equation"])*)
neuper@37906: 
neuper@37906: val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
neuper@37924: val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: (*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: (*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"A = a * b"))*)
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: (*val f = Form' (FormKF (~1,EdUndef,4,Nundef,"[b = A / a]"))*)
neuper@37906: 
neuper@37906: ------------------------------------------------------------------------*)
neuper@37906: 
neuper@37906: (*val f =
neuper@37906: Error' (Error_ "Refine_Tacitly [\"univariate\",\"equation\"] not applicable")*)
neuper@37906: 
neuper@37906: 
neuper@37906: (*----postponed.15.5.03 run scripts for maximum-example: univariate equation
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn e; 
neuper@37906: 
neuper@37906: val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
neuper@37906: 
neuper@37924: val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);
neuper@37924: val pits = get_obj g_pbl pt [];writeln(itms2str_ ctxt pits);
neuper@37906: 
neuper@37924: val mits = get_obj g_met pt (fst p);writeln(itms2str_ ctxt mits);
neuper@37924: val mits = get_obj g_met pt [];writeln(itms2str_ ctxt mits);
neuper@37906: 
neuper@37906: itms2args thy ["DiffApp","max_by_calculus"] mits;
neuper@37906: 
neuper@37906: val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906: 
neuper@37906: ---*)
neuper@37906: 
neuper@37906: "--------- autoCalc .. scripts for maximum-example ---------------";
neuper@37906: "--------- autoCalc .. scripts for maximum-example ---------------";
neuper@37906: "--------- autoCalc .. scripts for maximum-example ---------------";
neuper@37906: (*++++++++ see systest/inform.sml 'complete_metitms' ++++++++*)
neuper@37906:  states:=[];
neuper@37906: val fmz =
neuper@37906:     ["fixedValues [r=Arbfix]","maximum A",
neuper@37906:      "valuesFor [a,b]",
neuper@37906:      "relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",
neuper@37906:      "relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",
neuper@37906:      "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
neuper@37906: 
neuper@37906:      "boundVariable a","boundVariable b","boundVariable alpha",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "interval {x::real. 0 <= x & x <= 2*r}",
neuper@37906:      "interval {x::real. 0 <= x & x <= pi}",
neuper@37906:      "errorBound (eps=(0::real))"];
neuper@37906: val (dI',pI',mI') =
neuper@37906:   ("DiffApp.thy",["maximum_of","function"],
neuper@37906:    ["DiffApp","max_by_calculus"]);
neuper@37906: 
neuper@37906:  CalcTree [(fmz, (dI',pI',mI'))];
neuper@37906:  Iterator 1; moveActiveRoot 1;
neuper@37906:  autoCalculate 1 CompleteCalcHead;
neuper@37906:  refFormula 1 (get_pos 1 1); 
neuper@37906: 
neuper@37906:  fetchProposedTactic 1;
neuper@37906:  autoCalculate 1 (Step 1);
neuper@37906: 
neuper@37906:  fetchProposedTactic 1;
neuper@37906:  autoCalculate 1 (Step 1);
neuper@37906:  (*Subproblem on_interval maximum_of function*)
neuper@37906:  autoCalculate 1 CompleteCalcHead;
neuper@37906: 
neuper@37906:  fetchProposedTactic 1;
neuper@37906:  val ((pt,p),_) = get_calc 1;
neuper@37906:  val mits = get_obj g_met pt (fst p);
neuper@37924:  writeln (itms2str_ ctxt mits);
neuper@37906: (*
neuper@37924:  if itms2str_ ctxt 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 ()
neuper@37906:  else raise error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
neuper@37906: *)
neuper@37906:  (*FIXME: the environments contain identifers, and NOT values ?!?!?*)
neuper@37906: (* WN051209 while extending 'fun step' for initac, this became better ...
neuper@37924:  if itms2str_ ctxt 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 ()
neuper@37906:  else raise error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
neuper@37906: *)
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
neuper@37906: "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
neuper@37906: "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
neuper@37906: str2term
neuper@37906:   "Script Maximum_value(fix_::bool list)(m_::real) (rs_::bool list)\
neuper@37906:    \      (v_::real) (itv_::real set) (err_::bool) =          \ 
neuper@37906:    \ (let e_ = (hd o (filterVar m_)) rs_;              \
neuper@37906:    \      t_ = (if 1 < length_ rs_                            \
neuper@37906:    \           then (SubProblem (Reals_,[make,function],[no_met])\
neuper@37906:    \                     [real_ m_, real_ v_, bool_list_ rs_])\
neuper@37906:    \           else (hd rs_));                                \
neuper@37906:    \      (mx_::real) = SubProblem (Reals_,[on_interval,max_of,function], \
neuper@37906:    \                                [Isac,maximum_on_interval])\
neuper@37906:    \                               [bool_ t_, real_ v_, real_set_ itv_]\
neuper@37906:    \ in ((SubProblem (Reals_,[find_values,tool],[Isac,find_values])   \
neuper@37906:    \      [real_ mx_, real_ (Rhs t_), real_ v_, real_ m_,     \
neuper@37906:    \       bool_list_ (dropWhile (ident e_) rs_)])::bool list))";
neuper@37906: 
neuper@37906: val fix_ = (str2term "fix_::bool list", 
neuper@37906: 	    str2term "[r=Arbfix]");
neuper@37906: val m_   = (str2term "m_::real", 
neuper@37906: 	    str2term "A");
neuper@37906: val rs_  = (str2term "rs_::bool list", 
neuper@37906: 	    str2term "[A = a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]");
neuper@37906: val v_   = (str2term "v_::real", 
neuper@37906: 	    str2term "b");
neuper@37906: val itv_ = (str2term "itv_::real set", 
neuper@37906: 	    str2term "{x::real. 0 <= x & x <= 2*r}");
neuper@37906: val err_ = (str2term "err_::bool", 
neuper@37906: 	    str2term "eps=0");
neuper@37906: val env = [fix_, m_, rs_ ,v_, itv_, err_];
neuper@37906: 
neuper@37906: (*--- 1.line in script ---*)
neuper@37906: val t = str2term "(hd o (filterVar m_)) (rs_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "(hd o filterVar A) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
neuper@37906: val Some (s',_) = rewrite_set_ thy false list_rls s;
neuper@37906: val s'' = term2str s';
neuper@37906: if s''="A = a * b" then () else raise error "new behaviour with list_rls 1.1.";
neuper@37906: val env = env @ [(str2term "e_::bool",str2term "A = a * b")];
neuper@37906: 
neuper@37906: (*--- 2.line: condition alone ---*)
neuper@37906: val t = str2term "1 < length_ (rs_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
neuper@37906: val Some (s',_) = rewrite_set_ thy false list_rls s;
neuper@37906: val s'' = term2str s';
neuper@37906: if s''="True" then () else raise error "new behaviour with list_rls 1.2.";
neuper@37906: 
neuper@37906: (*--- 2.line in script ---*)
neuper@37906: val t = str2term 
neuper@37906: 	    "(if 1 < length_ rs_                            \
neuper@37906:    \           then (SubProblem (Reals_,[make,function],[no_met])\
neuper@37906:    \                     [real_ m_, real_ v_, bool_list_ rs_])\
neuper@37906:    \           else (hd rs_))";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "if 1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]\
neuper@37906: \then SubProblem (Reals_, [make, function], [no_met])\
neuper@37906: \      [real_ A, real_ b,\
neuper@37906: \       bool_list_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]\
neuper@37906: \else hd [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
neuper@37906: val Some (s',_) = rewrite_set_ thy false list_rls s;
neuper@37906: val s'' = term2str s';
neuper@37906: if s'' = 
neuper@37906: "SubProblem (Reals_, [make, function], [no_met])\n\
neuper@37906: \ [real_ A, real_ b,\n\
neuper@37906: \  bool_list_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]" then ()
neuper@37906: else raise error "new behaviour with list_rls 1.3.";
neuper@37906: val env = env @ [(str2term "t_::bool",
neuper@37906: 		  str2term "A = (2*sqrt(r^^^2-(b/2)^^^2)) * b")];
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
neuper@37906: "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
neuper@37906: "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
neuper@37906: str2term
neuper@37906:    "Script Make_fun_by_explicit (f_::real) (v_::real)         \
neuper@37906:    \      (eqs_::bool list) =                                 \
neuper@37906:    \ (let h_  = (hd o (filterVar f_)) eqs_;                   \
neuper@37906:    \      e_1 = hd (dropWhile (ident h_) eqs_);               \
neuper@37906:    \      vs_ = dropWhile (ident f_) (Vars h_);                \
neuper@37906:    \      v_1 = hd (dropWhile (ident v_) vs_);                \
neuper@37906:    \      (s_1::bool list)=(SubProblem(Reals_,[univar,equation],[no_met])\
neuper@37906:    \                          [bool_ e_1, real_ v_1])\
neuper@37906:    \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
neuper@37906: val f_ = (str2term "f_::real", 
neuper@37906: 	  str2term "A");
neuper@37906: val v_ = (str2term "v_::real", 
neuper@37906: 	  str2term "b");
neuper@37906: val eqs_=(str2term "eqs_::bool list", 
neuper@37906: 	  str2term "[A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]");
neuper@37906: val env = [f_, v_, eqs_];
neuper@37906: 
neuper@37906: (*--- 1.line in script ---*)
neuper@37906: val t = str2term "(hd o (filterVar v_)) (eqs_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906:      "(hd o filterVar b) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "A = a * b" then () else raise error "new behaviour with list_rls 2.1";
neuper@37906: val env = env @ [(str2term "h_::bool", str2term s')];
neuper@37906: 
neuper@37906: (*--- 2.line in script ---*)
neuper@37906: val t = str2term "hd (dropWhile (ident h_) (eqs_::bool list))";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906: 	    "hd (dropWhile (ident (A = a * b))\
neuper@37906: 	    \     [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2])";
neuper@37906: mem_rls "dropWhile_Cons" list_rls;
neuper@37906: mem_rls "Atools.ident" list_rls;
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2" then () 
neuper@37906: else raise error "new behaviour with list_rls 2.2";
neuper@37906: val env = env @ [(str2term "e_1::bool", str2term s')];
neuper@37906: 
neuper@37906: (*--- 3.line in script ---*)
neuper@37906: val t = str2term "dropWhile (ident f_) (Vars (h_::bool))";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term "dropWhile (ident A) (Vars (A = a * b))";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "[a, b]" then () else raise error "new behaviour with list_rls 2.3";
neuper@37906: val env = env @ [(str2term "vs_::real list", str2term s')];
neuper@37906: 
neuper@37906: (*--- 4.line in script ---*)
neuper@37906: val t = str2term "hd (dropWhile (ident v_) vs_)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term "hd (dropWhile (ident b) [a, b])";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "a" then () else raise error "new behaviour with list_rls 2.4.";
neuper@37906: val env = env @ [(str2term "v_1::real", str2term s')];
neuper@37906: 
neuper@37906: (*--- 5.line in script ---*)
neuper@37906: val t = str2term "(SubProblem(Reals_,[univar,equation],[no_met])\
neuper@37906: 		 \           [bool_ e_1, real_ v_1])";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "SubProblem (Reals_, [univar, equation], [no_met])\n\
neuper@37906: \ [bool_ ((a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2), real_ a]";
neuper@37906: val env = env @ [(str2term "s_1::bool list", 
neuper@37906: 		  str2term "[a = 2 * sqrt (r^^^2 - (b/2)^^^2)]")];
neuper@37906: 
neuper@37906: (*--- 6.line in script ---*)
neuper@37906: val t = str2term "Substitute [(v_1 = (rhs o hd) (s_1::bool list))] (h_::bool)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906: "Substitute [(a = (rhs o hd) [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)])]\n\
neuper@37906: \ (A = a * b)";
neuper@37906: mem_rls "Tools.rhs" list_rls;
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "Substitute [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)] (A = a * b)" 
neuper@37906: then () else raise error "new behaviour with list_rls 2.6.";
neuper@37906: 
neuper@37906: 
neuper@37906: "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
neuper@37906: "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
neuper@37906: "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
neuper@37906: str2term
neuper@37906:   "Script Make_fun_by_new_variable (f_::real) (v_::real)     \
neuper@37906:    \      (eqs_::bool list) =                                 \
neuper@37906:    \(let h_ = (hd o (filterVar f_)) eqs_;             \
neuper@37906:    \     es_ = dropWhile (ident h_) eqs_;                    \
neuper@37906:    \     vs_ = dropWhile (ident f_) (Vars h_);                \
neuper@37906:    \     v_1 = nth_ 1 vs_;                                   \
neuper@37906:    \     v_2 = nth_ 2 vs_;                                   \
neuper@37906:    \     e_1 = (hd o (filterVar v_1)) es_;            \
neuper@37906:    \     e_2 = (hd o (filterVar v_2)) es_;            \
neuper@37906:    \  (s_1::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
neuper@37906:    \                    [bool_ e_1, real_ v_1]);\
neuper@37906:    \  (s_2::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
neuper@37906:    \                    [bool_ e_2, real_ v_2])\
neuper@37906:    \in Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] h_)";
neuper@37906: val f_ = (str2term "f_::real", 
neuper@37906: 	  str2term "A");
neuper@37906: val v_ = (str2term "v_::real", 
neuper@37906: 	  str2term "alpha");
neuper@37906: val eqs_=(str2term "eqs_::bool list", 
neuper@37906: 	  str2term "[A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]");
neuper@37906: val env = [f_, v_, eqs_];
neuper@37906: 
neuper@37906: (*--- 1.line in script ---*)
neuper@37906: val t = str2term "(hd o (filterVar (f_::real))) (eqs_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906: "(hd o filterVar A) [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
neuper@37906: trace_rewrite:=true;
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: trace_rewrite:=false;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "A = a * b" then() else raise error "new behaviour with list_rls 3.1.";
neuper@37906: val env = env @ [(str2term "h_::bool", str2term s')];
neuper@37906: 
neuper@37906: (*--- 2.line in script ---*)
neuper@37906: val t = str2term "dropWhile (ident (h_::bool)) (eqs_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906: "dropWhile (ident (A = a * b))\
neuper@37906: \ [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "[a / 2 = r * sin alpha, b / 2 = r * cos alpha]" 
neuper@37906: then () else raise error "new behaviour with list_rls 3.2.";
neuper@37906: val env = env @ [(str2term "es_::bool list", str2term s')];
neuper@37906: 
neuper@37906: (*--- 3.line in script ---*)
neuper@37906: val t = str2term "dropWhile (ident (f_::real)) (Vars (h_::bool))";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term "dropWhile (ident A) (Vars (A = a * b))";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "[a, b]" then () else raise error "new behaviour with list_rls 3.3.";
neuper@37906: val env = env @ [(str2term "vs_::real list", str2term s')];
neuper@37906: 
neuper@37906: (*--- 4.line in script ---*)
neuper@37906: val t = str2term "nth_ 1 vs_";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term "nth_ 1 [a, b]";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "a" then () else raise error "new behaviour with list_rls 3.4.";
neuper@37906: val env = env @ [(str2term "v_1", str2term s')];
neuper@37906: 
neuper@37906: (*--- 5.line in script ---*)
neuper@37906: val t = str2term "nth_ 2 vs_";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term "nth_ 2 [a, b]";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "b" then () else raise error "new behaviour with list_rls 3.5.";
neuper@37906: val env = env @ [(str2term "v_2", str2term s')];
neuper@37906: 
neuper@37906: (*--- 6.line in script ---*)
neuper@37906: val t = str2term "(hd o (filterVar v_1)) (es_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906: 	   "(hd o filterVar a) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "a / 2 = r * sin alpha" then () 
neuper@37906: else raise error "new behaviour with list_rls 3.6.";
neuper@37906: val e_1 = str2term "e_1::bool";
neuper@37906: val env = env @ [(e_1, str2term s')];
neuper@37906: 
neuper@37906: (*--- 7.line in script ---*)
neuper@37906: val t = str2term "(hd o (filterVar v_2)) (es_::bool list)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: val t = str2term 
neuper@37906: 	  "(hd o filterVar b) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
neuper@37906: val Some (t',_) = rewrite_set_ thy false list_rls t;
neuper@37906: val s' = term2str t';
neuper@37906: if s' = "b / 2 = r * cos alpha" then () 
neuper@37906: else raise error "new behaviour with list_rls 3.7.";
neuper@37906: val env = env @ [(str2term "e_2::bool", str2term s')];
neuper@37906: 
neuper@37906: (*--- 8.line in script ---*)
neuper@37906: val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\
neuper@37906: 		 \            [bool_ e_1, real_ v_1])";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "SubProblem (Reals_, [univar, equation], [no_met])\
neuper@37906: 	    \ [bool_ (a / 2 = r * sin alpha), real_ a]";
neuper@37906: val s_1 = str2term "[a = 2*r*sin alpha]";
neuper@37906: val env = env @ [(str2term "s_1::bool list", s_1)];
neuper@37906: 
neuper@37906: (*--- 9.line in script ---*)
neuper@37906: val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\
neuper@37906:    \                    [bool_ e_2, real_ v_2])";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "SubProblem (Reals_, [univar, equation], [no_met])\
neuper@37906: 	    \ [bool_ (b / 2 = r * cos alpha), real_ b]";
neuper@37906: val s_2 = str2term "[b = 2*r*cos alpha]";
neuper@37906: val env = env @ [(str2term "s_2::bool list", s_2)];
neuper@37906: 
neuper@37906: (*--- 10.line in script ---*)
neuper@37906: val t = str2term 
neuper@37906: "Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] (h_::bool)";
neuper@37906: val s = subst_atomic env t;
neuper@37906: term2str s;
neuper@37906: "Substitute\n [(a = (rhs o hd) [a = 2 * r * sin alpha]),\
neuper@37906: \              (b = (rhs o hd) [b = 2 * r * cos alpha])] (A = a * b)";
neuper@37906: val Some (s',_) = rewrite_set_ thy false list_rls s;
neuper@37906: val s'' = term2str s';
neuper@37906: if s'' = 
neuper@37906: "Substitute [a = 2 * r * sin alpha, b = 2 * r * cos alpha] (A = a * b)"
neuper@37906: then () else raise error "new behaviour with list_rls 3.10.";
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: 
neuper@37906: