t@42195
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neuper@37906
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(* tests for IsacKnowledge/DiffApp
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author Walther Neuper 000301
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(c) due to copyright terms
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use"../smltest/IsacKnowledge/diffapp.sml";
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use"diffapp.sml";
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*)
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"Contents----------------------------------------------";
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" Specify_Problem (match_itms_oris) ";
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" test specify, fmz <> [] ";
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neuper@37906
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" test specify, fmz = [] ";
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neuper@37906
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" problemtypes + formalizations ";
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"-------------------- ptree of {(a,b). is-max ... ----------------";
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"--------- me .. scripts for maximum-example ---------------------";
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"--------- autoCalc .. scripts for maximum-example ---------------";
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"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
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"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
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"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
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" #################################################### ";
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" problemtypes + formalizations ";
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" #################################################### ";
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" -------------- [maximum_of,function] --------------- ";
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val pbt =
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t@42195
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["fixedValues f_ix","maximum m_m","valuesFor v_s","relations r_s"];
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t@42195
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(*=== inhibit exn 110722=============================================================
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map (the o (parseold thy)) pbt;
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t@42195
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=== inhibit exn 110722=============================================================*)
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val fmz =
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["fixedValues [r=Arbfix]","maximum A",
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"valuesFor [a,b]",
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"relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
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"relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
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"relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
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neuper@37906
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"boundVariable a","boundVariable b","boundVariable alpha",
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"interval {x::real. 0 <= x & x <= 2*r}",
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"interval {x::real. 0 <= x & x <= 2*r}",
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"interval {x::real. 0 <= x & x <= pi}",
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"errorBound (eps=(0::real))"];
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t@42195
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(*=== inhibit exn 110722=============================================================
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map (the o (parseold thy)) fmz;
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" -------------- [make,function] -------------- ";
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t@42195
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=== inhibit exn 110722=============================================================*)
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val pbt =
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neuper@37994
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["functionOf f_f","boundVariable v_v","equalities eqs",
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t@42195
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"functionTerm f_0_0"];
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t@42195
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(*=== inhibit exn 110722=============================================================
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map (the o (parseold thy)) pbt;
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val fmz12 =
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["functionOf A","boundVariable a","boundVariable b",
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"equalities [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
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(*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];
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map (the o (parseold thy)) fmz12;
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val fmz3 =
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["functionOf A","boundVariable a","boundVariable b",
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"equalities [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
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(*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];
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map (the o (parseold thy)) fmz3;
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" --------- [univar,equation] --------- ";
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val pbt =
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t@42195
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["equality e_e","solveFor v_v","solutions v_i_i"];
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map (the o (parseold thy)) pbt;
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val fmz =
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["equality ((a/2)^^^2 + (b/2)^^^2 = r^^^2)",
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"solveFor b","solutions b_i"];
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map (the o (parseold thy)) fmz;
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neuper@37906
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" ---- [on_interval,maximum_of,function] ---- ";
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neuper@37906
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val pbt =
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t@42195
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["functionTerm t_t","boundVariable v_v","interval itv_v",
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t@42195
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"errorBound err_r","maxArgument v_0"];
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neuper@37906
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map (the o (parseold thy)) pbt;
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neuper@37906
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val fmz12 =
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[(*28.11.00: "functionTerm (A_0 = a*sqrt(#4*r^^^#2 - a^^^#2))",*)
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"functionTerm (a*sqrt(4*r^^^2 - a^^^2))",
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(*28.11.00: "functionTerm (A_0 = b*sqrt(#4*r^^^#2 - b^^^#2))",*)
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"functionTerm (b*sqrt(4*r^^^2 - b^^^2))",
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"boundVariable a","boundVariable b",
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"interval {x::real. 0 <= x & x <= 2*r}",
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"errorBound (eps=0)","maxArgument (a_0=Undef)"];
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map (the o (parseold thy)) fmz12;
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val fmz3 =
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[(*28.11.00: "functionTerm (A_0 = (#2*r*sin alpha)*(#2*r*cos alpha))",*)
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"functionTerm ((2*r*sin alpha)*(2*r*cos alpha))",
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"boundVariable alpha",
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"interval {x::real. 0 <= x & x <= pi}",
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"errorBound (eps=0)","maxArgument (a_0=Undef)"];
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map (the o (parseold thy)) fmz3;
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neuper@37906
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" --------- [derivative_of,function] --------- ";
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neuper@37906
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val pbt =
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["functionTerm f_f","boundVariable v_v","derivative f_f'"];
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map (the o (parseold thy)) pbt;
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val fmz =
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[(*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)
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"functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",
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"boundVariable a",
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(*28.11.00: "derivative (A_0'=Undef)"*)"derivative (Undef)"];
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map (the o (parseold thy)) fmz;
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neuper@37906
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" --------- [find_values,tool] --------- ";
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neuper@37906
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val pbt =
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t@42195
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["maxArgument ma_a","functionTerm f_f","boundVariable v_v",
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t@42195
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"valuesFor vls_s","additionalRels r_s"];
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map (the o (parseold thy)) pbt;
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val fmz1 =
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["maxArgument (a_0=(srqt 2)*r)",
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(*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)
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"functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",
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neuper@37906
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"boundVariable a",
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"valuesFor [a,b]","maximum A",
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"additionalRels [(a/2)^^^2 + (b/2)^^^2 = r^^^2]"];
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map (the o (parseold thy)) fmz1;
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neuper@37906
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t@42166
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=== inhibit exn 110722=============================================================*)
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"-------------------- ptree of {(a,b). is-max ... --------------------------";
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"-------------------- ptree of {(a,b). is-max ... --------------------------";
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"-------------------- ptree of {(a,b). is-max ... --------------------------";
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neuper@37906
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(* Teil von max-on-surface.sml,
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der nach Init_Proof -> prep_ori wieder l"auft
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(f"ur tests mit neuer pos')
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use"test-max-surf1.sml";
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Compiler.Control.Print.printDepth:=7; (*4 is default*)
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Compiler.Control.Print.printDepth:=4; (*4 is default*)
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*)
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neuper@37906
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neuper@37906
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(* --vvv-- ausgeliehen von test-root-equ/sml *)
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val loc = e_istate;
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val (dI',pI',mI') =
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neuper@37991
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("Script",["sqroot-test","univariate","equation"],
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["Script","squ-equ-test2"]);
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neuper@37906
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val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
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"solveFor x","errorBound (eps=0)",
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"solutions L"];
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(*
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val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
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val ((p,p_),_,_,_,_,(_,pt,_)) = do_ (mI,m) e_pos'[1](e_scr,EmptyPtree,[]);
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neuper@37906
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--^^^-- ausgeliehen von test-root-equ/sml *)
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neuper@37906
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(*-------------- 9.6.03 --- cappend_ ... term -------irreparabler test
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neuper@37906
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val (pt,_) =
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neuper@37906
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cappend_problem EmptyPtree [] loc ([],(dI',pI',mI'));
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neuper@37906
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val pos = (lev_on o lev_dn) [];
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neuper@37906
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(* val pos = ([1]) *)
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neuper@37906
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val (pt,_) = cappend_parent pt pos loc "{(a,b). is-max ..."
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neuper@37906
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Empty_Tac TransitiveB;
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neuper@37906
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val pos = (lev_on o lev_dn) pos;
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neuper@37906
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(*val pos = ([1,1])*)
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neuper@37906
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val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-max ..."
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neuper@37906
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Empty_Tac ("[1,1]:{(a,b). is-extremum ...",[]) Complete;
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neuper@37906
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val pos = lev_on pos;
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neuper@37906
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(*val pos = ([1,2])*)
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neuper@37906
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val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-extremum ..."
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neuper@37906
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Empty_Tac ("[1,2]:{(a,b). f_x(a,b) ...",[]) Complete;
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neuper@37906
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val pos = lev_up pos;
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neuper@37906
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(*val pos = ([1])*)
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neuper@37906
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val (pt,_) = append_result pt pos e_istate ("[1#]:{(a,b). f_x(a,b) ...",[])
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Complete;
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neuper@37906
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167 |
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neuper@37906
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val pos = lev_on pos;
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neuper@37906
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(*val pos = ([2]) *)
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neuper@37906
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val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x(a,b) ..."
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neuper@37906
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Empty_Tac ("[2]:{(a,b). f_x & f_xx &...",[]) Complete;
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neuper@37906
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val pos = lev_on pos;
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neuper@37906
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(*al pos = [3] : pos*)
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neuper@37906
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val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x & f_xx &..."
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neuper@37906
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Empty_Tac TransitiveB;
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neuper@37906
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val pos = (lev_on o lev_dn) pos;
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neuper@37906
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(*pos = ([3,1]) *)
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neuper@37906
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val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx & ..."
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neuper@37906
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Empty_Tac ("[3,1]:{(a,b). f_x & f_xx } cup ...",[]) Complete;
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neuper@37906
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val pos = lev_on pos;
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neuper@37906
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(*pos = ([3,2]) *)
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neuper@37906
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val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx } cup.."
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neuper@37906
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183 |
Empty_Tac ("[3,2]:{(a,b). f_x ..} cup ...",[]) Complete;
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neuper@37906
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184 |
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neuper@37906
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val pos = lev_up pos;
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neuper@37906
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(*pos = ([3]) *)
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neuper@37906
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val (pt,_) = append_result pt pos e_istate ("[3#]:{(a,b). f_x ..} cup..",[])
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neuper@37906
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Complete;
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neuper@37906
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val pos = lev_on pos;
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neuper@37906
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(*val pos = [4] : pos *)
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neuper@37906
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val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x ..} cup ..."
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neuper@37906
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192 |
Empty_Tac IntersectB;
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neuper@37906
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val pos = (lev_on o lev_dn) pos;
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neuper@37906
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(*val pos = ([4,1]) *)
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neuper@37906
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val (pt,_) = cappend_parent pt pos loc "set_1 = ..."
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neuper@37906
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196 |
Empty_Tac SequenceB;
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neuper@37906
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197 |
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neuper@37906
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198 |
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neuper@37906
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199 |
val pos = (lev_on o lev_dn) pos;
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neuper@37906
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200 |
(*val pos = ([4,1,1]) *)
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neuper@37906
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201 |
val (pt,_) = cappend_parent(*pbl*) pt pos loc"f_x = d/dx x^3 ..."
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neuper@37906
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202 |
Empty_Tac TransitiveB;
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neuper@37906
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203 |
val pos = (lev_on o lev_dn) pos;
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neuper@37906
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204 |
(*val pos = ([4,1,1,1]) *)
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neuper@37906
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205 |
val (pt,_) = cappend_parent pt pos loc "d/dx x^3 ..."
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neuper@37906
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206 |
Empty_Tac TransitiveB;
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neuper@37906
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207 |
val pos = (lev_on o lev_dn) pos;
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neuper@37906
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208 |
(*val pos = ([4,1,1,1,1]) *)
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neuper@37906
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209 |
val (pt,_) = cappend_atomic pt pos loc "d/dx x^3 ..."
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neuper@37906
|
210 |
Empty_Tac ("[4,1,1,1,1]:3x^2 + d/dx ...",[]) Complete;
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neuper@37906
|
211 |
val pos = lev_on pos;
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neuper@37906
|
212 |
(*val pos = ([4,1,1,1,2]) *)
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neuper@37906
|
213 |
val (pt,_) = cappend_atomic pt pos loc "3x^2 + d/dx ..."
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neuper@37906
|
214 |
Empty_Tac ("[4,1,1,1,2]:3x^2 + 0 + d/dx ...",[]) Complete;
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neuper@37906
|
215 |
val pos = lev_on pos;
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neuper@37906
|
216 |
(*pos = ([4,1,1,1,3]) *)
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neuper@37906
|
217 |
val (pt,_) = cappend_atomic pt pos loc "3x^2 + 0 + d/dx ..."
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neuper@37906
|
218 |
Empty_Tac ("[4,1,1,1,3]:3x^2 + 0 -3 ...",[]) Complete;
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neuper@37906
|
219 |
"--- 1 ---";
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neuper@37906
|
220 |
val pos = lev_up pos;
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neuper@37906
|
221 |
(*pos = ([4,1,1,1]) *)
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neuper@37906
|
222 |
val (pt,_) = append_result pt pos e_istate ("[4,1,1,1#]:3x^2 -3.",[])Complete;
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neuper@37906
|
223 |
"--- 2 ---";
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neuper@37906
|
224 |
val pos = lev_up pos;
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neuper@37906
|
225 |
(*val pos = ([4,1,1]) *)
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neuper@37906
|
226 |
val (pt,_) = append_result pt pos e_istate ("[4,1,1#]:found 3x^2 -3 ...",[])
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neuper@37906
|
227 |
Complete;
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neuper@37906
|
228 |
"--- 3 ---";
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neuper@37906
|
229 |
val pos = lev_on pos;
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neuper@37906
|
230 |
(*val pos = ([4,1,2]+) *)
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neuper@37906
|
231 |
val (pt,_) = cappend_parent(*pbl*) pt pos loc "f_y = d/dy x^3 ..."
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neuper@37906
|
232 |
Empty_Tac TransitiveB;
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neuper@37906
|
233 |
"--- 4 ---";
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neuper@37906
|
234 |
writeln (pr_ptree pr_short pt);
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neuper@37906
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235 |
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neuper@37906
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236 |
(*
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neuper@37906
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237 |
. ----- pblobj -----
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neuper@37906
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238 |
1. {(a,b). is-max ...
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neuper@37906
|
239 |
1.1. {(a,b). is-max ...
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neuper@37906
|
240 |
1.2. {(a,b). is-extremum ...
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neuper@37906
|
241 |
2. {(a,b). f_x(a,b) ...
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neuper@37906
|
242 |
3. {(a,b). f_x & f_xx &...
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neuper@37906
|
243 |
3.1. {(a,b). f_x & f_xx & ...
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neuper@37906
|
244 |
3.2. {(a,b). f_x & f_xx } cup..
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neuper@37906
|
245 |
4. {(a,b). f_x ..} cup ...
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neuper@37906
|
246 |
4.1. set_1 = ...
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neuper@37906
|
247 |
4.1.1. f_x = d/dx x^3 ...
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neuper@37906
|
248 |
4.1.1.1. d/dx x^3 ...
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neuper@37906
|
249 |
4.1.1.1.1. d/dx x^3 ...
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neuper@37906
|
250 |
4.1.1.1.2. 3x^2 + d/dx ...
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neuper@37906
|
251 |
4.1.1.1.3. 3x^2 + 0 + d/dx ...
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neuper@37906
|
252 |
4.1.2. f_y = d/dy x^3 ...
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neuper@37906
|
253 |
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neuper@37906
|
254 |
use"test-max-surf1.sml";
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neuper@37906
|
255 |
*)
|
neuper@37906
|
256 |
-------------- 9.6.03 --- cappend_ ... term -------irreparabler test---*)
|
neuper@37906
|
257 |
|
neuper@37906
|
258 |
|
neuper@37906
|
259 |
"--------- me .. scripts for maximum-example ---------------------";
|
neuper@37906
|
260 |
"--------- me .. scripts for maximum-example ---------------------";
|
neuper@37906
|
261 |
"--------- me .. scripts for maximum-example ---------------------";
|
neuper@37906
|
262 |
|
neuper@37906
|
263 |
val fmz =
|
neuper@37906
|
264 |
["fixedValues [r=Arbfix]","maximum A",
|
neuper@37906
|
265 |
"valuesFor [a,b]",
|
neuper@37906
|
266 |
"relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
|
neuper@37906
|
267 |
"relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",
|
neuper@37906
|
268 |
"relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
|
neuper@37906
|
269 |
|
neuper@37906
|
270 |
"boundVariable a","boundVariable b","boundVariable alpha",
|
neuper@37906
|
271 |
"interval {x::real. 0 <= x & x <= 2*r}",
|
neuper@37906
|
272 |
"interval {x::real. 0 <= x & x <= 2*r}",
|
neuper@37906
|
273 |
"interval {x::real. 0 <= x & x <= pi}",
|
neuper@37906
|
274 |
"errorBound (eps=(0::real))"];
|
neuper@37906
|
275 |
val (dI',pI',mI') =
|
neuper@37991
|
276 |
("DiffApp",["maximum_of","function"],
|
neuper@37906
|
277 |
["DiffApp","max_by_calculus"]);
|
neuper@37906
|
278 |
|
neuper@37906
|
279 |
val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
|
t@42166
|
280 |
(*=== inhibit exn 110722=============================================================
|
neuper@37906
|
281 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
282 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
283 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
284 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@38043
|
285 |
val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => OldGoals.print_exn e;
|
neuper@37906
|
286 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
287 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
288 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
289 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
290 |
case nxt of (_, Specify_Method ["DiffApp","max_by_calculus"]) => ()
|
neuper@38031
|
291 |
| _ => error "diffapp.sml: max-exp me, nxt = Specify_Method";
|
neuper@37906
|
292 |
|
neuper@37906
|
293 |
val oris = fst3 (get_obj g_origin pt (fst p)); writeln(oris2str oris);
|
neuper@37924
|
294 |
val pits = get_obj g_pbl pt (fst p); writeln(itms2str_ ctxt pits);
|
neuper@37906
|
295 |
|
neuper@37906
|
296 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37924
|
297 |
val mits = get_obj g_met pt (fst p); writeln(itms2str_ ctxt mits);
|
neuper@37906
|
298 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
299 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
300 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
301 |
case nxt of (_,Apply_Method ["DiffApp","max_by_calculus"] ) => ()
|
neuper@38031
|
302 |
| _ => error "diffapp.sml: max-exp me, nxt = Apply_Method";
|
neuper@37906
|
303 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
t@42166
|
304 |
=== inhibit exn 110722=============================================================*)
|
neuper@37906
|
305 |
|
neuper@37926
|
306 |
(*since 0508 Apply_Method does the 1st step, if NONE init_form -------------
|
neuper@37991
|
307 |
(*val nxt = ("Subproblem",Subproblem ("DiffApp",["make","function"]))*)
|
neuper@37906
|
308 |
val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn_G e;
|
neuper@37906
|
309 |
(*val nxt = ("Refine_Tacitly",Refine_Tacitly ["make","function"])*)
|
neuper@37906
|
310 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
311 |
(*val nxt = ("Model_Problem",Model_Problem ["by_explicit","make","function"])*)
|
neuper@37906
|
312 |
----------------------------------------------------------------------------*)
|
neuper@37906
|
313 |
case nxt of (_, Model_Problem(*["by_explicit", "make", "function"]*)) => ()
|
neuper@38031
|
314 |
| _ => error "diffapp.sml: max-exp me, nxt = Model_Problem";
|
neuper@37906
|
315 |
|
t@42166
|
316 |
(*=== inhibit exn 110722=============================================================
|
neuper@37906
|
317 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
318 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
319 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
320 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
321 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
t@42166
|
322 |
=== inhibit exn 110722=============================================================*)
|
neuper@37906
|
323 |
|
neuper@37906
|
324 |
val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
|
neuper@37924
|
325 |
val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);
|
neuper@37906
|
326 |
|
t@42166
|
327 |
(*=== inhibit exn 110722=============================================================
|
neuper@37906
|
328 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
329 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
330 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
331 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
332 |
case nxt of (_, Apply_Method ["DiffApp", "make_fun_by_explicit"]) => ()
|
neuper@38031
|
333 |
| _ => error "diffapp.sml: max-exp Apply_Method ([1], Met) ";
|
t@42166
|
334 |
=== inhibit exn 110722=============================================================*)
|
neuper@37906
|
335 |
|
neuper@37906
|
336 |
(*----since WN050901 (ie. corr. mathengine#nxt_specify_ ..nxt_spec Pbl->p_
|
neuper@37906
|
337 |
we get at ...
|
neuper@37906
|
338 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
339 |
...
|
neuper@37906
|
340 |
### assod: NotAss m= Subproblem' ,
|
neuper@37906
|
341 |
stac= Substitute
|
neuper@37906
|
342 |
[(b, (rhs o hd)
|
neuper@37906
|
343 |
(Subproblem (thy, [normalize, polynomial, univariate, equation])))]
|
neuper@37906
|
344 |
(hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
|
neuper@37906
|
345 |
*** stac2tac_ TODO: no match for Substitute
|
neuper@37906
|
346 |
*** [(b, (rhs o hd)
|
neuper@37906
|
347 |
*** (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
|
neuper@37906
|
348 |
*** (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
|
neuper@37906
|
349 |
Exception- ERROR raised
|
neuper@37906
|
350 |
|
neuper@37906
|
351 |
############################################################################
|
neuper@37906
|
352 |
# presumerably didnt work before either, but not detected due to Emtpy_Tac #
|
neuper@37906
|
353 |
############################################################################
|
neuper@37906
|
354 |
|
neuper@37991
|
355 |
(*val nxt = Subproblem ("DiffApp",["univariate","equation"])) *)
|
neuper@37906
|
356 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
357 |
(*val nxt = Refine_Tacitly ["univariate","equation"])*)
|
neuper@37906
|
358 |
|
neuper@37906
|
359 |
val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
|
neuper@37924
|
360 |
val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);
|
neuper@37906
|
361 |
|
neuper@37906
|
362 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
363 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
364 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
365 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
366 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
367 |
(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)
|
neuper@37906
|
368 |
|
neuper@37906
|
369 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
370 |
(*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"A = a * b"))*)
|
neuper@37906
|
371 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
372 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
373 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
374 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
375 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
376 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
377 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
378 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
379 |
(*val f = Form' (FormKF (~1,EdUndef,4,Nundef,"[b = A / a]"))*)
|
neuper@37906
|
380 |
|
neuper@37906
|
381 |
------------------------------------------------------------------------*)
|
neuper@37906
|
382 |
|
neuper@37906
|
383 |
(*val f =
|
neuper@37906
|
384 |
Error' (Error_ "Refine_Tacitly [\"univariate\",\"equation\"] not applicable")*)
|
neuper@37906
|
385 |
|
neuper@37906
|
386 |
|
t@42166
|
387 |
(*----postponed.15.5.03 run scripts for maximum-example: univariate equation*)
|
t@42166
|
388 |
(*=== inhibit exn 110722=============================================================
|
neuper@37906
|
389 |
|
neuper@38043
|
390 |
val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => OldGoals.print_exn e;
|
t@42166
|
391 |
=== inhibit exn 110722=============================================================*)
|
neuper@37906
|
392 |
|
neuper@37906
|
393 |
val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);
|
neuper@37906
|
394 |
|
neuper@37924
|
395 |
val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);
|
neuper@37924
|
396 |
val pits = get_obj g_pbl pt [];writeln(itms2str_ ctxt pits);
|
neuper@37906
|
397 |
|
neuper@37924
|
398 |
val mits = get_obj g_met pt (fst p);writeln(itms2str_ ctxt mits);
|
neuper@37924
|
399 |
val mits = get_obj g_met pt [];writeln(itms2str_ ctxt mits);
|
neuper@37906
|
400 |
|
t@42166
|
401 |
(*=== inhibit exn 110722=============================================================
|
neuper@37906
|
402 |
itms2args thy ["DiffApp","max_by_calculus"] mits;
|
neuper@37906
|
403 |
|
neuper@37906
|
404 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
t@42166
|
405 |
=== inhibit exn 110722=============================================================*)
|
neuper@37906
|
406 |
|
t@42166
|
407 |
(*---*)
|
neuper@37906
|
408 |
|
neuper@37906
|
409 |
"--------- autoCalc .. scripts for maximum-example ---------------";
|
neuper@37906
|
410 |
"--------- autoCalc .. scripts for maximum-example ---------------";
|
neuper@37906
|
411 |
"--------- autoCalc .. scripts for maximum-example ---------------";
|
neuper@37906
|
412 |
(*++++++++ see systest/inform.sml 'complete_metitms' ++++++++*)
|
neuper@37906
|
413 |
states:=[];
|
neuper@37906
|
414 |
val fmz =
|
neuper@37906
|
415 |
["fixedValues [r=Arbfix]","maximum A",
|
neuper@37906
|
416 |
"valuesFor [a,b]",
|
neuper@37906
|
417 |
"relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",
|
neuper@37906
|
418 |
"relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",
|
neuper@37906
|
419 |
"relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",
|
neuper@37906
|
420 |
|
neuper@37906
|
421 |
"boundVariable a","boundVariable b","boundVariable alpha",
|
neuper@37906
|
422 |
"interval {x::real. 0 <= x & x <= 2*r}",
|
neuper@37906
|
423 |
"interval {x::real. 0 <= x & x <= 2*r}",
|
neuper@37906
|
424 |
"interval {x::real. 0 <= x & x <= pi}",
|
neuper@37906
|
425 |
"errorBound (eps=(0::real))"];
|
neuper@37906
|
426 |
val (dI',pI',mI') =
|
neuper@37991
|
427 |
("DiffApp",["maximum_of","function"],
|
neuper@37906
|
428 |
["DiffApp","max_by_calculus"]);
|
neuper@37906
|
429 |
|
neuper@37906
|
430 |
CalcTree [(fmz, (dI',pI',mI'))];
|
neuper@37906
|
431 |
Iterator 1; moveActiveRoot 1;
|
neuper@37906
|
432 |
autoCalculate 1 CompleteCalcHead;
|
neuper@37906
|
433 |
refFormula 1 (get_pos 1 1);
|
neuper@37906
|
434 |
|
neuper@37906
|
435 |
fetchProposedTactic 1;
|
neuper@37906
|
436 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
437 |
|
neuper@37906
|
438 |
fetchProposedTactic 1;
|
neuper@37906
|
439 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
440 |
(*Subproblem on_interval maximum_of function*)
|
neuper@37906
|
441 |
autoCalculate 1 CompleteCalcHead;
|
neuper@37906
|
442 |
|
neuper@37906
|
443 |
fetchProposedTactic 1;
|
neuper@37906
|
444 |
val ((pt,p),_) = get_calc 1;
|
neuper@37906
|
445 |
val mits = get_obj g_met pt (fst p);
|
neuper@37924
|
446 |
writeln (itms2str_ ctxt mits);
|
neuper@37906
|
447 |
(*
|
neuper@37995
|
448 |
if itms2str_ ctxt mits = "[\n(1 ,[1] ,true ,#Given ,Cor functionEq (hd r_s) ,(t_, [hd r_s])),\n(2 ,[1] ,true ,#Given ,Cor boundVariable v_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@38031
|
449 |
else error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
|
neuper@37906
|
450 |
*)
|
neuper@37906
|
451 |
(*FIXME: the environments contain identifers, and NOT values ?!?!?*)
|
neuper@37906
|
452 |
(* WN051209 while extending 'fun step' for initac, this became better ...
|
neuper@37995
|
453 |
if itms2str_ ctxt mits = "[\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(f_ix, [[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] ,(v_s, [[a],[b]])),\n(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2] ,(r_s, [[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@38031
|
454 |
else error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
|
neuper@37906
|
455 |
*)
|
neuper@37906
|
456 |
|
neuper@37906
|
457 |
|
neuper@37906
|
458 |
|
neuper@37906
|
459 |
"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
|
neuper@37906
|
460 |
"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
|
neuper@37906
|
461 |
"--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
|
neuper@37906
|
462 |
str2term
|
t@42203
|
463 |
"Script Maximum_value(f_ix::bool list)(m_m::real) (r_s::bool list)\
|
t@42203
|
464 |
\ (v_v::real) (itv_v::real set) (err_r::bool) = \
|
t@42203
|
465 |
\ (let e_e = (hd o (filterVar m_m)) r_s; \
|
t@42203
|
466 |
\ t_t = (if 1 < length_h r_s \
|
t@42203
|
467 |
\ then (SubProblem (Reals_s,[make,function],[no_met])\
|
t@42203
|
468 |
\ [REAL m_m, REAL v_v, BOOL_LIST r_s])\
|
neuper@37995
|
469 |
\ else (hd r_s)); \
|
t@42203
|
470 |
\ (mx_x::real) = SubProblem (Reals_s,[on_interval,max_of,function], \
|
neuper@37906
|
471 |
\ [Isac,maximum_on_interval])\
|
t@42203
|
472 |
\ [BOOL t_t, REAL v_v, REAL_SET itv_v]\
|
t@42203
|
473 |
\ in ((SubProblem (Reals_s,[find_values,tool],[Isac,find_values]) \
|
t@42203
|
474 |
\ [REAL mx_x, REAL (Rhs t_t), REAL v_v, REAL m_m, \
|
neuper@37995
|
475 |
\ BOOL_LIST (dropWhile (ident e_e) r_s)])::bool list))";
|
t@42203
|
476 |
(*=== inhibit exn 110722=============================================================
|
neuper@37906
|
477 |
|
neuper@37995
|
478 |
val f_ix = (str2term "f_ix::bool list",
|
neuper@37906
|
479 |
str2term "[r=Arbfix]");
|
neuper@37906
|
480 |
val m_ = (str2term "m_::real",
|
neuper@37906
|
481 |
str2term "A");
|
neuper@37995
|
482 |
val r_s = (str2term "rs_::bool list",
|
neuper@37906
|
483 |
str2term "[A = a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]");
|
neuper@37991
|
484 |
val v_v = (str2term "v_v::real",
|
neuper@37906
|
485 |
str2term "b");
|
neuper@37991
|
486 |
val itv_ = (str2term "itv_v::real set",
|
neuper@37906
|
487 |
str2term "{x::real. 0 <= x & x <= 2*r}");
|
neuper@37906
|
488 |
val err_ = (str2term "err_::bool",
|
neuper@37906
|
489 |
str2term "eps=0");
|
neuper@37995
|
490 |
val env = [f_ix, m_, r_s ,v_, itv_, err_];
|
neuper@37906
|
491 |
|
neuper@37906
|
492 |
(*--- 1.line in script ---*)
|
neuper@37995
|
493 |
val t = str2term "(hd o (filterVar m_)) (r_s::bool list)";
|
neuper@37906
|
494 |
val s = subst_atomic env t;
|
neuper@37906
|
495 |
term2str s;
|
neuper@37906
|
496 |
"(hd o filterVar A) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
|
neuper@37926
|
497 |
val SOME (s',_) = rewrite_set_ thy false list_rls s;
|
neuper@37906
|
498 |
val s'' = term2str s';
|
neuper@38031
|
499 |
if s''="A = a * b" then () else error "new behaviour with list_rls 1.1.";
|
neuper@37906
|
500 |
val env = env @ [(str2term "e_::bool",str2term "A = a * b")];
|
neuper@37906
|
501 |
|
neuper@37906
|
502 |
(*--- 2.line: condition alone ---*)
|
neuper@37995
|
503 |
val t = str2term "1 < length_ (r_s::bool list)";
|
neuper@37906
|
504 |
val s = subst_atomic env t;
|
neuper@37906
|
505 |
term2str s;
|
neuper@37906
|
506 |
"1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
|
neuper@37926
|
507 |
val SOME (s',_) = rewrite_set_ thy false list_rls s;
|
neuper@37906
|
508 |
val s'' = term2str s';
|
neuper@41928
|
509 |
if s''="HOL.True" then () else error "new behaviour with list_rls 1.2.";
|
neuper@37906
|
510 |
|
neuper@37906
|
511 |
(*--- 2.line in script ---*)
|
neuper@37906
|
512 |
val t = str2term
|
neuper@37995
|
513 |
"(if 1 < length_ r_s \
|
neuper@37906
|
514 |
\ then (SubProblem (Reals_,[make,function],[no_met])\
|
neuper@37995
|
515 |
\ [REAL m_, REAL v_v, BOOL_LIST r_s])\
|
neuper@37995
|
516 |
\ else (hd r_s))";
|
neuper@37906
|
517 |
val s = subst_atomic env t;
|
neuper@37906
|
518 |
term2str s;
|
neuper@37906
|
519 |
"if 1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]\
|
neuper@37906
|
520 |
\then SubProblem (Reals_, [make, function], [no_met])\
|
neuper@37984
|
521 |
\ [REAL A, REAL b,\
|
neuper@37984
|
522 |
\ BOOL_LIST [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]\
|
neuper@37906
|
523 |
\else hd [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
|
neuper@37926
|
524 |
val SOME (s',_) = rewrite_set_ thy false list_rls s;
|
neuper@37906
|
525 |
val s'' = term2str s';
|
neuper@37906
|
526 |
if s'' =
|
neuper@37906
|
527 |
"SubProblem (Reals_, [make, function], [no_met])\n\
|
neuper@37984
|
528 |
\ [REAL A, REAL b,\n\
|
neuper@37984
|
529 |
\ BOOL_LIST [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]" then ()
|
neuper@38031
|
530 |
else error "new behaviour with list_rls 1.3.";
|
neuper@37906
|
531 |
val env = env @ [(str2term "t_::bool",
|
neuper@37906
|
532 |
str2term "A = (2*sqrt(r^^^2-(b/2)^^^2)) * b")];
|
neuper@37906
|
533 |
|
neuper@37906
|
534 |
|
neuper@37906
|
535 |
|
neuper@37906
|
536 |
"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
|
neuper@37906
|
537 |
"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
|
neuper@37906
|
538 |
"---------------------- 1.5.03: Make_fun_by_explicit ---------------------";
|
neuper@37906
|
539 |
str2term
|
neuper@37994
|
540 |
"Script Make_fun_by_explicit (f_f::real) (v_v::real) \
|
neuper@37994
|
541 |
\ (eqs::bool list) = \
|
neuper@37994
|
542 |
\ (let h_ = (hd o (filterVar f_)) eqs; \
|
neuper@37994
|
543 |
\ e_1 = hd (dropWhile (ident h_) eqs); \
|
neuper@37995
|
544 |
\ v_s = dropWhile (ident f_) (Vars h_); \
|
neuper@37995
|
545 |
\ v_1 = hd (dropWhile (ident v_v) v_s); \
|
neuper@37906
|
546 |
\ (s_1::bool list)=(SubProblem(Reals_,[univar,equation],[no_met])\
|
neuper@37984
|
547 |
\ [BOOL e_1, REAL v_1])\
|
neuper@37906
|
548 |
\ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
|
neuper@37994
|
549 |
val f_ = (str2term "f_f::real",
|
neuper@37906
|
550 |
str2term "A");
|
neuper@37991
|
551 |
val v_v = (str2term "v_v::real",
|
neuper@37906
|
552 |
str2term "b");
|
neuper@37994
|
553 |
val eqs=(str2term "eqs::bool list",
|
neuper@37906
|
554 |
str2term "[A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]");
|
neuper@37994
|
555 |
val env = [f_f, v_v, eqs];
|
neuper@37906
|
556 |
|
neuper@37906
|
557 |
(*--- 1.line in script ---*)
|
neuper@37994
|
558 |
val t = str2term "(hd o (filterVar v_v)) (eqs::bool list)";
|
neuper@37906
|
559 |
val s = subst_atomic env t;
|
neuper@37906
|
560 |
term2str s;
|
neuper@37906
|
561 |
val t = str2term
|
neuper@37906
|
562 |
"(hd o filterVar b) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
|
neuper@37926
|
563 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
564 |
val s' = term2str t';
|
neuper@38031
|
565 |
if s' = "A = a * b" then () else error "new behaviour with list_rls 2.1";
|
neuper@37906
|
566 |
val env = env @ [(str2term "h_::bool", str2term s')];
|
neuper@37906
|
567 |
|
neuper@37906
|
568 |
(*--- 2.line in script ---*)
|
neuper@37994
|
569 |
val t = str2term "hd (dropWhile (ident h_) (eqs::bool list))";
|
neuper@37906
|
570 |
val s = subst_atomic env t;
|
neuper@37906
|
571 |
term2str s;
|
neuper@37906
|
572 |
val t = str2term
|
neuper@37906
|
573 |
"hd (dropWhile (ident (A = a * b))\
|
neuper@37906
|
574 |
\ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2])";
|
neuper@37906
|
575 |
mem_rls "dropWhile_Cons" list_rls;
|
neuper@37906
|
576 |
mem_rls "Atools.ident" list_rls;
|
neuper@37926
|
577 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
578 |
val s' = term2str t';
|
neuper@37906
|
579 |
if s' = "(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2" then ()
|
neuper@38031
|
580 |
else error "new behaviour with list_rls 2.2";
|
neuper@37906
|
581 |
val env = env @ [(str2term "e_1::bool", str2term s')];
|
neuper@37906
|
582 |
|
neuper@37906
|
583 |
(*--- 3.line in script ---*)
|
neuper@37906
|
584 |
val t = str2term "dropWhile (ident f_) (Vars (h_::bool))";
|
neuper@37906
|
585 |
val s = subst_atomic env t;
|
neuper@37906
|
586 |
term2str s;
|
neuper@37906
|
587 |
val t = str2term "dropWhile (ident A) (Vars (A = a * b))";
|
neuper@37926
|
588 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
589 |
val s' = term2str t';
|
neuper@38031
|
590 |
if s' = "[a, b]" then () else error "new behaviour with list_rls 2.3";
|
neuper@37906
|
591 |
val env = env @ [(str2term "vs_::real list", str2term s')];
|
neuper@37906
|
592 |
|
neuper@37906
|
593 |
(*--- 4.line in script ---*)
|
neuper@37995
|
594 |
val t = str2term "hd (dropWhile (ident v_v) v_s)";
|
neuper@37906
|
595 |
val s = subst_atomic env t;
|
neuper@37906
|
596 |
term2str s;
|
neuper@37906
|
597 |
val t = str2term "hd (dropWhile (ident b) [a, b])";
|
neuper@37926
|
598 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
599 |
val s' = term2str t';
|
neuper@38031
|
600 |
if s' = "a" then () else error "new behaviour with list_rls 2.4.";
|
neuper@37906
|
601 |
val env = env @ [(str2term "v_1::real", str2term s')];
|
neuper@37906
|
602 |
|
neuper@37906
|
603 |
(*--- 5.line in script ---*)
|
neuper@37906
|
604 |
val t = str2term "(SubProblem(Reals_,[univar,equation],[no_met])\
|
neuper@37984
|
605 |
\ [BOOL e_1, REAL v_1])";
|
neuper@37906
|
606 |
val s = subst_atomic env t;
|
neuper@37906
|
607 |
term2str s;
|
neuper@37906
|
608 |
"SubProblem (Reals_, [univar, equation], [no_met])\n\
|
neuper@37984
|
609 |
\ [BOOL ((a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2), REAL a]";
|
neuper@37906
|
610 |
val env = env @ [(str2term "s_1::bool list",
|
neuper@37906
|
611 |
str2term "[a = 2 * sqrt (r^^^2 - (b/2)^^^2)]")];
|
neuper@37906
|
612 |
|
neuper@37906
|
613 |
(*--- 6.line in script ---*)
|
neuper@37906
|
614 |
val t = str2term "Substitute [(v_1 = (rhs o hd) (s_1::bool list))] (h_::bool)";
|
neuper@37906
|
615 |
val s = subst_atomic env t;
|
neuper@37906
|
616 |
term2str s;
|
neuper@37906
|
617 |
val t = str2term
|
neuper@37906
|
618 |
"Substitute [(a = (rhs o hd) [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)])]\n\
|
neuper@37906
|
619 |
\ (A = a * b)";
|
neuper@37906
|
620 |
mem_rls "Tools.rhs" list_rls;
|
neuper@37926
|
621 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
622 |
val s' = term2str t';
|
neuper@37906
|
623 |
if s' = "Substitute [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)] (A = a * b)"
|
neuper@38031
|
624 |
then () else error "new behaviour with list_rls 2.6.";
|
neuper@37906
|
625 |
|
neuper@37906
|
626 |
|
neuper@37906
|
627 |
"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
|
neuper@37906
|
628 |
"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
|
neuper@37906
|
629 |
"---------------------- 2.5.03: Make_fun_by_new_variable -----------------";
|
neuper@37906
|
630 |
str2term
|
neuper@37994
|
631 |
"Script Make_fun_by_new_variable (f_f::real) (v_v::real) \
|
neuper@37994
|
632 |
\ (eqs::bool list) = \
|
neuper@37994
|
633 |
\(let h_ = (hd o (filterVar f_)) eqs; \
|
neuper@37994
|
634 |
\ es_ = dropWhile (ident h_) eqs; \
|
neuper@37995
|
635 |
\ v_s = dropWhile (ident f_) (Vars h_); \
|
neuper@37995
|
636 |
\ v_1 = nth_ 1 v_s; \
|
neuper@37995
|
637 |
\ v_2 = nth_ 2 v_s; \
|
neuper@37906
|
638 |
\ e_1 = (hd o (filterVar v_1)) es_; \
|
neuper@37906
|
639 |
\ e_2 = (hd o (filterVar v_2)) es_; \
|
neuper@37906
|
640 |
\ (s_1::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
|
neuper@37984
|
641 |
\ [BOOL e_1, REAL v_1]);\
|
neuper@37906
|
642 |
\ (s_2::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
|
neuper@37984
|
643 |
\ [BOOL e_2, REAL v_2])\
|
neuper@37906
|
644 |
\in Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] h_)";
|
neuper@37994
|
645 |
val f_ = (str2term "f_f::real",
|
neuper@37906
|
646 |
str2term "A");
|
neuper@37991
|
647 |
val v_v = (str2term "v_v::real",
|
neuper@37906
|
648 |
str2term "alpha");
|
neuper@37994
|
649 |
val eqs=(str2term "eqs::bool list",
|
neuper@37906
|
650 |
str2term "[A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]");
|
neuper@37994
|
651 |
val env = [f_f, v_v, eqs];
|
neuper@37906
|
652 |
|
neuper@37906
|
653 |
(*--- 1.line in script ---*)
|
neuper@37994
|
654 |
val t = str2term "(hd o (filterVar (f_f::real))) (eqs::bool list)";
|
neuper@37906
|
655 |
val s = subst_atomic env t;
|
neuper@37906
|
656 |
term2str s;
|
neuper@37906
|
657 |
val t = str2term
|
neuper@37906
|
658 |
"(hd o filterVar A) [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
|
neuper@37906
|
659 |
trace_rewrite:=true;
|
neuper@37926
|
660 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
661 |
trace_rewrite:=false;
|
neuper@37906
|
662 |
val s' = term2str t';
|
neuper@38031
|
663 |
if s' = "A = a * b" then() else error "new behaviour with list_rls 3.1.";
|
neuper@37906
|
664 |
val env = env @ [(str2term "h_::bool", str2term s')];
|
neuper@37906
|
665 |
|
neuper@37906
|
666 |
(*--- 2.line in script ---*)
|
neuper@37994
|
667 |
val t = str2term "dropWhile (ident (h_::bool)) (eqs::bool list)";
|
neuper@37906
|
668 |
val s = subst_atomic env t;
|
neuper@37906
|
669 |
term2str s;
|
neuper@37906
|
670 |
val t = str2term
|
neuper@37906
|
671 |
"dropWhile (ident (A = a * b))\
|
neuper@37906
|
672 |
\ [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
|
neuper@37926
|
673 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
674 |
val s' = term2str t';
|
neuper@37906
|
675 |
if s' = "[a / 2 = r * sin alpha, b / 2 = r * cos alpha]"
|
neuper@38031
|
676 |
then () else error "new behaviour with list_rls 3.2.";
|
neuper@37906
|
677 |
val env = env @ [(str2term "es_::bool list", str2term s')];
|
neuper@37906
|
678 |
|
neuper@37906
|
679 |
(*--- 3.line in script ---*)
|
neuper@37994
|
680 |
val t = str2term "dropWhile (ident (f_f::real)) (Vars (h_::bool))";
|
neuper@37906
|
681 |
val s = subst_atomic env t;
|
neuper@37906
|
682 |
term2str s;
|
neuper@37906
|
683 |
val t = str2term "dropWhile (ident A) (Vars (A = a * b))";
|
neuper@37926
|
684 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
685 |
val s' = term2str t';
|
neuper@38031
|
686 |
if s' = "[a, b]" then () else error "new behaviour with list_rls 3.3.";
|
neuper@37906
|
687 |
val env = env @ [(str2term "vs_::real list", str2term s')];
|
neuper@37906
|
688 |
|
neuper@37906
|
689 |
(*--- 4.line in script ---*)
|
neuper@37995
|
690 |
val t = str2term "nth_ 1 v_s";
|
neuper@37906
|
691 |
val s = subst_atomic env t;
|
neuper@37906
|
692 |
term2str s;
|
neuper@37906
|
693 |
val t = str2term "nth_ 1 [a, b]";
|
neuper@37926
|
694 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
695 |
val s' = term2str t';
|
neuper@38031
|
696 |
if s' = "a" then () else error "new behaviour with list_rls 3.4.";
|
neuper@37906
|
697 |
val env = env @ [(str2term "v_1", str2term s')];
|
neuper@37906
|
698 |
|
neuper@37906
|
699 |
(*--- 5.line in script ---*)
|
neuper@37995
|
700 |
val t = str2term "nth_ 2 v_s";
|
neuper@37906
|
701 |
val s = subst_atomic env t;
|
neuper@37906
|
702 |
term2str s;
|
neuper@37906
|
703 |
val t = str2term "nth_ 2 [a, b]";
|
neuper@37926
|
704 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
705 |
val s' = term2str t';
|
neuper@38031
|
706 |
if s' = "b" then () else error "new behaviour with list_rls 3.5.";
|
neuper@37906
|
707 |
val env = env @ [(str2term "v_2", str2term s')];
|
neuper@37906
|
708 |
|
neuper@37906
|
709 |
(*--- 6.line in script ---*)
|
neuper@37906
|
710 |
val t = str2term "(hd o (filterVar v_1)) (es_::bool list)";
|
neuper@37906
|
711 |
val s = subst_atomic env t;
|
neuper@37906
|
712 |
term2str s;
|
neuper@37906
|
713 |
val t = str2term
|
neuper@37906
|
714 |
"(hd o filterVar a) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
|
neuper@37926
|
715 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
716 |
val s' = term2str t';
|
neuper@37906
|
717 |
if s' = "a / 2 = r * sin alpha" then ()
|
neuper@38031
|
718 |
else error "new behaviour with list_rls 3.6.";
|
neuper@37906
|
719 |
val e_1 = str2term "e_1::bool";
|
neuper@37906
|
720 |
val env = env @ [(e_1, str2term s')];
|
neuper@37906
|
721 |
|
neuper@37906
|
722 |
(*--- 7.line in script ---*)
|
neuper@37906
|
723 |
val t = str2term "(hd o (filterVar v_2)) (es_::bool list)";
|
neuper@37906
|
724 |
val s = subst_atomic env t;
|
neuper@37906
|
725 |
term2str s;
|
neuper@37906
|
726 |
val t = str2term
|
neuper@37906
|
727 |
"(hd o filterVar b) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";
|
neuper@37926
|
728 |
val SOME (t',_) = rewrite_set_ thy false list_rls t;
|
neuper@37906
|
729 |
val s' = term2str t';
|
neuper@37906
|
730 |
if s' = "b / 2 = r * cos alpha" then ()
|
neuper@38031
|
731 |
else error "new behaviour with list_rls 3.7.";
|
neuper@37906
|
732 |
val env = env @ [(str2term "e_2::bool", str2term s')];
|
neuper@37906
|
733 |
|
neuper@37906
|
734 |
(*--- 8.line in script ---*)
|
neuper@37906
|
735 |
val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\
|
neuper@37984
|
736 |
\ [BOOL e_1, REAL v_1])";
|
neuper@37906
|
737 |
val s = subst_atomic env t;
|
neuper@37906
|
738 |
term2str s;
|
neuper@37906
|
739 |
"SubProblem (Reals_, [univar, equation], [no_met])\
|
neuper@37984
|
740 |
\ [BOOL (a / 2 = r * sin alpha), REAL a]";
|
neuper@37906
|
741 |
val s_1 = str2term "[a = 2*r*sin alpha]";
|
neuper@37906
|
742 |
val env = env @ [(str2term "s_1::bool list", s_1)];
|
neuper@37906
|
743 |
|
neuper@37906
|
744 |
(*--- 9.line in script ---*)
|
neuper@37906
|
745 |
val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\
|
neuper@37984
|
746 |
\ [BOOL e_2, REAL v_2])";
|
neuper@37906
|
747 |
val s = subst_atomic env t;
|
neuper@37906
|
748 |
term2str s;
|
neuper@37906
|
749 |
"SubProblem (Reals_, [univar, equation], [no_met])\
|
neuper@37984
|
750 |
\ [BOOL (b / 2 = r * cos alpha), REAL b]";
|
neuper@37906
|
751 |
val s_2 = str2term "[b = 2*r*cos alpha]";
|
neuper@37906
|
752 |
val env = env @ [(str2term "s_2::bool list", s_2)];
|
neuper@37906
|
753 |
|
neuper@37906
|
754 |
(*--- 10.line in script ---*)
|
neuper@37906
|
755 |
val t = str2term
|
neuper@37906
|
756 |
"Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] (h_::bool)";
|
neuper@37906
|
757 |
val s = subst_atomic env t;
|
neuper@37906
|
758 |
term2str s;
|
neuper@37906
|
759 |
"Substitute\n [(a = (rhs o hd) [a = 2 * r * sin alpha]),\
|
neuper@37906
|
760 |
\ (b = (rhs o hd) [b = 2 * r * cos alpha])] (A = a * b)";
|
neuper@37926
|
761 |
val SOME (s',_) = rewrite_set_ thy false list_rls s;
|
neuper@37906
|
762 |
val s'' = term2str s';
|
neuper@37906
|
763 |
if s'' =
|
neuper@37906
|
764 |
"Substitute [a = 2 * r * sin alpha, b = 2 * r * cos alpha] (A = a * b)"
|
neuper@38031
|
765 |
then () else error "new behaviour with list_rls 3.10.";
|
neuper@37906
|
766 |
|
neuper@37906
|
767 |
|
neuper@37906
|
768 |
|
t@42166
|
769 |
===== inhibit exn 110722===========================================================*)
|
t@42195
|
770 |
|
t@42203
|
771 |
|