(* tests for IsacKnowledge/DiffApp

    author Walther Neuper 000301

    (c) due to copyright terms

    use"../smltest/IsacKnowledge/diffapp.sml";

    use"diffapp.sml";

 *)

 "Contents----------------------------------------------";

 "              Specify_Problem (match_itms_oris)       ";

 "              test specify, fmz <> []                  ";

 "              test specify, fmz = []                  ";

 "          problemtypes + formalizations               ";

 "-------------------- ptree of {(a,b). is-max ... ----------------";

 "--------- me .. scripts for maximum-example ---------------------";

 "--------- autoCalc .. scripts for maximum-example ---------------";

 "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";

 "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";

 "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";

 (*=== inhibit exn ?=============================================================

 " #################################################### ";

 "          problemtypes + formalizations               ";

 " #################################################### ";

 " -------------- [maximum_of,function] --------------- ";

 val pbt = 

     ["fixedValues f_ix","maximum m_","valuesFor v_s","relations r_s"];

 map (the o (parseold thy)) pbt;

 val fmz =

     ["fixedValues [r=Arbfix]","maximum A",

      "valuesFor [a,b]",

      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",

      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",

      "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",

      "boundVariable a","boundVariable b","boundVariable alpha",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "interval {x::real. 0 <= x & x <= pi}",

      "errorBound (eps=(0::real))"];

 map (the o (parseold thy)) fmz;

 " -------------- [make,function] -------------- ";

 val pbt = 

     ["functionOf f_f","boundVariable v_v","equalities eqs",

      "functionTerm f_0_"];

 map (the o (parseold thy)) pbt;

 val fmz12 =

     ["functionOf A","boundVariable a","boundVariable b",

      "equalities [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",

      (*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];

 map (the o (parseold thy)) fmz12;

 val fmz3 =

     ["functionOf A","boundVariable a","boundVariable b",

      "equalities [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",

      (*28.11.00: "functionTerm (A_0=Undef)"*)"functionTerm (Undef)"];

 map (the o (parseold thy)) fmz3;

 " --------- [univar,equation] --------- ";

 val pbt = 

     ["equality e_e","solveFor v_v","solutions v_i_"];

 map (the o (parseold thy)) pbt;

 val fmz =

     ["equality ((a/2)^^^2 + (b/2)^^^2 = r^^^2)",

      "solveFor b","solutions b_i"];

 map (the o (parseold thy)) fmz;

 " ---- [on_interval,maximum_of,function] ---- ";

 val pbt = 

     ["functionTerm t_","boundVariable v_v","interval itv_",

      "errorBound err_","maxArgument v_0"];

 map (the o (parseold thy)) pbt;

 val fmz12 =

     [(*28.11.00: "functionTerm (A_0 = a*sqrt(#4*r^^^#2 - a^^^#2))",*)

      "functionTerm (a*sqrt(4*r^^^2 - a^^^2))",

      (*28.11.00: "functionTerm (A_0 = b*sqrt(#4*r^^^#2 - b^^^#2))",*)

      "functionTerm (b*sqrt(4*r^^^2 - b^^^2))",

      "boundVariable a","boundVariable b",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "errorBound (eps=0)","maxArgument (a_0=Undef)"];

 map (the o (parseold thy)) fmz12;

 val fmz3 =

     [(*28.11.00: "functionTerm (A_0 = (#2*r*sin alpha)*(#2*r*cos alpha))",*)

      "functionTerm ((2*r*sin alpha)*(2*r*cos alpha))",

      "boundVariable alpha",

      "interval {x::real. 0 <= x & x <= pi}",

      "errorBound (eps=0)","maxArgument (a_0=Undef)"];

 map (the o (parseold thy)) fmz3;

 " --------- [derivative_of,function] --------- ";

 val pbt = 

     ["functionTerm f_f","boundVariable v_v","derivative f_f'"];

 map (the o (parseold thy)) pbt;

 val fmz =

     [(*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)

      "functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",

      "boundVariable a",

      (*28.11.00: "derivative (A_0'=Undef)"*)"derivative (Undef)"];

 map (the o (parseold thy)) fmz;

 " --------- [find_values,tool] --------- ";

 val pbt = 

     ["maxArgument ma_","functionTerm f_f","boundVariable v_v",

      "valuesFor vls_","additionalRels r_s"];

 map (the o (parseold thy)) pbt;

 val fmz1 =

     ["maxArgument (a_0=(srqt 2)*r)",

      (*28.11.00: "functionTerm (A_0=a*#2*sqrt r^^^#2 - (a//#2)^^^#2)",*)

      "functionTerm (a*2*sqrt r^^^2 - (a/2)^^^2)",

      "boundVariable a",

      "valuesFor [a,b]","maximum A",

      "additionalRels [(a/2)^^^2 + (b/2)^^^2 = r^^^2]"];

 map (the o (parseold thy)) fmz1;

 "-------------------- ptree of {(a,b). is-max ... --------------------------";

 "-------------------- ptree of {(a,b). is-max ... --------------------------";

 "-------------------- ptree of {(a,b). is-max ... --------------------------";

 (* Teil von max-on-surface.sml,

    der nach Init_Proof -> prep_ori wieder l"auft

    (f"ur tests mit neuer pos')

    use"test-max-surf1.sml";

    Compiler.Control.Print.printDepth:=7; (*4 is default*)

    Compiler.Control.Print.printDepth:=4; (*4 is default*)

    *)

 (* --vvv-- ausgeliehen von test-root-equ/sml *)

 val loc = e_istate;

 val (dI',pI',mI') =

   ("Script",["sqroot-test","univariate","equation"],

    ["Script","squ-equ-test2"]);

 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",

 	   "solveFor x","errorBound (eps=0)",

 	   "solutions L"];

 (*

 val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

 val ((p,p_),_,_,_,_,(_,pt,_)) = do_ (mI,m) e_pos'[1](e_scr,EmptyPtree,[]);

  --^^^-- ausgeliehen von test-root-equ/sml *)

 (*-------------- 9.6.03 --- cappend_ ... term -------irreparabler test

 val (pt,_) = 

   cappend_problem EmptyPtree [] loc ([],(dI',pI',mI'));

 val pos = (lev_on o lev_dn) [];

 (* val pos = ([1]) *)

 val (pt,_) = cappend_parent pt pos loc "{(a,b). is-max ..." 

     Empty_Tac TransitiveB;

 val pos = (lev_on o lev_dn) pos;

 (*val pos = ([1,1])*)

 val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-max ..." 

     Empty_Tac ("[1,1]:{(a,b). is-extremum ...",[]) Complete;

 val pos = lev_on pos;

 (*val pos = ([1,2])*)

 val (pt,_) = cappend_atomic pt pos loc "{(a,b). is-extremum ..." 

     Empty_Tac ("[1,2]:{(a,b). f_x(a,b) ...",[]) Complete;

 val pos = lev_up pos;

 (*val pos = ([1])*)

 val (pt,_) = append_result pt pos e_istate ("[1#]:{(a,b). f_x(a,b) ...",[])

     Complete;

 val pos = lev_on pos;

 (*val pos = ([2]) *)

 val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x(a,b) ..." 

     Empty_Tac ("[2]:{(a,b). f_x & f_xx &...",[]) Complete;

 val pos = lev_on pos;

 (*al pos = [3] : pos*)

 val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x & f_xx &..." 

     Empty_Tac TransitiveB;

 val pos = (lev_on o lev_dn) pos;

 (*pos = ([3,1]) *)

 val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx & ..." 

     Empty_Tac ("[3,1]:{(a,b). f_x & f_xx } cup ...",[]) Complete;

 val pos = lev_on pos;

 (*pos = ([3,2]) *)

 val (pt,_) = cappend_atomic pt pos loc "{(a,b). f_x & f_xx } cup.."

     Empty_Tac ("[3,2]:{(a,b). f_x ..} cup ...",[]) Complete;

 val pos = lev_up pos;

 (*pos = ([3]) *)

 val (pt,_) = append_result pt pos e_istate ("[3#]:{(a,b). f_x ..} cup..",[])

     Complete;

 val pos = lev_on pos;

 (*val pos = [4] : pos *)

 val (pt,_) = cappend_parent pt pos loc "{(a,b). f_x ..} cup ..." 

     Empty_Tac IntersectB;

 val pos = (lev_on o lev_dn) pos;

 (*val pos = ([4,1]) *)

 val (pt,_) = cappend_parent pt pos loc "set_1 = ..." 

     Empty_Tac SequenceB;

 val pos = (lev_on o lev_dn) pos;

 (*val pos = ([4,1,1]) *)

 val (pt,_) = cappend_parent(*pbl*) pt pos loc"f_x = d/dx x^3 ..."

     Empty_Tac TransitiveB;

 val pos = (lev_on o lev_dn) pos;

 (*val pos = ([4,1,1,1]) *)

 val (pt,_) = cappend_parent pt pos loc "d/dx x^3 ..." 

     Empty_Tac TransitiveB;

 val pos = (lev_on o lev_dn) pos;

 (*val pos = ([4,1,1,1,1]) *)

 val (pt,_) = cappend_atomic pt pos loc "d/dx x^3 ..." 

     Empty_Tac ("[4,1,1,1,1]:3x^2 + d/dx ...",[]) Complete;

 val pos = lev_on pos;

 (*val pos = ([4,1,1,1,2]) *)

 val (pt,_) = cappend_atomic pt pos loc "3x^2 + d/dx ..." 

     Empty_Tac ("[4,1,1,1,2]:3x^2 + 0 + d/dx ...",[]) Complete;

 val pos = lev_on pos;

 (*pos = ([4,1,1,1,3]) *)

 val (pt,_) = cappend_atomic pt pos loc "3x^2 + 0 + d/dx ..." 

     Empty_Tac ("[4,1,1,1,3]:3x^2 + 0 -3 ...",[]) Complete;

 "--- 1 ---";

 val pos = lev_up pos;

 (*pos = ([4,1,1,1]) *)

 val (pt,_) = append_result pt pos e_istate ("[4,1,1,1#]:3x^2 -3.",[])Complete;

 "--- 2 ---";

 val pos = lev_up pos;

 (*val pos = ([4,1,1]) *)

 val (pt,_) = append_result pt pos e_istate ("[4,1,1#]:found 3x^2 -3 ...",[])

     Complete;

 "--- 3 ---";

 val pos = lev_on pos;

 (*val pos = ([4,1,2]+) *)

 val (pt,_) = cappend_parent(*pbl*) pt pos loc "f_y = d/dy x^3 ..."

     Empty_Tac TransitiveB;

 "--- 4 ---";

 writeln (pr_ptree pr_short pt);

 (*

 .    ----- pblobj -----

 1.   {(a,b). is-max ...

 1.1.   {(a,b). is-max ...

 1.2.   {(a,b). is-extremum ...

 2.   {(a,b). f_x(a,b) ...

 3.   {(a,b). f_x & f_xx &...

 3.1.   {(a,b). f_x & f_xx & ...

 3.2.   {(a,b). f_x & f_xx } cup..

 4.   {(a,b). f_x ..} cup ...

 4.1.   set_1 = ...

 4.1.1.   f_x = d/dx x^3 ...

 4.1.1.1.   d/dx x^3 ...

 4.1.1.1.1.   d/dx x^3 ...

 4.1.1.1.2.   3x^2 + d/dx ...

 4.1.1.1.3.   3x^2 + 0 + d/dx ...

 4.1.2.   f_y = d/dy x^3 ...

  use"test-max-surf1.sml";

    *)

 -------------- 9.6.03 --- cappend_ ... term -------irreparabler test---*)

 "--------- me .. scripts for maximum-example ---------------------";

 "--------- me .. scripts for maximum-example ---------------------";

 "--------- me .. scripts for maximum-example ---------------------";

 val fmz =

     ["fixedValues [r=Arbfix]","maximum A",

      "valuesFor [a,b]",

      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",

      "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]",

      "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",

      "boundVariable a","boundVariable b","boundVariable alpha",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "interval {x::real. 0 <= x & x <= pi}",

      "errorBound (eps=(0::real))"];

 val (dI',pI',mI') =

   ("DiffApp",["maximum_of","function"],

    ["DiffApp","max_by_calculus"]);

 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => OldGoals.print_exn e;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 case nxt of (_, Specify_Method ["DiffApp","max_by_calculus"]) => ()

 	  | _ => error "diffapp.sml: max-exp me, nxt = Specify_Method";

 val oris = fst3 (get_obj g_origin pt (fst p)); writeln(oris2str oris);

 val pits = get_obj g_pbl pt (fst p); writeln(itms2str_ ctxt pits);

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val mits = get_obj g_met pt (fst p); writeln(itms2str_ ctxt mits);

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 case nxt of (_,Apply_Method ["DiffApp","max_by_calculus"] ) => ()

 	  | _ => error "diffapp.sml: max-exp me, nxt = Apply_Method";

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (*since 0508 Apply_Method does the 1st step, if NONE init_form -------------

 (*val nxt = ("Subproblem",Subproblem ("DiffApp",["make","function"]))*)

 val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => print_exn_G e;

 (*val nxt = ("Refine_Tacitly",Refine_Tacitly ["make","function"])*)

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (*val nxt = ("Model_Problem",Model_Problem ["by_explicit","make","function"])*)

 ----------------------------------------------------------------------------*)

 case nxt of (_, Model_Problem(*["by_explicit", "make", "function"]*)) => ()

 	  | _ => error "diffapp.sml: max-exp me, nxt = Model_Problem";

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);

 val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 case nxt of (_, Apply_Method ["DiffApp", "make_fun_by_explicit"]) => ()

 	  | _ => error "diffapp.sml: max-exp Apply_Method ([1], Met) ";

 (*----since WN050901 (ie. corr. mathengine#nxt_specify_ ..nxt_spec Pbl->p_

 we get at ...

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 ...

 ### assod: NotAss m= Subproblem'  ,

  stac= Substitute

  [(b, (rhs o hd)

        (Subproblem (thy, [normalize, polynomial, univariate, equation])))]

  (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))

 *** stac2tac_ TODO: no match for Substitute

 ***  [(b, (rhs o hd)

 ***        (Subproblem (thy, [normalize, polynomial, univariate, equation])))]

 ***  (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))

 Exception- ERROR raised

 ############################################################################

 # presumerably didnt work before either, but not detected due to Emtpy_Tac #

 ############################################################################

 (*val nxt = Subproblem ("DiffApp",["univariate","equation"]))   *)

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (*val nxt = Refine_Tacitly ["univariate","equation"])*)

 val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);

 val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"A = a * b"))*)

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (*val f = Form' (FormKF (~1,EdUndef,4,Nundef,"[b = A / a]"))*)

 ------------------------------------------------------------------------*)

 (*val f =

 Error' (Error_ "Refine_Tacitly [\"univariate\",\"equation\"] not applicable")*)

 (*----postponed.15.5.03 run scripts for maximum-example: univariate equation

 val (p,_,f,nxt,_,pt) = (me nxt p c pt) handle e => OldGoals.print_exn e; 

 val oris = fst3 (get_obj g_origin pt (fst p));writeln(oris2str oris);

 val pits = get_obj g_pbl pt (fst p);writeln(itms2str_ ctxt pits);

 val pits = get_obj g_pbl pt [];writeln(itms2str_ ctxt pits);

 val mits = get_obj g_met pt (fst p);writeln(itms2str_ ctxt mits);

 val mits = get_obj g_met pt [];writeln(itms2str_ ctxt mits);

 itms2args thy ["DiffApp","max_by_calculus"] mits;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 ---*)

 "--------- autoCalc .. scripts for maximum-example ---------------";

 "--------- autoCalc .. scripts for maximum-example ---------------";

 "--------- autoCalc .. scripts for maximum-example ---------------";

 (*++++++++ see systest/inform.sml 'complete_metitms' ++++++++*)

  states:=[];

 val fmz =

     ["fixedValues [r=Arbfix]","maximum A",

      "valuesFor [a,b]",

      "relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",

      "relations [A=a*b, (a/2)^2 + (b/2)^2 = r^2]",

      "relations [A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]",

      "boundVariable a","boundVariable b","boundVariable alpha",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "interval {x::real. 0 <= x & x <= 2*r}",

      "interval {x::real. 0 <= x & x <= pi}",

      "errorBound (eps=(0::real))"];

 val (dI',pI',mI') =

   ("DiffApp",["maximum_of","function"],

    ["DiffApp","max_by_calculus"]);

  CalcTree [(fmz, (dI',pI',mI'))];

  Iterator 1; moveActiveRoot 1;

  autoCalculate 1 CompleteCalcHead;

  refFormula 1 (get_pos 1 1); 

  fetchProposedTactic 1;

  autoCalculate 1 (Step 1);

  fetchProposedTactic 1;

  autoCalculate 1 (Step 1);

  (*Subproblem on_interval maximum_of function*)

  autoCalculate 1 CompleteCalcHead;

  fetchProposedTactic 1;

  val ((pt,p),_) = get_calc 1;

  val mits = get_obj g_met pt (fst p);

  writeln (itms2str_ ctxt mits);

 (*

  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 ()

  else error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";

 *)

  (*FIXME: the environments contain identifers, and NOT values ?!?!?*)

 (* WN051209 while extending 'fun step' for initac, this became better ...

  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 ()

  else error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";

 *)

 "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";

 "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";

 "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";

 str2term

   "Script Maximum_value(f_ix::bool list)(m_::real) (r_s::bool list)\

    \      (v_v::real) (itv_v::real set) (err_::bool) =          \ 

    \ (let e_e = (hd o (filterVar m_)) r_s;              \

    \      t_ = (if 1 < length_ r_s                            \

    \           then (SubProblem (Reals_,[make,function],[no_met])\

    \                     [REAL m_, REAL v_v, BOOL_LIST r_s])\

    \           else (hd r_s));                                \

    \      (mx_::real) = SubProblem (Reals_,[on_interval,max_of,function], \

    \                                [Isac,maximum_on_interval])\

    \                               [BOOL t_, REAL v_v, REAL_SET itv_]\

    \ in ((SubProblem (Reals_,[find_values,tool],[Isac,find_values])   \

    \      [REAL mx_, REAL (Rhs t_), REAL v_v, REAL m_,     \

    \       BOOL_LIST (dropWhile (ident e_e) r_s)])::bool list))";

 val f_ix = (str2term "f_ix::bool list", 

 	    str2term "[r=Arbfix]");

 val m_   = (str2term "m_::real", 

 	    str2term "A");

 val r_s  = (str2term "rs_::bool list", 

 	    str2term "[A = a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]");

 val v_v   = (str2term "v_v::real", 

 	    str2term "b");

 val itv_ = (str2term "itv_v::real set", 

 	    str2term "{x::real. 0 <= x & x <= 2*r}");

 val err_ = (str2term "err_::bool", 

 	    str2term "eps=0");

 val env = [f_ix, m_, r_s ,v_, itv_, err_];

 (*--- 1.line in script ---*)

 val t = str2term "(hd o (filterVar m_)) (r_s::bool list)";

 val s = subst_atomic env t;

 term2str s;

 "(hd o filterVar A) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";

 val SOME (s',_) = rewrite_set_ thy false list_rls s;

 val s'' = term2str s';

 if s''="A = a * b" then () else error "new behaviour with list_rls 1.1.";

 val env = env @ [(str2term "e_::bool",str2term "A = a * b")];

 (*--- 2.line: condition alone ---*)

 val t = str2term "1 < length_ (r_s::bool list)";

 val s = subst_atomic env t;

 term2str s;

 "1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";

 val SOME (s',_) = rewrite_set_ thy false list_rls s;

 val s'' = term2str s';

 if s''="HOL.True" then () else error "new behaviour with list_rls 1.2.";

 (*--- 2.line in script ---*)

 val t = str2term 

 	    "(if 1 < length_ r_s                            \

    \           then (SubProblem (Reals_,[make,function],[no_met])\

    \                     [REAL m_, REAL v_v, BOOL_LIST r_s])\

    \           else (hd r_s))";

 val s = subst_atomic env t;

 term2str s;

 "if 1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]\

 \then SubProblem (Reals_, [make, function], [no_met])\

 \      [REAL A, REAL b,\

 \       BOOL_LIST [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]\

 \else hd [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";

 val SOME (s',_) = rewrite_set_ thy false list_rls s;

 val s'' = term2str s';

 if s'' = 

 "SubProblem (Reals_, [make, function], [no_met])\n\

 \ [REAL A, REAL b,\n\

 \  BOOL_LIST [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]]" then ()

 else error "new behaviour with list_rls 1.3.";

 val env = env @ [(str2term "t_::bool",

 		  str2term "A = (2*sqrt(r^^^2-(b/2)^^^2)) * b")];

 "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";

 "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";

 "---------------------- 1.5.03: Make_fun_by_explicit ---------------------";

 str2term

    "Script Make_fun_by_explicit (f_f::real) (v_v::real)         \

    \      (eqs::bool list) =                                 \

    \ (let h_  = (hd o (filterVar f_)) eqs;                   \

    \      e_1 = hd (dropWhile (ident h_) eqs);               \

    \      v_s = dropWhile (ident f_) (Vars h_);                \

    \      v_1 = hd (dropWhile (ident v_v) v_s);                \

    \      (s_1::bool list)=(SubProblem(Reals_,[univar,equation],[no_met])\

    \                          [BOOL e_1, REAL v_1])\

    \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";

 val f_ = (str2term "f_f::real", 

 	  str2term "A");

 val v_v = (str2term "v_v::real", 

 	  str2term "b");

 val eqs=(str2term "eqs::bool list", 

 	  str2term "[A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]");

 val env = [f_f, v_v, eqs];

 (*--- 1.line in script ---*)

 val t = str2term "(hd o (filterVar v_v)) (eqs::bool list)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

      "(hd o filterVar b) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "A = a * b" then () else error "new behaviour with list_rls 2.1";

 val env = env @ [(str2term "h_::bool", str2term s')];

 (*--- 2.line in script ---*)

 val t = str2term "hd (dropWhile (ident h_) (eqs::bool list))";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

 	    "hd (dropWhile (ident (A = a * b))\

 	    \     [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2])";

 mem_rls "dropWhile_Cons" list_rls;

 mem_rls "Atools.ident" list_rls;

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2" then () 

 else error "new behaviour with list_rls 2.2";

 val env = env @ [(str2term "e_1::bool", str2term s')];

 (*--- 3.line in script ---*)

 val t = str2term "dropWhile (ident f_) (Vars (h_::bool))";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term "dropWhile (ident A) (Vars (A = a * b))";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "[a, b]" then () else error "new behaviour with list_rls 2.3";

 val env = env @ [(str2term "vs_::real list", str2term s')];

 (*--- 4.line in script ---*)

 val t = str2term "hd (dropWhile (ident v_v) v_s)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term "hd (dropWhile (ident b) [a, b])";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "a" then () else error "new behaviour with list_rls 2.4.";

 val env = env @ [(str2term "v_1::real", str2term s')];

 (*--- 5.line in script ---*)

 val t = str2term "(SubProblem(Reals_,[univar,equation],[no_met])\

 		 \           [BOOL e_1, REAL v_1])";

 val s = subst_atomic env t;

 term2str s;

 "SubProblem (Reals_, [univar, equation], [no_met])\n\

 \ [BOOL ((a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2), REAL a]";

 val env = env @ [(str2term "s_1::bool list", 

 		  str2term "[a = 2 * sqrt (r^^^2 - (b/2)^^^2)]")];

 (*--- 6.line in script ---*)

 val t = str2term "Substitute [(v_1 = (rhs o hd) (s_1::bool list))] (h_::bool)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

 "Substitute [(a = (rhs o hd) [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)])]\n\

 \ (A = a * b)";

 mem_rls "Tools.rhs" list_rls;

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "Substitute [a = 2 * sqrt (r ^^^ 2 - (b / 2) ^^^ 2)] (A = a * b)" 

 then () else error "new behaviour with list_rls 2.6.";

 "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";

 "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";

 "---------------------- 2.5.03: Make_fun_by_new_variable -----------------";

 str2term

   "Script Make_fun_by_new_variable (f_f::real) (v_v::real)     \

    \      (eqs::bool list) =                                 \

    \(let h_ = (hd o (filterVar f_)) eqs;             \

    \     es_ = dropWhile (ident h_) eqs;                    \

    \     v_s = dropWhile (ident f_) (Vars h_);                \

    \     v_1 = nth_ 1 v_s;                                   \

    \     v_2 = nth_ 2 v_s;                                   \

    \     e_1 = (hd o (filterVar v_1)) es_;            \

    \     e_2 = (hd o (filterVar v_2)) es_;            \

    \  (s_1::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\

    \                    [BOOL e_1, REAL v_1]);\

    \  (s_2::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\

    \                    [BOOL e_2, REAL v_2])\

    \in Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] h_)";

 val f_ = (str2term "f_f::real", 

 	  str2term "A");

 val v_v = (str2term "v_v::real", 

 	  str2term "alpha");

 val eqs=(str2term "eqs::bool list", 

 	  str2term "[A=a*b, a/2=r*sin alpha, b/2=r*cos alpha]");

 val env = [f_f, v_v, eqs];

 (*--- 1.line in script ---*)

 val t = str2term "(hd o (filterVar (f_f::real))) (eqs::bool list)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

 "(hd o filterVar A) [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";

 trace_rewrite:=true;

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 trace_rewrite:=false;

 val s' = term2str t';

 if s' = "A = a * b" then() else error "new behaviour with list_rls 3.1.";

 val env = env @ [(str2term "h_::bool", str2term s')];

 (*--- 2.line in script ---*)

 val t = str2term "dropWhile (ident (h_::bool)) (eqs::bool list)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

 "dropWhile (ident (A = a * b))\

 \ [A = a * b, a / 2 = r * sin alpha, b / 2 = r * cos alpha]";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "[a / 2 = r * sin alpha, b / 2 = r * cos alpha]" 

 then () else error "new behaviour with list_rls 3.2.";

 val env = env @ [(str2term "es_::bool list", str2term s')];

 (*--- 3.line in script ---*)

 val t = str2term "dropWhile (ident (f_f::real)) (Vars (h_::bool))";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term "dropWhile (ident A) (Vars (A = a * b))";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "[a, b]" then () else error "new behaviour with list_rls 3.3.";

 val env = env @ [(str2term "vs_::real list", str2term s')];

 (*--- 4.line in script ---*)

 val t = str2term "nth_ 1 v_s";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term "nth_ 1 [a, b]";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "a" then () else error "new behaviour with list_rls 3.4.";

 val env = env @ [(str2term "v_1", str2term s')];

 (*--- 5.line in script ---*)

 val t = str2term "nth_ 2 v_s";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term "nth_ 2 [a, b]";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "b" then () else error "new behaviour with list_rls 3.5.";

 val env = env @ [(str2term "v_2", str2term s')];

 (*--- 6.line in script ---*)

 val t = str2term "(hd o (filterVar v_1)) (es_::bool list)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

 	   "(hd o filterVar a) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "a / 2 = r * sin alpha" then () 

 else error "new behaviour with list_rls 3.6.";

 val e_1 = str2term "e_1::bool";

 val env = env @ [(e_1, str2term s')];

 (*--- 7.line in script ---*)

 val t = str2term "(hd o (filterVar v_2)) (es_::bool list)";

 val s = subst_atomic env t;

 term2str s;

 val t = str2term 

 	  "(hd o filterVar b) [a / 2 = r * sin alpha, b / 2 = r * cos alpha]";

 val SOME (t',_) = rewrite_set_ thy false list_rls t;

 val s' = term2str t';

 if s' = "b / 2 = r * cos alpha" then () 

 else error "new behaviour with list_rls 3.7.";

 val env = env @ [(str2term "e_2::bool", str2term s')];

 (*--- 8.line in script ---*)

 val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\

 		 \            [BOOL e_1, REAL v_1])";

 val s = subst_atomic env t;

 term2str s;

 "SubProblem (Reals_, [univar, equation], [no_met])\

 	    \ [BOOL (a / 2 = r * sin alpha), REAL a]";

 val s_1 = str2term "[a = 2*r*sin alpha]";

 val env = env @ [(str2term "s_1::bool list", s_1)];

 (*--- 9.line in script ---*)

 val t = str2term "(SubProblem (Reals_,[univar,equation],[no_met])\

    \                    [BOOL e_2, REAL v_2])";

 val s = subst_atomic env t;

 term2str s;

 "SubProblem (Reals_, [univar, equation], [no_met])\

 	    \ [BOOL (b / 2 = r * cos alpha), REAL b]";

 val s_2 = str2term "[b = 2*r*cos alpha]";

 val env = env @ [(str2term "s_2::bool list", s_2)];

 (*--- 10.line in script ---*)

 val t = str2term 

 "Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] (h_::bool)";

 val s = subst_atomic env t;

 term2str s;

 "Substitute\n [(a = (rhs o hd) [a = 2 * r * sin alpha]),\

 \              (b = (rhs o hd) [b = 2 * r * cos alpha])] (A = a * b)";

 val SOME (s',_) = rewrite_set_ thy false list_rls s;

 val s'' = term2str s';

 if s'' = 

 "Substitute [a = 2 * r * sin alpha, b = 2 * r * cos alpha] (A = a * b)"

 then () else error "new behaviour with list_rls 3.10.";

 ===== inhibit exn ?===========================================================*)