test/Tools/isac/Knowledge/rateq.sml
author Walther Neuper <walther.neuper@jku.at>
Mon, 23 Mar 2020 17:51:35 +0100
changeset 59835 df00a2b5c4cc
parent 59831 edf1643edde5
child 59839 0688613fc053
permissions -rw-r--r--
make Check_elementwise' idle wrt. Calc.T

Note: kept for covering general case in Ctree (step between two Check_Postcond)
     1 (* Title:  Test for rational equations
     2    Author: Richard Lang 2009
     3    (c) copyright due to lincense terms.
     4 *)
     5 
     6 "-----------------------------------------------------------------";
     7 "table of contents -----------------------------------------------";
     8 "-----------------------------------------------------------------";
     9 "----------- pbl: rational, univariate, equation ----------------";
    10 "----------- solve (1/x = 5, x) by me ---------------------------";
    11 "----------- S.68, Bsp.: 40, ((x)/(x - 8) + (x - 8)/(x) = 26/5)--";
    12 "----------- x / (x ^ 2 - 6 * x + 9) - 1 / (x ^ 2 - 3 * x) = 1 /x";
    13 "----------- ((5*x)/(x - 2) - x/(x+2)=(4::real)), incl. refine ---------------------------------";
    14 "-----------------------------------------------------------------";
    15 "-----------------------------------------------------------------";
    16 
    17 val thy = @{theory "RatEq"};
    18 val ctxt = Proof_Context.init_global thy;
    19 
    20 "------------ pbl: rational, univariate, equation ----------------";
    21 "------------ pbl: rational, univariate, equation ----------------";
    22 "------------ pbl: rational, univariate, equation ----------------";
    23 val t = (Thm.term_of o the o (parse thy)) "(1/b+1/x=1) is_ratequation_in  x";
    24 val SOME (t_, _) = rewrite_set_ thy  false RatEq_prls t;
    25 val result = term2str t_;
    26 if result <>  "True"  then error "rateq.sml: new behaviour 1:" else ();
    27 
    28 val t = (Thm.term_of o the o (parse thy)) "(sqrt(x)=1) is_ratequation_in  x";
    29 val SOME (t_, _) = rewrite_set_ thy  false RatEq_prls t;
    30 val result = term2str t_;
    31 if result <>  "False"  then error "rateq.sml: new behaviour 2:" else ();
    32 
    33 val t = (Thm.term_of o the o (parse thy)) "(x=-1) is_ratequation_in x";
    34 val SOME (t_,_) = rewrite_set_ thy  false RatEq_prls t;
    35 val result = term2str t_;
    36 if result <>  "False"  then error "rateq.sml: new behaviour 3:" else ();
    37 
    38 val t = (Thm.term_of o the o (parse thy)) "(3 + x^^^2 + 1/(x^^^2+3)=1) is_ratequation_in x";
    39 val SOME (t_,_) = rewrite_set_ thy  false RatEq_prls t;
    40 val result = term2str t_;
    41 if result <>  "True"  then error "rateq.sml: new behaviour 4:" else ();
    42 
    43 val result = match_pbl ["equality (x=(1::real))","solveFor x","solutions L"] 
    44   (get_pbt ["rational","univariate","equation"]); 
    45 case result of NoMatch' _  => ()  | _ => error "rateq.sml: new behaviour: 5";
    46 
    47 val result = match_pbl ["equality (3 + x^^^2 + 1/(x^^^2+3)=1)","solveFor x","solutions L"] 
    48   (get_pbt ["rational","univariate","equation"]); 
    49 case result of Matches' _  => ()  | _ => error "rateq.sml: new behaviour: 6";
    50 
    51 "------------ solve (1/x = 5, x) by me ---------------------------";
    52 "------------ solve (1/x = 5, x) by me ---------------------------";
    53 "------------ solve (1/x = 5, x) by me ---------------------------";
    54 val fmz = ["equality (1/x=(5::real))","solveFor x","solutions L"];
    55 val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);
    56 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
    57 (* val (p,_,f,nxt,_,pt) = me nxt p [1] pt;------------- now Refine_Tacitly*)
    58 (*  nxt = ("Model_Problem",Model_Problem ["rational","univariate","equation"]) *)
    59 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    60 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    61 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    62 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    63 
    64 case nxt of ("Rewrite_Set", Rewrite_Set "RatEq_eliminate") => () | _ => ((*not checked before*));
    65 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    66 (*
    67 WN120317.TODO dropped rateq: here "x ~= 0 should at_location to ctxt, but it does not:
    68  --- repair NO asms from rls RatEq_eliminate --- shows why.
    69 so it needs more effort to find out, how Check_elementwise worked in 2002, see below.
    70 *)
    71 
    72 (* val nxt = (_,Subproblem ("RatEq",["univariate","equation"] ======= *)
    73 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    74 (* val (p,_,f,nxt,_,pt) = me nxt p [1] pt;------------- now Refine_Tacitly*)
    75 (*val nxt = ("Model_Problem", Model_Problem ["normalise","polynomial","univariate","equation"])*) 
    76 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    77 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    78 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    79 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    80 (*val nxt = Apply_Method ["PolyEq", "normalise_poly"])*)
    81 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    82 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    83 (* val nxt = (_,Subproblem ("PolyEq",["polynomial","univariate","equation"]=======*)
    84 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    85 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    86 (*  ("Model_Problem", Model_Problem ["degree_1","polynomial","univariate","equation"])*)
    87 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    88 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    89 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    90 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    91 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    92 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    93 val (p''',_,f,nxt''',_,pt''') = me nxt p [1] pt;
    94 f2str f = "[x = 1 / 5]";
    95 case nxt of ("Check_elementwise", Check_elementwise "Assumptions") => () | _ => ((*not checked before*));
    96 "~~~~~ fun me, args:"; val (tac, (p:pos'), _, (pt:ctree)) = (nxt, p, c, pt);
    97 val (pt, p) = case Step.by_tactic tac (pt,p) of
    98 ("ok", (_, _, ptp)) => ptp | _ => error "--- solve (1/x = 5.. Step.by_tactic";
    99 "~~~~~ fun Step.do_next, args:"; val (ip as (_,p_), (ptp as (pt,p), tacis)) = (p, ((pt, e_pos'), []))
   100 val pIopt = get_pblID (pt,ip); (*= SOME ["rational", "univariate", "equation"]
   101                        1-1 associated to metID ["RatEq", "solve_rat_equation"]*)
   102 tacis; (*= []*)
   103 member op = [Pbl,Met] p_ andalso is_none (get_obj g_env pt (fst p)); (*= false*)
   104 "~~~~~ fun do_next, args:"; val (ptp as (pt, pos as (p, p_))) = (pt, ip);
   105 val thy' = get_obj g_domID pt (par_pblobj pt p);
   106 val (is, sc) = resume_prog thy' (p,p_) pt; (*is: which ctxt?*)
   107 "~~~~~ fun find_next_step, args:"; val () = ();
   108 (*----- outcommented during cleanup of args in lucas-interpreter.sml ------------------------\\* )
   109 "~~~~~ fun go_scan_up, args:"; val (thy, ptp, (Prog sc), E, l, ay, a, v) =
   110 (thy, ptp, sc, E, l, true, a, v);
   111 1 < length l; (*true*)
   112 val up = drop_last l;
   113 at_location up sc; (* = Const ("HOL.Let", *)
   114 "~~~~~ fun scan_up, args:"; val (thy, ptp, (scr as (Prog sc)), E, l, ay,
   115  (t as Const ("HOL.Let",_) $ _), a, v) = (thy, ptp, (Prog sc), E, up, ay, (at_location up sc), a, v);
   116 ay = Napp_; (*false*)
   117 val up = drop_last l;
   118 val (Const ("HOL.Let",_) $ e $ (Abs (i,T,body))) = at_location up sc; (*Const ("Prog_Tac.SubProblem",..*)
   119 val i = mk_Free (i, T);
   120 val E = Env.update E (i, v);
   121 "~~~~~ fun scan_dn, args:"; val ((thy as (th,sr)), (pt, p), E, l, t, a, v) =
   122   (thy, ptp, E, (up@[R,D]), body, a, v);
   123 "~~~~~ fun check_leaf, args:"; val (call, thy, srls, (E, (a, v)), t) = ("next ", th, sr, (E, (a, v)), t);
   124 "~~~~~ fun eval_leaf, args:"; val (E, a, v, 
   125 	  (t as (Const ("Prog_Tac.Check'_elementwise",_) $ _ $ _ ))) = (E, a, v, t);
   126 val Program.Tac tm = Program.Tac (subst_atomic E t);
   127 term2str tm = "Check_elementwise [x = 1 / 5] {v_v. Assumptions}";
   128 (*                                     ------ ^^^ ----- ? "x" ?*)
   129 "~~~~~ to check_leaf return val:"; val ((Program.Tac stac, a')) = ((Program.Tac (subst_atomic E t), NONE));
   130 val stac' = eval_prog_expr (assoc_thy thy) srls (subst_atomic (upd_env_opt E (a,v)) stac);
   131 term2str stac' = "Check_elementwise [x = 1 / 5] {v_v. Assumptions}";
   132 "~~~~~ to scan_dn return val:"; val ((a', Program.Tac stac)) = ((a', Program.Tac stac'));
   133 val m = LItool.tac_from_prog pt (assoc_thy th) stac;
   134 case m of Check_elementwise "Assumptions" => () | _ => (); (*m' = Empty_Tac_ ???!??? *);
   135 val (p''''', pt''''', m''''') = (p, pt, m);
   136 "~~~~~ fun applicable_in, args:"; val ((p,p_), pt, (m as Check_elementwise pred)) = (p, pt, m);
   137 member op = [Pbl,Met] p_; (* = false*)
   138         val pp = par_pblobj pt p; 
   139         val thy' = (get_obj g_domID pt pp):theory';
   140         val thy = assoc_thy thy'
   141         val metID = (get_obj g_metID pt pp)
   142         val {crls,...} =  get_met metID
   143         val (f,asm) = case p_ of Frm => (get_obj g_form pt p , [])
   144                                | Res => get_obj g_result pt p;
   145 term2str f = "[x = 1 / 5]"; (*the current formula*)
   146         val vp = (thy2ctxt thy, pred) |-> parseNEW |> the |> mk_set thy pt p f;
   147 val (bdv, asms) = vp;
   148 
   149 term2str bdv = "x";
   150 terms2str asms = (* asms from rewriting are missing : vvv *)
   151   ("[\"<not> matches (?a = 0) (1 = 5 * x) | ~ lhs (1 = 5 * x) is_poly_in x\",\"x = 1 / 5\"," ^
   152    "\"lhs (1 + -5 * x = 0) is_poly_in x\",\"lhs (1 + -5 * x = 0) has_degree_in x = 1\"," ^
   153    "\"1 / x = 5 is_ratequation_in x\"]");
   154 (*
   155 WN120317.TODO dropped rateq: ctxt should contain "x ~= 0 here, but it does not, see above.
   156 *)
   157 
   158 val Appl (Check_elementwise' (curr_form, pred, (res, asms))) = applicable_in p''''' pt''''' m''''';
   159 term2str curr_form = "[x = 1 / 5]";
   160 pred = "Assumptions";
   161 res = str2term "[]::bool list";
   162 asms = [];
   163 
   164 val (p,_,f,nxt,_,pt) = me nxt''' p''' [] pt'''; (*<<<----- this caused the error*)
   165 f2str f = "[]";
   166 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   167 
   168 if p = ([], Res) andalso f2str f = "[x = 1 / 5]"
   169 then case nxt of ("End_Proof'", End_Proof') => ()
   170   | _ => error "rateq.sml: new behaviour: [x = 1 / 5] 1"
   171 else error "rateq.sml: new behaviour: [x = 1 / 5] 2";
   172 ( *----- outcommented during cleanup of args in lucas-interpreter.sml ------------------------//*)
   173 
   174 "------------ S.68, Bsp.: 40, ((x)/(x - 8) + (x - 8)/(x) = 26/5)--";
   175 "------------ S.68, Bsp.: 40, ((x)/(x - 8) + (x - 8)/(x) = 26/5)--";
   176 "------------ S.68, Bsp.: 40, ((x)/(x - 8) + (x - 8)/(x) = 26/5)--";
   177 (*EP Schalk_II_p68_n40*)
   178 val fmz = ["equality ((x)/(x - 8) + (x - 8)/(x) = 26/(5::real))","solveFor x","solutions L"];
   179 val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);
   180 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   181 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   182 (* nxt = ("Model_Problem",Model_Problem ["rational","univariate","equation"])*)
   183 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   184 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   185 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   186 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   187 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   188 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   189 (* nxt = ("Subproblem",Subproblem ("RatEq",["univariate","equation"]))*)
   190 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   191 (* nxt = ("Model_Problem", Model_Problem ["normalise","polynomial","univariate","equation"])*)
   192 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   193 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   194 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   195 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   196 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   197 
   198 if p = ([4, 3], Pbl) then ()
   199 else
   200   (case nxt of
   201     ("Add_Given", Add_Given "solveFor x") =>
   202       (case f of
   203         PpcKF (Problem [], {Given = [Incompl "solveFor", Correct "equality (320 + 128 * x + -16 * x ^^^ 2 = 0)"], ...}) => ()
   204       | _ => error ("S.68, Bsp.: 40 PblObj changed"))
   205   | _ => error ("S.68, Bsp.: 40 changed nxt =" ^ tac2str (snd nxt)));
   206 
   207 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   208 (* ("Subproblem", Subproblem ("PolyEq",["polynomial","univariate","equation"])) *)
   209 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   210 (* nxt = ("Model_Problem", Model_Problem
   211      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
   212 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   213 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   214 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   215 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   216 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   217 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   218 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   219 if p = ([], Res) andalso f2str f = "[]" then () 
   220 else error "rateq.sml: new behaviour: [x = -2, x = 10]";
   221 
   222 "------------ x / (x ^ 2 - 6 * x + 9) - 1 / (x ^ 2 - 3 * x) = 1 /x";
   223 "------------ x / (x ^ 2 - 6 * x + 9) - 1 / (x ^ 2 - 3 * x) = 1 /x";
   224 "------------ x / (x ^ 2 - 6 * x + 9) - 1 / (x ^ 2 - 3 * x) = 1 /x";
   225 (*ER-7*) (*Schalk I s.87 Bsp 55b*)
   226 val fmz = ["equality (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)",
   227 	   "solveFor x","solutions L"];
   228 val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);
   229 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   230 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   231 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   232 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   233 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   234 case nxt of ("Apply_Method", Apply_Method ["RatEq", "solve_rat_equation"]) => ()
   235 | _ => error "55b root specification broken";
   236 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   237 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   238 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   239 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   240 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   241 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   242 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   243 case nxt of ("Apply_Method", Apply_Method ["PolyEq", "normalise_poly"]) => ()
   244 | _ => error "55b normalise_poly specification broken 1";
   245 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   246 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   247 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   248 if p = ([4, 3], Res) andalso f2str f = "-6 * x + 5 * x ^^^ 2 = 0"
   249 then
   250   ((case nxt of
   251     ("Subproblem", Subproblem ("PolyEq", ["bdv_only", "degree_2", "polynomial", "univariate", "equation"])) => ()
   252   | _ => error ("S.68, Bsp.: 40 nxt =" ^ tac2str (snd nxt))))
   253 else error "xxx";
   254 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   255 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   256 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   257 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   258 case nxt of ("Apply_Method", Apply_Method ["PolyEq", "solve_d2_polyeq_bdvonly_equation"]) => ()
   259 | _ => error "55b normalise_poly specification broken 2";
   260 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   261 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   262 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   263 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   264 
   265 f2str f = "[x = 0, x = 6 / 5]";                                                        (*= GUI*)
   266 case snd nxt of Check_elementwise "Assumptions" => () | _ => ((*not checked before*)); (*= GUI*)
   267 if terms2str (get_assumptions_ pt p) = "[\"x = 6 / 5\"," ^
   268   "\"x = 0\"," ^
   269   "\"lhs (-6 * x + 5 * x ^^^ 2 = 0) is_poly_in x\"," ^
   270   "\"lhs (-6 * x + 5 * x ^^^ 2 = 0) has_degree_in x = 2\"]"
   271 then () else error "rateq.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";
   272 
   273 (*
   274 WN120317.TODO dropped rateq: ctxt should contain "x ~= 0 here, but it does not.
   275 
   276 The step-into-source contains an error; this error can be detected by
   277 test --- 'trace_script' from outside 'fun me '---
   278 *)
   279 val (pt''', p''') = (pt, p);
   280 "~~~~~ fun me, args:"; val (tac, (p:pos'), _, (pt:ctree)) = (nxt, p, c, pt);
   281     val (pt, p) = case Step.by_tactic tac (pt,p) of
   282 		      ("ok", (_, _, ptp)) => ptp  | _ => error "error in test setup";
   283 "~~~~~ Step.do_next, args:"; val (((ip as (_,p_)):pos'), ((ptp as (pt,p), tacis):calcstate)) =
   284   (p, ((pt, e_pos'),[]));
   285 val pIopt = get_pblID (pt,ip);
   286 ip = ([],Res); (* = false*)
   287 tacis; (* = []*)
   288 member op = [Pbl,Met] p_ andalso is_none (get_obj g_env pt (fst p)); (* = false*)
   289 "~~~~~ and do_next, args:"; val ((ptp as (pt, pos as (p,p_)))) = ((pt,ip));
   290 e_metID = get_obj g_metID pt (par_pblobj pt p); (* = false*)
   291           val thy' = get_obj g_domID pt (par_pblobj pt p);
   292 	        val (is, sc) = resume_prog thy' (p,p_) pt;
   293 "~~~~~ fun find_next_step, args:"; val (thy, (ptp as (pt, pos as (p, _)):ctree * pos'),
   294   (sc as Prog (h $ body)), (Pstate (E,l,a,v,s,b), ctxt)) = ((thy',srls), (pt,pos), sc, is);
   295 (*----- outcommented during cleanup of args in lucas-interpreter.sml ------------------------\\* )
   296 l = []; (* = false*)
   297 "~~~~~ and go_scan_up, args:"; val (thy, ptp, (Prog sc), E, l, ay, a, v) =
   298   (thy, ptp, sc, E, l, true, a, v);
   299 1 < length l; (* = true*)
   300 val up = drop_last l; 
   301 (*val (t as Abs (_,_,_)) = *)(at_location up sc); 
   302 "~~~~~ fun scan_up, args:"; val (thy, ptp, scr, E, l, ay, (t as Abs (_,_,_)), a, v) =
   303   (thy, ptp, (Prog sc), E, up, ay, (at_location up sc), a, v);
   304 term2str t = "%L_La. Check_elementwise L_L {v_v. Assumptions}";
   305 "~~~~~ and go_scan_up, args:"; val (thy, ptp, (Prog sc), E, l, ay, a, v) =
   306   (thy, ptp, scr, E, l, ay, a, v);
   307 1 < length l; (* = true*)
   308 val up = drop_last l; 
   309 (*val (t as Const ("HOL.Let",_) $ e $ (Abs (i,T,b))) = *)(at_location up sc);
   310 "~~~~~ fun scan_up, args:"; val (thy, ptp, scr, E, l, ay,
   311     (t as Const ("HOL.Let",_) $ e $ (Abs (i,T,b))), a, v) = (thy, ptp, (Prog sc), E, up, ay, (at_location up sc), a, v);
   312 
   313 term2str t = "let L_La =\n      SubProblem (RatEqX, [univariate, equation], [no_met])\n       [BOOL e_e, REAL v_v]\nin Check_elementwise L_L {v_v. Assumptions}";
   314 
   315 (* comment from BEFORE Isabelle2002 --> 2011:
   316 scan_up thy ptp (Prog sc) E up ay (at_location up sc) a v;
   317 go_scan_up thy ptp scr E l ay a v;
   318 scan_up thy ptp (Prog sc) E up ay (at_location up sc) a v;
   319 go_scan_up thy ptp sc E l true a v;
   320 find_next_step sc (pt,pos) is (*is as (ist, ctxt) ---> ist ctxt*);
   321 Step_Solve.do_next (pt,ip);
   322 Step.do_next p ((pt, e_pos'),[]);
   323 *)
   324 val (p,_,f,nxt,_,pt) = me nxt p''' [1] pt''';
   325 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   326 
   327   if p = ([], Res) andalso f2str f = "[]"
   328   then case nxt of ("End_Proof'", End_Proof') => ()
   329     | _ => error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 55b [x = 6 / 5] 1"
   330   else error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 55b [x = 6 / 5] 2";
   331 ( *----- outcommented during cleanup of args in lucas-interpreter.sml ------------------------//*)
   332 
   333 
   334 "----------- ((5*x)/(x - 2) - x/(x+2)=(4::real)), incl. refine ---------------------------------";
   335 "----------- ((5*x)/(x - 2) - x/(x+2)=(4::real)), incl. refine ---------------------------------";
   336 "----------- ((5*x)/(x - 2) - x/(x+2)=(4::real)), incl. refine ---------------------------------";
   337 (*was in test/../usecases.sml*)
   338 val fmz = ["equality ((5*x)/(x - 2) - x/(x+2)=(4::real))", "solveFor x","solutions L"];
   339 val (dI',pI',mI') = ("RatEq", ["univariate","equation"], ["no_met"]);
   340 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   341 (*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   342 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   343 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   344 (*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Apply_Method ["RatEq", "solve_rat_equation"]*)
   345 (*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Rewrite_Set "RatEq_simplify":*)
   346 
   347 (*+*)if (get_istate_LI pt p |> istate2str) (* still specify-phase: found_accept = false ---------------------------------> vvvvv*)
   348 (*+*) = "Pstate ([\"\n(e_e, 5 * x / (x - 2) - x / (x + 2) = 4)\",\"\n(v_v, x)\"], [], e_rls, NONE, \n??.empty, ORundef, false, true)"
   349 (*+*)then () else error "rat-eq + subpbl: istate in specify-phase";
   350 
   351 (*[1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Rewrite_Set "norm_Rational"*)
   352 
   353 (*+*)if (get_istate_LI pt p |> istate2str) (* solve-phase: found_accept = true -----------------------------------------------------------------------------------------------> vvvvv*)
   354 (*+*) = "Pstate ([\"\n(e_e, 5 * x / (x - 2) - x / (x + 2) = 4)\",\"\n(v_v, x)\"], [R,L,R,L,L,R,R,R], e_rls, SOME e_e, \n5 * x / (x + -1 * 2) + -1 * x / (x + 2) = 4, ORundef, true, true)"
   355 (*+*)then () else error "rat-eq + subpbl: istate after found_accept";
   356 
   357 (*[2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Rewrite_Set "RatEq_eliminate"*)
   358 (*^^^ 2*05*)
   359 \<close> ML \<open>
   360 (*[3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Subproblem ("PolyEq", ["normalise", "polynomial", "univariate", "equation"])*)
   361 (*[4], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Model_Problem*)
   362 
   363 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   364 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   365 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   366 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   367 (*^^^ 2*10*)
   368 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   369 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   370 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   371 (**)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;(**)
   372 
   373 (*[4,3], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Specify_Method ["PolyEq", "solve_d1_polyeq_equation"]*)
   374 (*[4,3], Met*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Apply_Method ["PolyEq", "solve_d1_polyeq_equation"]*)
   375 (*^^^ 2*15*)
   376 (*[4,3,1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Rewrite_Set_Inst (["(''bdv'', x)"], "d1_polyeq_simplify")*)
   377 (*[4,3,1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Rewrite_Set "polyeq_simplify"*)
   378 (*[4,3,2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*Or_to_List*)
   379 (*[4,3,3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Check_elementwise "Assumptions"*)
   380 (*                       f = FormKF "[x = -4 / 3]" *)
   381 (*[4, 3, 4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Check_Postcond ["degree_1", "polynomial", "univariate", "equation"]*)
   382 (*[4, 3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Check_Postcond ["normalise", "polynomial", "univariate", "equation"]*)
   383 (*[4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Check_elementwise "Assumptions"*)
   384 (*[5], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*Check_Postcond ["rational", "univariate", "equation"]*)
   385 (*[], Res*)val (p,_,f,nxt,_,pt) = me nxt p [] pt;(*End_Proof'*)
   386 
   387 if p = ([], Res) andalso f2str f = "[x = -4 / 3]"
   388 then case nxt of End_Proof' => () | _ => error "rat-eq + subpbl: end CHANGED 1"
   389 else error "rat-eq + subpbl: end CHANGED 2";
   390