(* title:  Knowledge/polyminus.sml

   author: Walther Neuper

   WN071207,

   (c) due to copyright terms

*)

"--------------------------------------------------------";

"--------------------------------------------------------";

"table of contents --------------------------------------";

"--------------------------------------------------------";

"----------- fun identifier --------------------------------------------------------------------";

"----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

"----------- fun ist_monom ---------------------------------------------------------------------";

"----------- fun eval_ist_monom -------------------------";

"----------- watch order_add_mult  ----------------------";

"----------- build predicate for +- ordering ------------";

"----------- build fasse_zusammen -----------------------";

"----------- build verschoenere -------------------------";

"----------- met simplification for_polynomials with_minu";

"----------- me simplification.for_polynomials.with_minus";

"----------- pbl polynom vereinfachen p.33 --------------";

"----------- met probe fuer_polynom ---------------------";

"----------- pbl polynom probe --------------------------";

"----------- pbl klammer polynom vereinfachen p.34 ------";

"----------- try fun applyTactics -----------------------";

"----------- pbl binom polynom vereinfachen p.39 --------";

"----------- pbl binom polynom vereinfachen: cube -------";

"----------- Refine.refine Vereinfache -------------------------";

"----------- *** Problem.prep_input: syntax error in '#Where' of [v";

"--------------------------------------------------------";

"--------------------------------------------------------";

"--------------------------------------------------------";

val thy = @{theory "PolyMinus"};

val ctxt = Proof_Context.init_global thy;

"----------- fun identifier --------------------------------------------------------------------";

"----------- fun identifier --------------------------------------------------------------------";

"----------- fun identifier --------------------------------------------------------------------";

if identifier (TermC.str2term "12 ::real") = "12"     then () else error "identifier 1";

if identifier (TermC.str2term

  "5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g ::real") = "|||||||||||||"

                                                      then () else error "identifier 1a";

if identifier (TermC.str2term "a ::real") = "a"       then () else error "identifier 2";

if identifier (TermC.str2term "3 * a ::real") = "a"   then () else error "identifier 3";

if identifier (TermC.str2term "a \<up> 2 ::real") = "a"   then () else error "identifier 4";

if identifier (TermC.str2term "3*a \<up> 2 ::real") = "a" then () else error "identifier 5";

if identifier (TermC.str2term "a * b ::real") = "b"   then () else error "identifier 5b";

(*these are strange (see "specific monomials" in comment to fun.def.)..*)

if identifier (TermC.str2term "a*b ::real") = "b"     then () else error "identifier 6";

if identifier (TermC.str2term "(3*a*b) ::real") = "b" then () else error "identifier 7";

"----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

"----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

"----------- fun eval_kleiner, fun kleiner -----------------------------------------------------";

"a" < "b";

"ba" < "ab";

"123" < "a"; (*unused due to ---vvv*)

"12" < "3"; (*true !!!*)

" a kleiner b ==> (b + a) = (a + b)";

TermC.str2term "aaa";

TermC.str2term "222 * aaa";

case eval_kleiner 0 0 (TermC.str2term "123 kleiner 32") 0 of

    SOME ("123 kleiner 32 = False", _) => ()

  | _ => error "polyminus.sml: 12 kleiner 9 = False";

case eval_kleiner 0 0 (TermC.str2term "a kleiner b") 0 of

    SOME ("a kleiner b = True", _) => ()

  | _ => error "polyminus.sml: a kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(10*g) kleiner f") 0 of

    SOME ("10 * g kleiner f = False", _) => ()

  | _ => error "polyminus.sml: 10 * g kleiner f = False";

case eval_kleiner 0 0 (TermC.str2term "(a \<up> 2) kleiner b") 0 of

    SOME ("a \<up> 2 kleiner b = True", _) => ()

  | _ => error "polyminus.sml: a \<up> 2 kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(3*a \<up> 2) kleiner b") 0 of

    SOME ("3 * a \<up> 2 kleiner b = True", _) => ()

  | _ => error "polyminus.sml: 3 * a \<up> 2 kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(a*b) kleiner c") 0 of

    SOME ("a * b kleiner c = True", _) => ()

  | _ => error "polyminus.sml: a * b kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(3*a*b) kleiner c") 0 of

    SOME ("3 * a * b kleiner c = True", _) => ()

  | _ => error "polyminus.sml: 3 * a * b kleiner b = True";

val t = TermC.str2term "12 kleiner 5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * (g::real)";

val SOME ("12 kleiner 5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g = True", _) =

           eval_kleiner "aaa" "bbb" t "ccc";

"~~~~~ fun eval_kleiner , args:"; val (_, _, (p as (Const (\<^const_name>\<open>kleiner\<close>,_) $ a $ b)), _) =

  ("aaa", "bbb", t, "ccc");

    (*if*) TermC.is_num b (*else*);

   	(*if*) identifier a < identifier b  (*else*);

"~~~~~ fun identifier , args:"; val (t) = (a);

(*+*)case a of

  Const (\<^const_name>\<open>numeral\<close>, _) $ (Const (\<^const_name>\<open>num.Bit0\<close>, _) $

    (Const (\<^const_name>\<open>num.Bit0\<close>, _) $ (Const (\<^const_name>\<open>num.Bit1\<close>, _) $ Const (\<^const_name>\<open>num.One\<close>, _)))) => ()

| _ => error "eval_kleiner CHANGED";                                                 (*isa*)

"----------- fun ist_monom ---------------------------------------------------------------------";

"----------- fun ist_monom ---------------------------------------------------------------------";

"----------- fun ist_monom ---------------------------------------------------------------------";

val t = TermC.str2term "0 ::real";

 if ist_monom t then () else error "ist_monom 1";

val t = TermC.str2term "a";

if ist_monom t then () else error "ist_monom 2";

val t = TermC.str2term "2 * a";

if ist_monom t then () else error "ist_monom 3";

val t = TermC.str2term "2 * a * b";

if ist_monom t then () else error "ist_monom 4";

val t = TermC.str2term "a * b";

if ist_monom t then () else error "ist_monom 5";

(*not covered before NEW numerals*)

val t = TermC.str2term "2 * a \<up> 2 * b";

if ist_monom t then () else error "ist_monom 6";

(*not covered before NEW numerals*)

val t = TermC.str2term "a \<up> 2 * b \<up> 3";

if ist_monom t then () else error "ist_monom 7";

val t = TermC.str2term "a \<up> 2 * 4 * b \<up> 3 * 5";

if ist_monom t then () else error "ist_monom 8";

"----------- fun eval_ist_monom ----------------------------------";

"----------- fun eval_ist_monom ----------------------------------";

"----------- fun eval_ist_monom ----------------------------------";

case eval_ist_monom 0 0 (TermC.str2term "12 ist_monom") 0 of

    SOME ("12 ist_monom = True", _) => ()

  | _ => error "polyminus.sml: 12 ist_monom = True";

case eval_ist_monom 0 0 (TermC.str2term "a ist_monom") 0 of

    SOME ("a ist_monom = True", _) => ()

  | _ => error "polyminus.sml: a ist_monom = True";

case eval_ist_monom 0 0 (TermC.str2term "(3*a) ist_monom") 0 of

    SOME ("3 * a ist_monom = True", _) => ()

  | _ => error "polyminus.sml: 3 * a ist_monom = True";

case eval_ist_monom 0 0 (TermC.str2term "(a \<up> 2) ist_monom") 0 of 

   SOME ("a \<up> 2 ist_monom = True", _) => ()

  | _ => error "polyminus.sml: a \<up> 2 ist_monom = True";

case eval_ist_monom 0 0 (TermC.str2term "(3*a \<up> 2) ist_monom") 0 of

    SOME ("3 * a \<up> 2 ist_monom = True", _) => ()

  | _ => error "polyminus.sml: 3*a \<up> 2 ist_monom = True";

case eval_ist_monom 0 0 (TermC.str2term "(a*b) ist_monom") 0 of

    SOME ("a * b ist_monom = True", _) => ()

  | _ => error "polyminus.sml: a*b ist_monom = True";

case eval_ist_monom 0 0 (TermC.str2term "(3*a*b) ist_monom") 0 of

    SOME ("3 * a * b ist_monom = True", _) => ()

  | _ => error "polyminus.sml: 3*a*b ist_monom = True";

"----------- watch order_add_mult  -------------------------------";

"----------- watch order_add_mult  -------------------------------";

"----------- watch order_add_mult  -------------------------------";

"----- with these simple variables it works...";

val ctxt = @{context};

val t = TermC.str2term "((a + d) + c) + b";

val SOME (t,_) = rewrite_set_ ctxt false order_add_mult t; UnparseC.term t;

if UnparseC.term t = "a + (b + (c + d))" then ()

else error "polyminus.sml 1 watch order_add_mult";

"----- the same stepwise...";

val od = ord_make_polynomial true (@{theory "Poly"});

val t = TermC.str2term "((a + d) + c) + b";

"((a + d) + c) + b"; 

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.commute} t; UnparseC.term t;

"b + ((a + d) + c)";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.commute} t; UnparseC.term t;

"b + (c + (a + d))";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

"b + (a + (c + d))";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

"a + (b + (c + d))";

if UnparseC.term t = "a + (b + (c + d))" then ()

else error "polyminus.sml 2 watch order_add_mult";

"----- if parentheses are right, left_commute is (almost) sufficient...";

val t = TermC.str2term "a + (d + (c + b))";

"a + (d + (c + b))";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

"a + (c + (d + b))";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.commute} t;UnparseC.term t;

"a + (c + (b + d))";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty true @{thm add.left_commute} t;UnparseC.term t;

"a + (b + (c + d))";

"----- but we do not want the parentheses at right; thus: cond.rew.";

"WN0712707 complicated monomials do not yet work ...";

val t = TermC.str2term "((5*a + 4*d) + 3*c) + 2*b";

val SOME (t,_) = rewrite_set_ ctxt false order_add_mult t; UnparseC.term t;

if UnparseC.term t = "2 * b + (3 * c + (4 * d + 5 * a))" then ()

else error "polyminus.sml: order_add_mult changed";

"----- here we see rew_sub going into subterm with ord.rew....";

val od = ord_make_polynomial false (@{theory "Poly"});

val t = TermC.str2term "b + a + c + d";

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty false @{thm add.commute} t; UnparseC.term t;

val SOME (t,_) = rewrite_ ctxt od Rule_Set.empty false @{thm add.commute} t; UnparseC.term t;

(*@@@ rew_sub gosub: t = d + (b + a + c)

  @@@ rew_sub begin: t = b + a + c*)

"----------- build predicate for +- ordering ---------------------";

"----------- build predicate for +- ordering ---------------------";

"----------- build predicate for +- ordering ---------------------";

"a" < "b";

"ba" < "ab";

"123" < "a"; (*unused due to ---vvv*)

"12" < "3"; (*true !!!*)

" a kleiner b ==> (b + a) = (a + b)";

TermC.str2term "aaa";

TermC.str2term "222 * aaa";

case eval_kleiner 0 0 (TermC.str2term "123 kleiner 32") 0 of

    SOME ("123 kleiner 32 = False", _) => ()

  | _ => error "polyminus.sml: 12 kleiner 9 = False";

case eval_kleiner 0 0 (TermC.str2term "a kleiner b") 0 of

    SOME ("a kleiner b = True", _) => ()

  | _ => error "polyminus.sml: a kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(10*g) kleiner f") 0 of

    SOME ("10 * g kleiner f = False", _) => ()

  | _ => error "polyminus.sml: 10 * g kleiner f = False";

case eval_kleiner 0 0 (TermC.str2term "(a \<up> 2) kleiner b") 0 of

    SOME ("a \<up> 2 kleiner b = True", _) => ()

  | _ => error "polyminus.sml: a \<up> 2 kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(3*a \<up> 2) kleiner b") 0 of

    SOME ("3 * a \<up> 2 kleiner b = True", _) => ()

  | _ => error "polyminus.sml: 3 * a \<up> 2 kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(a*b) kleiner c") 0 of

    SOME ("a * b kleiner c = True", _) => ()

  | _ => error "polyminus.sml: a * b kleiner b = True";

case eval_kleiner 0 0 (TermC.str2term "(3*a*b) kleiner c") 0 of

    SOME ("3 * a * b kleiner c = True", _) => ()

  | _ => error "polyminus.sml: 3 * a * b kleiner b = True";

"======= compare tausche_plus with real_num_collect";

val od = Rewrite_Ord.function_empty;

val erls = erls_ordne_alphabetisch;

val t = TermC.str2term "b + a";

val SOME (t,_) = rewrite_ ctxt od erls false @{thm tausche_plus} t; UnparseC.term t;

if UnparseC.term t = "a + b" then ()

else error "polyminus.sml: ordne_alphabetisch1 b + a";

val erls = Atools_erls;

val t = TermC.str2term "2*a + 3*a";

val SOME (t,_) = rewrite_ ctxt od erls false @{thm real_num_collect} t; UnparseC.term t;

"======= test rewrite_, rewrite_set_";

(*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

val erls = erls_ordne_alphabetisch;

val t = TermC.str2term "b + a";

val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

if UnparseC.term t = "a + b" then ()

else error "polyminus.sml: ordne_alphabetisch a + b";

val t = TermC.str2term "2*b + a";

val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

if UnparseC.term t = "a + 2 * b" then ()

else error "polyminus.sml: ordne_alphabetisch a + 2 * b";

val t = TermC.str2term "a + c + b";

val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

if UnparseC.term t = "a + b + c" then ()

else error "polyminus.sml: ordne_alphabetisch a + b + c";

"======= rewrite goes into subterms";

val t = TermC.str2term "a + c + b + d ::real";

val SOME (t,_) = rewrite_ ctxt od erls false @{thm tausche_plus_plus} t; UnparseC.term t;

if UnparseC.term t = "a + b + c + d" then ()

else error "polyminus.sml: ordne_alphabetisch1 a + b + c + d";

val t = TermC.str2term "a + c + d + b";

val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; UnparseC.term t;

if UnparseC.term t = "a + b + c + d" then ()

else error "polyminus.sml: ordne_alphabetisch2 a + b + c + d";

"======= here we see rew_sub going into subterm with cond.rew....";

val t = TermC.str2term "b + a + c + d";

val SOME (t,_) = rewrite_ ctxt od erls false @{thm tausche_plus} t; UnparseC.term t;

if UnparseC.term t = "a + b + c + d" then ()

else error "polyminus.sml: ordne_alphabetisch3 a + b + c + d";

"======= compile rls for the most complicated terms";

val t = TermC.str2term "5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12";

"5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

val SOME (t,_) = rewrite_set_ ctxt false ordne_alphabetisch t; 

if UnparseC.term t = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g"

then () else error "polyminus.sml: ordne_alphabetisch finished";

"----------- build fasse_zusammen --------------------------------";

"----------- build fasse_zusammen --------------------------------";

"----------- build fasse_zusammen --------------------------------";

val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";

val SOME (t,_) = rewrite_set_ ctxt false fasse_zusammen t;

if UnparseC.term t = "3 + - 2 * e + 2 * f + 2 * g" then ()

else error "polyminus.sml: fasse_zusammen finished";

"----------- build verschoenere ----------------------------------";

"----------- build verschoenere ----------------------------------";

"----------- build verschoenere ----------------------------------";

val t = TermC.str2term "3 + - 2 * e + 2 * f + 2 * g";

val SOME (t,_) = rewrite_set_ ctxt false verschoenere t;

if UnparseC.term t = "3 - 2 * e + 2 * f + 2 * g" then ()

else error "polyminus.sml: verschoenere 3 + - 2 * e ...";

"----------- met simplification for_polynomials with_minus -------";

"----------- met simplification for_polynomials with_minus -------";

"----------- met simplification for_polynomials with_minus -------";

val str = 

"Program SimplifyScript (t_t::real) =                \

\  (((Try (Rewrite_Set ordne_alphabetisch False)) #>     \

\    (Try (Rewrite_Set fasse_zusammen False)) #>     \

\    (Try (Rewrite_Set verschoenere False))) t_t)"

val sc = (inst_abs o (TermC.parseNEW' ctxt)) str;

TermC.atomty sc;

"----------- me simplification.for_polynomials.with_minus";

"----------- me simplification.for_polynomials.with_minus";

"----------- me simplification.for_polynomials.with_minus";

val c = [];

val (p,_,f,nxt,_,pt) = 

      CalcTreeTEST 

        [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

           "normalform N"],

	          ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	           ["simplification", "for_polynomials", "with_minus"]))];

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;

if f2str f = "3 - 2 * e + 2 * f + 2 * g" 

then case nxt of End_Proof' => () | _ =>  error "me simplification.for_polynomials.with_minus 1"

else error "polyminus.sml: me simplification.for_polynomials.with_minus 2";

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- 140 c ---";

reset_states ();

CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso 

   UnparseC.term (get_obj g_res pt (fst p)) = "3 - 2 * e + 2 * f + 2 * g"

then () else error "polyminus.sml: Vereinfache (3 - 2 * e + 2 * f...";

"======= 140 d ---";

reset_states ();

CalcTree [(["Term (-r - 2*s - 3*t + 5 + 4*r + 8*s - 5*t - 2)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso 

   UnparseC.term (get_obj g_res pt (fst p)) = "3 + 3 * r + 6 * s - 8 * t"

then () else error "polyminus.sml: Vereinfache 140 d)";

"======= 139 c ---";

reset_states ();

CalcTree [(["Term (3*e - 6*f - 8*e - 4*f + 5*e + 7*f)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso 

   UnparseC.term (get_obj g_res pt (fst p)) = "- (3 * f)"

then () else error "polyminus.sml: Vereinfache 139 c)";

"======= 139 b ---";

reset_states ();

CalcTree [(["Term (8*u - 5*v - 5*u + 7*v - 6*u - 3*v)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso 

   UnparseC.term (get_obj g_res pt (fst p)) = "- 3 * u - v"

then () else error "polyminus.sml: Vereinfache 139 b)";

"======= 138 a ---";

reset_states ();

CalcTree [(["Term (2*u - 3*v - 6*u + 5*v)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso 

   UnparseC.term (get_obj g_res pt (fst p)) = "- 4 * u + 2 * v"

then () else error "polyminus.sml: Vereinfache 138 a)";

"----------- met probe fuer_polynom ------------------------------";

"----------- met probe fuer_polynom ------------------------------";

"----------- met probe fuer_polynom ------------------------------";

val str = 

"Program ProbeScript (e_e::bool) (w_s::bool list) =\

\ (let e_e = Take e_e;                             \

\      e_e = Substitute w_s e_e                    \

\ in (Repeat((Try (Repeat (Calculate ''TIMES''))) #>  \

\            (Try (Repeat (Calculate ''PLUS''))) #>  \

\            (Try (Repeat (Calculate ''MINUS''))))) e_e)"

val sc = (inst_abs o (TermC.parseNEW' ctxt)) str;

TermC.atomty sc;

"----------- pbl polynom probe -----------------------------------";

"----------- pbl polynom probe -----------------------------------";

"----------- pbl polynom probe -----------------------------------";

reset_states ();

CalcTree [(["Pruefe ((5::int)*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12 =\

	    \3 - 2 * e + 2 * f + 2 * (g::int))",

	    "mitWert [e = (1::int), f = (2::int), g = (3::int)]",

	    "Geprueft b"],

	   ("PolyMinus",["polynom", "probe"],

	    ["probe", "fuer_polynom"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

(* autoCalculate 1 CompleteCalcHead;

   autoCalculate 1 (Steps 1);

   autoCalculate 1 (Steps 1);

   val ((pt,p),_) = get_calc 1; UnparseC.term (get_obj g_res pt (fst p));

@@@@@WN081114 gives "??.empty", all "Pruefe" are the same,

although analogies work in interface.sml: FIXME.WN081114 in "Pruefe"*)

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

if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "11 = 11"

then () else error "polyminus.sml: Probe 11 = 11";

Test_Tool.show_pt pt;

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

reset_states ();

CalcTree [(["Term (2*u - 5 - (3 - 4*u) + (8*u + 9))",

	    "normalform N"],

	   ("PolyMinus",["klammer", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_parentheses"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

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

if p = ([], Res) andalso 

   UnparseC.term (get_obj g_res pt (fst p)) = "1 + 14 * u"

then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";

Test_Tool.show_pt pt;

"======= probe p.34 -----";

reset_states ();

CalcTree [(["Pruefe (2*u - 5 - (3 - 4*u) + (8*u + 9) = 1 + 14 * (u::int))",

	    "mitWert [u = (2::int)]",

	    "Geprueft b"],

	   ("PolyMinus",["polynom", "probe"],

	    ["probe", "fuer_polynom"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

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

if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "29 = 29"

then () else error "polyminus.sml: Probe 29 = 29";

Test_Tool.show_pt pt;

"----------- try fun applyTactics --------------------------------";

"----------- try fun applyTactics --------------------------------";

"----------- try fun applyTactics --------------------------------";

reset_states ();

CalcTree [(["Term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalcHead;

autoCalculate 1 (Steps 1);

autoCalculate 1 (Steps 1);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 1  \<up> ";

fetchApplicableTactics 1 0 p;

val appltacs = specific_from_prog pt p;

applyTactic 1 p (hd appltacs) (*addiere_x_plus_minus*);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 2  \<up> ";

(*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

val erls = erls_ordne_alphabetisch;

val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

val SOME (t',_) = 

    rewrite_ ctxt Rewrite_Ord.function_empty erls false @{thm tausche_minus} t;

UnparseC.term t';     "- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f - 8 * g + 10 * g";

val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

val NONE = 

    rewrite_ ctxt Rewrite_Ord.function_empty erls false @{thm tausche_minus_plus} t;

val t = TermC.str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

val SOME (t',_) = 

    rewrite_set_ ctxt false ordne_alphabetisch t;

UnparseC.term t';     "- 9 + 12 + 5 * e - 7 * e - 8 * g + 10 * g + (- 4 + 6) * f";

applyTactic 1 p (hd (specific_from_prog pt p)) (*tausche_minus*);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 3  \<up> ";

applyTactic 1 p (hd (specific_from_prog pt p)) (**);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 4  \<up> ";

applyTactic 1 p (hd (specific_from_prog pt p)) (**);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 5  \<up> ";

applyTactic 1 p (hd (specific_from_prog pt p)) (**);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 6  \<up> ";

(*<CALCMESSAGE> failure </CALCMESSAGE>

applyTactic 1 p (hd (specific_from_prog pt p)) (**);

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

"----- 7  \<up> ";

*)

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

(*independent from failure above: met_simp_poly_minus not confluent:

(([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

(([], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f))]

~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

val ([], Res) = p;

val "2 * g + (3 - 2 * e + 2 * f)" = get_obj g_res pt (fst p) |> UnparseC.term;

(* ---------^^^--- not quite perfect*)

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

reset_states ();

CalcTree [(["Term (- (8 * g) + 10 * g + h)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "2 * g + h"

then () else error "polyminus.sml: addiere_vor_minus";

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

reset_states ();

CalcTree [(["Term (- (8 * g) + 10 * g + f)",

	    "normalform N"],

	   ("PolyMinus",["plus_minus", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "f + 2 * g"

then () else error "polyminus.sml: tausche_vor_plus";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

val thy = @{theory};

val rls = klammern_ausmultiplizieren;

val t = TermC.str2term "(3 * a + 2) * (4 * a - 1::real)";

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

"3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

val rls = discard_parentheses;

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

"3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

val rls = ordne_monome;

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

"3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

(*

val t = TermC.str2term "3 * a * 4 * a";

val rls = ordne_monome;

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

*)

val rls = klammern_aufloesen;

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

"3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

val rls = ordne_alphabetisch;

(*TODO: make is_monom more general, a*a=a^2, ...*)

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

"3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

(*STOPPED.WN080104

val rls = fasse_zusammen;

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

val rls = verschoenere;

val SOME (t,_) = rewrite_set_ ctxt false rls t; UnparseC.term t;

*)

(*@@@@@@@*)

reset_states ();

CalcTree [(["Term ((3*a + 2) * (4*a - 1))",

	    "normalform N"],

	   ("PolyMinus",["binom_klammer", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_parentheses_mult"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso

   UnparseC.term (get_obj g_res pt (fst p)) =(*"- 2 + 12 * a \<up> 2 + 5 * a" with OLD numerals*)

                                               "- 2 + 5 * a + 12 * a \<up> 2"

then () else error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";

"----------- pbl binom polynom vereinfachen: cube ----------------";

"----------- pbl binom polynom vereinfachen: cube ----------------";

"----------- pbl binom polynom vereinfachen: cube ----------------";

reset_states ();

CalcTree [(["Term (8*(a - q) + a - 2*q + 3*(a - 2*q))", "normalform N"],

	   ("PolyMinus",["binom_klammer", "polynom", "vereinfachen"],

	    ["simplification", "for_polynomials", "with_parentheses_mult"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;

if p = ([], Res) andalso UnparseC.term (get_obj g_res pt (fst p)) = "12 * a - 16 * q" 

then () else error "pbl binom polynom vereinfachen: cube";

"----------- Refine.refine Vereinfache ----------------------------------";

"----------- Refine.refine Vereinfache ----------------------------------";

"----------- Refine.refine Vereinfache ----------------------------------";

val fmz = ["Term (8*(a - q) + a - 2*q + 3*(a - 2*(q::real)))", "normalform (N::real)"];

(*default_print_depth 11;*)

val matches = Refine.refine fmz ["vereinfachen"];

(*default_print_depth 3;*)

"----- go into details, if it seems not to work -----";

"--- does the predicate evaluate correctly ?";

val t = TermC.str2term 

	    "matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q + 3 * (a - 2 * (q::real)))";

val ma = eval_matchsub "" "Prog_Expr.matchsub" t ctxt;

case ma of

    SOME ("matchsub (?a * (?b - ?c)) (8 * (a - q) + \

	  \a - 2 * q + 3 * (a - 2 * q)) = True", _) => ()

  | _ => error "polyminus.sml matchsub (?a * (?b - ?c)...A";

"--- does the respective prls rewrite ?";

val prls = Rule_Set.append_rules "prls_pbl_vereinf_poly" Rule_Set.empty 

	     [Eval ("Poly.is_polyexp", eval_is_polyexp ""),

	      Eval ("Prog_Expr.matchsub", eval_matchsub ""),

	      Thm ("or_true",@{thm or_true}),

	      (*"(?a | True) = True"*)

	      Thm ("or_false",@{thm or_false}),

	      (*"(?a | False) = ?a"*)

	      Thm ("not_true", @{thm not_true}),

	      (*"(~ True) = False"*)

	      Thm ("not_false", @{thm not_false})

	      (*"(~ False) = True"*)];

(*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

val SOME (t', _) = rewrite_set_ ctxt false prls t;

"--- does the respective prls rewrite the whole predicate ?";

val t = TermC.str2term 

	    "Not (matchsub (?a * (?b + ?c)) (8 * (a - q) + a - 2 * q) | \

	    \     matchsub (?a * (?b - ?c)) (8 * (a - q) + a - 2 * q) | \

	    \     matchsub ((?b + ?c) * ?a) (8 * (a - q) + a - 2 * q) | \

	    \     matchsub ((?b - ?c) * ?a) (8 * (a - q) + a - 2 * q) )";

(*Rewrite.trace_on := true; ..stopped Test_Isac.thy*)

val SOME (t', _) = rewrite_set_ ctxt false prls t;

if UnparseC.term t' = "False" then ()

else error "polyminus.sml Not (matchsub (?a * (?b + ?c)) (8 ...";

"----------- *** Problem.prep_input: syntax error in '#Where' of [v";

"----------- *** Problem.prep_input: syntax error in '#Where' of [v";

"----------- *** Problem.prep_input: syntax error in '#Where' of [v";

(*see test/../termC.sml for details*)

val t = TermC.parse_patt thy "t_t is_polyexp";

val t = TermC.parse_patt thy ("Not (matchsub (?a + (?b + ?c)) t_t | " ^

	                "     matchsub (?a + (?b - ?c)) t_t | " ^

	                "     matchsub (?a - (?b + ?c)) t_t | " ^

	                "     matchsub (?a + (?b - ?c)) t_t )");

(*show_types := true;

if UnparseC.term t = "~ (matchsub ((?a::real) + ((?b::real) + (?c::real))) (t_t::real) |\n   matchsub (?a + (?b - ?c)) t_t |\n   matchsub (?a - (?b + ?c)) t_t | matchsub (?a + (?b - ?c)) t_t)"

then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";

show_types := false;*)

if UnparseC.term t =

  "\<not> (matchsub (?a + (?b + ?c)) t_t \<or>\n        " ^

  "matchsub (?a + (?b - ?c)) t_t \<or>\n        " ^

  "matchsub (?a - (?b + ?c)) t_t \<or> " ^

  "matchsub (?a + (?b - ?c)) t_t)"

then () else error "polyminus.sml type-structure of \"?a :: real\" changed 1";