wneuper/isa: comparison test/Tools/isac/IsacKnowledge/rational.sml

equal deleted inserted replaced

-:d957275620d4
+:e6fc98fbcb85
 --------------------------------------------------------------------------!!!*)
 (*-----versuche 13.3.03-----
 val t = str2term "1 - x^^^2 - 5 * x^^^5";
 val vs=(((map free2str) o vars) t);
-val Some ml = expanded2poly t vs;
+val SOME ml = expanded2poly t vs;
 poly2term (ml, vs);
 poly2term'(rev(sort (mv_geq LEX_) (ml)),vs);
 poly2term'([(~5,[5]),(~1,[2]),(1,[0])], vs);
 monom2term((~5,[5]),vs);
 monom2term((~1,[2]),vs);
 		   powerproduct2term(is, vs);
 term2str ttt;
 -------versuche 13.3.03-----*)
 val t = str2term "1 - x^^^2 - 5 * x^^^5";
-val Some t' = expanded2polynomial t; term2str t';
+val SOME t' = expanded2polynomial t; term2str t';
 "1 + - 1 * x ^^^ 2 + - 5 * x ^^^ 5";
 val t = str2term "1 - x";
-val Some t' = expanded2polynomial t; term2str t';
+val SOME t' = expanded2polynomial t; term2str t';
 "1 + - 1 * x";
 val t = str2term "1 + (-1) * x";
-val Some t' = expanded2polynomial t; term2str t';
+val SOME t' = expanded2polynomial t; term2str t';
 "1 + - 1 * x";
 val t = (term_of o the o (parse thy)) "1 + (-1) * x ^^^ 2 + (-5) * x ^^^5";
-val Some t' = polynomial2expanded t; term2str t';
+val SOME t' = polynomial2expanded t; term2str t';
 "1 - x ^^^ 2 - 5 * x ^^^ 5";
 " external calculating functions test ";
 " external calculating functions test ";
 " external calculating functions test ";
 val t1 = (term_of o the o (parse thy)) "((3 * x^^^2 + 6 *x + 3) / (2*x + 2))";
-val Some (t1',asm)= factout_p_ thy t1;
+val SOME (t1',asm)= factout_p_ thy t1;
 term2str t1'; terms2str asm;
 "(3 + 3 * x) * (1 + 1 * x) / (2 * (1 + 1 * x))";
 "[]";
-val Some (t1',asm)= cancel_p_ thy t1;
+val SOME (t1',asm)= cancel_p_ thy t1;
 term2str t1'; terms2str asm;
 "(3 + 3 * x) / 2";
 "[\"1 + 1 * x ~= 0\"]";
 val t = (term_of o the o (parse thy)) "((-3 * x^^^2 + 6 *x - 3) / (2*x - 2))";
-val Some (t',asm)= cancel_ thy t;
+val SOME (t',asm)= cancel_ thy t;
 term2str t'; terms2str asm;
 "(3 - 3 * x) / 2";
 "[\"-1 + x ~= 0\"]";
-val Some (t',asm)= factout_ thy t;
+val SOME (t',asm)= factout_ thy t;
 term2str t'; terms2str asm;
 "(3 - 3 * x) * (-1 + x) / (2 * (-1 + x))";
 "[]";
 val t = str2term "((x+ (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";
-val Some (t',asm) = add_fraction_p_ thy t;
+val SOME (t',asm) = add_fraction_p_ thy t;
 term2str t'; terms2str asm;
 "(2 + 2 * x ^^^ 2) / (-1 + 1 * x ^^^ 2)";
 "[]";
-val Some (t',asm) = common_nominator_p_ thy t;
+val SOME (t',asm) = common_nominator_p_ thy t;
 term2str t'; terms2str asm;
 "(-1 + 1 * x) * (-1 + 1 * x) / ((1 + 1 * x) * (-1 + 1 * x)) +\n(1 + 1 * x) * (1 + 1 * x) / ((1 + 1 * x) * (-1 + 1 * x))";
 "[]";
 val t = str2term "((x - 1) / (x + 1)) + ((x + 1) / (x - 1))";
-val Some (t',asm) = add_fraction_ thy t;
+val SOME (t',asm) = add_fraction_ thy t;
 term2str t'; terms2str asm;
 "(2 + 2 * x ^^^ 2) / (-1 + x ^^^ 2)";
 "[]";
-val Some (t',asm) = common_nominator_ thy t;
+val SOME (t',asm) = common_nominator_ thy t;
 term2str t'; terms2str asm;
 "(-1 + x) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(1 + x) * (1 + x) / ((1 + x) * (-1 + x))";
 "[]";
 val t = str2term "((1) / (2*x + 2)) + ((1) / (2*x + (-2))) + ((1) / ( x^^^2 + (-1)))+((1) / (x^^^2 + (-2)*x + 1))";
-val Some (t',asm) = common_nominator_p_ thy t;
+val SOME (t',asm) = common_nominator_p_ thy t;
 term2str t'; terms2str asm;
 "1 * (1 + -2 * x + 1 * x ^^^ 2) /\n((-1 + 1 * x) * (2 * ((-1 + 1 * x) * (1 + 1 * x)))) +\n(1 * (-1 + 1 * x ^^^ 2) /\n ((-1 + 1 * x) * (2 * ((-1 + 1 * x) * (1 + 1 * x)))) +\n (1 * (-2 + 2 * x) / ((-1 + 1 * x) * (2 * ((-1 + 1 * x) * (1 + 1 * x)))) +\n  1 * (#";
 "[]";
-val Some (t',asm) = add_fraction_p_ thy t;
+val SOME (t',asm) = add_fraction_p_ thy t;
 term2str t'; terms2str asm;
 "1 * x / (1 + -2 * x + 1 * x ^^^ 2)";
 "[\"1 + 1 * x ~= 0\"]";
-val Some(t',asm) = norm_rational_ thy t;
+val SOME(t',asm) = norm_rational_ thy t;
 term2str t'; terms2str asm;
 "1 * x / (1 + -2 * x + 1 * x ^^^ 2)";
 "[\"1 + 1 * x ~= 0\"]";
 val t3 = (term_of o the o (parse thy)) "((1) / (2*x + 2)) + ((1) / (2*x - 2)) + ((1) / ( x^^^2 - 1))+((1) / (x^^^2 - 2 * x + 1))";
-val Some (t3',_) = common_nominator_ thy t3;
+val SOME (t3',_) = common_nominator_ thy t3;
-val Some (t3'',_) = add_fraction_ thy t3;
+val SOME (t3'',_) = add_fraction_ thy t3;
 (term2str t3');
 (term2str t3'');
-val Some(t4,t5) = norm_expanded_rat_ thy t3;
+val SOME(t4,t5) = norm_expanded_rat_ thy t3;
 term2str t4;
 term2str (hd(t5));
 val t=(term_of o the o (parse thy)) "(9 - x^^^2)/(9 - 6*x + x^^^2)";
-val Some (t',_) = factout_ thy t;
+val SOME (t',_) = factout_ thy t;
-val Some (t'',_) = cancel_ thy t;
+val SOME (t'',_) = cancel_ thy t;
 term2str t';
 term2str t'';
 "(3 + x) * (3 - x) / ((3 - x) * (3 - x))";
 "(3 + x) / (3 - x)";
 val t=(term_of o the o (parse thy))
 	    "(9 - x^^^2) / (9 - 6*x + x^^^2) + 1 / (3 - x)";
-val Some (t',_) = common_nominator_ thy t;
+val SOME (t',_) = common_nominator_ thy t;
-val Some (t'',_) = add_fraction_ thy t;
+val SOME (t'',_) = add_fraction_ thy t;
 term2str t';
 term2str t'';
 "(9 - x ^^^ 2) / ((3 - x) * (3 - x)) + 1 * (3 - x) / ((3 - x) * (3 - x))";
 "(4 + x) / (3 - x)";
 (*WN021016 added -----vv---*)
 val t = str2term "(9 - x^^^2) / (9 - 6*x + x^^^2) + 1";
-val Some (t',_) = common_nominator_ thy t;
+val SOME (t',_) = common_nominator_ thy t;
-val Some (t'',_) = add_fraction_ thy t;
+val SOME (t'',_) = add_fraction_ thy t;
 term2str t' = "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2) +\n1\
 		\ * (9 - 6 * x + x ^^^ 2) / (9 - 6 * x + x ^^^ 2)" (*true*);
 term2str t'' = "6 / (3 - x)" (*true*);
 val t = str2term "1 + (9 - x^^^2) / (9 - 6*x + x^^^2)";
-val Some (t',_) = common_nominator_ thy t;
+val SOME (t',_) = common_nominator_ thy t;
-val Some (t'',_) = add_fraction_ thy t;
+val SOME (t'',_) = add_fraction_ thy t;
 term2str t' = "1 * (9 - 6 * x + x ^^^ 2) / (9 - 6 * x + x ^^^ 2) +\n\
 		\(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)" (*true*);
 term2str t'' = "6 / (3 - x)" (*true*);
 (*WN021016 added -----^^---*)
-(*WN030602 added -----vv--- no rewrite -> None !*)
+(*WN030602 added -----vv--- no rewrite -> NONE !*)
 val t = str2term "1 / a";
-val None =  cancel_p_ thy t;
+val NONE =  cancel_p_ thy t;
-val None = rewrite_set_ thy false cancel_p t;
+val NONE = rewrite_set_ thy false cancel_p t;
 (*WN.2.6.03 added -------^^---*)
 val t = str2term "(y^^^2 - x^^^2)/(y^^^2 - 2*y*x + x^^^2)";
-val Some (t',_) = factout_ thy t;
+val SOME (t',_) = factout_ thy t;
-val Some (t'',_) = cancel_ thy t;
+val SOME (t'',_) = cancel_ thy t;
 term2str t' = "(y + x) * (y - x) / ((y - x) * (y - x))"(*true*);
 term2str t'' = "(y + x) / (y - x)";
 val t = str2term "(y^^^2 - x^^^2)/(y^^^2 - 2*y*x + x^^^2) + 1 / (y - x)";
-val Some (t',_) = common_nominator_ thy t;
+val SOME (t',_) = common_nominator_ thy t;
-val Some (t'',_) = add_fraction_ thy t;
+val SOME (t'',_) = add_fraction_ thy t;
 term2str t' =
 "(-1 * x ^^^ 2 + y ^^^ 2) / ((-1 * x + y) * (-1 * x + y)) +\n1\
 \ * (-1 * x + y) / ((-1 * x + y) * (-1 * x + y))" (*true*);
 term2str t'' = "(-1 - x - y) / (x - y)" (*true*);
 val t = str2term "(x^^^2 - y^^^2)/(x^^^2 - 2*x*y + y^^^2) + 1 / (x - y)";
-val Some (t',_) = common_nominator_ thy t;
+val SOME (t',_) = common_nominator_ thy t;
-val Some (t'',_) = add_fraction_ thy t;
+val SOME (t'',_) = add_fraction_ thy t;
 if term2str t' = "(-1 * y ^^^ 2 + x ^^^ 2) / ((-1 * y + x) * (-1 * y + x))\
 \ +\n1 * (-1 * y + x) / ((-1 * y + x) * (-1 * y + x))" then ()
 else raise error "rational.sml lex-ord 1";
 if term2str t'' = "(-1 - y - x) / (y - x)" then ()
 else raise error "rational.sml lex-ord 2";
 (*WN.16.10.02 WN070905 lexicographische Ordnung erhalten ! SK.ord*)
 val t = str2term "(x^^^2 - y^^^2)/(x^^^2 - 2*x*y + y^^^2)";
-val Some (t',_) = norm_expanded_rat_ thy t;
+val SOME (t',_) = norm_expanded_rat_ thy t;
 if term2str t' = "(x + y) / (x - y)" then ()
 else raise error "rational.sml term2poly: invalid x ^^^ 2 - y ^^^ 2 1";
-(*val Some (t'',_) = norm_rational_ thy t;
+(*val SOME (t'',_) = norm_rational_ thy t;
 *** RATIONALS_TERM2POLY_EXCEPTION: Invalid Polynomial
 WN.16.10.02 ?! + WN060831???SK4
 WN070905 *** term2poly: invalid = x ^^^ 2 - y ^^^ 2*)
 val t = str2term "(9 - x^^^2)/(9 - 6*x + x^^^2) + (1)/(3 + x)";
-val Some (t',_) = norm_expanded_rat_ thy t;
+val SOME (t',_) = norm_expanded_rat_ thy t;
 if term2str t' = "(12 + 5 * x + x ^^^ 2) / (9 - x ^^^ 2)" then ()
 else raise error "rational.sml (9 - x^^^2)/(9 - 6*x + x^^^2) +...";
-(*val Some (t'',_) = norm_rational_ thy t;
+(*val SOME (t'',_) = norm_rational_ thy t;
 *** RATIONALS_TERM2POLY_EXCEPTION: Invalid Polynomial WN.16.10.02 ?!
 WN070906 *** term2poly: invalid = 9 - x ^^^ 2 SK.term2poly*)
 val t=(term_of o the o (parse thy))
 	    "(9 + (-1)* x^^^2)/(9 + (-1)* 6*x + x^^^2) + (1)/(3 + x)";
-val Some (t',_) = norm_expanded_rat_ thy t;
+val SOME (t',_) = norm_expanded_rat_ thy t;
-val Some (t'',_) = norm_rational_ thy t;
+val SOME (t'',_) = norm_rational_ thy t;
 term2str t';
 term2str t'';
 "(12 + 5 * x + x ^^^ 2) / (9 - x ^^^ 2)";
 "(12 + 5 * x + x ^^^ 2) / (9 + (-1) * x ^^^ 2)";
 val e188a = the (rewrite_set thy' false "cancel" e188a');
 is_expanded (parse_rat "8 * x + -8");
 (* e188a = ("8 / 9",["not ((-1) + x = 0)"]) then () 13.3.03*)
 if e188a = ("8 / 9",["-1 + x ~= 0"]) then ()
 else raise error "rational.sml: e188a new behaviour";
-val Some (t,_) = rewrite_set thy' false mp
+val SOME (t,_) = rewrite_set thy' false mp
 			     "(8*((-1) + x))/(9*((-1) + x))";
 print("b)\n");
 val e188b'="(-15 + 5 * x) / (-18 + 6 * x)";(*SRC*)
-val Some (t,_) = rewrite_set thy' false "cancel" e188b';
+val SOME (t,_) = rewrite_set thy' false "cancel" e188b';
 t = "5 / 6" (*true*);
 print("c)\n");
 val e188c'="( a + -1 * b ) / ( b + -1 * a )";
 val e188c = the (rewrite_set thy' false "cancel_p" e188c');
 (*is_expanded (parse_rat "a + -1 * b");*)
-val Some (t,_) =
+val SOME (t,_) =
 rewrite_set thy' false mp "((-1)*(b + (-1) * a))/(1*(b + (-1) * a))";
 if t= "(a + -1 * b) / (-1 * a + b)"  then()
 else raise error "rational.sml: e188c new behaviour";
 print("\n\nexample 190:\n");
 print("c)\n");
 val e190c'="( 27 * a^^^3 + 9 * a^^^2 + 3 * a + 1 ) / ( 27 * a^^^3 + 18 * a^^^2 + 3 * a )";
 val e190c = the (rewrite_set thy' false "cancel" e190c');
-val Some (t,_) = rewrite_set thy' false mp "((1 + 9 * a ^^^ 2)*(1 + 3 * a))/((3 * a + 9 * a ^^^ 2)*(1 + 3 * a))";
+val SOME (t,_) = rewrite_set thy' false mp "((1 + 9 * a ^^^ 2)*(1 + 3 * a))/((3 * a + 9 * a ^^^ 2)*(1 + 3 * a))";
 if t = "(1 + 3 * a + 9 * a ^^^ 2 + 27 * a ^^^ 3) /\n(3 * a + 18 * a ^^^ 2 + 27 * a ^^^ 3)" then ()
 else raise error "rational.sml: e190c new behaviour";
 print("\n\nexample 191:\n");
 print("a)\n");
 val e191a = the (rewrite_set thy' false "cancel" e191a');
 is_expanded (parse_rat "x^^^2 + -1 * y^^^2");
 false;
 is_expanded (parse_rat "x + y");
 true; -----------*)
-val Some (t,_) = rewrite_set thy' false mp "((x + (-1) * y)*(x + y))/((1)*(x + y))";
+val SOME (t,_) = rewrite_set thy' false mp "((x + (-1) * y)*(x + y))/((1)*(x + y))";
 (* t="(x ^^^ 2 + -1 * y ^^^ 2) / (x + y)" then() WN.13.3.03*)
 if t="(x ^^^ 2 + -1 * y ^^^ 2) / (x + y)" then()
 else raise error "rational.sml: e191a new behaviour";
 print("c)\n");
 false;
 is_expanded (parse_rat "25 + -30*x + 9*x^^^2");
 false;
 is_expanded (parse_rat "-25 + 9*x^^^2");
 true;------------*)
-val Some (t,_) = rewrite_set thy' false mp "(((-5) + 3 * x)*((-5) + 3 * x))/((5 + 3 * x)*((-5) + 3 * x))";
+val SOME (t,_) = rewrite_set thy' false mp "(((-5) + 3 * x)*((-5) + 3 * x))/((5 + 3 * x)*((-5) + 3 * x))";
 (* t="(25 + ((-30) * x + 9 * x ^^^ 2)) / ((-25) + 9 * x ^^^ 2)"then() 13.3.03*)
 if t= "(25 + -30 * x + 9 * x ^^^ 2) / (-25 + 9 * x ^^^ 2)" then()
 else raise error "rational.sml: 'e191c' new behaviour";
 print("b)\n");
 val e192b'="( 7 * x^^^3 + -1 * x^^^2 * y ) / ( 7 * x * y^^^2 + -1 *  y^^^3 )";
 (*WN.23.10.02-------
 val e192b = the (rewrite_set thy' false "cancel" e192b');
 -------------------*)
-val Some (t',_) = rewrite_set thy' false mp "((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
+val SOME (t',_) = rewrite_set thy' false mp "((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
 if t' = "(7 * x ^^^ 3 + -1 * x ^^^ 2 * y) / (7 * x * y ^^^ 2 + -1 * y ^^^ 3)"
 (*"(-1 * y * x ^^^ 2 + 7 * x ^^^ 3) / (-1 * y ^^^ 3 + 7 * x * y ^^^ 2)"WN050929*)
 then () else raise error "rational.sml: 'e192b' new behaviour";
 (*^^^ works with MG's simplifier vvv*)
 val t =str2term"((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
-val Some (t',_) = rewrite_set_ Isac.thy false make_polynomial t;
+val SOME (t',_) = rewrite_set_ Isac.thy false make_polynomial t;
 if term2str t' = "(7 * x ^^^ 3 + -1 * x ^^^ 2 * y) / (7 * x * y ^^^ 2 + -1 * y ^^^ 3)" then () else raise error "rational.sml: 'e192b'MG new behaviour";
 print("\n\nexample 193:\n");
 print("a)\n");
 val e193b'="( x^^^2 + -8 * x + 16 ) / ( 2 * x^^^2 + -32 )";
 (*WN.23.10.02-------
 val e193b = the (rewrite_set thy' false "cancel" e193b');
 print("c)\n");
 val e193c'="( 2 * x + -50 * x^^^3 ) / ( 25 * x^^^2 + -10 * x + 1 )";
-val Some(t,_) = rewrite_set thy' false "cancel" e193c';
+val SOME(t,_) = rewrite_set thy' false "cancel" e193c';
 -------------------*)
 val wn01 = "(-25 + 9*x^^^2)/(5 + 3*x)";
-val Some (t,_) = rewrite_set thy' false "cancel" wn01;
+val SOME (t,_) = rewrite_set thy' false "cancel" wn01;
 (* t = "((-5) + 3 * x) / 1" then () WN.13.3.03*)
 if t = "(-5 + 3 * x) / 1" then ()
 else raise error "rational.sml: new behav. in cancel wn01";
 if est1 = ("-1 / 1",[]) then ()
 else raise error "new behaviour in rational.sml: est1'";
 val t = (term_of o the o (parse thy))
 "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
-val Some (t',_) = factout_ thy t;
+val SOME (t',_) = factout_ thy t;
 term2str t';
 "(3 + x) * (3 - x) / ((3 - x) * (3 - x))";
 "-------- reverse rewrite ----------------------------------------";
 	      "(9 - x ^^^ 2) / (9 + 6 * x + x ^^^ 2)";
 val Rrls {scr=Rfuns {init_state=ini,locate_rule=loc,
 		       next_rule=nex,normal_form=nor,...},...} = cancel;
 (*normal_form produces the result in ONE step*)
-val Some (t',_) = nor t;
+val SOME (t',_) = nor t;
 term2str t';
 (*initialize the interpreter state used by the 'me'*)
 val (t,_,revsets,_) = ini t;
 (*find the rule 'r' to apply to term 't'*)
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 (*val r = Thm ("sym_#mult_2_3","6 = 2 * 3") : rule*)
 (*check, if the rule 'r' applied by the user to 't' belongs to the ruleset;
 if the rule is OK, the term resulting from applying the rule is returned,too;
 there might be several rule applications inbetween,
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
 "(9 - x ^^^ 2) / (3 ^^^ 2 + 6 * x + x ^^^ 2)";
 (*find the next rule to apply*)
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 (*val r = Thm ("sym_#power_3_2","9 = 3 ^^^ 2") : rule*)
 (*check the next rule*)
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
 "(3 ^^^ 2 - x ^^^ 2) / (3 ^^^ 2 + 6 * x + x ^^^ 2)";
 (*find and check the next rules, rewrite*)
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
 "(3 ^^^ 2 - x ^^^ 2) / (3 ^^^ 2 + 2 * 3 * x + x ^^^ 2)";
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
 "(3 - x) * (3 + x) / (3 ^^^ 2 + 2 * 3 * x + x ^^^ 2)";
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
 "(3 - x) * (3 + x) / ((3 + x) * (3 + x))";
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 val (r,(t,asm))::_ = loc revsets t r;
 val ss = term2str t;
 if ss = "(3 - x) / (3 + x)" then ()
 else raise error "rational.sml: new behav. in rev-set cancel";
 terms2str asm;
 val t = str2term "(9 + (-1)*x^^^2) / (9 + ((-6)*x + x^^^2))";
 val Rrls {scr=Rfuns {init_state=ini,locate_rule=loc,
 		       next_rule=nex,normal_form=nor,...},...} = cancel_p;
 (*normal_form produces the result in ONE step*)
-val Some (t',_) = nor t;
+val SOME (t',_) = nor t;
 term2str t' = "(3 + 1 * x) / (3 + -1 * x)";
 (*initialize the interpreter state used by the 'me'*)
-val Some (t', asm) = cancel_p_ thy t;
+val SOME (t', asm) = cancel_p_ thy t;
 term2str t' = "(3 + x) / (3 + -1 * x)" (*true*);
 terms2str asm = "[\"3 + -1 * x ~= 0\"]" (*true*);
 val (t,_,revsets,_) = ini t;
 (* WN.10.10.02: dieser Fall terminiert nicht
 WN060823 'init_state' requires rewriting on specified location in the term
 print_depth 99; Rfuns; print_depth 3;
 WN060831 cycling "sym_order_mult_rls_" "sym_real_mult_assoc"
 as was with make_polynomial before ?!?*)
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 eq_Thm (r, Thm ("sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))",
 		mk_thm Rational.thy "9 = 3 ^^^ 2"));
 (*WN060831 *** id_of_thm
 Exception- ERROR raised ...
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
-val Some r = nex revsets t;
+val SOME r = nex revsets t;
 val (r,(t,asm))::_ = loc revsets t r;
 term2str t;
 *)
 print "\n\n\n******************  all tests successfull  *************************\n";
 (*WN.17.3.03 =========================================================vvv---*)
 "-------- norm_Rational ------------------------------------------";
 "-------- norm_Rational ------------------------------------------";
 "-------- norm_Rational ------------------------------------------";
 val t = str2term "(3*x+5)/18 - x/2  - -(3*x - 2)/9 = 0";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "1 / 18 = 0" then () else raise error "rational.sml 1";
 val t = str2term "(17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "(237 + 65 * x) / 36 = 0" then ()
 else raise error "rational.sml 2";
 val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 - (6*x)^^^2 + 29";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 (*before 040209:if term2str t' = "(23 + (35 * x + -72 * x ^^^ 2)) / 1"then()*)
 if term2str t' = "23 + 35 * x + -72 * x ^^^ 2" then ()
 else raise error "rational.sml 3";
 (*trace_rewrite:=true;*)
 val t = str2term "Not (6*x is_atom)";
-val Some (t',_) = rewrite_set_ thy false powers_erls t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false powers_erls t; term2str t';
 "True";
 val t = str2term "1 < 2";
-val Some (t',_) = rewrite_set_ thy false powers_erls t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false powers_erls t; term2str t';
 "True";
 val t = str2term "(6*x)^^^2";
-val Some (t',_) = rewrite_ thy dummy_ord powers_erls false
+val SOME (t',_) = rewrite_ thy dummy_ord powers_erls false
 			   (num_str realpow_def_atom) t;
 term2str t';
 trace_rewrite:=false;
 val t = str2term "-1 * (-2 * (5 / 2 * (13 * x / 2)))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "65 * x / 2" then () else raise error "rational.sml 4";
 val t = str2term "1 - ((13*x)/2 - 5/2)^^^2";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 (*bef.040209: if term2str t' = "(-21 + (130 * x + -169 * x ^^^ 2)) / 4"then()*)
 if term2str t' = "(-21 + 130 * x + -169 * x ^^^ 2) / 4" then ()
 else raise error "rational.sml 5";
 (*SRAM Schalk I, p.92 Nr. 609a*)
 val t = str2term "2*(3 - x/5)/3 - 4*(1 - x/3) - x/3 - 2*(x/2 - 1/4)/27 +5/54";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "(-255 + 112 * x) / 135" then ()
 else raise error "rational.sml 6";
 (*SRAM Schalk I, p.92 Nr. 610c*)
 val t = str2term "((x- 1)/(x+1) + 1) / ((x- 1)/(x+1) - (x+1)/(x- 1)) - 2";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "(-3 + -1 * x) / 2" then () else raise error "rational.sml 7";
 (*SRAM Schalk I, p.92 Nr. 476a*)
 val t = str2term "(x^^^2/(1 - x^^^2) + 1)/(x/(1 - x) + 1) *\
 		 \ (1 + x)";(*. a/b : c/d translated to a/b * d/c .*)
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 (*if term2str t' = "1 / 1" then () else raise error "rational.sml 8";3.6.03*)
 if term2str t' = "1" then () else raise error "rational.sml 8";
 (*............................vvv---TODO: sollte gehen mit poly_order *)
 (*Schalk I, p.92 Nr. 472a*)
 val t = str2term "((8*x^^^2 - 32*y^^^2)/(2*x + 4*y))/((4*x - 8*y)/(x + y))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "x + y" then () else raise error "rational.sml p.92 Nr. 472a";
 (*Schalk I, p.70 Nr. 480b; a/b : c/d translated to a/b * d/c*)
 val t = str2term "((12*x*y/(9*x^^^2 - y^^^2))/\
 		 \(1/(3*x - y)^^^2 - 1/(3*x + y)^^^2)) *\
 		 \(1/(x - 5*y)^^^2 - 1/(x + 5*y)^^^2)/\
 		 \(20*x*y/(x^^^2 - 25*y^^^2))";
 (*... nicht simpl, zerlegt ...*)
 val t = str2term "((12*x*y/(9*x^^^2 - y^^^2))/\
 		 \(1/(3*x - y)^^^2 - 1/(3*x + y)^^^2))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 "(-12 * (x * y ^^^ 3) + 108 * (x * (y * x ^^^ 2))) / (12 * (x * y))";
 (*                             ~~~~~~~~~~ poly_order notwendig!*)
 val t = str2term "(1/(x - 5*y)^^^2 - 1/(x + 5*y)^^^2)/\
 		 \(20*x*y/(x^^^2 - 25*y^^^2))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 "(-500 * (x * y ^^^ 3) /\n (x ^^^ 4 + (625 * y ^^^ 4 + -50 * (x ^^^ 2 * y ^^^ 2))) +\n 20 * (x * (y * x ^^^ 2)) /\n (x ^^^ 4 + (625 * y ^^^ 4 + -50 * (x ^^^ 2 * y ^^^ 2)))) /\n(20 * (x * y))";
 trace_rewrite:=true;
 trace_rewrite:=false;
 "nonterm.SK6 ----- SK060904-2a non-termination of add_fraction_p_";
 (*WN.2.6.03 from rlang.sml 56a
 val t = str2term "(a + b * x) / (a + -1 * (b * x)) + (-1 * a + b * x) / (a + b * x) = 4 * (a * b) / (a ^^^ 2 + -1 * b ^^^ 2)";
-val None = rewrite_set_ thy false common_nominator_p t;
+val NONE = rewrite_set_ thy false common_nominator_p t;
 WN060831 nonterm.SK7
 val t = str2term "(a + b * x) / (a + -1 * (b * x)) + (-1 * a + b * x) / (a + b * x)";
-val None = add_fraction_p_ thy t;
+val NONE = add_fraction_p_ thy t;
 *)
 (* ------------------------------------------------------------------- *)
 (*---------vvv------------ MG: ab 1.7.03 ----------------vvv-----------*)
 "-------- numeral rationals --------------------------------------";
 "-------- numeral rationals --------------------------------------";
 (*SRA Schalk I, p.40 Nr. 164b *)
 val t = str2term "(47/6 - 76/9 + 13/4)/(35/12)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) = "19 / 21" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 1";
 (*SRA Schalk I, p.40 Nr. 166a *)
 val t = str2term "((5/4)/(4+22/7) + 37/20)*(110/3 - 110/9 * 23/11)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) = "45 / 2" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 2";
 "-------- cancellation -------------------------------------------";
 (* e190c Stefan K.*)
 val t = str2term
 "((1 + 9 * a ^^^ 2)*(1 + 3 * a))/((3 * a + 9 * a ^^^ 2)*(1 + 3 * a))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(1 + 9 * a ^^^ 2) / (3 * a + 9 * a ^^^ 2)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 3";
 (* e192b Stefan K.*)
 val t = str2term
 "((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "x ^^^ 2 / y ^^^ 2"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 4";
 (*SRC Schalk I, p.66 Nr. 379c *)
 val t = str2term
 "(a - b)/(b - a)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "-1"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 5";
 (*SRC Schalk I, p.66 Nr. 380b *)
 val t = str2term
 "15*(3*x+3)*(4*x+9)/(12*(2*x+7)*(5*x+5))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(27 + 12 * x) / (28 + 8 * x)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 6";
 (*Schalk I, p.60 Nr. 215c *)
 (* Falsches Ergebnis: rechnet lange und cancel_p kann nicht weiter krzen!!!*)
 (* WN060831????MG1
 val t = str2term "(a+b)^^^4*(x - y)/((x - y)^^^3*(a+b)^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(a ^^^ 4 * x + -1 * a ^^^ 4 * y + 4 * a ^^^ 3 * b * x + -4 * a ^^^ 3 * b * y + 6 * a ^^^ 2 * b ^^^ 2 * x + -6 * a ^^^ 2 * b ^^^ 2 * y + 4 * a * b ^^^ 3 * x + -4 * a * b ^^^ 3 * y + b ^^^ 4 * x + -1 * b ^^^ 4 * y) /(a ^^^ 2 * x ^^^ 3 + -3 * a ^^^ 2 * x ^^^ 2 * y + 3 * a ^^^ 2 * x * y ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 3 + 2 * a * b * x ^^^ 3 + -6 * a * b * x ^^^ 2 * y + 6 * a * b * x * y ^^^ 2 + -2 * a * b * y ^^^ 3 + b ^^^ 2 * x ^^^ 3 + -3 * b ^^^ 2 * x ^^^ 2 * y + 3 * b ^^^ 2 * x * y ^^^ 2 + -1 * b ^^^ 2 * y ^^^ 3)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 7";
 *)
 (*val t = str2term
 "(a ^^^ 4 * x + -1 * a ^^^ 4 * y + 4 * a ^^^ 3 * b * x + -4 * a ^^^ 3 * b * y + 6 * a ^^^ 2 * b ^^^ 2 * x + -6 * a ^^^ 2 * b ^^^ 2 * y + 4 * a * b ^^^ 3 * x + -4 * a * b ^^^ 3 * y + b ^^^ 4 * x + -1 * b ^^^ 4 * y) /(a ^^^ 2 * x ^^^ 3 + -3 * a ^^^ 2 * x ^^^ 2 * y + 3 * a ^^^ 2 * x * y ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 3 + 2 * a * b * x ^^^ 3 + -6 * a * b * x ^^^ 2 * y + 6 * a * b * x * y ^^^ 2 + -2 * a * b * y ^^^ 3 + b ^^^ 2 * x ^^^ 3 + -3 * b ^^^ 2 * x ^^^ 2 * y + 3 * b ^^^ 2 * x * y ^^^ 2 + -1 * b ^^^ 2 * y ^^^ 3)"
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;*)
 (* uncaught exception nonexhaustive binding failure
 raised at: stdIn:93.1-93.51 *)
 (*Schalk I, p.66 Nr. 381a *)
 (* ACHTUNG: rechnet ca. 2 Minuten !!! *)
 (* WN060831???MG2
 val t = str2term "18*(a+b)^^^3*(a - b)^^^2/(72*(a - b)^^^3*(a+b)^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(a + b) / (4 * a + -4 * b)"
 then () else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 8";
 *)
 (*SRC Schalk I, p.66 Nr. 381b *)
 val t = str2term
 "(4*x^^^2 - 20*x + 25)/(2*x - 5)^^^3";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "-1 / (5 + -2 * x)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 9";
 (*SRC Schalk I, p.66 Nr. 381c *)
 val t = str2term
 "(27*a^^^3+9*a^^^2+3*a+1)/(27*a^^^3+18*a^^^2+3*a)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(1 + 9 * a ^^^ 2) / (3 * a + 9 * a ^^^ 2)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 10";
 (*SRC Schalk I, p.66 Nr. 383a *)
 val t = str2term
 "(5*a^^^2 - 5*a*b)/(a - b)^^^2";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "5 * a / (a + -1 * b)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 11";
 "-------- common denominator -------------------------------------";
 (*SRA Schalk I, p.67 Nr. 403a *)
 val t = str2term
 "4/x - 3/y - 1";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(-3 * x + 4 * y + -1 * x * y) / (x * y)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 12";
 (*SRA Schalk I, p.67 Nr. 407b *)
 val t = str2term
 "(2*a+3*b)/(b*c) + (3*c+a)/(a*c) - (2*a^^^2+3*b*c)/(a*b*c)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "4 / c"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 13";
 (*SRA Schalk I, p.67 Nr. 410b *)
 val t = str2term
 "1/(x+1) + 1/(x+2) - 2/(x+3)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(5 + 3 * x) / (6 + 11 * x + 6 * x ^^^ 2 + x ^^^ 3)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 14";
 (*SRA Schalk I, p.67 Nr. 413b *)
 val t = str2term
 "(1+x)/(1 - x) - (1 - x)/(1+x) + 2*x/(1 - x^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "6 * x / (1 + -1 * x ^^^ 2)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 15";
 (*SRA Schalk I, p.68 Nr. 414a *)
 val t = str2term
 "(x + 2)/(x - 1) + (x - 3)/(x - 2) - (x + 1)/((x - 1)*(x - 2))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(-2 + -5 * x + 2 * x ^^^ 2) / (2 + -3 * x + x ^^^ 2)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 16";
 (*SRA Schalk I, p.68 Nr. 423a *)
 val t = str2term
 "(2*x+3*y)/x + (4*x^^^3 - x*y^^^2 - 3*y^^^3)/(x^^^3 - 2*x^^^2*y+x*y^^^2) - (5*x+6*y)/(x - y)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "1"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 17";
 (*SRA Schalk I, p.68 Nr. 428b *)
 val t = str2term
 "1/(a - b)^^^2 + 1/(a+b)^^^2 - 2/(a^^^2 - b^^^2) - 4*(b^^^2 - 1)/(a^^^2 - b^^^2)^^^2";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "4 / (a ^^^ 4 + -2 * a ^^^ 2 * b ^^^ 2 + b ^^^ 4)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 18";
 (*SRA Schalk I, p.68 Nr. 430b *)
 val t = str2term
 "a^^^2/(a - 3*b) - 108*a*b^^^3/((a+3*b)*(a^^^2 - 9*b^^^2)) - 9*b^^^2*(a - 3*b)/(a+3*b)^^^2";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "a + 3 * b"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 19";
 (*SRA Schalk I, p.68 Nr. 432 *)
 val t = str2term
 "(a^^^2+a*b)/(a^^^2 - b^^^2) - (b^^^2 - a*b)/(b^^^2 - a^^^2) + a^^^2*(a - b)/(a^^^3 - a^^^2*b) - 2*a*(a^^^2 - b^^^2)/(a^^^3 - a*b^^^2) - 2*b^^^2/(a^^^2 - b^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "0"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 20";
 (*Eigenes*)
 val t = str2term
 "3*a/(a*b) + x/y";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(3 * y + b * x) / (b * y)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 21";
 "-------- multiply and cancel ------------------------------------";
 (*SRM Schalk I, p.68 Nr. 436a *)
 val t = str2term
 "3*(x+y)/(15*(x - y)) * 25*(x - y)^^^2/(18*(x+y)^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(5 * x + -5 * y) / (18 * x + 18 * y)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 22";
 (*SRM.test Schalk I, p.68 Nr. 436b *)
 (*WN060420???MG3 crashes with method 'simplify' in
 IsacCore > Simplification > Rational Terms > Multiplication > No.2*)
 val t = str2term "5*a*(a - b)^^^2*(a + b)^^^3/(7*b*(a - b)^^^3) * 7*b/(a + b)^^^3";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "5 * a / (a + -1 * b)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 23";
 (*Schalk I, p.68 Nr. 437a *)
 val t = str2term "(3*a - 4*b)/(4*c+3*e) * (3*a+4*b)/(9*a^^^2 - 16*b^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 if (term2str t) = "1 / (4 * c + 3 * e)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 24";
 "----- S.K. corrected non-termination 060904";
 val t = str2term "(3*a - 4*b) * (3*a+4*b)/((4*c+3*e)*(9*a^^^2 - 16*b^^^2))";
-val Some (t',_) = rewrite_set_ thy false make_polynomial t;
+val SOME (t',_) = rewrite_set_ thy false make_polynomial t;
 if term2str t' = "(9 * a ^^^ 2 + -16 * b ^^^ 2) /\n(36 * a ^^^ 2 * c + 27 * a ^^^ 2 * e + -64 * b ^^^ 2 * c +\n -48 * b ^^^ 2 * e)" then ()
 else raise error "rational.sml.sml: S.K.8..corrected 060904-6";
 "----- S.K. corrected non-termination of cancel_p_";
 val t'' = str2term "(9 * a ^^^ 2 + -16 * b ^^^ 2) /\
 \(36 * a^^^2 * c + (27 * a^^^2 * e + (-64 * b^^^2 * c + -48 * b^^^2 * e)))";
-val Some (t',_) = rewrite_set_ thy false cancel_p t'';
+val SOME (t',_) = rewrite_set_ thy false cancel_p t'';
 if term2str t' = "1 / (4 * c + 3 * e)" then ()
 else raise error "rational.sml.sml: diff.behav. in cancel_p S.K.8";
 (**)
 (*Schalk I, p.68 Nr. 437b *)
 (* nonterm.SK9 loops: cancel_p kann nicht weiter kuerzen!!! *)
 val t'' = str2term "(a + b)/(x^^^2 - y^^^2) * ((x - y)^^^2/(a^^^2 - b^^^2))";
-(* val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t'';
+(* val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t'';
 *)
 (*a casual output from above*)
 val t = str2term
 "(a * x ^^^ 2 + -2 * a * x * y + a * y ^^^ 2 + b * x ^^^ 2 + -2 * b * x * y + b * y ^^^ 2) /(a ^^^ 2 * x ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 2 + -1 * b ^^^ 2 * x ^^^ 2 + b ^^^ 2 * y ^^^ 2)";
 (* WN060831 nonterm.SK10
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;
 *)
 (*SRM Schalk I, p.68 Nr. 438a *)
 val t = str2term
 "x*y/(x*y - y^^^2)*(x^^^2 - x*y)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "x ^^^ 2"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 24";
 (*SRM Schalk I, p.68 Nr. 439b *)
 val t = str2term
 "(4*x^^^2+4*x+1)*((x^^^2 - 2*x^^^3)/(4*x^^^2+2*x))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(x + -4 * x ^^^ 3) / 2"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 25";
 (*SRM Schalk I, p.68 Nr. 440a *)
 val t = str2term
 "(x^^^2 - 2*x)/(x^^^2 - 3*x) * (x - 3)^^^2/(x^^^2 - 4)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(-3 + x) / (2 + x)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 26";
 "----- Schalk I, p.68 Nr. 440b SK11 works since 0707xx";
 val t = str2term
 "(a^^^3 - 9*a)/(a^^^3*b - a*b^^^3)*(a^^^2*b+a*b^^^2)/(a+3)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
 if term2str t = "(-3 * a + a ^^^ 2) / (a + -1 * b)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational 27";
 "----- SK12 works since 0707xx";
 val t = str2term "(a^^^3 - 9*a)*(a^^^2*b+a*b^^^2)/((a^^^3*b - a*b^^^3)*(a+3))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
 if term2str t' = "(-3 * a + a ^^^ 2) / (a + -1 * b)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational 28";
 "-------- common denominator and multiplication ------------------";
 (*----------------------------------------------------------------------*)
 (*SRAM Schalk I, p.69 Nr. 441b *)
 val t = str2term "(4*a/3 + 3*b^^^2/a^^^3 + b/(4*a))*(4*b/(3*a))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(36 * b ^^^ 3 + 3 * a ^^^ 2 * b ^^^ 2 + 16 * a ^^^ 4 * b) / (9 * a ^^^ 4)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 28";
 (*SRAM Schalk I, p.69 Nr. 442b *)
 val t = str2term "(15*a^^^2/x^^^3 - 5*b^^^4/x^^^2 + 25*c^^^2/x)*(x^^^3/(5*a*b^^^3*c^^^3)) + 1/c^^^3 * (b*x/a - 3*a/b^^^3)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "5 * x ^^^ 2 / (a * b ^^^ 3 * c)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 29";
 (*SRAM Schalk I, p.69 Nr. 443b *)
 val t = str2term "(a/2 + b/3)*(b/3 - a/2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(-9 * a ^^^ 2 + 4 * b ^^^ 2) / 36"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 30";
 (*SRAM Schalk I, p.69 Nr. 445b *)
 val t = str2term "(a^^^2/9 + 2*a/(3*b) + 4/b^^^2)*(a/3 - 2/b) + 8/b^^^3";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "a ^^^ 3 / 27"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 31";
 (*SRAM Schalk I, p.69 Nr. 446b *)
 val t = str2term "(x/(5*x + 4*y) - y/(5*x - 4*y) + 1)*(25*x^^^2 - 16*y^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "30 * x ^^^ 2 + -9 * x * y + -20 * y ^^^ 2"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 32";
 (*SRAM Schalk I, p.69 Nr. 449a *)(*Achtung: rechnet ca 8 Sekunden*)
 val t = str2term
 "(2*x^^^2/(3*y)+x/y^^^2)*(4*x^^^4/(9*y^^^2)+x^^^2/y^^^4)*(2*x^^^2/(3*y) - x/y^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(-81 * x ^^^ 4 + 16 * x ^^^ 8 * y ^^^ 4) / (81 * y ^^^ 8)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 33";
 (*SRAM Schalk I, p.69 Nr. 450a *)
 val t = str2term
 "(4*x/(3*y)+2*y/(3*x))^^^2 - (2*y/(3*x) - 2*x/y)*(2*y/(3*x)+2*x/y)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(52 * x ^^^ 2 + 16 * y ^^^ 2) / (9 * y ^^^ 2)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 34";
 "-------- double fractions ---------------------------------------";
 (*SRD Schalk I, p.69 Nr. 454b *)
 val t = str2term
 "((2 - x)/(2*a)) / (2*a/(x - 2))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(-4 + 4 * x + -1 * x ^^^ 2) / (4 * a ^^^ 2)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 35";
 (*SRD Schalk I, p.69 Nr. 455a *)
 val t = str2term
 "(a^^^2 + 1)/(a^^^2 - 1) / ((a+1)/(a - 1))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(1 + a ^^^ 2) / (1 + 2 * a + a ^^^ 2)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 36";
 "----- Schalk I, p.69 Nr. 455b";
 val t = str2term "(x^^^2 - 4)/(y^^^2 - 9)/((2+x)/(3 - y))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 if term2str t = "(2 + -1 * x) / (3 + y)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 37";
 "----- SK060904-1a non-termination of cancel_p_ ?: worked before 0707xx";
 val t = str2term "(x^^^2 - 4)*(3 - y)/((y^^^2 - 9)*(2+x))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
 if term2str t = "(2 + -1 * x) / (3 + y)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 37b";
 "----- ?: worked before 0707xx";
 val t = str2term "(3 + -1 * y) / (-9 + y ^^^ 2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
 if term2str t = "-1 / (3 + y)" then ()
 else raise error "rational.sml: -1 / (3 + y) norm_Rational";
 (*SRD Schalk I, p.69 Nr. 456b *)
 val t = str2term
 "(b^^^3 - b^^^2)/(b^^^2+b)/(b^^^2 - 1)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) = "b / (1 + 2 * b + b ^^^ 2)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 38";
 (*SRD Schalk I, p.69 Nr. 457b *)
 val t = str2term
 "(16*a^^^2 - 9*b^^^2)/(2*a+3*a*b) / ((4*a+3*b)/(4*a^^^2 - 9*a^^^2*b^^^2))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "8 * a ^^^ 2 + -6 * a * b + -12 * a ^^^ 2 * b + 9 * a * b ^^^ 2"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 39";
 "----- Schalk I, p.69 Nr. 458b works since 0707";
 val t = str2term
 "(2*a^^^2*x - a^^^2)/(a*x - b*x) / (b^^^2*(2*x - 1)/(x*(a - b)))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
 if term2str t = "a ^^^ 2 / b ^^^ 2" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 39b";
 (*SRD Schalk I, p.69 Nr. 459b *)
 val t = str2term "(a^^^2 - b^^^2)/(a*b) / (4*(a+b)^^^2/a)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
 if term2str t = "(a + -1 * b) / (4 * a * b + 4 * b ^^^ 2)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 41";
 (*Schalk I, p.69 Nr. 460b nonterm.SK
 val t = str2term
 "(9*(x^^^2 - 8*x+16)/(4*(y^^^2 - 2*y+1)))/((3*x - 12)/(16*y - 16))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 if term2str t =
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 42";
 val t = str2term
 "9*(x^^^2 - 8*x+16)*(16*y - 16)/(4*(y^^^2 - 2*y+1)*(3*x - 12))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
 ... non terminating.
-val Some (t',_) = rewrite_set_ thy false make_polynomial t;
+val SOME (t',_) = rewrite_set_ thy false make_polynomial t;
 "(-2304 + 1152 * x + 2304 * y + -144 * x ^^^ 2 + -1152 * x * y + 144 * x ^^^ 2 * y) /(-48 + 12 * x + 96 * y + -24 * x * y + -48 * y ^^^ 2 + 12 * x * y ^^^ 2)";
-val Some (t,_) = rewrite_set_ thy false cancel_p t';
+val SOME (t,_) = rewrite_set_ thy false cancel_p t';
 ... non terminating.*)
 (*SRD Schalk I, p.70 Nr. 472a *)
 val t = str2term "((8*x^^^2 - 32*y^^^2)/(2*x + 4*y))/\
 		 \((4*x - 8*y)/(x + y))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "x + y"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 43";
 (*----------------------------------------------------------------------*)
 (*SRD Schalk I, p.69 Nr. 461a *)
 val t = str2term
 "(2/(x+3) + 2/(x - 3)) / (8*x/(x^^^2 - 9))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "1 / 2"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 44";
 (*SRD Schalk I, p.69 Nr. 464b *)
 val t = str2term
 "(a - a/(a - 2)) / (a + a/(a - 2))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(3 + -1 * a) / (1 + -1 * a)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 45";
 (*SRD Schalk I, p.69 Nr. 465b *)
 val t = str2term
 "((x+3*y)/9 + (4*y^^^2 - 9*z^^^2)/(16*x)) /(x/9+y/6+z/4)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(4 * x + 6 * y + -9 * z) / (4 * x)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 46";
 (*SRD Schalk I, p.69 Nr. 466b *)
 val t = str2term
 "((1 - 7*(x - 2)/(x^^^2 - 4)) / (6/(x+2))) / (3/(x+5)+30/(x^^^2 - 25))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "(25 + -10 * x + x ^^^ 2) / 18"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 47";
 (*SRD Schalk I, p.70 Nr. 469 *)
 val t = str2term
 "3*b^^^2/(4*a^^^2 - 8*a*b + 4*b^^^2)/(a/(a^^^2*b - b^^^3) + (a - b)/(4*a*b^^^2+4*b^^^3) - 1/(4*b^^^2))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "3 * b ^^^ 3 / (2 * a + -2 * b)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 48";
 (*SRD.test Schalk I, p.70 Nr. 476b *) (* Rechenzeit: 10 sec *)
 (*WN060419 crashes with method 'simplify' ????SK*)
 val t = str2term
 "((a^^^2 - b^^^2)/(2*a*b)+2*a*b/(a^^^2 - b^^^2))/((a^^^2+b^^^2)/(2*a*b)+1) / ((a^^^2+b^^^2)^^^2/(a+b)^^^2)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
 if term2str t = "1 / (a ^^^ 2 + -1 * b ^^^ 2)" then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 49";
 "----- Schalk I, p.70 Nr. 477a";
 (* MG Achtung: terme explodieren; Bsp zu komplex;
 L???ung sollte (ziemlich grosser) Faktorisierter Ausdruck sein
 val t = str2term "b*y/(b - 2*y)/((b^^^2 - y^^^2)/(b+2*y)) /\
 		 \(b^^^2*y+b*y^^^2)*(a+x)^^^2/((b^^^2 - 4*y^^^2)*(a+2*x)^^^2)";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
 val t = str2term "b*y*(b+2*y)*(b^^^2 - 4*y^^^2)*(a+2*x)^^^2 / \
 		 \((b - 2*y)*(b^^^2 - y^^^2)*(b^^^2*y+b*y^^^2)*(a+x)^^^2)";
-val Some (t,_) = rewrite_set_ thy false make_polynomial t;
+val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
 ????SK ???MG*)
 "----- Schalk I, p.70 Nr. 478b ----- Rechenzeit: 5 sec";
 val t = str2term "(a - (a*b+b^^^2)/(a+b))/(b+(a - b)/(1+(a+b)/(a - b))) / \
 		 \((a - a^^^2/(a+b))/(a+(a*b)/(a - b)))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t',_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 if term2str t' =
 "(2 * a ^^^ 3 + 2 * a ^^^ 2 * b) / (a ^^^ 2 * b + b ^^^ 3)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 51";
 (*Schalk I, p.70 Nr. 480a *)
 (* Achtung: rechnet ewig; cancel_p kann nicht krzen: WN060831 nonterm.SK00
 val t = str2term
 "(1/x+1/y+1/z)/(1/x - 1/y - 1/z) / (2*x^^^2/(x^^^2 - z^^^2)/(x/(x+z)+x/(x - z)))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 52";
 (*MG Berechne Zwischenergebnisse: WN060831 nonterm.SK00*)
 val t = str2term
 "(1/x+1/y+1/z)/(1/x - 1/y - 1/z)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 "(x ^^^ 2 * y ^^^ 2 * z + x ^^^ 2 * y * z ^^^ 2 + x * y ^^^ 2 * z ^^^ 2) /
 (-1 * x ^^^ 2 * y ^^^ 2 * z + -1 * x ^^^ 2 * y * z ^^^ 2 + x * y ^^^ 2 * z ^^^ 2)";
 val t = str2term
 "2*x^^^2/(x^^^2 - z^^^2)/(x/(x+z)+x/(x - z))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 "1"
 (* SK 1. Ausdruck kann nicht weiter gekrzt werden; cancel_p !!!*)
 ###  rls: cancel_p on:
 GC #3.61.81.101.197.17503:   (0 ms)
 *** RATIONALS_DIRECT_CANCEL_EXCEPTION: Invalid fraction
 val t = str2term
 "(x^^^2 * (y^^^2 * z) + x^^^2 * (y * z^^^2) + x * (y^^^2 * z^^^2)) / (-1 * (x^^^2 * (y^^^2 * z)) + -1 * (x^^^2 * (y * z^^^2)) + x * (y^^^2 * z^^^2))";
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;
 (*uncaught exception nonexhaustive binding failure*)
 (* Das kann er aber krzen !!????: *)
 val t = str2term
 "(x^^^2 * (y^^^2 * z) +  x * (y^^^2 * z^^^2)) / (-1 * (x^^^2 * (y * z^^^2)) + x * (y^^^2 * z^^^2))";
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;
 "(-1 * (y * x) + -1 * (z * y)) / (1 * (z * x) + -1 * (z * y))";
 *)
 (*--------------------------------------------------------------------*)
 (*Schalk I, p.60 Nr. 215d *)
 (* Achtung: rechnet ewig ...
 val t = str2term "(a-b)^^^3 * (x+y)^^^4 / ((x+y)^^^2 * (a-b)^^^5)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t; noterm.SK
 *)
 (* Kein Wunder, denn Z???ler und Nenner extra als Polynom dargestellt ergibt:*)
 (*
 val t = str2term "(a-b)^^^3 * (x+y)^^^4";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 "a^^^3 * x^^^4 + 4 * a^^^3 * x^^^3 * y +\n6 * a^^^3 * x^^^2 * y^^^2 +\n4 * a^^^3 * x * y^^^3 +\na^^^3 * y^^^4 +\n-3 * a^^^2 * b * x^^^4 +\n-12 * a^^^2 * b * x^^^3 * y +\n-18 * a^^^2 * b * x^^^2 * y^^^2 +\n-12 * a^^^2 * b * x * y^^^3 +\n-3 * a^^^2 * b * y^^^4 +\n3 * a * b^^^2 * x^^^4 +\n12 * a * b^^^2 * x^^^3 * y +\n18 * a * b^^^2 * x^^^2 * y^^^2 +\n12 * a * b^^^2 * x * y^^^3 +\n3 * a * b^^^2 * y^^^4 +\n-1 * b^^^3 * x^^^4 +\n-4 * b^^^3 * x^^^3 * y +\n-6 * b^^^3 * x^^^2 * y^^^2 +\n-4 * b^^^3 * x * y^^^3 +\n-1 * b^^^3 * y^^^4";
 val t = str2term "((x+y)^^^2 * (a-b)^^^5)";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 "a^^^5 * x^^^2 + 2 * a^^^5 * x * y + a^^^5 * y^^^2 +\n-5 * a^^^4 * b * x^^^2 +\n-10 * a^^^4 * b * x * y +\n-5 * a^^^4 * b * y^^^2 +\n10 * a^^^3 * b^^^2 * x^^^2 +\n20 * a^^^3 * b^^^2 * x * y +\n10 * a^^^3 * b^^^2 * y^^^2 +\n-10 * a^^^2 * b^^^3 * x^^^2 +\n-20 * a^^^2 * b^^^3 * x * y +\n-10 * a^^^2 * b^^^3 * y^^^2 +\n5 * a * b^^^4 * x^^^2 +\n10 * a * b^^^4 * x * y +\n5 * a * b^^^4 * y^^^2 +\n-1 * b^^^5 * x^^^2 +\n-2 * b^^^5 * x * y +\n-1 * b^^^5 * y^^^2";
 *)
 (*anscheinend macht dem Rechner das Krzen diese Bruches keinen Spass mehr ...*)
 (*Schalk I, p.70 Nr. 480b
 val t = str2term "((12*x*y/(9*x^^^2 - y^^^2))/\
 		 \(1/(3*x - y)^^^2 - 1/(3*x + y)^^^2)) *\
 		 \(1/(x - 5*y)^^^2 - 1/(x + 5*y)^^^2)/\
 		 \(20*x*y/(x^^^2 - 25*y^^^2))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 SK.nonterm
 Kann nicht weiter vereinfacht werden !!!!?? *)
 (*--------------------------------------------------------------------*)
 "---- MGs test set";
 val t = str2term " (1 + x^^^5) / (y + x) + x^^^3 / x ";
-val Some (t,_) = rewrite_set_ thy false common_nominator_p t;
+val SOME (t,_) = rewrite_set_ thy false common_nominator_p t;
 if term2str t = "(1 + x ^^^ 3 + x ^^^ 5 + y * x ^^^ 2) / (x + y)" then()
 else raise error "";
 (*--------------------------------------------------------------------*)
 (* cancel_p liefert nicht immer Polynomnormalform (2): WN060831???SK3b
 ---> Sortierung FALSCH !!  *)
 val t = str2term "b^^^3 * a^^^5/a ";
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;
 "1 * (a^^^4 * b^^^3) / 1"; (*OK*)
 val t = str2term "b^^^3 * a^^^5/b ";
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;
 "1 * (b^^^2 * a^^^5) / 1"; (*cancel_p sortiert hier falsch um!*)
 (* Problem liegt NICHT bei ord_make_polynomial! (siehe folgende Bsple) *)
 (*
 (* cancel_p liefert nicht immer Polynomnormalform (2): WN060831???SK3c
 ---> erzeugt berflssige "1 * ..."
 val t = str2term "-1 / (3 + y)";
 (*~~         *)
-val Some (t,_) = rewrite_set_ thy false cancel_p t;
+val SOME (t,_) = rewrite_set_ thy false cancel_p t;
 term2str t;
 "-1 / (3 + 1 * y)";
 (********* Das ist das PROBLEM !!!!!!!??? *******************)
 (* -1 im Z???ler der Angabe verursacht das Problem !*)
 *)
 (* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - *)
 "----- MGs test set";
 val t = str2term "(a^^^2 + -1)/(a+1)";
-val Some (t',_) = rewrite_set_ thy false cancel_p t;
+val SOME (t',_) = rewrite_set_ thy false cancel_p t;
 if term2str t' = "(-1 + a) / 1" then ()
 else raise error "rational.sml MG tests 3d";
 "----- NOT TERMINATING ?: worked before 0707xx";
 val t = str2term "(a^^^2 - 1)*(b + 1) / ((b^^^2 - 1)*(a+1))";
-val Some (t'',_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t'',_) = rewrite_set_ thy false norm_Rational t;
 if term2str t'' = "(1 + -1 * a) / (1 + -1 * b)" then ()
 else raise error "rational.sml MG tests 3e";
 "----- corrected SK060905";
 val t = str2term "(4*x^^^2 - 20*x + 25)/(2*x - 5)^^^3";
-val Some (t',_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t',_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 if term2str t' = "-1 / (5 + -2 * x)" then ()
 else raise error "rational.sml corrected SK060905";
 "--------------------------------------------------------------------";
 "--------------------------------------------------------------------";
 (*SRAM Schalk I, p.69 Nr. 442b --- abgewandelt*)
 val t = str2term
 "(15*a^^^4/(a*x^^^3) - 5*a*((b^^^4 - 5*c^^^2*x)/x^^^2))*(x^^^3/(5*a*b^^^3*c^^^3)) + a/c^^^3 * (x*(b/a) - 3*b*(a/b^^^4))";
-val Some (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
+val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
 term2str t;
 if (term2str t) =
 "5 * x ^^^ 2 / (b ^^^ 3 * c)"
 then ()
 else raise error "rational.sml.sml: diff.behav. in norm_Rational_mg 53";
 else raise error "rational.sml: interSteps cancel_p rev_rew_p";
 val p = ([2,1,9],Res);
 getTactic 1 p;
 val (_, tac, _) = pt_extract (pt, p);
-(*case tac of Some (Rewrite ("sym_real_plus_binom_times1", _)) => ()
+(*case tac of SOME (Rewrite ("sym_real_plus_binom_times1", _)) => ()
 WN060905*)
-case tac of Some (Rewrite ("sym_real_add_mult_distrib2", _)) => ()
+case tac of SOME (Rewrite ("sym_real_add_mult_distrib2", _)) => ()
 | _ => raise error "rational.sml: getTactic, sym_real_plus_binom_times1";
 "-------- investigate rulesets for cancel_p ----------------------";
 "-------- investigate rulesets for cancel_p ----------------------";
 val thy = Rational.thy;
 "---------------- (a^^^2 + -1*b^^^2) / (a^^^2 + -2*a*b + b^^^2)";
 val t = str2term "(a^^^2 + -1*b^^^2) / (a^^^2 + -2*a*b + b^^^2)";
 val tt = str2term "(1 * a + 1 * b) * (1 * a + -1 * b)"(*numerator only*);
 "----- with rewrite_set_";
-val Some (tt',asm) = rewrite_set_ thy false make_polynomial tt;
+val SOME (tt',asm) = rewrite_set_ thy false make_polynomial tt;
 term2str tt'= "a ^^^ 2 + -1 * b ^^^ 2" (*true*);
 val tt = str2term "((1 * a + -1 * b) * (1 * a + -1 * b))"(*denominator only*);
-val Some (tt',asm) = rewrite_set_ thy false make_polynomial tt;
+val SOME (tt',asm) = rewrite_set_ thy false make_polynomial tt;
 term2str tt' = "a ^^^ 2 + -2 * a * b + b ^^^ 2" (*true*);
 "----- with make_deriv";
-val Some (tt, _) = factout_p_ Isac.thy t; term2str tt =
+val SOME (tt, _) = factout_p_ Isac.thy t; term2str tt =
 "(1 * a + 1 * b) * (1 * a + -1 * b) / ((1 * a + -1 * b) * (1 * a + -1 * b))";
 (*
 "--- with ruleset as before 060829";
 val {rules, rew_ord=(_,ro),...} =
 rep_rls (assoc_rls "make_polynomial");
-val der = make_deriv thy Atools_erls rules ro None tt;
+val der = make_deriv thy Atools_erls rules ro NONE tt;
 print_depth 99; map (term2str o #1) der; print_depth 3;
 print_depth 99; map (rule2str o #2) der; print_depth 3;
 ... did not terminate"*)
 "--- with simpler ruleset";
 val {rules, rew_ord=(_,ro),...} =
 rep_rls (assoc_rls "rev_rew_p");
-val der = make_deriv thy Atools_erls rules ro None tt;
+val der = make_deriv thy Atools_erls rules ro NONE tt;
 print_depth 99; writeln (deriv2str der); print_depth 3;
 print_depth 99; map (term2str o #1) der; print_depth 3;
 "...,(-1 * b ^^^ 2 + a ^^^ 2) / (-2 * (a * b) + a ^^^ 2 + (-1 * b) ^^^ 2) ]";
 print_depth 99; map (rule2str o #2) der; print_depth 3;
 print_depth 99; map (term2str o #1 o #3) der; print_depth 3;
-val der = make_deriv thy Atools_erls rules ro None
+val der = make_deriv thy Atools_erls rules ro NONE
 		     (str2term "(1 * a + 1 * b) * (1 * a + -1 * b)");
 print_depth 99; writeln (deriv2str der); print_depth 3;
 val {rules, rew_ord=(_,ro),...} =
 rep_rls (assoc_rls "rev_rew_p");
-val der = make_deriv thy Atools_erls rules ro None
+val der = make_deriv thy Atools_erls rules ro NONE
 		     (str2term "(1 * a + -1 * b) * (1 * a + -1 * b)");
 print_depth 99; writeln (deriv2str der); print_depth 3;
 print_depth 99; map (term2str o #1) der; print_depth 3;
 (*WN060829 ...postponed*)
 val (thy, eval_rls) = (Rational.thy, Atools_erls)(*see 'fun init_state'*);
 val Rrls {scr = Rfuns {init_state,...},...} = assoc_rls "cancel_p";
 "----- see  Rational.ML, local cancel_p, fun init_state";
 val t = str2term "(a^^^2 + (-1)*b^^^2) / (a^^^2 + (-2)*a*b + b^^^2)";
-val Some (t',_) = factout_p_ thy t; term2str t';
+val SOME (t',_) = factout_p_ thy t; term2str t';
 (*
-val rtas = reverse_deriv thy eval_rls rules ro None t';
+val rtas = reverse_deriv thy eval_rls rules ro NONE t';
 writeln(trtas2str rst);
 *)
 "----- see  Rational.ML, local cancel_p, fun init_state";
 val t = str2term "a^^^2 / a";
-val Some (t',_) = factout_p_ thy t;
+val SOME (t',_) = factout_p_ thy t;
 term2str t' = "a * a / (1 * a)" (*true*);
 (*... can be canceled with
 real_mult_div_cancel2 ?k ~= 0 ==> ?m * ?k / (?n * ?k) = ?m / ?n"*)
 (* sml/ME/rewtools.sml:
-val rtas = reverse_deriv thy Atools_erls rules ro None t';
+val rtas = reverse_deriv thy Atools_erls rules ro NONE t';
 writeln (deri2str rtas);
 *)
 "-------- SK 060904 ----------------------------------------------";
 "-------- SK 060904 ----------------------------------------------";
 "----- order on polynomials -- input + output";
 val thy = Isac.thy;
 val t = str2term "(a + -1 * b) / (-1 * a + b)";
-val Some (t', _) = factout_p_ thy t; term2str t';
+val SOME (t', _) = factout_p_ thy t; term2str t';
-val Some (t', _) = cancel_p_ thy t; term2str t';
+val SOME (t', _) = cancel_p_ thy t; term2str t';
 val t = str2term "a*b*c*d / (d*e*f*g)";
-val Some (t', _) = cancel_p_ thy t; term2str t';
+val SOME (t', _) = cancel_p_ thy t; term2str t';
 val t = str2term "a*(b*(c*d)) / (b*(e*(f*g)))";
-val Some (t', _) = cancel_p_ thy t; term2str t';
+val SOME (t', _) = cancel_p_ thy t; term2str t';
 (*???order.SK  ???*)
 "----- SK060904-1a non-termination of cancel_p_ ? worked before 0707xx";
 val t = str2term "(x^^^2 - 4)*(3 - y) / ((y^^^2 - 9)*(2+x))";
-val Some (t',_) = rewrite_set_ thy false norm_Rational t;
+val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
 if term2str t' = "(2 + -1 * x) / (3 + y)" then ()
 else raise error "rational.sml SK060904-1a worked since 0707xx";
 "----- SK060904-1b non-termination of cancel_p_ ... worked before 0707xx";
 val t = str2term "(9 * a ^^^ 2 + -16 * b ^^^ 2) /\
 \(36 * a^^^2 * c + (27 * a^^^2 * e + (-64 * b^^^2 * c + -48 * b^^^2 * e)))";
-val Some (t',_) = cancel_p_ thy t;
+val SOME (t',_) = cancel_p_ thy t;
 if term2str t' = "1 / (4 * c + 3 * e)" then ()
 else raise error "rational.sml SK060904-1b";
 "----- SK060904-2a non-termination of add_fraction_p_";
 val t = str2term " (a + b * x) / (a + -1 * (b * x)) +  \
 		 \ (-1 * a + b * x) / (a + b * x)      ";
 (* nonterm.SK
-val Some (t',_) = rewrite_set_ thy false common_nominator_p t;
+val SOME (t',_) = rewrite_set_ thy false common_nominator_p t;
 common_nominator_p_ thy t;
 " (a + b * x)*(a + b * x) / ((a + -1 * (b * x))*(a + -1 * (b * x))) +  \
 \ (-1 * a + b * x)*(a + -1 * (b * x)) / ((a + b * x)*(-1 * a + b * x)) ";

branch	isac-update-Isa09-2
changeset 37926	e6fc98fbcb85
parent 37906	e2b23ba9df13