src/sml/systest/testdaten.sml
branchgriesmayer
changeset 338 90390fecbe74
child 709 f5b966aa0b4e
equal deleted inserted replaced
337:53c9925d2d9c 338:90390fecbe74
       
     1 (* testdaten f"ur isac demo0
       
     2    WN 31.10.00, .., 18.1.01
       
     3    use"tests/testdaten.sml";
       
     4    use"testdaten.sml";
       
     5 
       
     6    proofs:= []; dials:=([],[],[]); 
       
     7   *)
       
     8 " _________________ exampel [x=4]: Rules 4.2.01a________________ ";
       
     9 " _________________ exampel [x=4]: Rules 4.2.01b________________ ";
       
    10 " _________________ exampel [x=4]: tutor active ________________ ";
       
    11 " _________________ exampel [x=4] ________________ ";
       
    12 " _________________ exampel [x =(-12)/5] ________________ ";
       
    13 " _________________ exampel [x =(-12)/5] Auto ________________ ";
       
    14 " ----------------- d_d x (x ^^^ 2 + 3 * x + 4) ----------------- ";
       
    15 " ----------------- d_d x (x ^^^ 2 + x + 1 / x ^^^ 2) ----------------- ";
       
    16 " ----------------- Schalk III S.62 Nr. 51a) --------- ";
       
    17 " ----------------- Schalk III S.144 Nr. 408b) --------- ";
       
    18 " ----------------- Schalk III S.137 Nr. 359g) --------- ";
       
    19 
       
    20 
       
    21 
       
    22 
       
    23 
       
    24 " _________________ exampel [x=4]: Rules 4.2.01a________________ ";
       
    25 " _________________ exampel [x=4]: Rules 4.2.01a________________ ";
       
    26 val (_,uI,0,0,[],[New_User],_) = StdinSML 0 0 0 0 New_User;
       
    27 val (_,_,pI,0,[],[New_Proof],_) = StdinSML uI 0 0 0 New_Proof;
       
    28 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
       
    29 	   "solveFor x","errorBound (eps=0)",
       
    30 	   "solutions L"];
       
    31 val (dI',pI',mI') =
       
    32   ("Test.thy",["squareroot","univariate","equation","test"],
       
    33    ("Test.thy","sqrt-equ-test"));
       
    34 "--- 0 ---";
       
    35 StdinSML uI pI 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
    36 "--- 1 ---";
       
    37 StdinSML uI pI ~1 ~1 (Command Accept);
       
    38 (* square_equation_left 
       
    39 "#9 + #4 * x = (sqrt x + sqrt (#5 + x)) ^^^ #2"*)
       
    40 "--- 2 ---";
       
    41 StdinSML uI pI ~2 ~2 (Command Rules);
       
    42 "--- 3 ---";
       
    43 StdinSML uI pI ~2 ~2 (RuleFK (Rewrite_Set "Test_simplify"));
       
    44 "--- 4 ---";
       
    45 val (_,_,_,_,_,[Error_ _ (*"Error_ Test_simplify not applicable to ..*),
       
    46     Request "apply a rule !"],_) =
       
    47 StdinSML uI pI ~3 ~3 (RuleFK (Rewrite_Set "Test_simplify"));
       
    48 
       
    49 
       
    50 " _________________ exampel [x=4]: Rules 4.2.01b________________ ";
       
    51 " _________________ exampel [x=4]: Rules 4.2.01b________________ ";
       
    52 val (_,uI,0,0,[],[New_User],_) = StdinSML 0 0 0 0 New_User;
       
    53 val (_,_,pI,0,[],[New_Proof],_) = StdinSML uI 0 0 0 New_Proof;
       
    54 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
       
    55 	   "solveFor x","errorBound (eps=0)",
       
    56 	   "solutions L"];
       
    57 val (dI',pI',mI') =
       
    58   ("Test.thy",["squareroot","univariate","equation","test"],
       
    59    ("Test.thy","sqrt-equ-test"));
       
    60 "--- 0 ---";
       
    61 StdinSML uI pI 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
    62 "--- 1 ---";
       
    63 StdinSML uI pI ~1 ~1 (Command Accept);
       
    64 (* square_equation_left 
       
    65 "#9 + #4 * x = (sqrt x + sqrt (#5 + x)) ^^^ #2"*)
       
    66 "--- 2 ---";
       
    67 StdinSML uI pI ~2 ~2 (Command Rules);
       
    68 "--- 3 ---";
       
    69 val (_,_,_,_,_,
       
    70    [Error_ _ (*"Error_ 'square_equation_left' not applicable to: #9 *),
       
    71     Select _, Request "select a rule !"],_) =
       
    72 StdinSML uI pI ~2 ~2 (RuleFK (Rewrite ("square_equation_left","")));
       
    73 
       
    74 
       
    75 " _________________ exampel [x=4]: tutor active ________________ ";
       
    76 " _________________ exampel [x=4]: tutor active ________________ ";
       
    77 val (_,uI,0,0,[],[New_User],_) = StdinSML 0 0 0 0 New_User;
       
    78 val (_,_,pI,0,[],[New_Proof],_) = StdinSML uI 0 0 0 New_Proof;
       
    79 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
       
    80 	   "solveFor x","errorBound (eps=0)",
       
    81 	   "solutions L"];
       
    82 val (dI',pI',mI') =
       
    83   ("Test.thy",["squareroot","univariate","equation","test"],
       
    84    ("Test.thy","sqrt-equ-test"));
       
    85 "--- s1 ---";
       
    86 StdinSML uI pI 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
    87 "--- 1 ---";
       
    88 StdinSML uI pI ~1 ~1 (Command Accept);
       
    89 (* square_equation_left 
       
    90 "#9 + #4 * x = (sqrt x + sqrt (#5 + x)) ^^^ #2"*)
       
    91 "--- 2 ---";
       
    92 StdinSML uI pI ~2 ~2 (Command Accept);
       
    93 (* Test_simplify 
       
    94 "#9 + #4 * x = #5 + (#2 * x + #2 * sqrt (x ^^^ #2 + #5 * x))"*)
       
    95 "--- 3 ---";
       
    96 StdinSML uI pI ~3 ~3 (Command Accept);
       
    97 (* rearrange_assoc 
       
    98 "#9 + #4 * x = #5 + #2 * x + #2 * sqrt (x ^^^ #2 + #5 * x)"*)
       
    99 "--- 4 ---";
       
   100 StdinSML uI pI ~4 ~4 (Command Accept);
       
   101 (* isolate_root 
       
   102 "sqrt (x ^^^ #2 + #5 * x) = (#5 + #2 * x + #-1 * (#9 + #4 * x)) // (#-1 *#2)"*)
       
   103 "--- 5 ---";
       
   104 StdinSML uI pI ~5 ~5 (Command Accept);
       
   105 (* Test_simplify 
       
   106 "sqrt (x ^^^ #2 + #5 * x) = #2 + x"*)
       
   107 "--- 6 ---";
       
   108 StdinSML uI pI ~6 ~6 (Command Accept);
       
   109 (* square_equation_left 
       
   110 "x ^^^ #2 + #5 * x = (#2 + x) ^^^ #2"*)
       
   111 "--- 7 ---";
       
   112 StdinSML uI pI ~7 ~7 (Command Accept);
       
   113 (* Test_simplify 
       
   114 "x ^^^ #2 + #5 * x = #4 + (x ^^^ #2 + #4 * x)"*)
       
   115 "--- 8 ---";
       
   116 StdinSML uI pI ~8 ~8 (Command Accept);
       
   117 (* rearrange_assoc 
       
   118 "x ^^^ #2 + #5 * x = #4 + x ^^^ #2 + #4 * x"*)
       
   119 "--- 9 ---";
       
   120 StdinSML uI pI ~9 ~9 (Command Accept);
       
   121 (* Test_simplify 
       
   122 "x ^^^ #2 + #5 * x = #4 + (x ^^^ #2 + #4 * x)"*)
       
   123 "--- 10 ---";
       
   124 StdinSML uI pI ~10 ~10 (Command Accept);
       
   125 (* norm_equation
       
   126 "x ^^^ #2 + #5 * x + #-1 * (#4 + (x ^^^ #2 + #4 * x)) = #0"*)
       
   127 "--- 11 ---";
       
   128 StdinSML uI pI ~11 ~11 (Command Accept);
       
   129 (* Test_simplify
       
   130  "#-4 + x = #0"*)
       
   131 "--- 12 ---";
       
   132 StdinSML uI pI ~12 ~12 (Command Accept);
       
   133 (* isolate_bdv
       
   134 "x = #0 + #-1 * #-4" *)
       
   135 "--- 13 ---";
       
   136 StdinSML uI pI ~13 ~13 (Command Accept);
       
   137 (* Test_simplify
       
   138 "x = #4" *)
       
   139 "--- 14 ---";
       
   140 StdinSML uI pI ~14 ~14 (Command Accept);
       
   141 val (_,_,1,~14,[],[RuleKF (_,m),FormKF (_,_,_,_,f),Request "Accept ?"],_) = it;
       
   142 if m = Check_Postcond ["squareroot","univariate","equation","test"] 
       
   143    andalso f = "[x = 4]" then () 
       
   144 else raise error "new behaviour in: exampel [x=4]: tutor active";
       
   145 "--- 15 ---";
       
   146 StdinSML uI pI ~15 ~15 (Command Accept);
       
   147 (* Request "start another example"*)
       
   148 
       
   149 (*---- after restruct. kb 18.9.02 ---- (same is in test-FE...)
       
   150 " _________________ exampel [x=4] ________________ ";
       
   151 " _________________ exampel [x=4] ________________ ";
       
   152 proofs:= []; dials:=([],[],[]); 
       
   153 StdinSML 0 0 0 0 New_User;
       
   154 StdinSML 1 0 0 0 New_Proof;
       
   155 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",
       
   156 	   "solveFor x","errorBound (eps=0)",
       
   157 	   "solutions L"];
       
   158 val (dI',pI',mI') =
       
   159   ("Test.thy",["squareroot","univariate","equation","test"],
       
   160    ("Test.thy","sqrt-equ-test"));
       
   161 "--- s1 ---";
       
   162 val (_,1,1,1,[],[_,_,FormKF (_,_,_,_,f),req],_) =
       
   163 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   164 
       
   165 StdinSML 1 1 ~1 ~1 (Command ActivePlus);
       
   166 StdinSML 1 1 ~1 ~1 (Command ActivePlus);
       
   167 StdinSML 1 1 ~1 ~1 (Command ActivePlus);
       
   168 StdinSML 1 1 ~1 ~1 (Command ActivePlus);(*acti=4..SelRule*)
       
   169 
       
   170 "--- !!! x1 --- strange choice"; (* hier nochmals spec !*)
       
   171 StdinSML 1 1 ~1  ~1 (RuleFK (Rewrite_Set "norm_equation"));
       
   172 "--- !!! x2 --- ME knows nxt_step";
       
   173 StdinSML 1 1 ~2  ~2 (RuleFK (Rewrite_Set "Test_simplify"));
       
   174 "--- !!! x3 --- helpless !!!";
       
   175 val (_,_,_,_,_,[FormKF (_,_,_,_,res),_,requ],_) =
       
   176 StdinSML 1 1 ~3  ~3 (RuleFK (Rewrite_Set "rearrange_assoc"));
       
   177 "--- !!! x4 ---";
       
   178 val (_,_,_,_,_,[FormKF (_,_,_,_,res),_,requ],_) =
       
   179 StdinSML 1 1 ~4  ~4 (RuleFK (Rewrite_Set "isolate_root"));
       
   180 "--- !!! x5 --- back at original equation !!!";
       
   181 val (_,_,_,_,_,[FormKF (_,_,_,_,res),_,requ],_) =
       
   182 StdinSML 1 1 ~5   ~5 (RuleFK (Rewrite_Set "Test_simplify"));
       
   183 if res="sqrt (9 + 4 * x) = sqrt x + sqrt (5 + x)"
       
   184 then () else raise error "new behaviour in test-example";
       
   185 "--- !!! x6 --- not applicable";
       
   186 val (_,_,_,_,_,[Error_ err,_,requ],_) =
       
   187 StdinSML 1 1 ~6  ~6 (RuleFK (Rewrite_Set "Test_simplify"));
       
   188 (*val (_,_,_,_,_,[RuleKF r,requ],_) =*)
       
   189 val (_,_,_,_,_,ios,_) =
       
   190 StdinSML 1 1 ~6 ~6 (Command YourTurn);
       
   191 StdinSML 1 1 ~7 ~7 (Command Accept);
       
   192 StdinSML 1 1 ~8 ~8 (Command Accept);
       
   193 StdinSML 1 1 ~9 ~9 (Command Accept);
       
   194 StdinSML 1 1 ~10 ~10 (Command Accept);
       
   195 StdinSML 1 1 ~11 ~11 (Command Accept);
       
   196 StdinSML 1 1 ~12 ~12 (Command Accept);
       
   197 StdinSML 1 1 ~13 ~13 (Command Accept);
       
   198 StdinSML 1 1 ~14 ~14 (Command Accept);
       
   199 StdinSML 1 1 ~15 ~15 (Command Accept);
       
   200 StdinSML 1 1 ~16 ~16 (Command Accept);
       
   201 StdinSML 1 1 ~17 ~17 (Command Accept);
       
   202 StdinSML 1 1 ~18 ~18 (Command Accept);
       
   203 StdinSML 1 1 ~19 ~19 (Command Accept);
       
   204 val (_,1,1,_,[],[FormKF (_,_,_,_,f),Request "Accept ?"],_) = it;
       
   205 if f="[x = 4]" then () else raise error "new behaviour in test-example[x=4]";
       
   206 
       
   207 val (_,1,1,~20,[],[Request "start another example",End_Proof],_) =
       
   208 StdinSML 1 1 ~20 ~20 (Command Accept);
       
   209 -------------------------------------------------------------------*)
       
   210 
       
   211 
       
   212 
       
   213 " _________________ exampel [x =(-12)/5] ________________ ";
       
   214 " _________________ exampel [x =(-12)/5] ________________ ";
       
   215 proofs:= []; dials:=([],[],[]); 
       
   216 StdinSML 0 0 0 0 New_User;
       
   217 StdinSML 1 0 0 0 New_Proof;
       
   218 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(-3+x))",
       
   219 	   "solveFor x","errorBound (eps=0)",
       
   220 	   "solutions L"];
       
   221 val (dI',pI',mI') =
       
   222   ("Test.thy",["squareroot","univariate","equation","test"],
       
   223    ("Test.thy","sqrt-equ-test"));
       
   224 "--- s1 ---";
       
   225 val (_,1,1,1,[],[_,_,FormKF (_,_,_,_,f),req],_) =
       
   226 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   227 
       
   228 StdinSML 1 1 ~1 ~1 (Command SpeedMinus);
       
   229 StdinSML 1 1 ~1 ~1 (Command SpeedMinus);
       
   230 StdinSML 1 1 ~1 ~1 (Command Accept);(*->rule*)
       
   231 StdinSML 1 1 ~1 ~1 (Command Accept);(*->form*)
       
   232 val (_,_,_,_,_,dats,_) =
       
   233 StdinSML 1 1 ~2 ~2 (Command Accept);(*->rule*)
       
   234 StdinSML 1 1 ~2 ~2 (Command Accept);(*->form*)
       
   235 
       
   236 
       
   237 StdinSML 1 1 ~3 ~3 (Command ActivePlus);
       
   238 StdinSML 1 1 ~3 ~3 (Command ActivePlus);(*act=2: SelRule..PutRuleRes,Tt*)
       
   239 StdinSML 1 1 ~3 ~3 (RuleFK (Rewrite_Set "rearrange_assoc"));
       
   240 StdinSML 1 1 ~4 ~4 (Command Accept);
       
   241 StdinSML 1 1 ~4 ~4 (RuleFK (Rewrite_Set "isolate_root"));
       
   242 StdinSML 1 1 ~5 ~5 (Command Accept);
       
   243 StdinSML 1 1 ~5 ~5 (RuleFK (Rewrite_Set "Test_simplify"));
       
   244 StdinSML 1 1 ~6 ~6 (Command Accept);
       
   245 
       
   246 
       
   247 StdinSML 1 1 ~6 ~6 (Command SpeedPlus);
       
   248 StdinSML 1 1 ~6 ~6 (Command SpeedPlus);(*act=2: SelRule..SelRule*)
       
   249 StdinSML 1 1 ~6 ~6 (RuleFK (Rewrite ("square_equation_left","")));
       
   250 StdinSML 1 1 ~7 ~7 (RuleFK (Rewrite_Set "Test_simplify"));
       
   251 StdinSML 1 1 ~8 ~8 (RuleFK (Rewrite_Set "rearrange_assoc"));
       
   252 
       
   253 
       
   254 StdinSML 1 1 ~9 ~9 (Command YourTurn);
       
   255 StdinSML 1 1 ~10 ~10 (Command Accept);
       
   256 StdinSML 1 1 ~11 ~11 (Command Accept);
       
   257 StdinSML 1 1 ~12 ~12 (Command Accept);
       
   258 StdinSML 1 1 ~13 ~13 (Command Accept);
       
   259 StdinSML 1 1 ~14 ~14 (Command Accept);
       
   260 val (_,_,_,_,_,dats,_) =
       
   261 StdinSML 1 1 ~15 ~15 (Command Accept);
       
   262 if dats=[Request "start another example",End_Proof] then () 
       
   263 else raise error "new behaviour in test-example 1: [x =(-12)/5]";
       
   264 
       
   265 
       
   266 " _________________ exampel [x =(-12)/5] Auto ________________ ";
       
   267 " _________________ exampel [x =(-12)/5] Auto ________________ ";
       
   268 proofs:= []; dials:=([],[],[]); 
       
   269 StdinSML 0 0 0 0 New_User;
       
   270 StdinSML 1 0 0 0 New_Proof;
       
   271 val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(-3+x))",
       
   272 	   "solveFor x","errorBound (eps=0)",
       
   273 	   "solutions L"];
       
   274 val (dI',pI',mI') =
       
   275   ("Test.thy",["squareroot","univariate","equation","test"],
       
   276    ("Test.thy","sqrt-equ-test"));
       
   277 val Script sc = (#scr o get_met) ("Test.thy","sqrt-equ-test");
       
   278 writeln(term2str sc);
       
   279 "--- s1 ---";
       
   280 val (_,1,1,1,[],[_,_,FormKF (_,_,_,_,f),req],_) =
       
   281 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   282 
       
   283 val (_,_,_,_,_,dats,_) = StdinSML 1 1 ~1 ~1 (Command Auto);
       
   284 val FormKF (~16,Protect,0,Nundef,res) = 
       
   285     (last_elem o drop_last o drop_last) dats;
       
   286 if res=(*"[]"*)"[x = -12 / 5]" then () 
       
   287 else raise error "new behaviour in test-example 2: [x =(-12)/5]";
       
   288 
       
   289 
       
   290 
       
   291 " ----------------- differentiate ----------------- ";
       
   292 " ----------------- d_d x (x ^^^ 2 + 3 * x + 4) ----------------- ";
       
   293 proofs:= []; dials:=([],[],[]); 
       
   294 StdinSML 0 0 0 0 New_User;
       
   295 StdinSML 1 0 0 0 New_Proof;
       
   296 val fmz = ["functionTerm (d_d x (x ^^^ 2 + 3 * x + 4))", 
       
   297 	   "differentiateFor x","derivative f_'_"];
       
   298 val (dI',pI',mI') =
       
   299   ("Diff.thy",["derivative_of","function"],
       
   300    ("Diff.thy","differentiate_on_R"));
       
   301 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   302 (*FormKF (~10,Protect,0,Nundef,"#3 + #2 * x")*)
       
   303 (* 25.4.01: remove Error with NotAppl
       
   304  StdinSML 1 1 ~1  ~1 (RuleFK (Rewrite_Set "Test_simplify"));  
       
   305  StdinSML 1 1 ~2  ~2 (RuleFK (Rewrite_Inst (["(bdv,x)"],("diff_sum",""))));
       
   306  StdinSML 1 1 ~3  ~3 (RuleFK (Rewrite_Inst (["(bdv,x)"],("diff_const",""))));
       
   307 uncaught exception TYPE ...
       
   308 
       
   309 val uI=1;val pI=1;val acI= ~3;val cI= ~3;
       
   310 val dat=(RuleFK (Rewrite_Inst (["(bdv,x)"],("diff_const",""))));;
       
   311 *)
       
   312 
       
   313 
       
   314 (*18.4.01 tests mit speed*)
       
   315 
       
   316 StdinSML 1 1 ~1 ~1 (Command Accept);
       
   317 	 
       
   318 StdinSML 1 1 ~2 ~2 (Command SpeedPlus);
       
   319 StdinSML 1 1 ~2 ~2 (Command Accept);
       
   320 	 
       
   321 StdinSML 1 1 ~4 ~4 (Command SpeedMinus);
       
   322 StdinSML 1 1 ~4 ~4 (Command Accept);
       
   323 	 
       
   324 StdinSML 1 1 ~5 ~5 (Command Accept);
       
   325 (**)
       
   326 val xxx = StdinSML 1 1 ~6 ~6 (Command Auto);
       
   327 if xxx = ("@@@@@begin@@@@@",1,1,~6,[],
       
   328    [FormKF (~7,Protect,1,Nundef,"2 * x ^^^ (2 - 1) + 3 * d_d x x + 0"),
       
   329     FormKF (~8,Protect,1,Nundef,"2 * x ^^^ (2 - 1) + 3 * 1 + 0"),
       
   330     FormKF (~9,Protect,1,Nundef,"3 + 2 * x"),
       
   331     FormKF (~10,Protect,0,Nundef,"3 + 2 * x"),
       
   332     Request "start another example",End_Proof],"@@@@@end@@@@@")
       
   333 then () else writeln "new behaviour in example d_d x (x ^^^ 2 + 3 * x + 4), SpeedPlus/Minus";
       
   334 
       
   335 
       
   336 " ----------------- d_d x (x ^^^ 2 + x + 1 / x ^^^ 2) ----------------- ";
       
   337 proofs:= []; dials:=([],[],[]); 
       
   338 StdinSML 0 0 0 0 New_User;
       
   339 StdinSML 1 0 0 0 New_Proof;
       
   340 val fmz = ["functionTerm (d_d x (x ^^^ 2 + x + 1 / x ^^^ 2))", 
       
   341 	   "differentiateFor x","derivative f_'_"];
       
   342 val (dI',pI',mI') =
       
   343   ("Diff.thy",["derivative_of","function"],
       
   344    ("Diff.thy","differentiate_on_R"));
       
   345 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   346 StdinSML 1 1 ~1 ~1 (Command Auto);
       
   347 (*FormKF (~12,Protect,0,Nundef,"#1 + (#2 * x + #-2 * x ^^^ #-3)")*)
       
   348 
       
   349 " ----------------- Schalk III S.62 Nr. 34a) --------- ";
       
   350 proofs:= []; dials:=([],[],[]); 
       
   351 StdinSML 0 0 0 0 New_User;
       
   352 StdinSML 1 0 0 0 New_Proof;
       
   353 val fmz = ["functionTerm (d_d x ((5 * x ^^^ 2 - 2) * (7 * x + 1)))", 
       
   354 	   "differentiateFor x","derivative f_'_"];
       
   355 val (dI',pI',mI') =
       
   356   ("Diff.thy",["derivative_of","function"],
       
   357    ("Diff.thy","differentiate_on_R"));
       
   358 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   359 StdinSML 1 1 ~1 ~1 (Command Auto);
       
   360 
       
   361 
       
   362 " ----------------- Schalk III S.62 Nr. 51a) --------- ";
       
   363 proofs:= []; dials:=([],[],[]); 
       
   364 StdinSML 0 0 0 0 New_User;
       
   365 StdinSML 1 0 0 0 New_Proof;
       
   366 val fmz = ["functionTerm (d_d x ((x+1)/(x- 1)))", 
       
   367 	   "differentiateFor x","derivative f_'_"];
       
   368 val (dI',pI',mI') =
       
   369   ("Diff.thy",["derivative_of","function"],
       
   370    ("Diff.thy","differentiate_on_R"));
       
   371 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   372 StdinSML 1 1 ~1 ~1 (Command Auto);
       
   373 (*"#-1 // (#1 + (x ^^^ #2 + #-2 * x)) +\n(x // (#1 + (x ^^^ #2 + #-2 * x)) +\n (#1 + x) * (#-1 // (#1 + (x ^^^ #2 + #-2 * x))))" ----- simplification !?!*)
       
   374 
       
   375 
       
   376 " ----------------- Schalk III S.144 Nr. 408b) --------- ";
       
   377 proofs:= []; dials:=([],[],[]); 
       
   378 StdinSML 0 0 0 0 New_User;
       
   379 StdinSML 1 0 0 0 New_Proof;
       
   380 val fmz = ["functionTerm (d_d x (x ^^^ 2 * (ln ((sin x) ^^^ 2))))", 
       
   381 	   "differentiateFor x","derivative f_'_"];
       
   382 val (dI',pI',mI') =
       
   383   ("Diff.thy",["derivative_of","function"],
       
   384    ("Diff.thy","differentiate_on_R"));
       
   385 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   386 StdinSML 1 1 ~1 ~1 (Command Auto);
       
   387 (*"#2 * (x * ln (sin x ^^^ #2)) +\ncos x * (sin x * (x ^^^ #2 * (#2 // sin x ^^^ #2)))"---- cancel sin x !!!*)
       
   388 
       
   389 
       
   390 " ----------------- Schalk III S.137 Nr. 359g) --------- ";
       
   391 proofs:= []; dials:=([],[],[]); 
       
   392 StdinSML 0 0 0 0 New_User;
       
   393 StdinSML 1 0 0 0 New_Proof;
       
   394 val fmz = ["functionTerm (d_d x (sqrt (cos (3*x))))", 
       
   395 	   "differentiateFor x","derivative f_'_"];
       
   396 val (dI',pI',mI') =
       
   397   ("Diff.thy",["derivative_of","function"],
       
   398    ("Diff.thy","differentiate_on_R"));
       
   399 StdinSML 1 1 1 1 (RuleFK (Init_Proof (fmz,(dI',pI',mI'))));
       
   400 StdinSML 1 1 ~1 ~1 (Command Auto);