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src/Tools/isac/Knowledge/Diff.thy
author Walther Neuper <neuper@ist.tugraz.at>
Wed, 08 Sep 2010 17:17:29 +0200
branchisac-update-Isa09-2
changeset 37993 e4796b1125fb
parent 37991 028442673981
child 38031 460c24a6a6ba
permissions -rw-r--r--
updated Knowledge/Diff.thy 
     1 (* differentiation over the reals

     2    author: Walther Neuper

     3    000516   

     4  *)

     5 

     6 theory Diff imports Calculus Trig LogExp Rational Root Poly Atools begin

     7 

     8 ML {*

     9 @{term "sin x"}

    10 *}

    11 

    12 consts

    13 

    14   d_d           :: "[real, real]=> real"

    15 (*sin, cos      :: "real => real"      already in Isabelle2009-2*)

    16 (*

    17   log, ln       :: "real => real"

    18   nlog          :: "[real, real] => real"

    19   exp           :: "real => real"         ("E'_ ^^^ _" 80)

    20 *)

    21   (*descriptions in the related problems*)

    22   derivativeEq  :: "bool => una"

    23 

    24   (*predicates*)

    25   primed        :: "'a => 'a" (*"primed A" -> "A'"*)

    26 

    27   (*the CAS-commands, eg. "Diff (2*x^^^3, x)", 

    28 			  "Differentiate (A = s * (a - s), s)"*)

    29   Diff           :: "[real * real] => real"

    30   Differentiate  :: "[bool * real] => bool"

    31 

    32   (*subproblem and script-name*)

    33   differentiate  :: "[ID * (ID list) * ID, real,real] => real"

    34                	   ("(differentiate (_)/ (_ _ ))" 9)

    35   DiffScr        :: "[real,real,  real] => real"

    36                    ("((Script DiffScr (_ _ =))// (_))" 9)

    37   DiffEqScr      :: "[bool,real,  bool] => bool"

    38                    ("((Script DiffEqScr (_ _ =))// (_))" 9)

    39 

    40 text {*a variant of the derivatives defintion:

    41 

    42   d_d            :: "(real => real) => (real => real)"

    43 

    44   advantages:

    45 (1) no variable 'bdv' on the meta-level required

    46 (2) chain_rule "d_d (%x. (u (v x))) = (%x. (d_d u)) (v x) * d_d v"

    47 (3) and no specialized chain-rules required like

    48     diff_sin_chain "d_d bdv (sin u)    = cos u * d_d bdv u"

    49 

    50   disadvantage: d_d (%x. 1 + x^2) = ... differs from high-school notation

    51 *}

    52 

    53 axioms (*stated as axioms, todo: prove as theorems

    54         'bdv' is a constant on the meta-level  *)

    55   diff_const:     "[| Not (bdv occurs_in a) |] ==> d_d bdv a = 0"

    56   diff_var:       "d_d bdv bdv = 1"

    57   diff_prod_const:"[| Not (bdv occurs_in u) |] ==>  

    58 					 d_d bdv (u * v) = u * d_d bdv v"

    59 

    60   diff_sum:       "d_d bdv (u + v)     = d_d bdv u + d_d bdv v"

    61   diff_dif:       "d_d bdv (u - v)     = d_d bdv u - d_d bdv v"

    62   diff_prod:      "d_d bdv (u * v)     = d_d bdv u * v + u * d_d bdv v"

    63   diff_quot:      "Not (v = 0) ==> (d_d bdv (u / v) =  

    64 	           (d_d bdv u * v - u * d_d bdv v) / v ^^^ 2)"

    65 

    66   diff_sin:       "d_d bdv (sin bdv)   = cos bdv"

    67   diff_sin_chain: "d_d bdv (sin u)     = cos u * d_d bdv u"

    68   diff_cos:       "d_d bdv (cos bdv)   = - sin bdv"

    69   diff_cos_chain: "d_d bdv (cos u)     = - sin u * d_d bdv u"

    70   diff_pow:       "d_d bdv (bdv ^^^ n) = n * (bdv ^^^ (n - 1))"

    71   diff_pow_chain: "d_d bdv (u ^^^ n)   = n * (u ^^^ (n - 1)) * d_d bdv u"

    72   diff_ln:        "d_d bdv (ln bdv)    = 1 / bdv"

    73   diff_ln_chain:  "d_d bdv (ln u)      = d_d bdv u / u"

    74   diff_exp:       "d_d bdv (exp bdv)   = exp bdv"

    75   diff_exp_chain: "d_d bdv (exp u)     = exp u * d_d x u"

    76 (*

    77   diff_sqrt      "d_d bdv (sqrt bdv)  = 1 / (2 * sqrt bdv)"

    78   diff_sqrt_chain"d_d bdv (sqrt u)    = d_d bdv u / (2 * sqrt u)"

    79 *)

    80   (*...*)

    81 

    82   frac_conv:       "[| bdv occurs_in b; 0 < n |] ==>  

    83 		    a / (b ^^^ n) = a * b ^^^ (-n)"

    84   frac_sym_conv:   "n < 0 ==> a * b ^^^ n = a / b ^^^ (-n)"

    85 

    86   sqrt_conv_bdv:   "sqrt bdv = bdv ^^^ (1 / 2)"

    87   sqrt_conv_bdv_n: "sqrt (bdv ^^^ n) = bdv ^^^ (n / 2)"

    88   sqrt_conv:       "bdv occurs_in u ==> sqrt u = u ^^^ (1 / 2)"

    89   sqrt_sym_conv:   "u ^^^ (a / 2) = sqrt (u ^^^ a)"

    90 

    91   root_conv:       "bdv occurs_in u ==> nroot n u = u ^^^ (1 / n)"

    92   root_sym_conv:   "u ^^^ (a / b) = nroot b (u ^^^ a)"

    93 

    94   realpow_pow_bdv: "(bdv ^^^ b) ^^^ c = bdv ^^^ (b * c)"

    95 

    96 ML {*

    97 val thy = @{theory};

    98 

    99 (** eval functions **)

   100 

   101 fun primed (Const (id, T)) = Const (id ^ "'", T)

   102   | primed (Free (id, T)) = Free (id ^ "'", T)

   103   | primed t = raise error ("primed called with arg = '"^ term2str t ^"'");

   104 

   105 (*("primed", ("Diff.primed", eval_primed "#primed"))*)

   106 fun eval_primed _ _ (p as (Const ("Diff.primed",_) $ t)) _ =

   107     SOME ((term2str p) ^ " = " ^ term2str (primed t),

   108 	  Trueprop $ (mk_equality (p, primed t)))

   109   | eval_primed _ _ _ _ = NONE;

   110 

   111 calclist':= overwritel (!calclist', 

   112    [("primed", ("Diff.primed", eval_primed "#primed"))

   113     ]);

   114 *}

   115 ML {*

   116 (** rulesets **)

   117 

   118 (*.converts a term such that differentiation works optimally.*)

   119 val diff_conv =   

   120     Rls {id="diff_conv", 

   121 	 preconds = [], 

   122 	 rew_ord = ("termlessI",termlessI), 

   123 	 erls = append_rls "erls_diff_conv" e_rls 

   124 			   [Calc ("Atools.occurs'_in", eval_occurs_in ""),

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

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

   127 			    Calc ("op <",eval_equ "#less_"),

   128 			    Thm ("and_true",num_str @{thm and_true}),

   129 			    Thm ("and_false",num_str @{thm and_false})

   130 			    ], 

   131 	 srls = Erls, calc = [],

   132 	 rules = [Thm ("frac_conv", num_str @{thm frac_conv}),

   133 		  Thm ("sqrt_conv_bdv", num_str @{thm sqrt_conv_bdv}),

   134 		  Thm ("sqrt_conv_bdv_n", num_str @{thm sqrt_conv_bdv_n}),

   135 		  Thm ("sqrt_conv", num_str @{thm sqrt_conv}),

   136 		  Thm ("root_conv", num_str @{thm root_conv}),

   137 		  Thm ("realpow_pow_bdv", num_str @{thm realpow_pow_bdv}),

   138 		  Calc ("op *", eval_binop "#mult_"),

   139 		  Thm ("rat_mult",num_str @{thm rat_mult}),

   140 		  (*a / b * (c / d) = a * c / (b * d)*)

   141 		  Thm ("times_divide_eq_right",num_str @{thm times_divide_eq_right}),

   142 		  (*?x * (?y / ?z) = ?x * ?y / ?z*)

   143 		  Thm ("times_divide_eq_left",num_str @{thm times_divide_eq_left})

   144 		  (*?y / ?z * ?x = ?y * ?x / ?z*)

   145 		 ],

   146 	 scr = EmptyScr};

   147 *}

   148 ML {*

   149 (*.beautifies a term after differentiation.*)

   150 val diff_sym_conv =   

   151     Rls {id="diff_sym_conv", 

   152 	 preconds = [], 

   153 	 rew_ord = ("termlessI",termlessI), 

   154 	 erls = append_rls "erls_diff_sym_conv" e_rls 

   155 			   [Calc ("op <",eval_equ "#less_")

   156 			    ], 

   157 	 srls = Erls, calc = [],

   158 	 rules = [Thm ("frac_sym_conv", num_str @{thm frac_sym_conv}),

   159 		  Thm ("sqrt_sym_conv", num_str @{thm sqrt_sym_conv}),

   160 		  Thm ("root_sym_conv", num_str @{thm root_sym_conv}),

   161 		  Thm ("sym_real_mult_minus1",

   162 		       num_str (@{thm real_mult_minus1} RS @{thm sym})),

   163 		      (*- ?z = "-1 * ?z"*)

   164 		  Thm ("rat_mult",num_str @{thm rat_mult}),

   165 		  (*a / b * (c / d) = a * c / (b * d)*)

   166 		  Thm ("times_divide_eq_right",num_str @{thm times_divide_eq_right}),

   167 		  (*?x * (?y / ?z) = ?x * ?y / ?z*)

   168 		  Thm ("times_divide_eq_left",num_str @{thm times_divide_eq_left}),

   169 		  (*?y / ?z * ?x = ?y * ?x / ?z*)

   170 		  Calc ("op *", eval_binop "#mult_")

   171 		 ],

   172 	 scr = EmptyScr};

   173 

   174 (*..*)

   175 val srls_diff = 

   176     Rls {id="srls_differentiate..", 

   177 	 preconds = [], 

   178 	 rew_ord = ("termlessI",termlessI), 

   179 	 erls = e_rls, 

   180 	 srls = Erls, calc = [],

   181 	 rules = [Calc("Tools.lhs", eval_lhs "eval_lhs_"),

   182 		  Calc("Tools.rhs", eval_rhs "eval_rhs_"),

   183 		  Calc("Diff.primed", eval_primed "Diff.primed")

   184 		  ],

   185 	 scr = EmptyScr};

   186 *}

   187 ML {*

   188 (*..*)

   189 val erls_diff = 

   190     append_rls "erls_differentiate.." e_rls

   191                [Thm ("not_true",num_str @{thm not_true}),

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

   193 		

   194 		Calc ("Atools.ident",eval_ident "#ident_"),    

   195 		Calc ("Atools.is'_atom",eval_is_atom "#is_atom_"),

   196 		Calc ("Atools.occurs'_in",eval_occurs_in ""),

   197 		Calc ("Atools.is'_const",eval_const "#is_const_")

   198 		];

   199 

   200 (*.rules for differentiation, _no_ simplification.*)

   201 val diff_rules =

   202     Rls {id="diff_rules", preconds = [], rew_ord = ("termlessI",termlessI), 

   203 	 erls = erls_diff, srls = Erls, calc = [],

   204 	 rules = [Thm ("diff_sum",num_str @{thm diff_sum}),

   205 		  Thm ("diff_dif",num_str @{thm diff_dif}),

   206 		  Thm ("diff_prod_const",num_str @{thm diff_prod_const}),

   207 		  Thm ("diff_prod",num_str @{thm diff_prod}),

   208 		  Thm ("diff_quot",num_str @{thm diff_quot}),

   209 		  Thm ("diff_sin",num_str @{thm diff_sin}),

   210 		  Thm ("diff_sin_chain",num_str @{thm diff_sin_chain}),

   211 		  Thm ("diff_cos",num_str @{thm diff_cos}),

   212 		  Thm ("diff_cos_chain",num_str @{thm diff_cos_chain}),

   213 		  Thm ("diff_pow",num_str @{thm diff_pow}),

   214 		  Thm ("diff_pow_chain",num_str @{thm diff_pow_chain}),

   215 		  Thm ("diff_ln",num_str @{thm diff_ln}),

   216 		  Thm ("diff_ln_chain",num_str @{thm diff_ln_chain}),

   217 		  Thm ("diff_exp",num_str @{thm diff_exp}),

   218 		  Thm ("diff_exp_chain",num_str @{thm diff_exp_chain}),

   219 (*

   220 		  Thm ("diff_sqrt",num_str @{thm diff_sqrt}),

   221 		  Thm ("diff_sqrt_chain",num_str @{thm diff_sqrt_chain}),

   222 *)

   223 		  Thm ("diff_const",num_str @{thm diff_const}),

   224 		  Thm ("diff_var",num_str @{thm diff_var})

   225 		  ],

   226 	 scr = EmptyScr};

   227 *}

   228 ML {*

   229 (*.normalisation for checking user-input.*)

   230 val norm_diff = 

   231     Rls {id="diff_rls", preconds = [], rew_ord = ("termlessI",termlessI), 

   232 	 erls = Erls, srls = Erls, calc = [],

   233 	 rules = [Rls_ diff_rules,

   234 		  Rls_ norm_Poly

   235 		  ],

   236 	 scr = EmptyScr};

   237 ruleset' := 

   238 overwritelthy @{theory} (!ruleset', 

   239 	    [("diff_rules", prep_rls norm_diff),

   240 	     ("norm_diff", prep_rls norm_diff),

   241 	     ("diff_conv", prep_rls diff_conv),

   242 	     ("diff_sym_conv", prep_rls diff_sym_conv)

   243 	     ]);

   244 

   245 *}

   246 ML {*

   247 (** problem types **)

   248 

   249 store_pbt

   250  (prep_pbt thy "pbl_fun" [] e_pblID

   251  (["function"], [], e_rls, NONE, []));

   252 

   253 store_pbt

   254  (prep_pbt thy "pbl_fun_deriv" [] e_pblID

   255  (["derivative_of","function"],

   256   [("#Given" ,["functionTerm f_f","differentiateFor v_v"]),

   257    ("#Find"  ,["derivative f_f'"])

   258   ],

   259   append_rls "e_rls" e_rls [],

   260   SOME "Diff (f_f, v_v)", [["diff","differentiate_on_R"],

   261 			 ["diff","after_simplification"]]));

   262 

   263 (*here "named" is used differently from Integration"*)

   264 store_pbt

   265  (prep_pbt thy "pbl_fun_deriv_nam" [] e_pblID

   266  (["named","derivative_of","function"],

   267   [("#Given" ,["functionEq f_f","differentiateFor v_v"]),

   268    ("#Find"  ,["derivativeEq f_f'"])

   269   ],

   270   append_rls "e_rls" e_rls [],

   271   SOME "Differentiate (f_f, v_v)", [["diff","differentiate_equality"]]));

   272 *}

   273 ML {*

   274 

   275 (** methods **)

   276 

   277 store_met

   278  (prep_met thy "met_diff" [] e_metID

   279  (["diff"], [],

   280    {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,

   281     crls = Atools_erls, nrls = norm_diff}, "empty_script"));

   282 

   283 store_met

   284  (prep_met thy "met_diff_onR" [] e_metID

   285  (["diff","differentiate_on_R"],

   286    [("#Given" ,["functionTerm f_f","differentiateFor v_v"]),

   287     ("#Find"  ,["derivative f_f'"])

   288     ],

   289    {rew_ord'="tless_true", rls' = erls_diff, calc = [], srls = e_rls, 

   290     prls=e_rls, crls = Atools_erls, nrls = norm_diff},

   291 "Script DiffScr (f_f::real) (v_v::real) =                          " ^

   292 " (let f_f' = Take (d_d v_v f_f)                                    " ^

   293 " in (((Try (Rewrite_Set_Inst [(bdv,v_v)] diff_conv False)) @@    " ^

   294 " (Repeat                                                        " ^

   295 "   ((Repeat (Rewrite_Inst [(bdv,v_v)] diff_sum        False)) Or " ^

   296 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_prod_const False)) Or " ^

   297 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_prod       False)) Or " ^

   298 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_quot       True )) Or " ^

   299 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_sin        False)) Or " ^

   300 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_sin_chain  False)) Or " ^

   301 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_cos        False)) Or " ^

   302 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_cos_chain  False)) Or " ^

   303 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_pow        False)) Or " ^

   304 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_pow_chain  False)) Or " ^

   305 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_ln         False)) Or " ^

   306 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_ln_chain   False)) Or " ^

   307 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_exp        False)) Or " ^

   308 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_exp_chain  False)) Or " ^

   309 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_const      False)) Or " ^

   310 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_var        False)) Or " ^

   311 "    (Repeat (Rewrite_Set             make_polynomial False)))) @@ " ^

   312 " (Try (Rewrite_Set_Inst [(bdv,v_v)] diff_sym_conv False)))) f_f')"

   313 ));

   314 *}

   315 ML {*

   316 store_met

   317  (prep_met thy "met_diff_simpl" [] e_metID

   318  (["diff","diff_simpl"],

   319    [("#Given" ,["functionTerm f_f","differentiateFor v_v"]),

   320     ("#Find"  ,["derivative f_f'"])

   321     ],

   322    {rew_ord'="tless_true", rls' = erls_diff, calc = [], srls = e_rls,

   323     prls=e_rls, crls = Atools_erls, nrls = norm_diff},

   324 "Script DiffScr (f_f::real) (v_v::real) =                          " ^

   325 " (let f_f' = Take (d_d v_v f_f)                                    " ^

   326 " in ((     " ^

   327 " (Repeat                                                        " ^

   328 "   ((Repeat (Rewrite_Inst [(bdv,v_v)] diff_sum        False)) Or " ^

   329 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_prod_const False)) Or " ^

   330 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_prod       False)) Or " ^

   331 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_quot       True )) Or " ^

   332 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_sin        False)) Or " ^

   333 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_sin_chain  False)) Or " ^

   334 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_cos        False)) Or " ^

   335 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_cos_chain  False)) Or " ^

   336 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_pow        False)) Or " ^

   337 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_pow_chain  False)) Or " ^

   338 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_ln         False)) Or " ^

   339 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_ln_chain   False)) Or " ^

   340 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_exp        False)) Or " ^

   341 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_exp_chain  False)) Or " ^

   342 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_const      False)) Or " ^

   343 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_var        False)) Or " ^

   344 "    (Repeat (Rewrite_Set             make_polynomial False))))  " ^

   345 " )) f_f')"

   346  ));

   347     

   348 store_met

   349  (prep_met thy "met_diff_equ" [] e_metID

   350  (["diff","differentiate_equality"],

   351    [("#Given" ,["functionEq f_f","differentiateFor v_v"]),

   352    ("#Find"  ,["derivativeEq f_f'"])

   353   ],

   354    {rew_ord'="tless_true", rls' = erls_diff, calc = [], 

   355     srls = srls_diff, prls=e_rls, crls=Atools_erls, nrls = norm_diff},

   356 "Script DiffEqScr (f_f::bool) (v_v::real) =                          " ^

   357 " (let f_f' = Take ((primed (lhs f_f)) = d_d v_v (rhs f_f))            " ^

   358 " in (((Try (Rewrite_Set_Inst [(bdv,v_v)] diff_conv False)) @@      " ^

   359 " (Repeat                                                          " ^

   360 "   ((Repeat (Rewrite_Inst [(bdv,v_v)] diff_sum        False)) Or   " ^

   361 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_dif        False)) Or   " ^

   362 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_prod_const False)) Or   " ^

   363 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_prod       False)) Or   " ^

   364 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_quot       True )) Or   " ^

   365 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_sin        False)) Or   " ^

   366 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_sin_chain  False)) Or   " ^

   367 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_cos        False)) Or   " ^

   368 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_cos_chain  False)) Or   " ^

   369 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_pow        False)) Or   " ^

   370 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_pow_chain  False)) Or   " ^

   371 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_ln         False)) Or   " ^

   372 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_ln_chain   False)) Or   " ^

   373 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_exp        False)) Or   " ^

   374 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_exp_chain  False)) Or   " ^

   375 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_const      False)) Or   " ^

   376 "    (Repeat (Rewrite_Inst [(bdv,v_v)] diff_var        False)) Or   " ^

   377 "    (Repeat (Rewrite_Set             make_polynomial False)))) @@ " ^

   378 " (Try (Rewrite_Set_Inst [(bdv,v_v)] diff_sym_conv False)))) f_f')"

   379 ));

   380 

   381 store_met

   382  (prep_met thy "met_diff_after_simp" [] e_metID

   383  (["diff","after_simplification"],

   384    [("#Given" ,["functionTerm f_f","differentiateFor v_v"]),

   385     ("#Find"  ,["derivative f_f'"])

   386     ],

   387    {rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, prls=e_rls,

   388     crls=Atools_erls, nrls = norm_Rational},

   389 "Script DiffScr (f_f::real) (v_v::real) =                          " ^

   390 " (let f_f' = Take (d_d v_v f_f)                                    " ^

   391 " in ((Try (Rewrite_Set norm_Rational False)) @@                 " ^

   392 "     (Try (Rewrite_Set_Inst [(bdv,v_v)] diff_conv False)) @@     " ^

   393 "     (Try (Rewrite_Set_Inst [(bdv,v_v)] norm_diff False)) @@     " ^

   394 "     (Try (Rewrite_Set_Inst [(bdv,v_v)] diff_sym_conv False)) @@ " ^

   395 "     (Try (Rewrite_Set norm_Rational False))) f_f')"

   396 ));

   397 

   398 

   399 (** CAS-commands **)

   400 

   401 (*.handle cas-input like "Diff (a * x^3 + b, x)".*)

   402 (* val (t, pairl) = strip_comb (str2term "Diff (a * x^3 + b, x)");

   403    val [Const ("Pair", _) $ t $ bdv] = pairl;

   404    *)

   405 fun argl2dtss [Const ("Pair", _) $ t $ bdv] =

   406     [((term_of o the o (parse thy)) "functionTerm", [t]),

   407      ((term_of o the o (parse thy)) "differentiateFor", [bdv]),

   408      ((term_of o the o (parse thy)) "derivative", 

   409       [(term_of o the o (parse thy)) "f_f'"])

   410      ]

   411   | argl2dtss _ = raise error "Diff.ML: wrong argument for argl2dtss";

   412 castab := 

   413 overwritel (!castab, 

   414 	    [((term_of o the o (parse thy)) "Diff",  

   415 	      (("Isac", ["derivative_of","function"], ["no_met"]), 

   416 	       argl2dtss))

   417 	     ]);

   418 

   419 (*.handle cas-input like "Differentiate (A = s * (a - s), s)".*)

   420 (* val (t, pairl) = strip_comb (str2term "Differentiate (A = s * (a - s), s)");

   421    val [Const ("Pair", _) $ t $ bdv] = pairl;

   422    *)

   423 fun argl2dtss [Const ("Pair", _) $ t $ bdv] =

   424     [((term_of o the o (parse thy)) "functionEq", [t]),

   425      ((term_of o the o (parse thy)) "differentiateFor", [bdv]),

   426      ((term_of o the o (parse thy)) "derivativeEq", 

   427       [(term_of o the o (parse thy)) "f_f'::bool"])

   428      ]

   429   | argl2dtss _ = raise error "Diff.ML: wrong argument for argl2dtss";

   430 castab := 

   431 overwritel (!castab, 

   432 	    [((term_of o the o (parse thy)) "Differentiate",  

   433 	      (("Isac", ["named","derivative_of","function"], ["no_met"]), 

   434 	       argl2dtss))

   435 	     ]);

   436 *}

   437 

   438 end
wneuper/isa