neuper@37906
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(* differentiation over the reals
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author: Walther Neuper
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000516
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*)
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theory Diff imports Calculus Trig LogExp Rational Root Poly Atools begin
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consts
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d_d :: "[real, real]=> real"
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sin, cos :: "real => real"
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(*
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log, ln :: "real => real"
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nlog :: "[real, real] => real"
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exp :: "real => real" ("E'_ ^^^ _" 80)
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*)
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(*descriptions in the related problems*)
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derivativeEq :: bool => una
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(*predicates*)
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primed :: "'a => 'a" (*"primed A" -> "A'"*)
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(*the CAS-commands, eg. "Diff (2*x^^^3, x)",
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"Differentiate (A = s * (a - s), s)"*)
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Diff :: "[real * real] => real"
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Differentiate :: "[bool * real] => bool"
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(*subproblem and script-name*)
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differentiate :: "[ID * (ID list) * ID, real,real] => real"
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("(differentiate (_)/ (_ _ ))" 9)
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DiffScr :: "[real,real, real] => real"
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("((Script DiffScr (_ _ =))// (_))" 9)
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DiffEqScr :: "[bool,real, bool] => bool"
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("((Script DiffEqScr (_ _ =))// (_))" 9)
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text {*a variant of the derivatives defintion:
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d_d :: "(real => real) => (real => real)"
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advantages:
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(1) no variable 'bdv' on the meta-level required
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(2) chain_rule "d_d (%x. (u (v x))) = (%x. (d_d u)) (v x) * d_d v"
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(3) and no specialized chain-rules required like
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diff_sin_chain "d_d bdv (sin u) = cos u * d_d bdv u"
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disadvantage: d_d (%x. 1 + x^2) = ... differs from high-school notation
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*}
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axioms (*stated as axioms, todo: prove as theorems
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'bdv' is a constant on the meta-level *)
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diff_const "[| Not (bdv occurs_in a) |] ==> d_d bdv a = 0"
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diff_var "d_d bdv bdv = 1"
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diff_prod_const"[| Not (bdv occurs_in u) |] ==>
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d_d bdv (u * v) = u * d_d bdv v"
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diff_sum "d_d bdv (u + v) = d_d bdv u + d_d bdv v"
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diff_dif "d_d bdv (u - v) = d_d bdv u - d_d bdv v"
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diff_prod "d_d bdv (u * v) = d_d bdv u * v + u * d_d bdv v"
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diff_quot "Not (v = 0) ==> (d_d bdv (u / v) =
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(d_d bdv u * v - u * d_d bdv v) / v ^^^ 2)"
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diff_sin "d_d bdv (sin bdv) = cos bdv"
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diff_sin_chain "d_d bdv (sin u) = cos u * d_d bdv u"
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diff_cos "d_d bdv (cos bdv) = - sin bdv"
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diff_cos_chain "d_d bdv (cos u) = - sin u * d_d bdv u"
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diff_pow "d_d bdv (bdv ^^^ n) = n * (bdv ^^^ (n - 1))"
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diff_pow_chain "d_d bdv (u ^^^ n) = n * (u ^^^ (n - 1)) * d_d bdv u"
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diff_ln "d_d bdv (ln bdv) = 1 / bdv"
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diff_ln_chain "d_d bdv (ln u) = d_d bdv u / u"
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diff_exp "d_d bdv (exp bdv) = exp bdv"
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diff_exp_chain "d_d bdv (exp u) = exp u * d_d x u"
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(*
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diff_sqrt "d_d bdv (sqrt bdv) = 1 / (2 * sqrt bdv)"
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diff_sqrt_chain"d_d bdv (sqrt u) = d_d bdv u / (2 * sqrt u)"
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*)
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(*...*)
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frac_conv "[| bdv occurs_in b; 0 < n |] ==>
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a / (b ^^^ n) = a * b ^^^ (-n)"
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frac_sym_conv "n < 0 ==> a * b ^^^ n = a / b ^^^ (-n)"
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sqrt_conv_bdv "sqrt bdv = bdv ^^^ (1 / 2)"
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sqrt_conv_bdv_n "sqrt (bdv ^^^ n) = bdv ^^^ (n / 2)"
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sqrt_conv "bdv occurs_in u ==> sqrt u = u ^^^ (1 / 2)"
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sqrt_sym_conv "u ^^^ (a / 2) = sqrt (u ^^^ a)"
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root_conv "bdv occurs_in u ==> nroot n u = u ^^^ (1 / n)"
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root_sym_conv "u ^^^ (a / b) = nroot b (u ^^^ a)"
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realpow_pow_bdv "(bdv ^^^ b) ^^^ c = bdv ^^^ (b * c)"
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ML {*
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(** eval functions **)
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fun primed (Const (id, T)) = Const (id ^ "'", T)
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| primed (Free (id, T)) = Free (id ^ "'", T)
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| primed t = raise error ("primed called with arg = '"^ term2str t ^"'");
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(*("primed", ("Diff.primed", eval_primed "#primed"))*)
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fun eval_primed _ _ (p as (Const ("Diff.primed",_) $ t)) _ =
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SOME ((term2str p) ^ " = " ^ term2str (primed t),
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Trueprop $ (mk_equality (p, primed t)))
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| eval_primed _ _ _ _ = NONE;
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calclist':= overwritel (!calclist',
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[("primed", ("Diff.primed", eval_primed "#primed"))
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]);
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(** rulesets **)
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(*.converts a term such that differentiation works optimally.*)
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val diff_conv =
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Rls {id="diff_conv",
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preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = append_rls "erls_diff_conv" e_rls
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[Calc ("Atools.occurs'_in", eval_occurs_in ""),
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neuper@37966
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Thm ("not_true",num_str @{not_true),
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Thm ("not_false",num_str @{not_false),
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Calc ("op <",eval_equ "#less_"),
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Thm ("and_true",num_str @{and_true),
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Thm ("and_false",num_str @{and_false)
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],
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srls = Erls, calc = [],
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rules = [Thm ("frac_conv", num_str @{frac_conv),
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Thm ("sqrt_conv_bdv", num_str @{sqrt_conv_bdv),
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Thm ("sqrt_conv_bdv_n", num_str @{sqrt_conv_bdv_n),
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Thm ("sqrt_conv", num_str @{sqrt_conv),
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Thm ("root_conv", num_str @{root_conv),
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Thm ("realpow_pow_bdv", num_str @{realpow_pow_bdv),
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Calc ("op *", eval_binop "#mult_"),
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Thm ("rat_mult",num_str @{rat_mult),
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(*a / b * (c / d) = a * c / (b * d)*)
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Thm ("times_divide_eq_right",num_str @{thm times_divide_eq_right}),
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(*?x * (?y / ?z) = ?x * ?y / ?z*)
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Thm ("times_divide_eq_left",num_str @{thm times_divide_eq_left})
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(*?y / ?z * ?x = ?y * ?x / ?z*)
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(*
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Thm ("", num_str @{),*)
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],
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scr = EmptyScr};
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(*.beautifies a term after differentiation.*)
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val diff_sym_conv =
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Rls {id="diff_sym_conv",
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preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = append_rls "erls_diff_sym_conv" e_rls
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[Calc ("op <",eval_equ "#less_")
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],
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srls = Erls, calc = [],
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rules = [Thm ("frac_sym_conv", num_str @{frac_sym_conv),
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Thm ("sqrt_sym_conv", num_str @{sqrt_sym_conv),
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Thm ("root_sym_conv", num_str @{root_sym_conv),
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Thm ("sym_real_mult_minus1",
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num_str @{(real_mult_minus1 RS sym)),
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(*- ?z = "-1 * ?z"*)
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Thm ("rat_mult",num_str @{rat_mult),
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(*a / b * (c / d) = a * c / (b * d)*)
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Thm ("times_divide_eq_right",num_str @{thm times_divide_eq_right}),
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(*?x * (?y / ?z) = ?x * ?y / ?z*)
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Thm ("times_divide_eq_left",num_str @{thm times_divide_eq_left}),
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(*?y / ?z * ?x = ?y * ?x / ?z*)
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Calc ("op *", eval_binop "#mult_")
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],
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scr = EmptyScr};
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(*..*)
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val srls_diff =
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Rls {id="srls_differentiate..",
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preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = e_rls,
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srls = Erls, calc = [],
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rules = [Calc("Tools.lhs", eval_lhs "eval_lhs_"),
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Calc("Tools.rhs", eval_rhs "eval_rhs_"),
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Calc("Diff.primed", eval_primed "Diff.primed")
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],
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scr = EmptyScr};
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(*..*)
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val erls_diff =
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append_rls "erls_differentiate.." e_rls
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[Thm ("not_true",num_str @{not_true),
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Thm ("not_false",num_str @{not_false),
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Calc ("Atools.ident",eval_ident "#ident_"),
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Calc ("Atools.is'_atom",eval_is_atom "#is_atom_"),
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Calc ("Atools.occurs'_in",eval_occurs_in ""),
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Calc ("Atools.is'_const",eval_const "#is_const_")
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];
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(*.rules for differentiation, _no_ simplification.*)
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val diff_rules =
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Rls {id="diff_rules", preconds = [], rew_ord = ("termlessI",termlessI),
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erls = erls_diff, srls = Erls, calc = [],
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rules = [Thm ("diff_sum",num_str @{diff_sum),
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Thm ("diff_dif",num_str @{diff_dif),
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Thm ("diff_prod_const",num_str @{diff_prod_const),
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Thm ("diff_prod",num_str @{diff_prod),
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Thm ("diff_quot",num_str @{diff_quot),
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Thm ("diff_sin",num_str @{diff_sin),
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Thm ("diff_sin_chain",num_str @{diff_sin_chain),
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Thm ("diff_cos",num_str @{diff_cos),
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Thm ("diff_cos_chain",num_str @{diff_cos_chain),
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Thm ("diff_pow",num_str @{diff_pow),
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Thm ("diff_pow_chain",num_str @{diff_pow_chain),
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Thm ("diff_ln",num_str @{diff_ln),
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Thm ("diff_ln_chain",num_str @{diff_ln_chain),
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Thm ("diff_exp",num_str @{diff_exp),
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Thm ("diff_exp_chain",num_str @{diff_exp_chain),
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(*
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Thm ("diff_sqrt",num_str @{diff_sqrt),
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Thm ("diff_sqrt_chain",num_str @{diff_sqrt_chain),
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*)
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Thm ("diff_const",num_str @{diff_const),
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Thm ("diff_var",num_str @{diff_var)
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],
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scr = EmptyScr};
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(*.normalisation for checking user-input.*)
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val norm_diff =
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Rls {id="diff_rls", preconds = [], rew_ord = ("termlessI",termlessI),
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erls = Erls, srls = Erls, calc = [],
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rules = [Rls_ diff_rules,
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Rls_ norm_Poly
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],
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scr = EmptyScr};
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ruleset' :=
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overwritelthy thy (!ruleset',
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[("diff_rules", prep_rls norm_diff),
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("norm_diff", prep_rls norm_diff),
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("diff_conv", prep_rls diff_conv),
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("diff_sym_conv", prep_rls diff_sym_conv)
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]);
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(** problem types **)
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store_pbt
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(prep_pbt (theory "Diff") "pbl_fun" [] e_pblID
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(["function"], [], e_rls, NONE, []));
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neuper@37954
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store_pbt
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neuper@37954
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(prep_pbt (theory "Diff") "pbl_fun_deriv" [] e_pblID
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(["derivative_of","function"],
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neuper@37954
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[("#Given" ,["functionTerm f_","differentiateFor v_"]),
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neuper@37954
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("#Find" ,["derivative f_'_"])
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],
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neuper@37954
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append_rls "e_rls" e_rls [],
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neuper@37954
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SOME "Diff (f_, v_)", [["diff","differentiate_on_R"],
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["diff","after_simplification"]]));
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neuper@37954
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(*here "named" is used differently from Integration"*)
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neuper@37954
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store_pbt
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neuper@37954
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(prep_pbt (theory "Diff") "pbl_fun_deriv_nam" [] e_pblID
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neuper@37954
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(["named","derivative_of","function"],
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neuper@37954
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[("#Given" ,["functionEq f_","differentiateFor v_"]),
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("#Find" ,["derivativeEq f_'_"])
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],
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append_rls "e_rls" e_rls [],
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SOME "Differentiate (f_, v_)", [["diff","differentiate_equality"]]));
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264 |
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265 |
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(** methods **)
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267 |
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store_met
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269 |
(prep_met (theory "Diff") "met_diff" [] e_metID
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(["diff"], [],
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{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
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crls = Atools_erls, nrls = norm_diff}, "empty_script"));
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273 |
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store_met
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(prep_met (theory "Diff") "met_diff_onR" [] e_metID
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(["diff","differentiate_on_R"],
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[("#Given" ,["functionTerm f_","differentiateFor v_"]),
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("#Find" ,["derivative f_'_"])
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],
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{rew_ord'="tless_true", rls' = erls_diff, calc = [], srls = e_rls,
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prls=e_rls, crls = Atools_erls, nrls = norm_diff},
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"Script DiffScr (f_::real) (v_::real) = " ^
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" (let f'_ = Take (d_d v_ f_) " ^
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" in (((Try (Rewrite_Set_Inst [(bdv,v_)] diff_conv False)) @@ " ^
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" (Repeat " ^
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" ((Repeat (Rewrite_Inst [(bdv,v_)] diff_sum False)) Or " ^
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_prod_const False)) Or " ^
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_prod False)) Or " ^
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_quot True )) Or " ^
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_sin False)) Or " ^
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_sin_chain False)) Or " ^
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292 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_cos False)) Or " ^
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293 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_cos_chain False)) Or " ^
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294 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_pow False)) Or " ^
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|
295 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_pow_chain False)) Or " ^
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neuper@37954
|
296 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_ln False)) Or " ^
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|
297 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_ln_chain False)) Or " ^
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|
298 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_exp False)) Or " ^
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|
299 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_exp_chain False)) Or " ^
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|
300 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_const False)) Or " ^
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|
301 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_var False)) Or " ^
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|
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" (Repeat (Rewrite_Set make_polynomial False)))) @@ " ^
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|
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" (Try (Rewrite_Set_Inst [(bdv,v_)] diff_sym_conv False)))) f'_)"
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|
304 |
));
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305 |
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306 |
store_met
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|
307 |
(prep_met (theory "Diff") "met_diff_simpl" [] e_metID
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|
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(["diff","diff_simpl"],
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|
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[("#Given" ,["functionTerm f_","differentiateFor v_"]),
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|
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("#Find" ,["derivative f_'_"])
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|
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],
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|
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{rew_ord'="tless_true", rls' = erls_diff, calc = [], srls = e_rls,
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|
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prls=e_rls, crls = Atools_erls, nrls = norm_diff},
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|
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"Script DiffScr (f_::real) (v_::real) = " ^
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|
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" (let f'_ = Take (d_d v_ f_) " ^
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|
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" in (( " ^
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|
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" (Repeat " ^
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|
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" ((Repeat (Rewrite_Inst [(bdv,v_)] diff_sum False)) Or " ^
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|
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_prod_const False)) Or " ^
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|
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_prod False)) Or " ^
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|
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" (Repeat (Rewrite_Inst [(bdv,v_)] diff_quot True )) Or " ^
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|
322 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_sin False)) Or " ^
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|
323 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_sin_chain False)) Or " ^
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|
324 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_cos False)) Or " ^
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neuper@37954
|
325 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_cos_chain False)) Or " ^
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neuper@37954
|
326 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_pow False)) Or " ^
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neuper@37954
|
327 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_pow_chain False)) Or " ^
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neuper@37954
|
328 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_ln False)) Or " ^
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neuper@37954
|
329 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_ln_chain False)) Or " ^
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neuper@37954
|
330 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_exp False)) Or " ^
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neuper@37954
|
331 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_exp_chain False)) Or " ^
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neuper@37954
|
332 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_const False)) Or " ^
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neuper@37954
|
333 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_var False)) Or " ^
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neuper@37954
|
334 |
" (Repeat (Rewrite_Set make_polynomial False)))) " ^
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|
335 |
" )) f'_)"
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|
336 |
));
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neuper@37954
|
337 |
|
neuper@37954
|
338 |
store_met
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neuper@37954
|
339 |
(prep_met (theory "Diff") "met_diff_equ" [] e_metID
|
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|
340 |
(["diff","differentiate_equality"],
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|
341 |
[("#Given" ,["functionEq f_","differentiateFor v_"]),
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|
342 |
("#Find" ,["derivativeEq f_'_"])
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|
343 |
],
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|
344 |
{rew_ord'="tless_true", rls' = erls_diff, calc = [],
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|
345 |
srls = srls_diff, prls=e_rls, crls=Atools_erls, nrls = norm_diff},
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neuper@37954
|
346 |
"Script DiffEqScr (f_::bool) (v_::real) = " ^
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|
347 |
" (let f'_ = Take ((primed (lhs f_)) = d_d v_ (rhs f_)) " ^
|
neuper@37954
|
348 |
" in (((Try (Rewrite_Set_Inst [(bdv,v_)] diff_conv False)) @@ " ^
|
neuper@37954
|
349 |
" (Repeat " ^
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neuper@37954
|
350 |
" ((Repeat (Rewrite_Inst [(bdv,v_)] diff_sum False)) Or " ^
|
neuper@37954
|
351 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_dif False)) Or " ^
|
neuper@37954
|
352 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_prod_const False)) Or " ^
|
neuper@37954
|
353 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_prod False)) Or " ^
|
neuper@37954
|
354 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_quot True )) Or " ^
|
neuper@37954
|
355 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_sin False)) Or " ^
|
neuper@37954
|
356 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_sin_chain False)) Or " ^
|
neuper@37954
|
357 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_cos False)) Or " ^
|
neuper@37954
|
358 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_cos_chain False)) Or " ^
|
neuper@37954
|
359 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_pow False)) Or " ^
|
neuper@37954
|
360 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_pow_chain False)) Or " ^
|
neuper@37954
|
361 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_ln False)) Or " ^
|
neuper@37954
|
362 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_ln_chain False)) Or " ^
|
neuper@37954
|
363 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_exp False)) Or " ^
|
neuper@37954
|
364 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_exp_chain False)) Or " ^
|
neuper@37954
|
365 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_const False)) Or " ^
|
neuper@37954
|
366 |
" (Repeat (Rewrite_Inst [(bdv,v_)] diff_var False)) Or " ^
|
neuper@37954
|
367 |
" (Repeat (Rewrite_Set make_polynomial False)))) @@ " ^
|
neuper@37954
|
368 |
" (Try (Rewrite_Set_Inst [(bdv,v_)] diff_sym_conv False)))) f'_)"
|
neuper@37954
|
369 |
));
|
neuper@37954
|
370 |
|
neuper@37954
|
371 |
store_met
|
neuper@37954
|
372 |
(prep_met (theory "Diff") "met_diff_after_simp" [] e_metID
|
neuper@37954
|
373 |
(["diff","after_simplification"],
|
neuper@37954
|
374 |
[("#Given" ,["functionTerm f_","differentiateFor v_"]),
|
neuper@37954
|
375 |
("#Find" ,["derivative f_'_"])
|
neuper@37954
|
376 |
],
|
neuper@37954
|
377 |
{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls, prls=e_rls,
|
neuper@37954
|
378 |
crls=Atools_erls, nrls = norm_Rational},
|
neuper@37954
|
379 |
"Script DiffScr (f_::real) (v_::real) = " ^
|
neuper@37954
|
380 |
" (let f'_ = Take (d_d v_ f_) " ^
|
neuper@37954
|
381 |
" in ((Try (Rewrite_Set norm_Rational False)) @@ " ^
|
neuper@37954
|
382 |
" (Try (Rewrite_Set_Inst [(bdv,v_)] diff_conv False)) @@ " ^
|
neuper@37954
|
383 |
" (Try (Rewrite_Set_Inst [(bdv,v_)] norm_diff False)) @@ " ^
|
neuper@37954
|
384 |
" (Try (Rewrite_Set_Inst [(bdv,v_)] diff_sym_conv False)) @@ " ^
|
neuper@37954
|
385 |
" (Try (Rewrite_Set norm_Rational False))) f'_)"
|
neuper@37954
|
386 |
));
|
neuper@37954
|
387 |
|
neuper@37954
|
388 |
|
neuper@37954
|
389 |
(** CAS-commands **)
|
neuper@37954
|
390 |
|
neuper@37954
|
391 |
(*.handle cas-input like "Diff (a * x^3 + b, x)".*)
|
neuper@37954
|
392 |
(* val (t, pairl) = strip_comb (str2term "Diff (a * x^3 + b, x)");
|
neuper@37954
|
393 |
val [Const ("Pair", _) $ t $ bdv] = pairl;
|
neuper@37954
|
394 |
*)
|
neuper@37954
|
395 |
fun argl2dtss [Const ("Pair", _) $ t $ bdv] =
|
neuper@37954
|
396 |
[((term_of o the o (parse thy)) "functionTerm", [t]),
|
neuper@37954
|
397 |
((term_of o the o (parse thy)) "differentiateFor", [bdv]),
|
neuper@37954
|
398 |
((term_of o the o (parse thy)) "derivative",
|
neuper@37954
|
399 |
[(term_of o the o (parse thy)) "f_'_"])
|
neuper@37954
|
400 |
]
|
neuper@37954
|
401 |
| argl2dtss _ = raise error "Diff.ML: wrong argument for argl2dtss";
|
neuper@37954
|
402 |
castab :=
|
neuper@37954
|
403 |
overwritel (!castab,
|
neuper@37954
|
404 |
[((term_of o the o (parse thy)) "Diff",
|
neuper@37954
|
405 |
(("Isac.thy", ["derivative_of","function"], ["no_met"]),
|
neuper@37954
|
406 |
argl2dtss))
|
neuper@37954
|
407 |
]);
|
neuper@37954
|
408 |
|
neuper@37954
|
409 |
(*.handle cas-input like "Differentiate (A = s * (a - s), s)".*)
|
neuper@37954
|
410 |
(* val (t, pairl) = strip_comb (str2term "Differentiate (A = s * (a - s), s)");
|
neuper@37954
|
411 |
val [Const ("Pair", _) $ t $ bdv] = pairl;
|
neuper@37954
|
412 |
*)
|
neuper@37954
|
413 |
fun argl2dtss [Const ("Pair", _) $ t $ bdv] =
|
neuper@37954
|
414 |
[((term_of o the o (parse thy)) "functionEq", [t]),
|
neuper@37954
|
415 |
((term_of o the o (parse thy)) "differentiateFor", [bdv]),
|
neuper@37954
|
416 |
((term_of o the o (parse thy)) "derivativeEq",
|
neuper@37954
|
417 |
[(term_of o the o (parse thy)) "f_'_::bool"])
|
neuper@37954
|
418 |
]
|
neuper@37954
|
419 |
| argl2dtss _ = raise error "Diff.ML: wrong argument for argl2dtss";
|
neuper@37954
|
420 |
castab :=
|
neuper@37954
|
421 |
overwritel (!castab,
|
neuper@37954
|
422 |
[((term_of o the o (parse thy)) "Differentiate",
|
neuper@37954
|
423 |
(("Isac.thy", ["named","derivative_of","function"], ["no_met"]),
|
neuper@37954
|
424 |
argl2dtss))
|
neuper@37954
|
425 |
]);
|
neuper@37954
|
426 |
*}
|
neuper@37954
|
427 |
|
neuper@37906
|
428 |
end
|