neuper@37906: (* integration over the reals neuper@37906: author: Walther Neuper neuper@37906: 050814, 08:51 neuper@37906: (c) due to copyright terms neuper@37906: *) neuper@37906: neuper@37954: theory Integrate imports Diff begin neuper@37906: neuper@37906: consts neuper@37906: neuper@37906: Integral :: "[real, real]=> real" ("Integral _ D _" 91) neuper@37906: (*new'_c :: "real => real" ("new'_c _" 66)*) neuper@37906: is'_f'_x :: "real => bool" ("_ is'_f'_x" 10) neuper@37906: neuper@37906: (*descriptions in the related problems*) neuper@37996: integrateBy :: "real => una" neuper@37996: antiDerivative :: "real => una" neuper@37996: antiDerivativeName :: "(real => real) => una" neuper@37906: neuper@37906: (*the CAS-command, eg. "Integrate (2*x^^^3, x)"*) neuper@37906: Integrate :: "[real * real] => real" neuper@37906: neuper@52148: axiomatization where neuper@37906: (*stated as axioms, todo: prove as theorems neuper@37906: 'bdv' is a constant handled on the meta-level neuper@37906: specifically as a 'bound variable' *) neuper@37906: neuper@52148: integral_const: "Not (bdv occurs_in u) ==> Integral u D bdv = u * bdv" and neuper@52148: integral_var: "Integral bdv D bdv = bdv ^^^ 2 / 2" and neuper@37906: neuper@37983: integral_add: "Integral (u + v) D bdv = neuper@52148: (Integral u D bdv) + (Integral v D bdv)" and neuper@37983: integral_mult: "[| Not (bdv occurs_in u); bdv occurs_in v |] ==> neuper@52148: Integral (u * v) D bdv = u * (Integral v D bdv)" and neuper@37906: (*WN080222: this goes into sub-terms, too ... neuper@37983: call_for_new_c: "[| Not (matches (u + new_c v) a); Not (a is_f_x) |] ==> neuper@37954: a = a + new_c a" neuper@37906: *) neuper@37983: integral_pow: "Integral bdv ^^^ n D bdv = bdv ^^^ (n+1) / (n + 1)" neuper@37906: wneuper@59472: ML \ neuper@37972: val thy = @{theory}; neuper@37972: neuper@37954: (** eval functions **) neuper@37954: neuper@37954: val c = Free ("c", HOLogic.realT); walther@59878: (*.create a new unique variable 'c..' in a term; for use by Rule.Eval in a rls; neuper@37954: an alternative to do this would be '(Try (Calculate new_c_) (new_c es__))' neuper@37954: in the script; this will be possible if currying doesnt take the value neuper@37954: from a variable, but the value '(new_c es__)' itself.*) neuper@37954: fun new_c term = neuper@37954: let fun selc var = neuper@40836: case (Symbol.explode o id_of) var of neuper@37954: "c"::[] => true walther@59875: | "c"::"_"::is => (case (TermC.int_opt_of_string o implode) is of neuper@37954: SOME _ => true neuper@37954: | NONE => false) neuper@37954: | _ => false; neuper@40836: fun get_coeff c = case (Symbol.explode o id_of) c of walther@59875: "c"::"_"::is => (the o TermC.int_opt_of_string o implode) is neuper@37954: | _ => 0; wneuper@59389: val cs = filter selc (TermC.vars term); neuper@37954: in neuper@37954: case cs of neuper@37954: [] => c neuper@37954: | [c] => Free ("c_2", HOLogic.realT) neuper@37954: | cs => neuper@37954: let val max_coeff = maxl (map get_coeff cs) neuper@37954: in Free ("c_"^string_of_int (max_coeff + 1), HOLogic.realT) end neuper@37954: end; neuper@37954: neuper@37954: (*WN080222 neuper@37954: (*("new_c", ("Integrate.new'_c", eval_new_c "#new_c_"))*) neuper@37954: fun eval_new_c _ _ (p as (Const ("Integrate.new'_c",_) $ t)) _ = walther@59868: SOME ((UnparseC.term p) ^ " = " ^ UnparseC.term (new_c p), neuper@37954: Trueprop $ (mk_equality (p, new_c p))) neuper@37954: | eval_new_c _ _ _ _ = NONE; neuper@37954: *) neuper@37954: neuper@37954: (*WN080222:*) neuper@37954: (*("add_new_c", ("Integrate.add'_new'_c", eval_add_new_c "#add_new_c_")) neuper@37954: add a new c to a term or a fun-equation; neuper@37954: this is _not in_ the term, because only applied to _whole_ term*) neuper@37954: fun eval_add_new_c (_:string) "Integrate.add'_new'_c" p (_:theory) = neuper@37954: let val p' = case p of neuper@41922: Const ("HOL.eq", T) $ lh $ rh => wneuper@59389: Const ("HOL.eq", T) $ lh $ TermC.mk_add rh (new_c rh) wneuper@59389: | p => TermC.mk_add p (new_c p) walther@59868: in SOME ((UnparseC.term p) ^ " = " ^ UnparseC.term p', wneuper@59390: HOLogic.Trueprop $ (TermC.mk_equality (p, p'))) neuper@37954: end neuper@37954: | eval_add_new_c _ _ _ _ = NONE; neuper@37954: neuper@37954: neuper@37954: (*("is_f_x", ("Integrate.is'_f'_x", eval_is_f_x "is_f_x_"))*) neuper@37954: fun eval_is_f_x _ _(p as (Const ("Integrate.is'_f'_x", _) neuper@37954: $ arg)) _ = wneuper@59389: if TermC.is_f_x arg walther@59868: then SOME ((UnparseC.term p) ^ " = True", wneuper@59390: HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True}))) walther@59868: else SOME ((UnparseC.term p) ^ " = False", wneuper@59390: HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False}))) neuper@37954: | eval_is_f_x _ _ _ _ = NONE; wneuper@59472: \ wneuper@59472: setup \KEStore_Elems.add_calcs s1210629013@52145: [("add_new_c", ("Integrate.add'_new'_c", eval_add_new_c "add_new_c_")), wneuper@59472: ("is_f_x", ("Integrate.is'_f'_x", eval_is_f_x "is_f_idextifier_"))]\ wneuper@59472: ML \ neuper@37954: (** rulesets **) neuper@37954: neuper@37954: (*.rulesets for integration.*) neuper@37954: val integration_rules = walther@59851: Rule_Def.Repeat {id="integration_rules", preconds = [], neuper@37954: rew_ord = ("termlessI",termlessI), walther@59851: erls = Rule_Def.Repeat {id="conditions_in_integration_rules", neuper@37954: preconds = [], neuper@37954: rew_ord = ("termlessI",termlessI), walther@59851: erls = Rule_Set.Empty, walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], neuper@37954: rules = [(*for rewriting conditions in Thm's*) walther@59878: Rule.Eval ("Prog_Expr.occurs'_in", Prog_Expr.eval_occurs_in "#occurs_in_"), walther@59871: Rule.Thm ("not_true", ThmC.numerals_to_Free @{thm not_true}), wneuper@59416: Rule.Thm ("not_false",@{thm not_false}) neuper@37954: ], walther@59878: scr = Rule.Empty_Prog}, walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], neuper@37954: rules = [ walther@59871: Rule.Thm ("integral_const", ThmC.numerals_to_Free @{thm integral_const}), walther@59871: Rule.Thm ("integral_var", ThmC.numerals_to_Free @{thm integral_var}), walther@59871: Rule.Thm ("integral_add", ThmC.numerals_to_Free @{thm integral_add}), walther@59871: Rule.Thm ("integral_mult", ThmC.numerals_to_Free @{thm integral_mult}), walther@59871: Rule.Thm ("integral_pow", ThmC.numerals_to_Free @{thm integral_pow}), walther@59878: Rule.Eval ("Groups.plus_class.plus", (**)eval_binop "#add_")(*for n+1*) neuper@37954: ], walther@59878: scr = Rule.Empty_Prog}; wneuper@59472: \ wneuper@59472: ML \ neuper@37954: val add_new_c = walther@59878: Rule_Set.Sequence {id="add_new_c", preconds = [], neuper@37954: rew_ord = ("termlessI",termlessI), walther@59851: erls = Rule_Def.Repeat {id="conditions_in_add_new_c", neuper@37954: preconds = [], neuper@37954: rew_ord = ("termlessI",termlessI), walther@59851: erls = Rule_Set.Empty, walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], walther@59878: rules = [Rule.Eval ("Prog_Expr.matches", Prog_Expr.eval_matches""), walther@59878: Rule.Eval ("Integrate.is'_f'_x", neuper@37954: eval_is_f_x "is_f_x_"), walther@59871: Rule.Thm ("not_true", ThmC.numerals_to_Free @{thm not_true}), walther@59871: Rule.Thm ("not_false", ThmC.numerals_to_Free @{thm not_false}) neuper@37954: ], walther@59878: scr = Rule.Empty_Prog}, walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], walther@59871: rules = [ (*Rule.Thm ("call_for_new_c", ThmC.numerals_to_Free @{thm call_for_new_c}),*) wneuper@59416: Rule.Cal1 ("Integrate.add'_new'_c", eval_add_new_c "new_c_") neuper@37954: ], walther@59878: scr = Rule.Empty_Prog}; wneuper@59472: \ wneuper@59472: ML \ neuper@37954: neuper@37954: (*.rulesets for simplifying Integrals.*) neuper@37954: neuper@37954: (*.for simplify_Integral adapted from 'norm_Rational_rls'.*) neuper@37954: val norm_Rational_rls_noadd_fractions = walther@59851: Rule_Def.Repeat {id = "norm_Rational_rls_noadd_fractions", preconds = [], walther@59857: rew_ord = ("dummy_ord",Rewrite_Ord.dummy_ord), walther@59851: erls = norm_rat_erls, srls = Rule_Set.Empty, calc = [], errpatts = [], wneuper@59416: rules = [(*Rule.Rls_ add_fractions_p_rls,!!!*) wneuper@59416: Rule.Rls_ (*rat_mult_div_pow original corrected WN051028*) walther@59851: (Rule_Def.Repeat {id = "rat_mult_div_pow", preconds = [], walther@59857: rew_ord = ("dummy_ord",Rewrite_Ord.dummy_ord), walther@59852: erls = (*FIXME.WN051028 Rule_Set.empty,*) walther@59852: Rule_Set.append_rules "Rule_Set.empty-is_polyexp" Rule_Set.empty walther@59878: [Rule.Eval ("Poly.is'_polyexp", neuper@37954: eval_is_polyexp "")], walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], walther@59871: rules = [Rule.Thm ("rat_mult", ThmC.numerals_to_Free @{thm rat_mult}), neuper@37954: (*"?a / ?b * (?c / ?d) = ?a * ?c / (?b * ?d)"*) walther@59871: Rule.Thm ("rat_mult_poly_l", ThmC.numerals_to_Free @{thm rat_mult_poly_l}), neuper@37954: (*"?c is_polyexp ==> ?c * (?a / ?b) = ?c * ?a / ?b"*) walther@59871: Rule.Thm ("rat_mult_poly_r", ThmC.numerals_to_Free @{thm rat_mult_poly_r}), neuper@37954: (*"?c is_polyexp ==> ?a / ?b * ?c = ?a * ?c / ?b"*) neuper@37954: wneuper@59416: Rule.Thm ("real_divide_divide1_mg", walther@59871: ThmC.numerals_to_Free @{thm real_divide_divide1_mg}), neuper@37954: (*"y ~= 0 ==> (u / v) / (y / z) = (u * z) / (y * v)"*) wneuper@59416: Rule.Thm ("divide_divide_eq_right", walther@59871: ThmC.numerals_to_Free @{thm divide_divide_eq_right}), neuper@37954: (*"?x / (?y / ?z) = ?x * ?z / ?y"*) wneuper@59416: Rule.Thm ("divide_divide_eq_left", walther@59871: ThmC.numerals_to_Free @{thm divide_divide_eq_left}), neuper@37954: (*"?x / ?y / ?z = ?x / (?y * ?z)"*) walther@59878: Rule.Eval ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"), neuper@37954: walther@59871: Rule.Thm ("rat_power", ThmC.numerals_to_Free @{thm rat_power}) neuper@37954: (*"(?a / ?b) ^^^ ?n = ?a ^^^ ?n / ?b ^^^ ?n"*) neuper@37954: ], walther@59878: scr = Rule.Empty_Prog neuper@37954: }), wneuper@59416: Rule.Rls_ make_rat_poly_with_parentheses, wneuper@59416: Rule.Rls_ cancel_p_rls,(*FIXME:cancel_p does NOT order sometimes*) wneuper@59416: Rule.Rls_ rat_reduce_1 neuper@37954: ], walther@59878: scr = Rule.Empty_Prog wneuper@59406: }; neuper@37954: neuper@37954: (*.for simplify_Integral adapted from 'norm_Rational'.*) neuper@37954: val norm_Rational_noadd_fractions = walther@59878: Rule_Set.Sequence {id = "norm_Rational_noadd_fractions", preconds = [], walther@59857: rew_ord = ("dummy_ord",Rewrite_Ord.dummy_ord), walther@59851: erls = norm_rat_erls, srls = Rule_Set.Empty, calc = [], errpatts = [], wneuper@59416: rules = [Rule.Rls_ discard_minus, wneuper@59416: Rule.Rls_ rat_mult_poly,(* removes double fractions like a/b/c *) wneuper@59416: Rule.Rls_ make_rat_poly_with_parentheses, (*WN0510 also in(#)below*) wneuper@59416: Rule.Rls_ cancel_p_rls, (*FIXME.MG:cancel_p does NOT order sometim*) wneuper@59416: Rule.Rls_ norm_Rational_rls_noadd_fractions,(* the main rls (#) *) wneuper@59416: Rule.Rls_ discard_parentheses1 (* mult only *) neuper@37954: ], walther@59878: scr = Rule.Empty_Prog wneuper@59406: }; neuper@37954: neuper@37954: (*.simplify terms before and after Integration such that neuper@37954: ..a.x^2/2 + b.x^3/3.. is made to ..a/2.x^2 + b/3.x^3.. (and NO neuper@37954: common denominator as done by norm_Rational or make_ratpoly_in. neuper@37954: This is a copy from 'make_ratpoly_in' with respective reduction of rules and neuper@37954: *1* expand the term, ie. distribute * and / over + neuper@37954: .*) neuper@37954: val separate_bdv2 = walther@59852: Rule_Set.append_rules "separate_bdv2" neuper@37954: collect_bdv walther@59871: [Rule.Thm ("separate_bdv", ThmC.numerals_to_Free @{thm separate_bdv}), neuper@37954: (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*) walther@59871: Rule.Thm ("separate_bdv_n", ThmC.numerals_to_Free @{thm separate_bdv_n}), walther@59871: Rule.Thm ("separate_1_bdv", ThmC.numerals_to_Free @{thm separate_1_bdv}), neuper@37954: (*"?bdv / ?b = (1 / ?b) * ?bdv"*) walther@59871: Rule.Thm ("separate_1_bdv_n", ThmC.numerals_to_Free @{thm separate_1_bdv_n})(*, neuper@37954: (*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*) wneuper@59416: *****Rule.Thm ("add_divide_distrib", walther@59871: ***** ThmC.numerals_to_Free @{thm add_divide_distrib}) neuper@37954: (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)----------*) neuper@37954: ]; neuper@37954: val simplify_Integral = walther@59878: Rule_Set.Sequence {id = "simplify_Integral", preconds = []:term list, walther@59857: rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), walther@59851: erls = Atools_erls, srls = Rule_Set.Empty, neuper@42451: calc = [], errpatts = [], walther@59871: rules = [Rule.Thm ("distrib_right", ThmC.numerals_to_Free @{thm distrib_right}), neuper@37954: (*"(?z1.0 + ?z2.0) * ?w = ?z1.0 * ?w + ?z2.0 * ?w"*) walther@59871: Rule.Thm ("add_divide_distrib", ThmC.numerals_to_Free @{thm add_divide_distrib}), neuper@37954: (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*) neuper@37954: (*^^^^^ *1* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*) wneuper@59416: Rule.Rls_ norm_Rational_noadd_fractions, wneuper@59416: Rule.Rls_ order_add_mult_in, wneuper@59416: Rule.Rls_ discard_parentheses, wneuper@59416: (*Rule.Rls_ collect_bdv, from make_polynomial_in*) wneuper@59416: Rule.Rls_ separate_bdv2, walther@59878: Rule.Eval ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e") neuper@37954: ], walther@59878: scr = Rule.Empty_Prog}; neuper@37954: neuper@37954: neuper@37954: (*simplify terms before and after Integration such that neuper@37954: ..a.x^2/2 + b.x^3/3.. is made to ..a/2.x^2 + b/3.x^3.. (and NO neuper@37954: common denominator as done by norm_Rational or make_ratpoly_in. neuper@37954: This is a copy from 'make_polynomial_in' with insertions from neuper@37954: 'make_ratpoly_in' neuper@37954: THIS IS KEPT FOR COMPARISON ............................................ s1210629013@55444: * val simplify_Integral = prep_rls'( walther@59878: * Rule_Set.Sequence {id = "", preconds = []:term list, walther@59857: * rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), walther@59851: * erls = Atools_erls, srls = Rule_Set.Empty, neuper@37954: * calc = [], (*asm_thm = [],*) wneuper@59416: * rules = [Rule.Rls_ expand_poly, wneuper@59416: * Rule.Rls_ order_add_mult_in, wneuper@59416: * Rule.Rls_ simplify_power, wneuper@59416: * Rule.Rls_ collect_numerals, wneuper@59416: * Rule.Rls_ reduce_012, walther@59871: * Rule.Thm ("realpow_oneI", ThmC.numerals_to_Free @{thm realpow_oneI}), wneuper@59416: * Rule.Rls_ discard_parentheses, wneuper@59416: * Rule.Rls_ collect_bdv, neuper@37954: * (*below inserted from 'make_ratpoly_in'*) walther@59852: * Rule.Rls_ (Rule_Set.append_rules "separate_bdv" neuper@37954: * collect_bdv walther@59871: * [Rule.Thm ("separate_bdv", ThmC.numerals_to_Free @{thm separate_bdv}), neuper@37954: * (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*) walther@59871: * Rule.Thm ("separate_bdv_n", ThmC.numerals_to_Free @{thm separate_bdv_n}), walther@59871: * Rule.Thm ("separate_1_bdv", ThmC.numerals_to_Free @{thm separate_1_bdv}), neuper@37954: * (*"?bdv / ?b = (1 / ?b) * ?bdv"*) walther@59871: * Rule.Thm ("separate_1_bdv_n", ThmC.numerals_to_Free @{thm separate_1_bdv_n})(*, neuper@37954: * (*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*) wneuper@59416: * Rule.Thm ("add_divide_distrib", walther@59871: * ThmC.numerals_to_Free @{thm add_divide_distrib}) neuper@37954: * (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)*) neuper@37954: * ]), walther@59878: * Rule.Eval ("Rings.divide_class.divide" , eval_cancel "#divide_e") neuper@37954: * ], walther@59878: * scr = Rule.Empty_Prog wneuper@59406: * }); neuper@37954: .......................................................................*) neuper@37954: neuper@37954: val integration = walther@59878: Rule_Set.Sequence {id="integration", preconds = [], neuper@37954: rew_ord = ("termlessI",termlessI), walther@59851: erls = Rule_Def.Repeat {id="conditions_in_integration", neuper@37954: preconds = [], neuper@37954: rew_ord = ("termlessI",termlessI), walther@59851: erls = Rule_Set.Empty, walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], neuper@37954: rules = [], walther@59878: scr = Rule.Empty_Prog}, walther@59851: srls = Rule_Set.Empty, calc = [], errpatts = [], wneuper@59416: rules = [ Rule.Rls_ integration_rules, wneuper@59416: Rule.Rls_ add_new_c, wneuper@59416: Rule.Rls_ simplify_Integral neuper@37954: ], walther@59878: scr = Rule.Empty_Prog}; s1210629013@55444: walther@59618: val prep_rls' = Auto_Prog.prep_rls @{theory}; wneuper@59472: \ wneuper@59472: setup \KEStore_Elems.add_rlss s1210629013@55444: [("integration_rules", (Context.theory_name @{theory}, prep_rls' integration_rules)), s1210629013@55444: ("add_new_c", (Context.theory_name @{theory}, prep_rls' add_new_c)), s1210629013@55444: ("simplify_Integral", (Context.theory_name @{theory}, prep_rls' simplify_Integral)), s1210629013@55444: ("integration", (Context.theory_name @{theory}, prep_rls' integration)), s1210629013@55444: ("separate_bdv2", (Context.theory_name @{theory}, prep_rls' separate_bdv2)), neuper@52125: neuper@52125: ("norm_Rational_noadd_fractions", (Context.theory_name @{theory}, s1210629013@55444: prep_rls' norm_Rational_noadd_fractions)), neuper@52125: ("norm_Rational_rls_noadd_fractions", (Context.theory_name @{theory}, wneuper@59472: prep_rls' norm_Rational_rls_noadd_fractions))]\ neuper@37954: neuper@37954: (** problems **) wneuper@59472: setup \KEStore_Elems.add_pbts walther@59898: [(Specify.prep_pbt thy "pbl_fun_integ" [] Spec.e_pblID s1210629013@55339: (["integrate","function"], s1210629013@55339: [("#Given" ,["functionTerm f_f", "integrateBy v_v"]), s1210629013@55339: ("#Find" ,["antiDerivative F_F"])], walther@59852: Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)], s1210629013@55339: SOME "Integrate (f_f, v_v)", s1210629013@55339: [["diff","integration"]])), s1210629013@55339: (*here "named" is used differently from Differentiation"*) walther@59898: (Specify.prep_pbt thy "pbl_fun_integ_nam" [] Spec.e_pblID s1210629013@55339: (["named","integrate","function"], s1210629013@55339: [("#Given" ,["functionTerm f_f", "integrateBy v_v"]), s1210629013@55339: ("#Find" ,["antiDerivativeName F_F"])], walther@59852: Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)], s1210629013@55339: SOME "Integrate (f_f, v_v)", wneuper@59472: [["diff","integration","named"]]))]\ s1210629013@55380: neuper@37954: (** methods **) wneuper@59545: wneuper@59504: partial_function (tailrec) integrate :: "real \ real \ real" wneuper@59504: where walther@59635: "integrate f_f v_v = ( walther@59635: let walther@59635: t_t = Take (Integral f_f D v_v) walther@59635: in walther@59635: (Rewrite_Set_Inst [(''bdv'', v_v)] ''integration'') t_t)" wneuper@59472: setup \KEStore_Elems.add_mets walther@59898: [Specify.prep_met thy "met_diffint" [] Spec.e_metID s1210629013@55373: (["diff","integration"], s1210629013@55373: [("#Given" ,["functionTerm f_f", "integrateBy v_v"]), ("#Find" ,["antiDerivative F_F"])], walther@59852: {rew_ord'="tless_true", rls'=Atools_erls, calc = [], srls = Rule_Set.empty, prls=Rule_Set.empty, walther@59852: crls = Atools_erls, errpats = [], nrls = Rule_Set.empty}, wneuper@59551: @{thm integrate.simps})] wneuper@59473: \ wneuper@59545: wneuper@59504: partial_function (tailrec) intergrate_named :: "real \ real \ (real \ real) \ bool" walther@59635: where walther@59635: "intergrate_named f_f v_v F_F =( walther@59635: let walther@59635: t_t = Take (F_F v_v = Integral f_f D v_v) walther@59635: in ( walther@59637: (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''simplify_Integral'')) #> walther@59635: (Rewrite_Set_Inst [(''bdv'', v_v)] ''integration'') walther@59635: ) t_t)" wneuper@59473: setup \KEStore_Elems.add_mets walther@59898: [Specify.prep_met thy "met_diffint_named" [] Spec.e_metID s1210629013@55373: (["diff","integration","named"], s1210629013@55373: [("#Given" ,["functionTerm f_f", "integrateBy v_v"]), s1210629013@55373: ("#Find" ,["antiDerivativeName F_F"])], walther@59852: {rew_ord'="tless_true", rls'=Atools_erls, calc = [], srls = Rule_Set.empty, prls=Rule_Set.empty, walther@59852: crls = Atools_erls, errpats = [], nrls = Rule_Set.empty}, wneuper@59551: @{thm intergrate_named.simps})] wneuper@59472: \ neuper@37954: neuper@37906: end