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(* chapter 'Biegelinie' from the textbook:
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Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.
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author: Walther Neuper 050826,
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(c) due to copyright terms
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*)
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theory Biegelinie imports Integrate Equation EqSystem Base_Tools begin
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consts
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qq :: "real => real" (* Streckenlast *)
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Q :: "real => real" (* Querkraft *)
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Q' :: "real => real" (* Ableitung der Querkraft *)
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M'_b :: "real => real" ("M'_b") (* Biegemoment *)
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M'_b' :: "real => real" ("M'_b'") (* Ableitung des Biegemoments *)
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y'' :: "real => real" (* 2.Ableitung der Biegeline *)
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y' :: "real => real" (* Neigung der Biegeline *)
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(*y :: "real => real" (* Biegeline *)*)
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EI :: "real" (* Biegesteifigkeit *)
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(*new Descriptions in the related problems*)
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Traegerlaenge :: "real => una"
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Streckenlast :: "real => una"
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BiegemomentVerlauf :: "bool => una"
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Biegelinie :: "(real => real) => una"
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AbleitungBiegelinie :: "(real => real) => una"
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Randbedingungen :: "bool list => una"
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RandbedingungenBiegung :: "bool list => una"
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RandbedingungenNeigung :: "bool list => una"
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RandbedingungenMoment :: "bool list => una"
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RandbedingungenQuerkraft :: "bool list => una"
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FunktionsVariable :: "real => una"
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Funktionen :: "bool list => una"
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Gleichungen :: "bool list => una"
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GleichungsVariablen :: "real list => una"
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(*Script-names*)
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Biegelinie2Script :: "[real, real, real, real => real, real => real, bool list, real list,
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bool] => bool"
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("((Script Biegelinie2Script (_ _ _ _ _ _ _=))// (_))" 9)
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Biege1xIntegrierenScript ::
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"[real,real,real,real=>real,bool list,bool list,bool list,
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bool] => bool"
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("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)
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Belastung2BiegelScript :: "[real,real,real=>real,real=>real,
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bool list] => bool list"
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("((Script Belastung2BiegelScript (_ _ _ _ =))// (_))" 9)
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SetzeRandbedScript :: "[bool list,bool list,
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bool list] => bool list"
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("((Script SetzeRandbedScript (_ _ =))// (_))" 9)
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axiomatization where
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Querkraft_Belastung: "Q' x = -qq x" and
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Belastung_Querkraft: "-qq x = Q' x" and
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Moment_Querkraft: "M_b' x = Q x" and
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Querkraft_Moment: "Q x = M_b' x" and
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Neigung_Moment: "y'' x = -M_b x/ EI" and
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Moment_Neigung: "M_b x = -EI * y'' x" and
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(*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)
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make_fun_explicit: "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"
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setup \<open>
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KEStore_Elems.add_thes
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[make_thy @{theory}
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_isa @{theory} ("IsacKnowledge", "Theorems")
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("Belastung_Querkraft", @{thm Belastung_Querkraft})
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("Moment_Neigung", @{thm Moment_Neigung})
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("Moment_Querkraft", @{thm Moment_Querkraft})
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("Neigung_Moment", @{thm Neigung_Moment})
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("Querkraft_Belastung", @{thm Querkraft_Belastung})
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("Querkraft_Moment", @{thm Querkraft_Moment})
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["Walther Neuper 2005 supported by a grant from NMI Austria"],
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make_thm @{theory} "IsacKnowledge" ("make_fun_explicit", @{thm make_fun_explicit})
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["Walther Neuper 2005 supported by a grant from NMI Austria"]]
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\<close>
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(** problems **)
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setup \<open>KEStore_Elems.add_pbts
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[(Specify.prep_pbt @{theory} "pbl_bieg" [] Celem.e_pblID
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(["Biegelinien"],
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[("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
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(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
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("#Find" ,["Biegelinie b_b"]),
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("#Relate",["Randbedingungen r_b"])],
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Rule.append_rls "e_rls" Rule.e_rls [], NONE, [["IntegrierenUndKonstanteBestimmen2"]])),
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(Specify.prep_pbt @{theory} "pbl_bieg_mom" [] Celem.e_pblID
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(["MomentBestimmte","Biegelinien"],
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[("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
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(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
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("#Find" ,["Biegelinie b_b"]),
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("#Relate",["RandbedingungenBiegung r_b","RandbedingungenMoment r_m"])
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],
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Rule.append_rls "e_rls" Rule.e_rls [], NONE, [["IntegrierenUndKonstanteBestimmen"]])),
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(Specify.prep_pbt @{theory} "pbl_bieg_momg" [] Celem.e_pblID
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(["MomentGegebene","Biegelinien"], [], Rule.append_rls "e_rls" Rule.e_rls [], NONE,
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[["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]])),
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(Specify.prep_pbt @{theory} "pbl_bieg_einf" [] Celem.e_pblID
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(["einfache","Biegelinien"], [], Rule.append_rls "e_rls" Rule.e_rls [], NONE,
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[["IntegrierenUndKonstanteBestimmen","4x4System"]])),
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(Specify.prep_pbt @{theory} "pbl_bieg_momquer" [] Celem.e_pblID
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(["QuerkraftUndMomentBestimmte","Biegelinien"], [], Rule.append_rls "e_rls" Rule.e_rls [], NONE,
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[["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]])),
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(Specify.prep_pbt @{theory} "pbl_bieg_vonq" [] Celem.e_pblID
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(["vonBelastungZu","Biegelinien"],
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[("#Given" ,["Streckenlast q_q","FunktionsVariable v_v"]),
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("#Find" ,["Funktionen funs'''"])],
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Rule.append_rls "e_rls" Rule.e_rls [], NONE, [["Biegelinien","ausBelastung"]])),
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(Specify.prep_pbt @{theory} "pbl_bieg_randbed" [] Celem.e_pblID
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(["setzeRandbedingungen","Biegelinien"],
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[("#Given" ,["Funktionen fun_s","Randbedingungen r_b"]),
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("#Find" ,["Gleichungen equs'''"])],
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Rule.append_rls "e_rls" Rule.e_rls [], NONE, [["Biegelinien","setzeRandbedingungenEin"]])),
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(Specify.prep_pbt @{theory} "pbl_equ_fromfun" [] Celem.e_pblID
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(["makeFunctionTo","equation"],
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[("#Given" ,["functionEq fu_n","substitution su_b"]),
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("#Find" ,["equality equ'''"])],
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Rule.append_rls "e_rls" Rule.e_rls [], NONE, [["Equation","fromFunction"]]))]\<close>
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ML \<open>
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(** methods **)
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val srls = Rule.Rls {id="srls_IntegrierenUnd..",
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preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = Rule.append_rls "erls_in_srls_IntegrierenUnd.." Rule.e_rls
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[(*for asm in NTH_CONS ...*)
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Rule.Calc ("Orderings.ord_class.less",eval_equ "#less_"),
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(*2nd NTH_CONS pushes n+-1 into asms*)
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Rule.Calc("Groups.plus_class.plus", eval_binop "#add_")
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],
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srls = Rule.Erls, calc = [], errpatts = [],
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rules = [Rule.Thm ("NTH_CONS",TermC.num_str @{thm NTH_CONS}),
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Rule.Calc("Groups.plus_class.plus", eval_binop "#add_"),
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Rule.Thm ("NTH_NIL",TermC.num_str @{thm NTH_NIL}),
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Rule.Calc("Tools.lhs", Tools.eval_lhs"eval_lhs_"),
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Rule.Calc("Tools.rhs", Tools.eval_rhs"eval_rhs_"),
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Rule.Calc("Atools.argument'_in",
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eval_argument_in "Atools.argument'_in")
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],
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scr = Rule.EmptyScr};
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val srls2 =
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Rule.Rls {id="srls_IntegrierenUnd..",
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preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = Rule.append_rls "erls_in_srls_IntegrierenUnd.." Rule.e_rls
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[(*for asm in NTH_CONS ...*)
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Rule.Calc ("Orderings.ord_class.less",eval_equ "#less_"),
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(*2nd NTH_CONS pushes n+-1 into asms*)
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Rule.Calc("Groups.plus_class.plus", eval_binop "#add_")
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],
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srls = Rule.Erls, calc = [], errpatts = [],
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rules = [Rule.Thm ("NTH_CONS",TermC.num_str @{thm NTH_CONS}),
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Rule.Calc("Groups.plus_class.plus", eval_binop "#add_"),
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Rule.Thm ("NTH_NIL", TermC.num_str @{thm NTH_NIL}),
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Rule.Calc("Tools.lhs", Tools.eval_lhs "eval_lhs_"),
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Rule.Calc("Atools.filter'_sameFunId",
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eval_filter_sameFunId "Atools.filter'_sameFunId"),
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(*WN070514 just for smltest/../biegelinie.sml ...*)
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Rule.Calc("Atools.sameFunId", eval_sameFunId "Atools.sameFunId"),
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Rule.Thm ("filter_Cons", TermC.num_str @{thm filter_Cons}),
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Rule.Thm ("filter_Nil", TermC.num_str @{thm filter_Nil}),
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Rule.Thm ("if_True", TermC.num_str @{thm if_True}),
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Rule.Thm ("if_False", TermC.num_str @{thm if_False}),
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Rule.Thm ("hd_thm", TermC.num_str @{thm hd_thm})
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],
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scr = Rule.EmptyScr};
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\<close>
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section \<open>Methods\<close>
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(* setup parent directory *)
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setup \<open>KEStore_Elems.add_mets
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[Specify.prep_met @{theory} "met_biege" [] Celem.e_metID
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(["IntegrierenUndKonstanteBestimmen"], [],
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{rew_ord'="tless_true", rls'= Rule.Erls, calc = [], srls = Rule.Erls, prls = Rule.Erls, crls =Rule.Erls,
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errpats = [], nrls = Rule.Erls},
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@{thm refl})]
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\<close>
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subsection \<open>Sub-problem "integrate and determine constants", nicely modularised\<close>
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partial_function (tailrec) biegelinie :: "real \<Rightarrow> real \<Rightarrow> real \<Rightarrow> (real \<Rightarrow> real) \<Rightarrow> bool list \<Rightarrow> real list \<Rightarrow> bool"
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where
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"biegelinie l q v b s vs =
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(let
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funs = SubProblem (''Biegelinie'', [''vonBelastungZu'', ''Biegelinien''],
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[''Biegelinien'', ''ausBelastung'']) [REAL q, REAL v]; \<comment> \<open>PROG +args\<close>
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equs = SubProblem (''Biegelinie'', [''setzeRandbedingungen'', ''Biegelinien''],
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[''Biegelinien'', ''setzeRandbedingungenEin'']) [BOOL_LIST funs, BOOL_LIST s];
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cons = SubProblem (''Biegelinie'', [''LINEAR'', ''system''], [''no_met''])
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[BOOL_LIST equs, REAL_LIST vs]; \<comment> \<open>PROG consts\<close>
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B = Take (lastI funs);
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B = ((Substitute cons) @@ (Rewrite_Set_Inst [(''bdv'', v)] ''make_ratpoly_in'' False)) B
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in B)"
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setup \<open>KEStore_Elems.add_mets
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[Specify.prep_met @{theory} "met_biege_2" [] Celem.e_metID
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(["IntegrierenUndKonstanteBestimmen2"],
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[("#Given" ,["Traegerlaenge l", "Streckenlast q",
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"FunktionsVariable v", "GleichungsVariablen vs", "AbleitungBiegelinie id_abl"]),
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(*("#Where",["0 < l"]), ...wait for < and handling Arbfix*)
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("#Find" ,["Biegelinie b"]),
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("#Relate",["Randbedingungen s"])],
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{rew_ord'="tless_true",
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rls' = Rule.append_rls "erls_IntegrierenUndK.." Rule.e_rls
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[Rule.Calc ("Atools.ident",eval_ident "#ident_"),
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Rule.Thm ("not_true",TermC.num_str @{thm not_true}),
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Rule.Thm ("not_false",TermC.num_str @{thm not_false})],
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calc = [],
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srls = Rule.append_rls "erls_IntegrierenUndK.." Rule.e_rls
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[Rule.Calc("Tools.rhs", Tools.eval_rhs"eval_rhs_"),
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Rule.Calc ("Atools.ident",eval_ident "#ident_"),
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Rule.Thm ("last_thmI",TermC.num_str @{thm last_thmI}),
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Rule.Thm ("if_True",TermC.num_str @{thm if_True}),
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Rule.Thm ("if_False",TermC.num_str @{thm if_False})],
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|
224 |
prls = Rule.Erls, crls = Atools_erls, errpats = [], nrls = Rule.Erls},
|
wneuper@59545
|
225 |
@{thm biegelinie.simps}
|
wneuper@59545
|
226 |
(*""Script Biegelinie2Script " ^
|
wneuper@59540
|
227 |
"(l::real) (q :: real) (v :: real) (id_abl::real\<Rightarrow>real) (b :: real => real) (s :: bool list) (vs :: real list) = " ^
|
wneuper@59504
|
228 |
" (let " ^
|
wneuper@59540
|
229 |
" (funs :: bool list) = (SubProblem (''Biegelinie'', " ^
|
wneuper@59540
|
230 |
" [''vonBelastungZu'', ''Biegelinien''], [''Biegelinien'', ''ausBelastung'']) " ^
|
wneuper@59540
|
231 |
" [REAL q, REAL v, REAL_REAL b, REAL_REAL id_abl]); " ^
|
wneuper@59540
|
232 |
" (equs :: bool list) = (SubProblem (''Biegelinie'', " ^
|
wneuper@59489
|
233 |
" [''setzeRandbedingungen'', ''Biegelinien''], [''Biegelinien'', ''setzeRandbedingungenEin'']) " ^
|
wneuper@59504
|
234 |
" [BOOL_LIST funs, BOOL_LIST s]); " ^
|
wneuper@59540
|
235 |
" (cons :: bool list) = (SubProblem (''Biegelinie'', " ^
|
wneuper@59540
|
236 |
" [''LINEAR'', ''system''], [''no_met'']) " ^
|
wneuper@59540
|
237 |
" [BOOL_LIST equs, REAL_LIST vs]); " ^
|
wneuper@59504
|
238 |
" B = Take (lastI funs); " ^
|
wneuper@59504
|
239 |
" B = ((Substitute cons) @@ " ^
|
wneuper@59540
|
240 |
" (Rewrite_Set_Inst [(''bdv'', v)] ''make_ratpoly_in'' False)) B " ^
|
wneuper@59545
|
241 |
" in B) "*))]
|
wneuper@59473
|
242 |
\<close>
|
wneuper@59473
|
243 |
setup \<open>KEStore_Elems.add_mets
|
wneuper@59473
|
244 |
[Specify.prep_met @{theory} "met_biege_intconst_2" [] Celem.e_metID
|
s1210629013@55373
|
245 |
(["IntegrierenUndKonstanteBestimmen","2xIntegrieren"], [],
|
wneuper@59416
|
246 |
{rew_ord'="tless_true", rls'=Rule.Erls, calc = [], srls = Rule.e_rls, prls=Rule.e_rls, crls = Atools_erls,
|
wneuper@59416
|
247 |
errpats = [], nrls = Rule.e_rls},
|
wneuper@59545
|
248 |
@{thm refl}),
|
wneuper@59406
|
249 |
Specify.prep_met @{theory} "met_biege_intconst_4" [] Celem.e_metID
|
s1210629013@55373
|
250 |
(["IntegrierenUndKonstanteBestimmen","4x4System"], [],
|
wneuper@59416
|
251 |
{rew_ord'="tless_true", rls'=Rule.Erls, calc = [], srls = Rule.e_rls, prls=Rule.e_rls, crls = Atools_erls,
|
wneuper@59416
|
252 |
errpats = [], nrls = Rule.e_rls},
|
wneuper@59545
|
253 |
@{thm refl}),
|
wneuper@59406
|
254 |
Specify.prep_met @{theory} "met_biege_intconst_1" [] Celem.e_metID
|
s1210629013@55373
|
255 |
(["IntegrierenUndKonstanteBestimmen","1xIntegrieren"], [],
|
wneuper@59416
|
256 |
{rew_ord'="tless_true", rls'=Rule.Erls, calc = [], srls = Rule.e_rls, prls=Rule.e_rls, crls = Atools_erls,
|
wneuper@59416
|
257 |
errpats = [], nrls = Rule.e_rls},
|
wneuper@59545
|
258 |
@{thm refl}),
|
wneuper@59406
|
259 |
Specify.prep_met @{theory} "met_biege2" [] Celem.e_metID
|
s1210629013@55373
|
260 |
(["Biegelinien"], [],
|
wneuper@59416
|
261 |
{rew_ord'="tless_true", rls'=Rule.Erls, calc = [], srls = Rule.e_rls, prls=Rule.e_rls, crls = Atools_erls,
|
wneuper@59416
|
262 |
errpats = [], nrls = Rule.e_rls},
|
wneuper@59545
|
263 |
@{thm refl})]
|
wneuper@59472
|
264 |
\<close>
|
wneuper@59429
|
265 |
subsection \<open>Compute the general bending line\<close>
|
wneuper@59429
|
266 |
|
wneuper@59544
|
267 |
partial_function (tailrec) belastung_zu_biegelinie :: "real \<Rightarrow> real \<Rightarrow> (real \<Rightarrow> real) \<Rightarrow> (real \<Rightarrow> real) \<Rightarrow> bool list"
|
wneuper@59504
|
268 |
where
|
wneuper@59544
|
269 |
"belastung_zu_biegelinie q__q v_v id_fun id_abl =
|
wneuper@59504
|
270 |
(let q___q = Take (qq v_v = q__q);
|
wneuper@59504
|
271 |
q___q = ((Rewrite ''sym_neg_equal_iff_equal'' True) @@
|
wneuper@59504
|
272 |
(Rewrite ''Belastung_Querkraft'' True)) q___q;
|
wneuper@59504
|
273 |
Q__Q = SubProblem (''Biegelinie'', [''named'', ''integrate'', ''function''],
|
wneuper@59504
|
274 |
[''diff'', ''integration'', ''named'']) [REAL (rhs q___q), REAL v_v, REAL_REAL Q];
|
wneuper@59504
|
275 |
M__M = Rewrite ''Querkraft_Moment'' True Q__Q;
|
wneuper@59504
|
276 |
M__M = SubProblem (''Biegelinie'', [''named'', ''integrate'', ''function''],
|
wneuper@59504
|
277 |
[''diff'', ''integration'', ''named'']) [REAL (rhs M__M), REAL v_v, REAL_REAL M_b];
|
wneuper@59504
|
278 |
N__N = ((Rewrite ''Moment_Neigung'' False) @@
|
wneuper@59504
|
279 |
(Rewrite ''make_fun_explicit'' False)) M__M;
|
wneuper@59504
|
280 |
N__N = SubProblem (''Biegelinie'', [''named'', ''integrate'', ''function''],
|
wneuper@59504
|
281 |
[''diff'', ''integration'', ''named''])
|
wneuper@59544
|
282 |
[REAL (rhs N__N), REAL v_v, REAL_REAL id_abl]; \<comment> \<open>PROG string\<close>
|
wneuper@59504
|
283 |
B__B = SubProblem (''Biegelinie'', [''named'', ''integrate'', ''function''],
|
wneuper@59504
|
284 |
[''diff'', ''integration'', ''named''])
|
wneuper@59544
|
285 |
[REAL (rhs N__N), REAL v_v, REAL_REAL id_fun] \<comment> \<open>PROG string\<close>
|
wneuper@59504
|
286 |
in [Q__Q, M__M, N__N, B__B])"
|
wneuper@59472
|
287 |
setup \<open>KEStore_Elems.add_mets
|
wneuper@59473
|
288 |
[Specify.prep_met @{theory} "met_biege_ausbelast" [] Celem.e_metID
|
s1210629013@55373
|
289 |
(["Biegelinien", "ausBelastung"],
|
wneuper@59540
|
290 |
[("#Given" ,["Streckenlast q__q", "FunktionsVariable v_v",
|
wneuper@59540
|
291 |
"Biegelinie id_fun", "AbleitungBiegelinie id_abl"]),
|
wneuper@59540
|
292 |
("#Find" ,["Funktionen fun_s"])],
|
s1210629013@55373
|
293 |
{rew_ord'="tless_true",
|
wneuper@59416
|
294 |
rls' = Rule.append_rls "erls_ausBelastung" Rule.e_rls
|
wneuper@59416
|
295 |
[Rule.Calc ("Atools.ident", eval_ident "#ident_"),
|
wneuper@59416
|
296 |
Rule.Thm ("not_true", TermC.num_str @{thm not_true}),
|
wneuper@59416
|
297 |
Rule.Thm ("not_false", TermC.num_str @{thm not_false})],
|
s1210629013@55373
|
298 |
calc = [],
|
wneuper@59416
|
299 |
srls = Rule.append_rls "srls_ausBelastung" Rule.e_rls
|
wneuper@59491
|
300 |
[Rule.Calc ("Tools.rhs", Tools.eval_rhs "eval_rhs_")],
|
wneuper@59416
|
301 |
prls = Rule.e_rls, crls = Atools_erls, errpats = [], nrls = Rule.e_rls},
|
wneuper@59545
|
302 |
@{thm belastung_zu_biegelinie.simps}
|
wneuper@59545
|
303 |
(*"Script Belastung2BiegelScript (q__q::real) (v_v::real) (id_fun::real\<Rightarrow>real) (id_abl::real\<Rightarrow>real) = " ^
|
wneuper@59540
|
304 |
" (let q___q = Take (qq v_v = q__q); " ^
|
wneuper@59540
|
305 |
" q___q = ((Rewrite ''sym_neg_equal_iff_equal'' True) @@ " ^
|
wneuper@59540
|
306 |
" (Rewrite ''Belastung_Querkraft'' True)) q___q; " ^
|
wneuper@59540
|
307 |
" (Q__Q:: bool) = " ^
|
wneuper@59540
|
308 |
" (SubProblem (''Biegelinie'',[''named'',''integrate'',''function''], " ^
|
wneuper@59540
|
309 |
" [''diff'',''integration'',''named'']) " ^
|
wneuper@59540
|
310 |
" [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
|
wneuper@59540
|
311 |
" M__M = Rewrite ''Querkraft_Moment'' True Q__Q; " ^
|
wneuper@59540
|
312 |
" (M__M::bool) = " ^
|
wneuper@59540
|
313 |
" (SubProblem (''Biegelinie'',[''named'',''integrate'',''function''], " ^
|
wneuper@59540
|
314 |
" [''diff'',''integration'',''named'']) " ^
|
wneuper@59540
|
315 |
" [REAL (rhs M__M), REAL v_v, REAL_REAL M_b]); " ^
|
wneuper@59540
|
316 |
" N__N = ((Rewrite ''Moment_Neigung'' False) @@ " ^
|
wneuper@59540
|
317 |
" (Rewrite ''make_fun_explicit'' False)) M__M; " ^
|
wneuper@59540
|
318 |
" (N__N:: bool) = " ^
|
wneuper@59540
|
319 |
" (SubProblem (''Biegelinie'',[''named'',''integrate'',''function''], " ^
|
wneuper@59498
|
320 |
" [''diff'',''integration'', ''named'']) " ^
|
wneuper@59540
|
321 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL id_abl]); " ^
|
wneuper@59540
|
322 |
" (B__B:: bool) = " ^
|
wneuper@59540
|
323 |
" (SubProblem (''Biegelinie'',[''named'',''integrate'',''function''], " ^
|
wneuper@59540
|
324 |
" [''diff'',''integration'',''named'']) " ^
|
wneuper@59540
|
325 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL id_fun]) " ^
|
wneuper@59545
|
326 |
" in [Q__Q, M__M, N__N, B__B]) "*))]
|
wneuper@59472
|
327 |
\<close>
|
wneuper@59429
|
328 |
subsection \<open>Substitute the constraints into the equations\<close>
|
wneuper@59429
|
329 |
|
wneuper@59504
|
330 |
partial_function (tailrec) setzte_randbedingungen :: "bool list \<Rightarrow> bool list \<Rightarrow> bool list"
|
wneuper@59504
|
331 |
where
|
wneuper@59504
|
332 |
"setzte_randbedingungen fun_s r_b =
|
wneuper@59504
|
333 |
(let b_1 = NTH 1 r_b;
|
wneuper@59504
|
334 |
f_s = filter_sameFunId (lhs b_1) fun_s;
|
wneuper@59504
|
335 |
e_1 = SubProblem (''Biegelinie'', [''makeFunctionTo'', ''equation''],
|
wneuper@59504
|
336 |
[''Equation'', ''fromFunction'']) [BOOL (hd f_s), BOOL b_1];
|
wneuper@59504
|
337 |
b_2 = NTH 2 r_b;
|
wneuper@59504
|
338 |
f_s = filter_sameFunId (lhs b_2) fun_s;
|
wneuper@59504
|
339 |
e_2 = SubProblem (''Biegelinie'', [''makeFunctionTo'', ''equation''],
|
wneuper@59504
|
340 |
[''Equation'', ''fromFunction'']) [BOOL (hd f_s), BOOL b_2];
|
wneuper@59504
|
341 |
b_3 = NTH 3 r_b;
|
wneuper@59504
|
342 |
f_s = filter_sameFunId (lhs b_3) fun_s;
|
wneuper@59504
|
343 |
e_3 = SubProblem (''Biegelinie'', [''makeFunctionTo'', ''equation''],
|
wneuper@59504
|
344 |
[''Equation'', ''fromFunction'']) [BOOL (hd f_s), BOOL b_3];
|
wneuper@59504
|
345 |
b_4 = NTH 4 r_b;
|
wneuper@59504
|
346 |
f_s = filter_sameFunId (lhs b_4) fun_s;
|
wneuper@59504
|
347 |
e_4 = SubProblem (''Biegelinie'', [''makeFunctionTo'', ''equation''],
|
wneuper@59504
|
348 |
[''Equation'', ''fromFunction'']) [BOOL (hd f_s), BOOL b_4]
|
wneuper@59504
|
349 |
in [e_1, e_2, e_3, e_4])"
|
wneuper@59472
|
350 |
setup \<open>KEStore_Elems.add_mets
|
wneuper@59473
|
351 |
[Specify.prep_met @{theory} "met_biege_setzrand" [] Celem.e_metID
|
s1210629013@55373
|
352 |
(["Biegelinien", "setzeRandbedingungenEin"],
|
s1210629013@55373
|
353 |
[("#Given" , ["Funktionen fun_s", "Randbedingungen r_b"]),
|
s1210629013@55373
|
354 |
("#Find" , ["Gleichungen equs'''"])],
|
wneuper@59416
|
355 |
{rew_ord'="tless_true", rls'=Rule.Erls, calc = [], srls = srls2, prls=Rule.e_rls, crls = Atools_erls,
|
wneuper@59416
|
356 |
errpats = [], nrls = Rule.e_rls},
|
wneuper@59545
|
357 |
@{thm setzte_randbedingungen.simps}
|
wneuper@59545
|
358 |
(*"Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
|
s1210629013@55373
|
359 |
" (let b_1 = NTH 1 r_b; " ^
|
s1210629013@55373
|
360 |
" f_s = filter_sameFunId (lhs b_1) fun_s; " ^
|
s1210629013@55373
|
361 |
" (e_1::bool) = " ^
|
wneuper@59489
|
362 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
363 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
364 |
" [BOOL (hd f_s), BOOL b_1]); " ^
|
s1210629013@55373
|
365 |
" b_2 = NTH 2 r_b; " ^
|
s1210629013@55373
|
366 |
" f_s = filter_sameFunId (lhs b_2) fun_s; " ^
|
s1210629013@55373
|
367 |
" (e_2::bool) = " ^
|
wneuper@59489
|
368 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
369 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
370 |
" [BOOL (hd f_s), BOOL b_2]); " ^
|
s1210629013@55373
|
371 |
" b_3 = NTH 3 r_b; " ^
|
s1210629013@55373
|
372 |
" f_s = filter_sameFunId (lhs b_3) fun_s; " ^
|
s1210629013@55373
|
373 |
" (e_3::bool) = " ^
|
wneuper@59489
|
374 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
375 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
376 |
" [BOOL (hd f_s), BOOL b_3]); " ^
|
s1210629013@55373
|
377 |
" b_4 = NTH 4 r_b; " ^
|
s1210629013@55373
|
378 |
" f_s = filter_sameFunId (lhs b_4) fun_s; " ^
|
s1210629013@55373
|
379 |
" (e_4::bool) = " ^
|
wneuper@59489
|
380 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
381 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
382 |
" [BOOL (hd f_s), BOOL b_4]) " ^
|
wneuper@59545
|
383 |
" in [e_1, e_2, e_3, e_4])"*)
|
s1210629013@55373
|
384 |
(* filter requires more than 1 sec !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
s1210629013@55373
|
385 |
"Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
|
s1210629013@55373
|
386 |
" (let b_1 = NTH 1 r_b; " ^
|
s1210629013@55373
|
387 |
" f_s = filter (sameFunId (lhs b_1)) fun_s; " ^
|
s1210629013@55373
|
388 |
" (e_1::bool) = " ^
|
wneuper@59489
|
389 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
390 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
391 |
" [BOOL (hd f_s), BOOL b_1]); " ^
|
s1210629013@55373
|
392 |
" b_2 = NTH 2 r_b; " ^
|
s1210629013@55373
|
393 |
" f_s = filter (sameFunId (lhs b_2)) fun_s; " ^
|
s1210629013@55373
|
394 |
" (e_2::bool) = " ^
|
wneuper@59489
|
395 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
396 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
397 |
" [BOOL (hd f_s), BOOL b_2]); " ^
|
s1210629013@55373
|
398 |
" b_3 = NTH 3 r_b; " ^
|
s1210629013@55373
|
399 |
" f_s = filter (sameFunId (lhs b_3)) fun_s; " ^
|
s1210629013@55373
|
400 |
" (e_3::bool) = " ^
|
wneuper@59489
|
401 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
402 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
403 |
" [BOOL (hd f_s), BOOL b_3]); " ^
|
s1210629013@55373
|
404 |
" b_4 = NTH 4 r_b; " ^
|
s1210629013@55373
|
405 |
" f_s = filter (sameFunId (lhs b_4)) fun_s; " ^
|
s1210629013@55373
|
406 |
" (e_4::bool) = " ^
|
wneuper@59489
|
407 |
" (SubProblem (''Biegelinie'',[''makeFunctionTo'',''equation'']," ^
|
wneuper@59489
|
408 |
" [''Equation'',''fromFunction'']) " ^
|
s1210629013@55373
|
409 |
" [BOOL (hd f_s), BOOL b_4]) " ^
|
wneuper@59429
|
410 |
" in [e_1,e_2,e_3,e_4])"*))]
|
wneuper@59472
|
411 |
\<close>
|
wneuper@59429
|
412 |
subsection \<open>Transform an equality into a function\<close>
|
wneuper@59429
|
413 |
|
wneuper@59504
|
414 |
(*(M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2) (M_b L = 0) -->
|
wneuper@59504
|
415 |
0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
wneuper@59504
|
416 |
partial_function (tailrec) function_to_equality :: "bool \<Rightarrow> bool \<Rightarrow> bool"
|
wneuper@59504
|
417 |
where
|
wneuper@59504
|
418 |
"function_to_equality fu_n su_b =
|
wneuper@59504
|
419 |
(let fu_n = Take fu_n;
|
wneuper@59504
|
420 |
bd_v = argument_in (lhs fu_n);
|
wneuper@59504
|
421 |
va_l = argument_in (lhs su_b);
|
wneuper@59504
|
422 |
eq_u = Substitute [bd_v = va_l] fu_n;
|
wneuper@59504
|
423 |
\<comment> \<open>([1], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2\<close>
|
wneuper@59504
|
424 |
eq_u = Substitute [su_b] eq_u
|
wneuper@59504
|
425 |
in (Rewrite_Set ''norm_Rational'' False) eq_u)"
|
wneuper@59472
|
426 |
setup \<open>KEStore_Elems.add_mets
|
wneuper@59473
|
427 |
[Specify.prep_met @{theory} "met_equ_fromfun" [] Celem.e_metID
|
s1210629013@55373
|
428 |
(["Equation","fromFunction"],
|
s1210629013@55373
|
429 |
[("#Given" ,["functionEq fu_n","substitution su_b"]),
|
s1210629013@55373
|
430 |
("#Find" ,["equality equ'''"])],
|
wneuper@59416
|
431 |
{rew_ord'="tless_true", rls'=Rule.Erls, calc = [],
|
wneuper@59416
|
432 |
srls = Rule.append_rls "srls_in_EquationfromFunc" Rule.e_rls
|
wneuper@59491
|
433 |
[Rule.Calc("Tools.lhs", Tools.eval_lhs "eval_lhs_"),
|
wneuper@59416
|
434 |
Rule.Calc("Atools.argument'_in", eval_argument_in "Atools.argument'_in")],
|
wneuper@59416
|
435 |
prls=Rule.e_rls, crls = Atools_erls, errpats = [], nrls = Rule.e_rls},
|
s1210629013@55373
|
436 |
(*(M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2) (M_b L = 0) -->
|
s1210629013@55373
|
437 |
0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
wneuper@59545
|
438 |
@{thm function_to_equality.simps}
|
wneuper@59545
|
439 |
(*"Script Function2Equality (fu_n::bool) (su_b::bool) =" ^
|
s1210629013@55373
|
440 |
" (let fu_n = Take fu_n; " ^
|
s1210629013@55373
|
441 |
" bd_v = argument_in (lhs fu_n); " ^
|
s1210629013@55373
|
442 |
" va_l = argument_in (lhs su_b); " ^
|
s1210629013@55373
|
443 |
" eq_u = (Substitute [bd_v = va_l]) fu_n; " ^
|
s1210629013@55373
|
444 |
(*([1], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
s1210629013@55373
|
445 |
" eq_u = (Substitute [su_b]) eq_u " ^
|
wneuper@59545
|
446 |
" in (Rewrite_Set ''norm_Rational'' False) eq_u) "*))]
|
wneuper@59472
|
447 |
\<close>
|
s1210629013@55373
|
448 |
|
neuper@37906
|
449 |
end
|
neuper@37906
|
450 |
|