neuper@42256: (* Title: Test_Z_Transform neuper@42256: Author: Jan Rocnik neuper@42256: (c) copyright due to lincense terms. neuper@42256: 12345678901234567890123456789012345678901234567890123456789012345678901234567890 neuper@42256: 10 20 30 40 50 60 70 80 neuper@42256: *) neuper@42256: neuper@42256: theory Test_Z_Transform imports Isac begin neuper@42256: neuper@42256: section {*trials towards Z transform *} neuper@42256: text{*===============================*} neuper@42256: subsection {*terms*} neuper@42256: ML {* neuper@42256: @{term "1 < || z ||"}; neuper@42256: @{term "z / (z - 1)"}; neuper@42256: @{term "-u -n - 1"}; neuper@42256: @{term "-u [-n - 1]"}; (*[ ] denotes lists !!!*) neuper@42256: @{term "z /(z - 1) = -u [-n - 1]"};Isac neuper@42256: @{term "1 < || z || ==> z / (z - 1) = -u [-n - 1]"}; neuper@42256: term2str @{term "1 < || z || ==> z / (z - 1) = -u [-n - 1]"}; neuper@42256: *} neuper@42256: ML {* neuper@42256: (*alpha --> "" *) neuper@42256: neuper@42256: @{term "\ "}; neuper@42256: @{term "\ "}; neuper@42256: @{term "\ "}; neuper@42256: @{term "\ "}; neuper@42256: term2str @{term "\ "}; neuper@42256: *} neuper@42256: neuper@42256: subsection {*rules*} neuper@42256: (*axiomatization "z / (z - 1) = -u [-n - 1]" Illegal variable name: "z / (z - 1) = -u [-n - 1]" *) neuper@42256: (*definition "z / (z - 1) = -u [-n - 1]" Bad head of lhs: existing constant "op /"*) neuper@42256: axiomatization where neuper@42256: rule1: "1 = \[n]" and neuper@42256: rule2: "|| z || > 1 ==> z / (z - 1) = u [n]" and neuper@42256: rule3: "|| z || < 1 ==> z / (z - 1) = -u [-n - 1]" and neuper@42256: rule4: "|| z || > || \ || ==> z / (z - \) = \^^^n * u [n]" and neuper@42256: rule5: "|| z || < || \ || ==> z / (z - \) = -(\^^^n) * u [-n - 1]" and neuper@42256: rule6: "|| z || > 1 ==> z/(z - 1)^^^2 = n * u [n]" neuper@42256: ML {* neuper@42256: @{thm rule1}; neuper@42256: @{thm rule2}; neuper@42256: @{thm rule3}; neuper@42256: @{thm rule4}; neuper@42256: *} neuper@42256: neuper@42256: subsection {*apply rules*} neuper@42256: ML {* neuper@42256: val inverse_Z = append_rls "inverse_Z" e_rls neuper@42256: [ Thm ("rule3",num_str @{thm rule3}), neuper@42256: Thm ("rule4",num_str @{thm rule4}), neuper@42256: Thm ("rule1",num_str @{thm rule1}) neuper@42256: ]; neuper@42256: neuper@42256: val t = str2term "z / (z - 1) + z / (z - \) + 1"; neuper@42256: val SOME (t', asm) = rewrite_set_ thy true inverse_Z t; neuper@42256: term2str t' = "z / (z - ?\ [?n]) + z / (z - \) + ?\ [?n]"; (*attention rule1 !!!*) neuper@42256: *} neuper@42256: ML {* neuper@42256: val (thy, ro, er) = (@{theory}, tless_true, eval_rls); neuper@42256: *} neuper@42256: ML {* neuper@42256: val SOME (t, asm1) = rewrite_ thy ro er true (num_str @{thm rule3}) t; neuper@42256: term2str t = "- ?u [- ?n - 1] + z / (z - \) + 1"; (*- real *) neuper@42256: term2str t; neuper@42256: *} neuper@42256: ML {* neuper@42256: val SOME (t, asm2) = rewrite_ thy ro er true (num_str @{thm rule4}) t; neuper@42256: term2str t = "- ?u [- ?n - 1] + \ ^^^ ?n * ?u [?n] + 1"; (*- real *) neuper@42256: term2str t; neuper@42256: *} neuper@42256: ML {* neuper@42256: val SOME (t, asm3) = rewrite_ thy ro er true (num_str @{thm rule1}) t; neuper@42256: term2str t = "- ?u [- ?n - 1] + \ ^^^ ?n * ?u [?n] + ?\ [?n]"; (*- real *) neuper@42256: term2str t; neuper@42256: *} neuper@42256: ML {* neuper@42256: terms2str (asm1 @ asm2 @ asm3); neuper@42256: *} neuper@42256: neuper@42256: section {*Prepare steps in CTP-based programming language*} neuper@42256: text{*===================================================*} neuper@42256: subsection {*prepare expression*} neuper@42256: ML {* neuper@42256: val ctxt = ProofContext.init_global @{theory}; neuper@42256: val ctxt = declare_constraints' [@{term "z::real"}] ctxt; neuper@42256: neuper@42256: val SOME fun1 = parseNEW ctxt "X z = 3 / (z - 1/4 + -1/8 * z ^^^ -1)"; term2str fun1; neuper@42256: val SOME fun1' = parseNEW ctxt "X z = 3 / (z - 1/4 + -1/8 * (1/z))"; term2str fun1'; neuper@42256: *} neuper@42256: neuper@42256: axiomatization where neuper@42256: ruleZY: "(X z = a / b) = (X' z = a / (z * b))" neuper@42256: neuper@42256: ML {* neuper@42256: val (thy, ro, er) = (@{theory}, tless_true, eval_rls); neuper@42256: val SOME (fun2, asm1) = rewrite_ thy ro er true @{thm ruleZY} fun1; term2str fun2; neuper@42256: val SOME (fun2', asm1) = rewrite_ thy ro er true @{thm ruleZY} fun1'; term2str fun2'; neuper@42256: neuper@42256: val SOME (fun3,_) = rewrite_set_ @{theory Isac} false norm_Rational fun2; neuper@42256: term2str fun3; (*fails on x^^^(-1) TODO*) neuper@42256: val SOME (fun3',_) = rewrite_set_ @{theory Isac} false norm_Rational fun2'; neuper@42256: term2str fun3'; (*OK*) neuper@42256: neuper@42256: val (_, expr) = HOLogic.dest_eq fun3'; term2str expr; neuper@42256: *} neuper@42256: neuper@42256: subsection {*solve equation*} neuper@42256: text {*this type of equation if too general for the present program*} neuper@42256: ML {* neuper@42256: "----------- Minisubplb/100-init-rootp (*OK*)bl.sml ---------------------"; neuper@42256: val denominator = parseNEW ctxt "z^^^2 - 1/4*z - 1/8 = 0"; neuper@42256: val fmz = ["equality (z^^^2 - 1/4*z - 1/8 = (0::real))", "solveFor z","solutions L"]; neuper@42256: val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]); neuper@42256: (* ^^^^^^^^^^^^^^^^^^^^^^ TODO: ISAC determines type of eq*) neuper@42256: *} neuper@42256: text {*Does the Equation Match the Specification ?*} neuper@42256: ML {* neuper@42256: match_pbl fmz (get_pbt ["univariate","equation"]); neuper@42256: *} neuper@42256: neuper@42256: ML {* neuper@42256: val denominator = parseNEW ctxt "-1/8 + -1/4*z + z^^^2 = 0"; neuper@42256: val fmz = (*specification*) neuper@42256: ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", (*equality*) neuper@42256: "solveFor z", (*bound variable*) neuper@42256: "solutions L"]; (*identifier for solution*) neuper@42256: (*liste der theoreme die zum lösen benötigt werden, aus isac, keine spezielle methode (no met)*) neuper@42256: val (dI',pI',mI') = neuper@42256: ("Isac", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]); neuper@42256: *} neuper@42256: text {*Does the Other Equation Match the Specification ?*} neuper@42256: ML {* neuper@42256: match_pbl fmz (get_pbt ["pqFormula","degree_2","polynomial","univariate","equation"]); neuper@42256: *} neuper@42256: text {*Solve Equation Stepwise*} neuper@42256: ML {* neuper@42256: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt =..,Check_elementwise "Assumptions")*) neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f; neuper@42256: (*[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2] TODO sqrt*) neuper@42256: show_pt pt; neuper@42256: val SOME f = parseNEW ctxt "[z = 1 / 8 + 3 / 8, z = 1 / 8 + -3 / 8]"; neuper@42256: *} neuper@42256: neuper@42256: subsection {*partial fraction decomposition*} neuper@42256: subsubsection {*solution of the equation*} neuper@42256: ML {* neuper@42256: val SOME solutions = parseNEW ctxt "[z=1/2, z=-1/4]"; neuper@42256: term2str solutions; neuper@42256: atomty solutions; neuper@42256: *} neuper@42256: neuper@42256: subsubsection {*get solutions out of list*} neuper@42256: text {*in isac's CTP-based programming language: let s_1 = NTH 1 solutions; s_2 = NTH 2...*} neuper@42256: ML {* neuper@42256: val Const ("List.list.Cons", _) $ s_1 $ (Const ("List.list.Cons", _) $ neuper@42256: s_2 $ Const ("List.list.Nil", _)) = solutions; neuper@42256: term2str s_1; neuper@42256: term2str s_2; neuper@42256: *} neuper@42256: neuper@42256: ML {* (*Solutions as Denominator --> Denominator1 = z - Zeropoint1, Denominator2 = z-Zeropoint2,...*) neuper@42256: val xx = HOLogic.dest_eq s_1; neuper@42256: val s_1' = HOLogic.mk_binop "Groups.minus_class.minus" xx; neuper@42256: val xx = HOLogic.dest_eq s_2; neuper@42256: val s_2' = HOLogic.mk_binop "Groups.minus_class.minus" xx; neuper@42256: term2str s_1'; neuper@42256: term2str s_2'; neuper@42256: *} neuper@42256: neuper@42256: subsubsection {*build expression*} neuper@42256: text {*in isac's CTP-based programming language: let s_1 = Take numerator / (s_1 * s_2)*} neuper@42256: ML {* neuper@42256: (*The Main Denominator is the multiplikation of the partial fraction denominators*) neuper@42256: val denominator' = HOLogic.mk_binop "Groups.times_class.times" (s_1', s_2') ; neuper@42256: val SOME numerator = parseNEW ctxt "3::real"; neuper@42256: neuper@42256: val expr' = HOLogic.mk_binop "Rings.inverse_class.divide" (numerator, denominator'); neuper@42256: term2str expr'; neuper@42256: *} neuper@42256: neuper@42256: subsubsection {*Ansatz - create partial fractions out of our expression*} neuper@42256: neuper@42256: axiomatization where neuper@42256: ansatz2: "n / (a*b) = A/a + B/(b::real)" and neuper@42256: multiply_eq2: "(n / (a*b) = A/a + B/b) = (a*b*(n / (a*b)) = a*b*(A/a + B/b))" neuper@42256: neuper@42256: ML {* neuper@42256: (*we use our ansatz2 to rewrite our expression and get an equilation with our expression on the left and the partial fractions of it on the right side*) neuper@42256: val SOME (t1,_) = rewrite_ @{theory Isac} e_rew_ord e_rls false @{thm ansatz2} expr'; neuper@42256: term2str t1; atomty t1; neuper@42256: val eq1 = HOLogic.mk_eq (expr', t1); neuper@42256: term2str eq1; neuper@42256: *} neuper@42256: ML {* neuper@42256: (*eliminate the demoninators by multiplying the left and the right side with the main denominator*) neuper@42256: val SOME (eq2,_) = rewrite_ @{theory Isac} e_rew_ord e_rls false @{thm multiply_eq2} eq1; neuper@42256: term2str eq2; neuper@42256: *} neuper@42256: ML {* neuper@42256: (*simplificatoin*) neuper@42256: val SOME (eq3,_) = rewrite_set_ @{theory Isac} false norm_Rational eq2; neuper@42256: term2str eq3; (*?A ?B not simplified*) neuper@42256: *} neuper@42256: ML {* neuper@42256: val SOME fract1 = neuper@42256: parseNEW ctxt "(z - 1 / 2) * (z - -1 / 4) * (A / (z - 1 / 2) + B / (z - -1 / 4))"; (*A B !*) neuper@42256: val SOME (fract2,_) = rewrite_set_ @{theory Isac} false norm_Rational fract1; neuper@42256: term2str fract2 = "(A + -2 * B + 4 * A * z + 4 * B * z) / 4"; neuper@42256: (*term2str fract2 = "A * (1 / 4 + z) + B * (-1 / 2 + z)" would be more traditional*) neuper@42256: *} neuper@42256: ML {* neuper@42256: val (numerator, denominator) = HOLogic.dest_eq eq3; neuper@42256: val eq3' = HOLogic.mk_eq (numerator, fract1); (*A B !*) neuper@42256: term2str eq3'; neuper@42256: (*MANDATORY: simplify (and remove denominator) otherwise 3 = 0*) neuper@42256: val SOME (eq3'' ,_) = rewrite_set_ @{theory Isac} false norm_Rational eq3'; neuper@42256: term2str eq3''; neuper@42256: *} neuper@42256: neuper@42256: subsubsection {*get first koeffizient*} neuper@42256: neuper@42256: ML {* neuper@42256: (*substitude z with the first zeropoint to get A*) neuper@42256: val SOME (eq4_1,_) = rewrite_terms_ @{theory Isac} e_rew_ord e_rls [s_1] eq3''; neuper@42256: term2str eq4_1; neuper@42256: neuper@42256: val SOME (eq4_2,_) = rewrite_set_ @{theory Isac} false norm_Rational eq4_1; neuper@42256: term2str eq4_2; neuper@42256: neuper@42256: val fmz = ["equality (3 = 3 * A / (4::real))", "solveFor A","solutions L"]; neuper@42256: val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]); neuper@42256: (*solve the simple linear equilation for A TODO: return eq, not list of eq*) neuper@42256: val (p,_,fa,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fa,nxt,_,pt) = me nxt p [] pt; neuper@42256: f2str fa; neuper@42256: *} neuper@42256: neuper@42256: subsubsection {*get second koeffizient*} neuper@42256: neuper@42256: ML {* neuper@42256: (*substitude z with the second zeropoint to get B*) neuper@42256: val SOME (eq4b_1,_) = rewrite_terms_ @{theory Isac} e_rew_ord e_rls [s_2] eq3''; neuper@42256: term2str eq4b_1; neuper@42256: neuper@42256: val SOME (eq4b_2,_) = rewrite_set_ @{theory Isac} false norm_Rational eq4b_1; neuper@42256: term2str eq4b_2; neuper@42256: *} neuper@42256: ML {* neuper@42256: (*solve the simple linear equilation for B TODO: return eq, not list of eq*) neuper@42256: val fmz = ["equality (3 = -3 * B / (4::real))", "solveFor B","solutions L"]; neuper@42256: val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]); neuper@42256: val (p,_,fb,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: val (p,_,fb,nxt,_,pt) = me nxt p [] pt; neuper@42256: f2str fb; neuper@42256: *} neuper@42256: neuper@42256: ML {* (*check koeffizients*) neuper@42256: if f2str fa = "[A = 4]" then () else error "part.fract. eq4_1"; neuper@42256: if f2str fb = "[B = -4]" then () else error "part.fract. eq4_1"; neuper@42256: *} neuper@42256: neuper@42256: subsubsection {*substitute expression with solutions*} neuper@42256: ML {* neuper@42256: *} neuper@42256: neuper@42256: section {*Implement the Specification and the Method*} neuper@42256: text{*==============================================*} neuper@42256: subsection{*Define the Specification*} neuper@42256: ML {* neuper@42256: val thy = @{theory}; neuper@42256: *} neuper@42256: ML {* neuper@42256: store_pbt neuper@42256: (prep_pbt thy "pbl_SP" [] e_pblID neuper@42256: (["SignalProcessing"], [], e_rls, NONE, [])); neuper@42256: store_pbt neuper@42256: (prep_pbt thy "pbl_SP_Ztrans" [] e_pblID neuper@42256: (["Z_Transform","SignalProcessing"], [], e_rls, NONE, [])); neuper@42256: store_pbt neuper@42256: (prep_pbt thy "pbl_SP_Ztrans_inv" [] e_pblID neuper@42256: (["inverse", "Z_Transform", "SignalProcessing"], neuper@42256: [("#Given" ,["equality X_eq"]), neuper@42256: ("#Find" ,["equality n_eq"]) neuper@42256: ], neuper@42256: append_rls "e_rls" e_rls [(*for preds in where_*)], NONE, neuper@42256: [["TODO: path to method"]])); neuper@42256: neuper@42256: show_ptyps(); neuper@42256: get_pbt ["inverse","Z_Transform","SignalProcessing"]; neuper@42256: *} neuper@42256: neuper@42256: subsection{*Define the (Dummy-)Method*} neuper@42256: subsection {*Define Name and Signature for the Method*} neuper@42256: consts neuper@42256: InverseZTransform :: "[bool, bool] => bool" neuper@42256: ("((Script InverseZTransform (_ =))// (_))" 9) neuper@42256: neuper@42256: ML {* neuper@42256: store_met neuper@42256: (prep_met thy "met_SP" [] e_metID neuper@42256: (["SignalProcessing"], [], neuper@42256: {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, neuper@42256: crls = e_rls, nrls = e_rls}, "empty_script")); neuper@42256: store_met neuper@42256: (prep_met thy "met_SP_Ztrans" [] e_metID neuper@42256: (["SignalProcessing", "Z_Transform"], [], neuper@42256: {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, neuper@42256: crls = e_rls, nrls = e_rls}, "empty_script")); neuper@42256: *} neuper@42256: ML {* neuper@42256: store_met neuper@42256: (prep_met thy "met_SP_Ztrans_inv" [] e_metID neuper@42256: (["SignalProcessing", "Z_Transform", "inverse"], [], neuper@42256: {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, neuper@42256: crls = e_rls, nrls = e_rls}, neuper@42256: "empty_script" neuper@42256: )); neuper@42256: val thy = @{theory}; (*latest version of thy required*) neuper@42256: store_met neuper@42256: (prep_met thy "met_SP_Ztrans_inv" [] e_metID neuper@42256: (["SignalProcessing", "Z_Transform", "inverse"], neuper@42256: [("#Given" ,["equality X_eq"]), neuper@42256: ("#Find" ,["equality n_eq"]) neuper@42256: ], neuper@42256: {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, neuper@42256: crls = e_rls, nrls = e_rls}, neuper@42256: "Script InverseZTransform (Xeq::bool) =" ^ neuper@42256: " (let X = Take Xeq;" ^ neuper@42256: " X = Rewrite ruleZY False X" ^ neuper@42256: " in X)" neuper@42256: )); neuper@42256: neuper@42256: show_mets(); neuper@42256: get_met ["SignalProcessing","Z_Transform","inverse"]; neuper@42256: *} neuper@42256: neuper@42256: neuper@42256: section {*Program in CTP-based language*} neuper@42256: text{*=================================*} neuper@42256: subsection {*Stepwise extend Program*} neuper@42256: ML {* neuper@42256: val str = neuper@42256: "Script InverseZTransform (Xeq::bool) =" ^ neuper@42256: " Xeq"; neuper@42256: *} neuper@42256: ML {* neuper@42256: val str = neuper@42256: "Script InverseZTransform (Xeq::bool) =" ^ neuper@42256: " (let X = Take Xeq;" ^ neuper@42256: " X = Rewrite ruleZY False X" ^ neuper@42256: " in X)"; neuper@42256: *} neuper@42256: ML {* neuper@42256: val thy = @{theory}; neuper@42256: val sc = ((inst_abs thy) o term_of o the o (parse thy)) str; neuper@42256: *} neuper@42256: ML {* neuper@42256: term2str sc; neuper@42256: atomty sc neuper@42256: *} neuper@42256: neuper@42256: neuper@42256: subsection {*Store Final Version of Program for Execution*} neuper@42256: ML {* neuper@42256: store_met neuper@42256: (prep_met thy "met_SP_Ztrans_inv" [] e_metID neuper@42256: (["SignalProcessing", "Z_Transform", "inverse"], neuper@42256: [("#Given" ,["equality X_eq"]), neuper@42256: ("#Find" ,["equality n_eq"]) neuper@42256: ], neuper@42256: {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, neuper@42256: crls = e_rls, nrls = e_rls}, neuper@42256: "Script InverseZTransform (Xeq::bool) =" ^ neuper@42256: " (let X = Take Xeq;" ^ neuper@42256: " X = Rewrite ruleZY False X" ^ neuper@42256: " in X)" neuper@42256: )); neuper@42256: *} neuper@42256: neuper@42256: neuper@42256: subsection {*Stepwise Execute the Program*} neuper@42256: neuper@42256: neuper@42256: neuper@42256: neuper@42256: neuper@42256: neuper@42256: neuper@42256: neuper@42256: section {*Write Tests for Crucial Details*} neuper@42256: text{*===================================*} neuper@42256: ML {* neuper@42256: neuper@42256: *} neuper@42256: neuper@42256: section {*Integrate Program into Knowledge*} neuper@42256: ML {* neuper@42256: neuper@42256: *} neuper@42256: neuper@42256: end neuper@42256: