1.1 --- a/src/Tools/isac/Knowledge/Inverse_Z_Transform.thy	Tue May 28 16:52:30 2019 +0200
     1.2 +++ b/src/Tools/isac/Knowledge/Inverse_Z_Transform.thy	Wed May 29 10:36:16 2019 +0200
     1.3 @@ -75,16 +75,17 @@
     1.4      [Specify.prep_met thy "met_SP" [] Celem.e_metID
     1.5        (["SignalProcessing"], [],
     1.6          {rew_ord'="tless_true", rls'= Rule.e_rls, calc = [], srls = Rule.e_rls, prls = Rule.e_rls, crls = Rule.e_rls,
     1.7 -          errpats = [], nrls = Rule.e_rls}, "empty_script"),
     1.8 +          errpats = [], nrls = Rule.e_rls}, @{thm refl}),
     1.9      Specify.prep_met thy "met_SP_Ztrans" [] Celem.e_metID
    1.10        (["SignalProcessing", "Z_Transform"], [],
    1.11          {rew_ord'="tless_true", rls'= Rule.e_rls, calc = [], srls = Rule.e_rls, prls = Rule.e_rls, crls = Rule.e_rls,
    1.12 -          errpats = [], nrls = Rule.e_rls}, "empty_script")]
    1.13 +          errpats = [], nrls = Rule.e_rls}, @{thm refl})]
    1.14  \<close>
    1.15 -(*ok
    1.16 -partial_function (tailrec) inverse_ztransform :: "bool \<Rightarrow> bool"
    1.17 +
    1.18 +(*WARNING: Additional type variable(s) in specification of "inverse_ztransform": 'a *)
    1.19 +partial_function (tailrec) inverse_ztransform :: "bool \<Rightarrow> real \<Rightarrow> bool"
    1.20    where
    1.21 -"inverse_ztransform X_eq =                                           \<comment> \<open>(1/z) instead of z ^^^ -1\<close>                
    1.22 +"inverse_ztransform X_eq z =                                           \<comment> \<open>(1/z) instead of z ^^^ -1\<close>                
    1.23   (let X = Take X_eq;                                                                
    1.24        X' = Rewrite ''ruleZY'' False X;                                         \<comment> \<open>z * denominator\<close>                          
    1.25        X' = (Rewrite_Set ''norm_Rational'' False) X';                                  \<comment> \<open>simplify\<close>                   
    1.26 @@ -96,7 +97,6 @@
    1.27        L_L = SubProblem (''Test'', [''LINEAR'',''univariate'',''equation'',''test''],         
    1.28                  [''Test'',''solve_linear'']) [BOOL equ, REAL z]               \<comment> \<open>PROG string\<close>
    1.29    in X) "
    1.30 -*)
    1.31  setup \<open>KEStore_Elems.add_mets
    1.32      [Specify.prep_met thy "met_SP_Ztrans_inv" [] Celem.e_metID
    1.33        (["SignalProcessing", "Z_Transform", "Inverse"],
    1.34 @@ -104,7 +104,8 @@
    1.35            ("#Find"  ,["stepResponse (n_eq::bool)"])],
    1.36          {rew_ord'="tless_true", rls'= Rule.e_rls, calc = [], srls = Rule.e_rls, prls = Rule.e_rls, crls = Rule.e_rls,
    1.37            errpats = [], nrls = Rule.e_rls},
    1.38 -        "Script InverseZTransform1 (X_eq::bool) =" ^ (*(1/z) instead of z ^^^ -1*)
    1.39 +        @{thm inverse_ztransform.simps}
    1.40 +	    (*"Script InverseZTransform1 (X_eq::bool) =" ^ (*(1/z) instead of z ^^^ -1*)
    1.41            " (let X = Take X_eq;" ^
    1.42            "      X' = Rewrite ''ruleZY'' False X;" ^ (*z * denominator*)
    1.43            "      X' = (Rewrite_Set ''norm_Rational'' False) X';" ^ (*simplify*)
    1.44 @@ -118,10 +119,9 @@
    1.45            "                         [''LINEAR'',''univariate'',''equation'',''test'']," ^
    1.46            "                         [''Test'',''solve_linear''])              " ^
    1.47            "                        [BOOL equ, REAL z])              " ^
    1.48 -          "  in X)")]
    1.49 +          "  in X)"*))]
    1.50  \<close>
    1.51  
    1.52 -(* ok
    1.53  partial_function (tailrec) inverse_ztransform2 :: "bool \<Rightarrow> real \<Rightarrow> bool"
    1.54    where
    1.55  "inverse_ztransform2 X_eq X_z =
    1.56 @@ -139,7 +139,6 @@
    1.57      X_zeq = Take (X_z = rhs pbz_eq);
    1.58      n_eq = (Rewrite_Set ''inverse_z'' False) X_zeq
    1.59    in n_eq)"
    1.60 -*)
    1.61  setup \<open>KEStore_Elems.add_mets
    1.62      [Specify.prep_met thy "met_SP_Ztrans_inv_sub" [] Celem.e_metID
    1.63        (["SignalProcessing", "Z_Transform", "Inverse_sub"],
    1.64 @@ -166,7 +165,8 @@
    1.65                      eval_factors_from_solution "#factors_from_solution")
    1.66                    ], scr = Rule.EmptyScr},
    1.67            prls = Rule.e_rls, crls = Rule.e_rls, errpats = [], nrls = norm_Rational},
    1.68 -        " Script InverseZTransform2 (X_eq::bool) (X_z::real) =               "^ (*([], Frm), Problem (Isac, [Inverse, Z_Transform, SignalProcessing])*)
    1.69 +        @{thm simplify.simps}
    1.70 +	    (*" Script InverseZTransform2 (X_eq::bool) (X_z::real) =               "^ (*([], Frm), Problem (Isac, [Inverse, Z_Transform, SignalProcessing])*)
    1.71          " (let X = Take X_eq;                                                "^ (*([1], Frm), X z = 3 / (z - 1 / 4 + -1 / 8 * (1 / z))*)
    1.72          "   X' = Rewrite ''ruleZY'' False X;                                 "^ (*([1], Res), ?X' z = 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))*)
    1.73          "   (X'_z::real) = lhs X';                                           "^ (*            ?X' z*)
    1.74 @@ -180,7 +180,7 @@
    1.75          "   pbz_eq = Rewrite ''ruleYZ'' False pbz_eq;                        "^ (*([3], Res), ?X' z = 4 * (?z / (z - 1 / 2)) + -4 * (?z / (z - -1 / 4))*)
    1.76          "   (X_zeq::bool) = Take (X_z = rhs pbz_eq);                         "^ (*([4], Frm), X_z = 4 * (z / (z - 1 / 2)) + -4 * (z / (z - -1 / 4))*)
    1.77          "   n_eq = (Rewrite_Set ''inverse_z'' False) X_zeq                   "^ (*([4], Res), X_z = 4 * (1 / 2) ^^^ ?n * ?u [?n] + -4 * (-1 / 4) ^^^ ?n * ?u [?n]*)
    1.78 -        " in n_eq)                                                           ")](*            X_z = 4 * (1 / 2) ^^^ n * u [n] + -4 * (-1 / 4) ^^^ n * u [n]*)
    1.79 +        " in n_eq)                                                           "*))](*            X_z = 4 * (1 / 2) ^^^ n * u [n] + -4 * (-1 / 4) ^^^ n * u [n]*)
    1.80  \<close>
    1.81  
    1.82  end