1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/doc-isac/jrocnik/Test_Complex.thy	Tue Sep 17 09:50:52 2013 +0200
     1.3 @@ -0,0 +1,113 @@
     1.4 +theory Test_Complex imports Isac begin
     1.5 +
     1.6 +section {*terms and operations*}
     1.7 +ML {*
     1.8 +  print_depth 999; @{term "Complex 1 (2::real)"};
     1.9 +*}
    1.10 +ML {*
    1.11 +@{term "Complex 1 2 + Complex 3 4"};
    1.12 +print_depth 999; str2term "Complex 1 2 + Complex 3 4"; print_depth 999;
    1.13 +*}
    1.14 +ML {*
    1.15 +@{term "Complex 1 2 * Complex 3 4"};
    1.16 +@{term "Complex 1 2 - Complex 3 4"};
    1.17 +@{term "Complex 1 2 / Complex 3 4"};
    1.18 +(*@{term "Complex 1 2 ^ Complex 3 4"};
    1.19 +  Type unification failed: Clash of types "complex" and "nat"
    1.20 +  Operator:  op ^ (Complex 1 2) :: nat \<Rightarrow> complex
    1.21 +  Operand:   Complex 3 4 :: complex*)
    1.22 +*}
    1.23 +ML {*
    1.24 +term2str @{term "Complex 1 2 + Complex 3 4"};
    1.25 +term2str @{term "Complex 1 2 / Complex 3 4"};
    1.26 +*}
    1.27 +
    1.28 +ML {*
    1.29 +val a = @{term "Complex 1 2"};
    1.30 +atomty a;
    1.31 +val a = str2term "Complex 1 2";
    1.32 +atomty a;
    1.33 +*}
    1.34 +ML {*
    1.35 +val b = @{term "Complex 3 4"};
    1.36 +val b = str2term "Complex 3 4";
    1.37 +(*a + (b::complex); ERROR: term + term*)
    1.38 +*}
    1.39 +
    1.40 +section {*use the operations for simplification*}
    1.41 +
    1.42 +
    1.43 +
    1.44 +subsection {*example 1 -- ADD*}
    1.45 +ML {*
    1.46 +  print_depth 1;
    1.47 +  val (thy, ro, er) = (@{theory}, tless_true, eval_rls);
    1.48 +*}
    1.49 +ML {*
    1.50 +  val thm = @{thm "complex_add"};
    1.51 +  val t = str2term "Complex 1 2 + Complex 3 4";
    1.52 +  val SOME _ = rewrite_ thy ro er true thm t;
    1.53 +  val SOME (t', _) = rewrite_ thy ro er true thm t;
    1.54 +  "Complex (1 + 3) (2 + 4)" = term2str t';
    1.55 +*}
    1.56 +
    1.57 +
    1.58 +
    1.59 +
    1.60 +subsection {*example 2 -- ADD, MULT*}
    1.61 +ML {*
    1.62 +
    1.63 +val Simplify_complex = append_rls "Simplify_complex" e_rls
    1.64 +  [ Thm  ("complex_add",num_str @{thm complex_add}),
    1.65 +		    Thm  ("complex_mult",num_str @{thm complex_mult}),
    1.66 +		    Rls_ norm_Poly
    1.67 +		  ];
    1.68 +
    1.69 +*}
    1.70 +ML {*
    1.71 +
    1.72 +val t = str2term "(Complex 1 2 * (Complex 3 4 + Complex 5 (6::real)))";
    1.73 +term2str t = "Complex 1 2 * (Complex 3 4 + Complex 5 6)";
    1.74 +atomty t;
    1.75 +
    1.76 +*}
    1.77 +ML {*
    1.78 +
    1.79 +
    1.80 +val SOME (t, _) = rewrite_set_ thy true Simplify_complex t;
    1.81 +
    1.82 +term2str t = "Complex -12 26";
    1.83 +atomty t;
    1.84 +
    1.85 +*}
    1.86 +
    1.87 +subsection {*example 3*}
    1.88 +ML {*
    1.89 +val Simplify_complex = append_rls "Simplify_complex" e_rls
    1.90 +  [ Thm  ("complex_mult",num_str @{thm complex_mult}),
    1.91 +    Thm  ("complex_inverse",num_str @{thm complex_inverse}),
    1.92 +		    Rls_ norm_Poly
    1.93 +		  ];
    1.94 +*}
    1.95 +ML {*
    1.96 +val t = str2term "inverse (Complex (2::real) (4::real))";
    1.97 +term2str t = "inverse Complex (2) (4)";
    1.98 +atomty t;
    1.99 +*}
   1.100 +ML {*
   1.101 +trace_rewrite := true;
   1.102 +val SOME (t, _) = rewrite_set_ thy true Simplify_complex t;
   1.103 +trace_rewrite := false;
   1.104 +term2str t = "Complex -12 26";
   1.105 +atomty t;
   1.106 +*}
   1.107 +
   1.108 +
   1.109 +
   1.110 +ML {*
   1.111 +trace_rewrite := true;
   1.112 +trace_rewrite := false;
   1.113 +*}
   1.114 +
   1.115 +end
   1.116 +