--- a/src/HOL/Complex/ComplexArith0.ML Sat Feb 14 02:06:12 2004 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,187 +0,0 @@
-(* Title: ComplexArith0.ML
- Author: Jacques D. Fleuriot
- Copyright: 2001 University of Edinburgh
- Description: Assorted facts that need binary literals
- Also, common factor cancellation (see e.g. HyperArith0)
-*)
-
-local
- open Complex_Numeral_Simprocs
-in
-
-val rel_complex_number_of = [eq_complex_number_of];
-
-
-structure CancelNumeralFactorCommon =
- struct
- val mk_coeff = mk_coeff
- val dest_coeff = dest_coeff 1
- val trans_tac = Real_Numeral_Simprocs.trans_tac
- val norm_tac = ALLGOALS (simp_tac (HOL_ss addsimps complex_minus_from_mult_simps @ mult_1s))
- THEN ALLGOALS (simp_tac (HOL_ss addsimps bin_simps@complex_mult_minus_simps))
- THEN ALLGOALS (simp_tac (HOL_ss addsimps mult_ac))
- val numeral_simp_tac = ALLGOALS (simp_tac (HOL_ss addsimps rel_complex_number_of@bin_simps))
- val simplify_meta_eq = simplify_meta_eq
- end
-
-
-structure DivCancelNumeralFactor = CancelNumeralFactorFun
- (open CancelNumeralFactorCommon
- val prove_conv = Bin_Simprocs.prove_conv
- val mk_bal = HOLogic.mk_binop "HOL.divide"
- val dest_bal = HOLogic.dest_bin "HOL.divide" complexT
- val cancel = mult_divide_cancel_left RS trans
- val neg_exchanges = false
-)
-
-
-structure EqCancelNumeralFactor = CancelNumeralFactorFun
- (open CancelNumeralFactorCommon
- val prove_conv = Bin_Simprocs.prove_conv
- val mk_bal = HOLogic.mk_eq
- val dest_bal = HOLogic.dest_bin "op =" complexT
- val cancel = field_mult_cancel_left RS trans
- val neg_exchanges = false
-)
-
-val complex_cancel_numeral_factors_relations =
- map prep_simproc
- [("complexeq_cancel_numeral_factor",
- ["(l::complex) * m = n", "(l::complex) = m * n"],
- EqCancelNumeralFactor.proc)];
-
-val complex_cancel_numeral_factors_divide = prep_simproc
- ("complexdiv_cancel_numeral_factor",
- ["((l::complex) * m) / n", "(l::complex) / (m * n)",
- "((number_of v)::complex) / (number_of w)"],
- DivCancelNumeralFactor.proc);
-
-val complex_cancel_numeral_factors =
- complex_cancel_numeral_factors_relations @
- [complex_cancel_numeral_factors_divide];
-
-end;
-
-
-Addsimprocs complex_cancel_numeral_factors;
-
-
-(*examples:
-print_depth 22;
-set timing;
-set trace_simp;
-fun test s = (Goal s; by (Simp_tac 1));
-
-
-test "9*x = 12 * (y::complex)";
-test "(9*x) / (12 * (y::complex)) = z";
-
-test "-99*x = 132 * (y::complex)";
-
-test "999*x = -396 * (y::complex)";
-test "(999*x) / (-396 * (y::complex)) = z";
-
-test "-99*x = -81 * (y::complex)";
-test "(-99*x) / (-81 * (y::complex)) = z";
-
-test "-2 * x = -1 * (y::complex)";
-test "-2 * x = -(y::complex)";
-test "(-2 * x) / (-1 * (y::complex)) = z";
-
-*)
-
-
-(** Declarations for ExtractCommonTerm **)
-
-local
- open Complex_Numeral_Simprocs
-in
-
-structure CancelFactorCommon =
- struct
- val mk_sum = long_mk_prod
- val dest_sum = dest_prod
- val mk_coeff = mk_coeff
- val dest_coeff = dest_coeff
- val find_first = find_first []
- val trans_tac = Real_Numeral_Simprocs.trans_tac
- val norm_tac = ALLGOALS (simp_tac (HOL_ss addsimps mult_1s@mult_ac))
- end;
-
-
-structure EqCancelFactor = ExtractCommonTermFun
- (open CancelFactorCommon
- val prove_conv = Bin_Simprocs.prove_conv
- val mk_bal = HOLogic.mk_eq
- val dest_bal = HOLogic.dest_bin "op =" complexT
- val simplify_meta_eq = cancel_simplify_meta_eq field_mult_cancel_left
-);
-
-
-structure DivideCancelFactor = ExtractCommonTermFun
- (open CancelFactorCommon
- val prove_conv = Bin_Simprocs.prove_conv
- val mk_bal = HOLogic.mk_binop "HOL.divide"
- val dest_bal = HOLogic.dest_bin "HOL.divide" complexT
- val simplify_meta_eq = cancel_simplify_meta_eq mult_divide_cancel_eq_if
-);
-
-val complex_cancel_factor =
- map prep_simproc
- [("complex_eq_cancel_factor", ["(l::complex) * m = n", "(l::complex) = m * n"],
- EqCancelFactor.proc),
- ("complex_divide_cancel_factor", ["((l::complex) * m) / n", "(l::complex) / (m * n)"],
- DivideCancelFactor.proc)];
-
-end;
-
-Addsimprocs complex_cancel_factor;
-
-
-(*examples:
-print_depth 22;
-set timing;
-set trace_simp;
-fun test s = (Goal s; by (Asm_simp_tac 1));
-
-test "x*k = k*(y::complex)";
-test "k = k*(y::complex)";
-test "a*(b*c) = (b::complex)";
-test "a*(b*c) = d*(b::complex)*(x*a)";
-
-
-test "(x*k) / (k*(y::complex)) = (uu::complex)";
-test "(k) / (k*(y::complex)) = (uu::complex)";
-test "(a*(b*c)) / ((b::complex)) = (uu::complex)";
-test "(a*(b*c)) / (d*(b::complex)*(x*a)) = (uu::complex)";
-
-(*FIXME: what do we do about this?*)
-test "a*(b*c)/(y*z) = d*(b::complex)*(x*a)/z";
-*)
-
-
-(** Division by 1, -1 **)
-
-Goal "x/-1 = -(x::complex)";
-by (Simp_tac 1);
-qed "complex_divide_minus1";
-Addsimps [complex_divide_minus1];
-
-Goal "-1/(x::complex) = - (1/x)";
-by (simp_tac (simpset() addsimps [complex_divide_def, inverse_minus_eq]) 1);
-qed "complex_minus1_divide";
-Addsimps [complex_minus1_divide];
-
-Goal "(x + - a = (0::complex)) = (x=a)";
-by (simp_tac (simpset() addsimps [diff_eq_eq,symmetric complex_diff_def]) 1);
-qed "complex_add_minus_iff";
-Addsimps [complex_add_minus_iff];
-
-Goal "(x+y = (0::complex)) = (y = -x)";
-by Auto_tac;
-by (dtac (sym RS (diff_eq_eq RS iffD2)) 1);
-by Auto_tac;
-qed "complex_add_eq_0_iff";
-AddIffs [complex_add_eq_0_iff];
-
-