author | paulson |
Wed, 28 Jan 2004 10:41:49 +0100 | |
changeset 14368 | 2763da611ad9 |
parent 14331 | 8dbbb7cf3637 |
child 14369 | c50188fe6366 |
permissions | -rw-r--r-- |
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1 |
(* Title: HOL/Integ/int_arith1.ML |
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ID: $Id$ |
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rearranged setup of arithmetic procedures, avoiding global reference values;
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Authors: Larry Paulson and Tobias Nipkow |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
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|
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Simprocs and decision procedure for linear arithmetic. |
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*) |
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14329 | 8 |
(** Misc ML bindings **) |
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||
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val NCons_Pls = thm"NCons_Pls"; |
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val NCons_Min = thm"NCons_Min"; |
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val NCons_BIT = thm"NCons_BIT"; |
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val number_of_Pls = thm"number_of_Pls"; |
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val number_of_Min = thm"number_of_Min"; |
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val number_of_BIT = thm"number_of_BIT"; |
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val bin_succ_Pls = thm"bin_succ_Pls"; |
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val bin_succ_Min = thm"bin_succ_Min"; |
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val bin_succ_BIT = thm"bin_succ_BIT"; |
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val bin_pred_Pls = thm"bin_pred_Pls"; |
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val bin_pred_Min = thm"bin_pred_Min"; |
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val bin_pred_BIT = thm"bin_pred_BIT"; |
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val bin_minus_Pls = thm"bin_minus_Pls"; |
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val bin_minus_Min = thm"bin_minus_Min"; |
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val bin_minus_BIT = thm"bin_minus_BIT"; |
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val bin_add_Pls = thm"bin_add_Pls"; |
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val bin_add_Min = thm"bin_add_Min"; |
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val bin_mult_Pls = thm"bin_mult_Pls"; |
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val bin_mult_Min = thm"bin_mult_Min"; |
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val bin_mult_BIT = thm"bin_mult_BIT"; |
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val zadd_ac = thms "Ring_and_Field.add_ac" |
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val zmult_ac = thms "Ring_and_Field.mult_ac" |
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val NCons_Pls_0 = thm"NCons_Pls_0"; |
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val NCons_Pls_1 = thm"NCons_Pls_1"; |
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val NCons_Min_0 = thm"NCons_Min_0"; |
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val NCons_Min_1 = thm"NCons_Min_1"; |
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val bin_succ_1 = thm"bin_succ_1"; |
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val bin_succ_0 = thm"bin_succ_0"; |
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val bin_pred_1 = thm"bin_pred_1"; |
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val bin_pred_0 = thm"bin_pred_0"; |
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val bin_minus_1 = thm"bin_minus_1"; |
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val bin_minus_0 = thm"bin_minus_0"; |
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val bin_add_BIT_11 = thm"bin_add_BIT_11"; |
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val bin_add_BIT_10 = thm"bin_add_BIT_10"; |
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val bin_add_BIT_0 = thm"bin_add_BIT_0"; |
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val bin_add_Pls_right = thm"bin_add_Pls_right"; |
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val bin_add_Min_right = thm"bin_add_Min_right"; |
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val bin_add_BIT_BIT = thm"bin_add_BIT_BIT"; |
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val bin_mult_1 = thm"bin_mult_1"; |
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val bin_mult_0 = thm"bin_mult_0"; |
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val number_of_NCons = thm"number_of_NCons"; |
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val number_of_succ = thm"number_of_succ"; |
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val number_of_pred = thm"number_of_pred"; |
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val number_of_minus = thm"number_of_minus"; |
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val number_of_add = thm"number_of_add"; |
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val diff_number_of_eq = thm"diff_number_of_eq"; |
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val number_of_mult = thm"number_of_mult"; |
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val double_number_of_BIT = thm"double_number_of_BIT"; |
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val int_numeral_0_eq_0 = thm"int_numeral_0_eq_0"; |
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val int_numeral_1_eq_1 = thm"int_numeral_1_eq_1"; |
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val zmult_minus1 = thm"zmult_minus1"; |
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val zmult_minus1_right = thm"zmult_minus1_right"; |
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val zminus_number_of_zmult = thm"zminus_number_of_zmult"; |
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val zminus_1_eq_m1 = thm"zminus_1_eq_m1"; |
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val zero_less_nat_eq = thm"zero_less_nat_eq"; |
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val eq_number_of_eq = thm"eq_number_of_eq"; |
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val iszero_number_of_Pls = thm"iszero_number_of_Pls"; |
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val nonzero_number_of_Min = thm"nonzero_number_of_Min"; |
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val iszero_number_of_BIT = thm"iszero_number_of_BIT"; |
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val iszero_number_of_0 = thm"iszero_number_of_0"; |
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val iszero_number_of_1 = thm"iszero_number_of_1"; |
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val less_number_of_eq_neg = thm"less_number_of_eq_neg"; |
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val not_neg_number_of_Pls = thm"not_neg_number_of_Pls"; |
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val neg_number_of_Min = thm"neg_number_of_Min"; |
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val neg_number_of_BIT = thm"neg_number_of_BIT"; |
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val le_number_of_eq_not_less = thm"le_number_of_eq_not_less"; |
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val zabs_number_of = thm"zabs_number_of"; |
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val zabs_0 = thm"zabs_0"; |
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val zabs_1 = thm"zabs_1"; |
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val number_of_reorient = thm"number_of_reorient"; |
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val add_number_of_left = thm"add_number_of_left"; |
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val mult_number_of_left = thm"mult_number_of_left"; |
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val add_number_of_diff1 = thm"add_number_of_diff1"; |
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val add_number_of_diff2 = thm"add_number_of_diff2"; |
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val less_iff_diff_less_0 = thm"less_iff_diff_less_0"; |
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val eq_iff_diff_eq_0 = thm"eq_iff_diff_eq_0"; |
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val le_iff_diff_le_0 = thm"le_iff_diff_le_0"; |
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val bin_mult_simps = thms"bin_mult_simps"; |
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val NCons_simps = thms"NCons_simps"; |
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val bin_arith_extra_simps = thms"bin_arith_extra_simps"; |
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val bin_arith_simps = thms"bin_arith_simps"; |
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val bin_rel_simps = thms"bin_rel_simps"; |
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val zless_imp_add1_zle = thm "zless_imp_add1_zle"; |
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val combine_common_factor = thm"combine_common_factor"; |
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val eq_add_iff1 = thm"eq_add_iff1"; |
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val eq_add_iff2 = thm"eq_add_iff2"; |
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val less_add_iff1 = thm"less_add_iff1"; |
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val less_add_iff2 = thm"less_add_iff2"; |
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val le_add_iff1 = thm"le_add_iff1"; |
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val le_add_iff2 = thm"le_add_iff2"; |
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structure Bin_Simprocs = |
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107 |
struct |
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fun prove_conv tacs sg (hyps: thm list) xs (t, u) = |
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if t aconv u then None |
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110 |
else |
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let val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u)) |
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in Some (Tactic.prove sg xs [] eq (K (EVERY tacs))) end |
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|
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114 |
fun prove_conv_nohyps tacs sg = prove_conv tacs sg []; |
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fun prove_conv_nohyps_novars tacs sg = prove_conv tacs sg [] []; |
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|
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fun prep_simproc (name, pats, proc) = |
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118 |
Simplifier.simproc (Theory.sign_of (the_context())) name pats proc; |
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119 |
|
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120 |
fun is_numeral (Const("Numeral.number_of", _) $ w) = true |
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| is_numeral _ = false |
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fun simplify_meta_eq f_number_of_eq f_eq = |
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mk_meta_eq ([f_eq, f_number_of_eq] MRS trans) |
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structure IntAbstractNumeralsData = |
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struct |
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val dest_eq = HOLogic.dest_eq o HOLogic.dest_Trueprop o concl_of |
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val is_numeral = is_numeral |
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val numeral_0_eq_0 = int_numeral_0_eq_0 |
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val numeral_1_eq_1 = int_numeral_1_eq_1 |
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val prove_conv = prove_conv_nohyps_novars |
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fun norm_tac simps = ALLGOALS (simp_tac (HOL_ss addsimps simps)) |
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val simplify_meta_eq = simplify_meta_eq |
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end |
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|
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structure IntAbstractNumerals = AbstractNumeralsFun (IntAbstractNumeralsData) |
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(*For addition, we already have rules for the operand 0. |
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Multiplication is omitted because there are already special rules for |
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both 0 and 1 as operands. Unary minus is trivial, just have - 1 = -1. |
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For the others, having three patterns is a compromise between just having |
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one (many spurious calls) and having nine (just too many!) *) |
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val eval_numerals = |
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map prep_simproc |
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[("int_add_eval_numerals", |
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["(m::int) + 1", "(m::int) + number_of v"], |
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IntAbstractNumerals.proc (number_of_add RS sym)), |
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("int_diff_eval_numerals", |
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["(m::int) - 1", "(m::int) - number_of v"], |
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IntAbstractNumerals.proc diff_number_of_eq), |
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("int_eq_eval_numerals", |
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["(m::int) = 0", "(m::int) = 1", "(m::int) = number_of v"], |
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IntAbstractNumerals.proc eq_number_of_eq), |
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("int_less_eval_numerals", |
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["(m::int) < 0", "(m::int) < 1", "(m::int) < number_of v"], |
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IntAbstractNumerals.proc less_number_of_eq_neg), |
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("int_le_eval_numerals", |
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["(m::int) <= 0", "(m::int) <= 1", "(m::int) <= number_of v"], |
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IntAbstractNumerals.proc le_number_of_eq_not_less)] |
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(*reorientation simprules using ==, for the following simproc*) |
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val meta_zero_reorient = zero_reorient RS eq_reflection |
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val meta_one_reorient = one_reorient RS eq_reflection |
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val meta_number_of_reorient = number_of_reorient RS eq_reflection |
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(*reorientation simplification procedure: reorients (polymorphic) |
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0 = x, 1 = x, nnn = x provided x isn't 0, 1 or a numeral.*) |
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fun reorient_proc sg _ (_ $ t $ u) = |
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case u of |
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Const("0", _) => None |
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| Const("1", _) => None |
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| Const("Numeral.number_of", _) $ _ => None |
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| _ => Some (case t of |
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Const("0", _) => meta_zero_reorient |
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| Const("1", _) => meta_one_reorient |
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| Const("Numeral.number_of", _) $ _ => meta_number_of_reorient) |
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|
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val reorient_simproc = |
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prep_simproc ("reorient_simproc", ["0=x", "1=x", "number_of w = x"], reorient_proc) |
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|
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end; |
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|
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185 |
|
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Addsimprocs Bin_Simprocs.eval_numerals; |
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Addsimprocs [Bin_Simprocs.reorient_simproc]; |
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|
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|
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structure Int_Numeral_Simprocs = |
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struct |
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|
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193 |
(*Maps 0 to Numeral0 and 1 to Numeral1 so that arithmetic in simprocs |
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194 |
isn't complicated by the abstract 0 and 1.*) |
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val numeral_syms = [int_numeral_0_eq_0 RS sym, int_numeral_1_eq_1 RS sym]; |
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val numeral_sym_ss = HOL_ss addsimps numeral_syms; |
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197 |
|
13462 | 198 |
fun rename_numerals th = |
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199 |
simplify numeral_sym_ss (Thm.transfer (the_context ()) th); |
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200 |
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201 |
(*Utilities*) |
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202 |
|
10693 | 203 |
fun mk_numeral n = HOLogic.number_of_const HOLogic.intT $ HOLogic.mk_bin n; |
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|
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205 |
(*Decodes a binary INTEGER*) |
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206 |
fun dest_numeral (Const("0", _)) = 0 |
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207 |
| dest_numeral (Const("1", _)) = 1 |
13462 | 208 |
| dest_numeral (Const("Numeral.number_of", _) $ w) = |
10890 | 209 |
(HOLogic.dest_binum w |
210 |
handle TERM _ => raise TERM("Int_Numeral_Simprocs.dest_numeral:1", [w])) |
|
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| dest_numeral t = raise TERM("Int_Numeral_Simprocs.dest_numeral:2", [t]); |
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|
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213 |
fun find_first_numeral past (t::terms) = |
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((dest_numeral t, rev past @ terms) |
215 |
handle TERM _ => find_first_numeral (t::past) terms) |
|
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| find_first_numeral past [] = raise TERM("find_first_numeral", []); |
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217 |
|
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val zero = mk_numeral 0; |
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val mk_plus = HOLogic.mk_binop "op +"; |
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|
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val uminus_const = Const ("uminus", HOLogic.intT --> HOLogic.intT); |
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222 |
|
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223 |
(*Thus mk_sum[t] yields t+0; longer sums don't have a trailing zero*) |
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224 |
fun mk_sum [] = zero |
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225 |
| mk_sum [t,u] = mk_plus (t, u) |
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| mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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|
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228 |
(*this version ALWAYS includes a trailing zero*) |
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229 |
fun long_mk_sum [] = zero |
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230 |
| long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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231 |
|
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232 |
val dest_plus = HOLogic.dest_bin "op +" HOLogic.intT; |
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|
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234 |
(*decompose additions AND subtractions as a sum*) |
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235 |
fun dest_summing (pos, Const ("op +", _) $ t $ u, ts) = |
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236 |
dest_summing (pos, t, dest_summing (pos, u, ts)) |
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237 |
| dest_summing (pos, Const ("op -", _) $ t $ u, ts) = |
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238 |
dest_summing (pos, t, dest_summing (not pos, u, ts)) |
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239 |
| dest_summing (pos, t, ts) = |
13462 | 240 |
if pos then t::ts else uminus_const$t :: ts; |
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241 |
|
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242 |
fun dest_sum t = dest_summing (true, t, []); |
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243 |
|
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244 |
val mk_diff = HOLogic.mk_binop "op -"; |
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245 |
val dest_diff = HOLogic.dest_bin "op -" HOLogic.intT; |
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246 |
|
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247 |
val one = mk_numeral 1; |
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248 |
val mk_times = HOLogic.mk_binop "op *"; |
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249 |
|
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250 |
fun mk_prod [] = one |
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251 |
| mk_prod [t] = t |
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252 |
| mk_prod (t :: ts) = if t = one then mk_prod ts |
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253 |
else mk_times (t, mk_prod ts); |
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|
254 |
|
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|
255 |
val dest_times = HOLogic.dest_bin "op *" HOLogic.intT; |
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|
256 |
|
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|
257 |
fun dest_prod t = |
13462 | 258 |
let val (t,u) = dest_times t |
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259 |
in dest_prod t @ dest_prod u end |
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260 |
handle TERM _ => [t]; |
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|
261 |
|
13462 | 262 |
(*DON'T do the obvious simplifications; that would create special cases*) |
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|
263 |
fun mk_coeff (k, ts) = mk_times (mk_numeral k, ts); |
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|
264 |
|
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|
265 |
(*Express t as a product of (possibly) a numeral with other sorted terms*) |
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|
266 |
fun dest_coeff sign (Const ("uminus", _) $ t) = dest_coeff (~sign) t |
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|
267 |
| dest_coeff sign t = |
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|
268 |
let val ts = sort Term.term_ord (dest_prod t) |
13462 | 269 |
val (n, ts') = find_first_numeral [] ts |
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|
270 |
handle TERM _ => (1, ts) |
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|
271 |
in (sign*n, mk_prod ts') end; |
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|
272 |
|
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|
273 |
(*Find first coefficient-term THAT MATCHES u*) |
13462 | 274 |
fun find_first_coeff past u [] = raise TERM("find_first_coeff", []) |
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275 |
| find_first_coeff past u (t::terms) = |
13462 | 276 |
let val (n,u') = dest_coeff 1 t |
277 |
in if u aconv u' then (n, rev past @ terms) |
|
278 |
else find_first_coeff (t::past) u terms |
|
279 |
end |
|
280 |
handle TERM _ => find_first_coeff (t::past) u terms; |
|
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|
281 |
|
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|
282 |
|
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Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
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|
283 |
(*Simplify Numeral0+n, n+Numeral0, Numeral1*n, n*Numeral1*) |
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|
284 |
val add_0s = map rename_numerals [zadd_0, zadd_0_right]; |
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|
285 |
val mult_1s = map rename_numerals [zmult_1, zmult_1_right] @ |
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|
286 |
[zmult_minus1, zmult_minus1_right]; |
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|
287 |
|
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|
288 |
(*To perform binary arithmetic. The "left" rewriting handles patterns |
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289 |
created by the simprocs, such as 3 * (5 * x). *) |
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290 |
val bin_simps = [int_numeral_0_eq_0 RS sym, int_numeral_1_eq_1 RS sym, |
13462 | 291 |
add_number_of_left, mult_number_of_left] @ |
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|
292 |
bin_arith_simps @ bin_rel_simps; |
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|
293 |
|
14113 | 294 |
(*Binary arithmetic BUT NOT ADDITION since it may collapse adjacent terms |
295 |
during re-arrangement*) |
|
296 |
val non_add_bin_simps = |
|
297 |
bin_simps \\ [add_number_of_left, number_of_add RS sym]; |
|
298 |
||
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|
299 |
(*To evaluate binary negations of coefficients*) |
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|
300 |
val zminus_simps = NCons_simps @ |
13462 | 301 |
[zminus_1_eq_m1, number_of_minus RS sym, |
302 |
bin_minus_1, bin_minus_0, bin_minus_Pls, bin_minus_Min, |
|
303 |
bin_pred_1, bin_pred_0, bin_pred_Pls, bin_pred_Min]; |
|
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|
304 |
|
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|
305 |
(*To let us treat subtraction as addition*) |
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|
306 |
val diff_simps = [zdiff_def, zminus_zadd_distrib, zminus_zminus]; |
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|
307 |
|
10713
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simproc bug fix: negative literals and large terms
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diff
changeset
|
308 |
(*push the unary minus down: - x * y = x * - y *) |
13462 | 309 |
val int_minus_mult_eq_1_to_2 = |
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|
310 |
[zmult_zminus, zmult_zminus_right RS sym] MRS trans |> standard; |
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|
311 |
|
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diff
changeset
|
312 |
(*to extract again any uncancelled minuses*) |
13462 | 313 |
val int_minus_from_mult_simps = |
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diff
changeset
|
314 |
[zminus_zminus, zmult_zminus, zmult_zminus_right]; |
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diff
changeset
|
315 |
|
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diff
changeset
|
316 |
(*combine unary minus with numeric literals, however nested within a product*) |
69c9fc1d11f2
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diff
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|
317 |
val int_mult_minus_simps = |
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diff
changeset
|
318 |
[zmult_assoc, zmult_zminus RS sym, int_minus_mult_eq_1_to_2]; |
69c9fc1d11f2
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paulson
parents:
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diff
changeset
|
319 |
|
9436
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|
320 |
(*Apply the given rewrite (if present) just once*) |
62bb04ab4b01
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|
321 |
fun trans_tac None = all_tac |
62bb04ab4b01
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changeset
|
322 |
| trans_tac (Some th) = ALLGOALS (rtac (th RS trans)); |
62bb04ab4b01
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|
323 |
|
62bb04ab4b01
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|
324 |
fun simplify_meta_eq rules = |
62bb04ab4b01
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parents:
diff
changeset
|
325 |
simplify (HOL_basic_ss addeqcongs[eq_cong2] addsimps rules) |
12975 | 326 |
o mk_meta_eq; |
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|
327 |
|
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parents:
diff
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|
328 |
structure CancelNumeralsCommon = |
62bb04ab4b01
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parents:
diff
changeset
|
329 |
struct |
13462 | 330 |
val mk_sum = mk_sum |
331 |
val dest_sum = dest_sum |
|
332 |
val mk_coeff = mk_coeff |
|
333 |
val dest_coeff = dest_coeff 1 |
|
334 |
val find_first_coeff = find_first_coeff [] |
|
9436
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parents:
diff
changeset
|
335 |
val trans_tac = trans_tac |
13462 | 336 |
val norm_tac = |
11868
56db9f3a6b3e
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paulson
parents:
11713
diff
changeset
|
337 |
ALLGOALS (simp_tac (HOL_ss addsimps numeral_syms@add_0s@mult_1s@ |
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
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diff
changeset
|
338 |
diff_simps@zminus_simps@zadd_ac)) |
14113 | 339 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps non_add_bin_simps@int_mult_minus_simps)) |
10713
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
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diff
changeset
|
340 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps int_minus_from_mult_simps@ |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
341 |
zadd_ac@zmult_ac)) |
13462 | 342 |
val numeral_simp_tac = ALLGOALS (simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
9436
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parents:
diff
changeset
|
343 |
val simplify_meta_eq = simplify_meta_eq (add_0s@mult_1s) |
62bb04ab4b01
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parents:
diff
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|
344 |
end; |
62bb04ab4b01
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parents:
diff
changeset
|
345 |
|
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
346 |
|
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
347 |
structure EqCancelNumerals = CancelNumeralsFun |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
348 |
(open CancelNumeralsCommon |
13485
acf39e924091
tuned prove_conv (error reporting done within meta_simplifier.ML);
wenzelm
parents:
13462
diff
changeset
|
349 |
val prove_conv = Bin_Simprocs.prove_conv |
9436
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
350 |
val mk_bal = HOLogic.mk_eq |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
351 |
val dest_bal = HOLogic.dest_bin "op =" HOLogic.intT |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
352 |
val bal_add1 = eq_add_iff1 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
353 |
val bal_add2 = eq_add_iff2 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
354 |
); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
355 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
356 |
structure LessCancelNumerals = CancelNumeralsFun |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
357 |
(open CancelNumeralsCommon |
13485
acf39e924091
tuned prove_conv (error reporting done within meta_simplifier.ML);
wenzelm
parents:
13462
diff
changeset
|
358 |
val prove_conv = Bin_Simprocs.prove_conv |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
359 |
val mk_bal = HOLogic.mk_binrel "op <" |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
360 |
val dest_bal = HOLogic.dest_bin "op <" HOLogic.intT |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
361 |
val bal_add1 = less_add_iff1 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
362 |
val bal_add2 = less_add_iff2 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
363 |
); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
364 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
365 |
structure LeCancelNumerals = CancelNumeralsFun |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
366 |
(open CancelNumeralsCommon |
13485
acf39e924091
tuned prove_conv (error reporting done within meta_simplifier.ML);
wenzelm
parents:
13462
diff
changeset
|
367 |
val prove_conv = Bin_Simprocs.prove_conv |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
368 |
val mk_bal = HOLogic.mk_binrel "op <=" |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
369 |
val dest_bal = HOLogic.dest_bin "op <=" HOLogic.intT |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
370 |
val bal_add1 = le_add_iff1 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
371 |
val bal_add2 = le_add_iff2 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
372 |
); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
373 |
|
13462 | 374 |
val cancel_numerals = |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
375 |
map Bin_Simprocs.prep_simproc |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
376 |
[("inteq_cancel_numerals", |
13462 | 377 |
["(l::int) + m = n", "(l::int) = m + n", |
378 |
"(l::int) - m = n", "(l::int) = m - n", |
|
379 |
"(l::int) * m = n", "(l::int) = m * n"], |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
380 |
EqCancelNumerals.proc), |
13462 | 381 |
("intless_cancel_numerals", |
382 |
["(l::int) + m < n", "(l::int) < m + n", |
|
383 |
"(l::int) - m < n", "(l::int) < m - n", |
|
384 |
"(l::int) * m < n", "(l::int) < m * n"], |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
385 |
LessCancelNumerals.proc), |
13462 | 386 |
("intle_cancel_numerals", |
387 |
["(l::int) + m <= n", "(l::int) <= m + n", |
|
388 |
"(l::int) - m <= n", "(l::int) <= m - n", |
|
389 |
"(l::int) * m <= n", "(l::int) <= m * n"], |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
390 |
LeCancelNumerals.proc)]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
391 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
392 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
393 |
structure CombineNumeralsData = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
394 |
struct |
13462 | 395 |
val add = op + : int*int -> int |
396 |
val mk_sum = long_mk_sum (*to work for e.g. 2*x + 3*x *) |
|
397 |
val dest_sum = dest_sum |
|
398 |
val mk_coeff = mk_coeff |
|
399 |
val dest_coeff = dest_coeff 1 |
|
14272
5efbb548107d
Tidying of the integer development; towards removing the
paulson
parents:
14271
diff
changeset
|
400 |
val left_distrib = combine_common_factor RS trans |
13485
acf39e924091
tuned prove_conv (error reporting done within meta_simplifier.ML);
wenzelm
parents:
13462
diff
changeset
|
401 |
val prove_conv = Bin_Simprocs.prove_conv_nohyps |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
402 |
val trans_tac = trans_tac |
13462 | 403 |
val norm_tac = |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
404 |
ALLGOALS (simp_tac (HOL_ss addsimps numeral_syms@add_0s@mult_1s@ |
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
405 |
diff_simps@zminus_simps@zadd_ac)) |
14113 | 406 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps non_add_bin_simps@int_mult_minus_simps)) |
10713
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
407 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps int_minus_from_mult_simps@ |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
408 |
zadd_ac@zmult_ac)) |
13462 | 409 |
val numeral_simp_tac = ALLGOALS |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
410 |
(simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
411 |
val simplify_meta_eq = simplify_meta_eq (add_0s@mult_1s) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
412 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
413 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
414 |
structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData); |
13462 | 415 |
|
416 |
val combine_numerals = |
|
417 |
Bin_Simprocs.prep_simproc |
|
418 |
("int_combine_numerals", ["(i::int) + j", "(i::int) - j"], CombineNumerals.proc); |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
419 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
420 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
421 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
422 |
Addsimprocs Int_Numeral_Simprocs.cancel_numerals; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
423 |
Addsimprocs [Int_Numeral_Simprocs.combine_numerals]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
424 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
425 |
(*examples: |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
426 |
print_depth 22; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
427 |
set timing; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
428 |
set trace_simp; |
13462 | 429 |
fun test s = (Goal s, by (Simp_tac 1)); |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
430 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
431 |
test "l + 2 + 2 + 2 + (l + 2) + (oo + 2) = (uu::int)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
432 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
433 |
test "2*u = (u::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
434 |
test "(i + j + 12 + (k::int)) - 15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
435 |
test "(i + j + 12 + (k::int)) - 5 = y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
436 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
437 |
test "y - b < (b::int)"; |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
438 |
test "y - (3*b + c) < (b::int) - 2*c"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
439 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
440 |
test "(2*x - (u*v) + y) - v*3*u = (w::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
441 |
test "(2*x*u*v + (u*v)*4 + y) - v*u*4 = (w::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
442 |
test "(2*x*u*v + (u*v)*4 + y) - v*u = (w::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
443 |
test "u*v - (x*u*v + (u*v)*4 + y) = (w::int)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
444 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
445 |
test "(i + j + 12 + (k::int)) = u + 15 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
446 |
test "(i + j*2 + 12 + (k::int)) = j + 5 + y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
447 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
448 |
test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + (vv::int)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
449 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
450 |
test "a + -(b+c) + b = (d::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
451 |
test "a + -(b+c) - b = (d::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
452 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
453 |
(*negative numerals*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
454 |
test "(i + j + -2 + (k::int)) - (u + 5 + y) = zz"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
455 |
test "(i + j + -3 + (k::int)) < u + 5 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
456 |
test "(i + j + 3 + (k::int)) < u + -6 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
457 |
test "(i + j + -12 + (k::int)) - 15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
458 |
test "(i + j + 12 + (k::int)) - -15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
459 |
test "(i + j + -12 + (k::int)) - -15 = y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
460 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
461 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
462 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
463 |
(** Constant folding for integer plus and times **) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
464 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
465 |
(*We do not need |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
466 |
structure Nat_Plus_Assoc = Assoc_Fold (Nat_Plus_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
467 |
structure Int_Plus_Assoc = Assoc_Fold (Int_Plus_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
468 |
because combine_numerals does the same thing*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
469 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
470 |
structure Int_Times_Assoc_Data : ASSOC_FOLD_DATA = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
471 |
struct |
13462 | 472 |
val ss = HOL_ss |
473 |
val eq_reflection = eq_reflection |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
474 |
val sg_ref = Sign.self_ref (Theory.sign_of (the_context ())) |
13462 | 475 |
val T = HOLogic.intT |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
476 |
val plus = Const ("op *", [HOLogic.intT,HOLogic.intT] ---> HOLogic.intT); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
477 |
val add_ac = zmult_ac |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
478 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
479 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
480 |
structure Int_Times_Assoc = Assoc_Fold (Int_Times_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
481 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
482 |
Addsimprocs [Int_Times_Assoc.conv]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
483 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
484 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
485 |
(** The same for the naturals **) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
486 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
487 |
structure Nat_Times_Assoc_Data : ASSOC_FOLD_DATA = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
488 |
struct |
13462 | 489 |
val ss = HOL_ss |
490 |
val eq_reflection = eq_reflection |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
491 |
val sg_ref = Sign.self_ref (Theory.sign_of (the_context ())) |
13462 | 492 |
val T = HOLogic.natT |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
493 |
val plus = Const ("op *", [HOLogic.natT,HOLogic.natT] ---> HOLogic.natT); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
494 |
val add_ac = mult_ac |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
495 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
496 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
497 |
structure Nat_Times_Assoc = Assoc_Fold (Nat_Times_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
498 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
499 |
Addsimprocs [Nat_Times_Assoc.conv]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
500 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
501 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
502 |
(*** decision procedure for linear arithmetic ***) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
503 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
504 |
(*---------------------------------------------------------------------------*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
505 |
(* Linear arithmetic *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
506 |
(*---------------------------------------------------------------------------*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
507 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
508 |
(* |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
509 |
Instantiation of the generic linear arithmetic package for int. |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
510 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
511 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
512 |
(* Update parameters of arithmetic prover *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
513 |
local |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
514 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
515 |
(* reduce contradictory <= to False *) |
13462 | 516 |
val add_rules = |
517 |
simp_thms @ bin_arith_simps @ bin_rel_simps @ |
|
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
518 |
[int_numeral_0_eq_0, int_numeral_1_eq_1, |
14368
2763da611ad9
converted Real/Lubs to Isar script. Converting arithmetic setup
paulson
parents:
14331
diff
changeset
|
519 |
zminus_0, zdiff_def, |
13462 | 520 |
zadd_zminus_inverse, zadd_zminus_inverse2, |
521 |
zmult_0, zmult_0_right, |
|
12482
d2848ccc9757
new rewrite rules for use by arith_tac to take care of uminus.
nipkow
parents:
12018
diff
changeset
|
522 |
zmult_1, zmult_1_right, |
d2848ccc9757
new rewrite rules for use by arith_tac to take care of uminus.
nipkow
parents:
12018
diff
changeset
|
523 |
zmult_zminus, zmult_zminus_right, |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
524 |
zminus_zadd_distrib, zminus_zminus, zmult_assoc, |
13499 | 525 |
int_0, int_1, int_Suc, zadd_int RS sym, zmult_int RS sym]; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
526 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
527 |
val simprocs = [Int_Times_Assoc.conv, Int_Numeral_Simprocs.combine_numerals]@ |
13462 | 528 |
Int_Numeral_Simprocs.cancel_numerals @ |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
529 |
Bin_Simprocs.eval_numerals; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
530 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
531 |
in |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
532 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
533 |
val int_arith_setup = |
10693 | 534 |
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} => |
14368
2763da611ad9
converted Real/Lubs to Isar script. Converting arithmetic setup
paulson
parents:
14331
diff
changeset
|
535 |
{add_mono_thms = add_mono_thms, |
10693 | 536 |
mult_mono_thms = mult_mono_thms, |
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
537 |
inj_thms = [zle_int RS iffD2,int_int_eq RS iffD2] @ inj_thms, |
14272
5efbb548107d
Tidying of the integer development; towards removing the
paulson
parents:
14271
diff
changeset
|
538 |
lessD = lessD @ [zless_imp_add1_zle], |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
539 |
simpset = simpset addsimps add_rules |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
540 |
addsimprocs simprocs |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
541 |
addcongs [if_weak_cong]}), |
10834 | 542 |
arith_inj_const ("IntDef.int", HOLogic.natT --> HOLogic.intT), |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
543 |
arith_discrete ("IntDef.int", true)]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
544 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
545 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
546 |
|
13462 | 547 |
val fast_int_arith_simproc = |
548 |
Simplifier.simproc (Theory.sign_of (the_context())) |
|
549 |
"fast_int_arith" ["(m::int) < n","(m::int) <= n", "(m::int) = n"] Fast_Arith.lin_arith_prover; |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
550 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
551 |
Addsimprocs [fast_int_arith_simproc] |
13462 | 552 |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
553 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
554 |
(* Some test data |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
555 |
Goal "!!a::int. [| a <= b; c <= d; x+y<z |] ==> a+c <= b+d"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
556 |
by (fast_arith_tac 1); |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
557 |
Goal "!!a::int. [| a < b; c < d |] ==> a-d+ 2 <= b+(-c)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
558 |
by (fast_arith_tac 1); |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
559 |
Goal "!!a::int. [| a < b; c < d |] ==> a+c+ 1 < b+d"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
560 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
561 |
Goal "!!a::int. [| a <= b; b+b <= c |] ==> a+a <= c"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
562 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
563 |
Goal "!!a::int. [| a+b <= i+j; a<=b; i<=j |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
564 |
\ ==> a+a <= j+j"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
565 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
566 |
Goal "!!a::int. [| a+b < i+j; a<b; i<j |] \ |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
567 |
\ ==> a+a - - -1 < j+j - 3"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
568 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
569 |
Goal "!!a::int. a+b+c <= i+j+k & a<=b & b<=c & i<=j & j<=k --> a+a+a <= k+k+k"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
570 |
by (arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
571 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
572 |
\ ==> a <= l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
573 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
574 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
575 |
\ ==> a+a+a+a <= l+l+l+l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
576 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
577 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
578 |
\ ==> a+a+a+a+a <= l+l+l+l+i"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
579 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
580 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
581 |
\ ==> a+a+a+a+a+a <= l+l+l+l+i+l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
582 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
583 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
584 |
\ ==> 6*a <= 5*l+i"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
585 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
586 |
*) |