diff options
Diffstat (limited to 'src/Util/Bool.v')
| -rw-r--r-- | src/Util/Bool.v | 43 |
1 files changed, 43 insertions, 0 deletions
diff --git a/src/Util/Bool.v b/src/Util/Bool.v new file mode 100644 index 000000000..031718c87 --- /dev/null +++ b/src/Util/Bool.v @@ -0,0 +1,43 @@ +(*** Boolean Utility Lemmas and Databases *) +Require Import Coq.Bool.Bool. + +(** For equalities of booleans *) +Create HintDb bool_congr discriminated. +(** For properties of booleans, with, e.g., [iff] *) +Create HintDb bool_congr_setoid discriminated. +(** For generic simplifications of things involving booleans, e.g., if-statements *) +Create HintDb boolsimplify discriminated. + +Hint Extern 1 => progress autorewrite with boolsimplify in * : boolsimplify. +Hint Extern 1 => progress autorewrite with bool_congr in * : bool_congr. +Hint Extern 1 => progress autorewrite with bool_congr_setoid in * : bool_congr_setoid. +Hint Extern 2 => progress rewrite_strat topdown hints bool_congr_setoid : bool_congr_setoid. + +Hint Rewrite Bool.andb_diag Bool.orb_diag Bool.eqb_reflx Bool.negb_involutive Bool.eqb_negb1 Bool.eqb_negb2 Bool.orb_true_r Bool.orb_true_l Bool.orb_false_r Bool.orb_false_l Bool.orb_negb_r Bool.andb_false_r Bool.andb_false_l Bool.andb_true_r Bool.andb_false_r Bool.andb_negb_r Bool.absorption_andb Bool.absorption_orb Bool.xorb_false_r Bool.xorb_false_l Bool.xorb_true_r Bool.xorb_true_l Bool.xorb_nilpotent : bool_congr. +Hint Rewrite Bool.negb_if : boolsimplify. +Hint Rewrite <- Bool.andb_if Bool.andb_lazy_alt Bool.orb_lazy_alt : boolsimplify. +Hint Rewrite Bool.not_true_iff_false Bool.not_false_iff_true Bool.eqb_true_iff Bool.eqb_false_iff Bool.negb_true_iff Bool.negb_false_iff Bool.orb_true_iff Bool.orb_false_iff Bool.andb_true_iff Bool.andb_false_iff Bool.xorb_negb_negb : bool_congr_setoid. + +Create HintDb push_orb discriminated. +Create HintDb pull_orb discriminated. +Create HintDb push_andb discriminated. +Create HintDb pull_andb discriminated. +Create HintDb push_negb discriminated. +Create HintDb pull_negb discriminated. +Hint Extern 1 => progress autorewrite with push_orb in * : push_orb. +Hint Extern 1 => progress autorewrite with pull_orb in * : pull_orb. +Hint Extern 1 => progress autorewrite with push_andb in * : push_andb. +Hint Extern 1 => progress autorewrite with pull_andb in * : pull_andb. +Hint Extern 1 => progress autorewrite with push_negb in * : push_negb. +Hint Extern 1 => progress autorewrite with pull_negb in * : pull_negb. +Hint Rewrite Bool.negb_orb Bool.negb_andb : push_negb. +Hint Rewrite Bool.xorb_negb_negb : pull_negb. +Hint Rewrite <- Bool.negb_orb Bool.negb_andb Bool.negb_xorb_l Bool.negb_xorb_r : pull_negb. +Hint Rewrite Bool.andb_orb_distrib_r Bool.andb_orb_distrib_l : push_andb. +Hint Rewrite <- Bool.orb_andb_distrib_r Bool.orb_andb_distrib_l : push_andb. +Hint Rewrite Bool.orb_andb_distrib_r Bool.orb_andb_distrib_l : pull_andb. +Hint Rewrite <- Bool.andb_orb_distrib_r Bool.andb_orb_distrib_l : pull_andb. +Hint Rewrite Bool.orb_andb_distrib_r Bool.orb_andb_distrib_l : push_orb. +Hint Rewrite <- Bool.andb_orb_distrib_r Bool.andb_orb_distrib_l : push_orb. +Hint Rewrite <- Bool.orb_andb_distrib_r Bool.orb_andb_distrib_l : pull_orb. +Hint Rewrite Bool.andb_orb_distrib_r Bool.andb_orb_distrib_l : pull_orb. |