diff options
| -rw-r--r-- | _CoqProject | 1 | ||||
| -rw-r--r-- | src/Util/Bool.v | 43 | ||||
| -rw-r--r-- | src/Util/ZUtil.v | 10 |
3 files changed, 53 insertions, 1 deletions
diff --git a/_CoqProject b/_CoqProject index 0d45357f9..fe9916326 100644 --- a/_CoqProject +++ b/_CoqProject @@ -62,6 +62,7 @@ src/Specific/GF25519.v src/Tactics/VerdiTactics.v src/Tactics/Algebra_syntax/Nsatz.v src/Util/AdditionChainExponentiation.v +src/Util/Bool.v src/Util/CaseUtil.v src/Util/Decidable.v src/Util/Equality.v 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. diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v index 0b1d097bb..b7547f150 100644 --- a/src/Util/ZUtil.v +++ b/src/Util/ZUtil.v @@ -24,7 +24,7 @@ Hint Resolve (fun a b H => proj1 (Z.mod_pos_bound a b H)) (fun a b H => proj2 (Z which can reasonably be said to "simplify" the goal, should go in this database. *) Create HintDb zsimplify discriminated. -Hint Rewrite Z.div_1_r Z.mul_1_r Z.mul_1_l Z.sub_diag Z.mul_0_r Z.mul_0_l Z.add_0_l Z.add_0_r Z.opp_involutive Z.sub_0_r Z_mod_same_full Z.sub_simpl_r Z.sub_simpl_l Z.add_opp_diag_r Z.add_opp_diag_l Zmod_0_l Z.add_simpl_r Z.add_simpl_l : zsimplify. +Hint Rewrite Z.div_1_r Z.mul_1_r Z.mul_1_l Z.sub_diag Z.mul_0_r Z.mul_0_l Z.add_0_l Z.add_0_r Z.opp_involutive Z.sub_0_r Z_mod_same_full Z.sub_simpl_r Z.sub_simpl_l Z.add_opp_diag_r Z.add_opp_diag_l Zmod_0_l Z.add_simpl_r Z.add_simpl_l Z.opp_0 : zsimplify. Hint Rewrite Z.div_mul Z.div_1_l Z.div_same Z.mod_same Z.div_small Z.mod_small Z.div_add Z.div_add_l Z.mod_add Z.div_0_l Z.mod_mod using lia : zsimplify. Hint Rewrite <- Z.opp_eq_mul_m1 : zsimplify. @@ -1162,6 +1162,14 @@ Module Z. reflexivity. Qed. + Lemma minus_distr_if (b : bool) x y : -(if b then x else y) = if b then -x else -y. + Proof. destruct b; reflexivity. Qed. + Hint Rewrite minus_distr_if : push_Zopp. + + Lemma minus_minus_one : - -1 = 1. + Proof. reflexivity. Qed. + Hint Rewrite minus_minus_one : zsimplify. + Lemma mul_mod_l a b n : n <> 0 -> (a * b) mod n = ((a mod n) * b) mod n. Proof. intros; rewrite (Z.mul_mod a b), (Z.mul_mod (a mod n) b) by lia. |