diff options
Diffstat (limited to 'src/Util/Decidable.v')
| -rw-r--r-- | src/Util/Decidable.v | 29 |
1 files changed, 16 insertions, 13 deletions
diff --git a/src/Util/Decidable.v b/src/Util/Decidable.v index 726b52b6b..9ab05699a 100644 --- a/src/Util/Decidable.v +++ b/src/Util/Decidable.v @@ -32,24 +32,24 @@ Local Ltac solve_decidable_transparent := solve_decidable_transparent_with first Local Hint Extern 0 => solve [ solve_decidable_transparent ] : typeclass_instances. -Global Instance dec_True : Decidable True := left I. -Global Instance dec_False : Decidable False := right (fun x => x). -Global Instance dec_or {A B} `{Decidable A, Decidable B} : Decidable (A \/ B). exact _. Defined. -Global Instance dec_and {A B} `{Decidable A, Decidable B} : Decidable (A /\ B). exact _. Defined. -Global Instance dec_impl {A B} `{Decidable (B \/ ~A)} : Decidable (A -> B) | 3. exact _. Defined. -Global Instance dec_impl_simple {A B} `{Decidable A, Decidable B} : Decidable (A -> B). exact _. Defined. -Global Instance dec_iff {A B} `{Decidable A, Decidable B} : Decidable (A <-> B). exact _. Defined. +Global Instance dec_True : Decidable True | 10 := left I. +Global Instance dec_False : Decidable False | 10 := right (fun x => x). +Global Instance dec_or {A B} `{Decidable A, Decidable B} : Decidable (A \/ B) | 10. exact _. Defined. +Global Instance dec_and {A B} `{Decidable A, Decidable B} : Decidable (A /\ B) | 10. exact _. Defined. +Global Instance dec_impl {A B} `{Decidable (B \/ ~A)} : Decidable (A -> B) | 10. exact _. Defined. +Global Instance dec_impl_simple {A B} `{Decidable A, Decidable B} : Decidable (A -> B) | 10. exact _. Defined. +Global Instance dec_iff {A B} `{Decidable A, Decidable B} : Decidable (A <-> B) | 10. exact _. Defined. Lemma dec_not {A} `{Decidable A} : Decidable (~A). Proof. solve_decidable_transparent. Defined. (** Disallow infinite loops of dec_not *) Hint Extern 0 (Decidable (~?A)) => apply (@dec_not A) : typeclass_instances. -Global Instance dec_eq_unit : DecidableRel (@eq unit). exact _. Defined. -Global Instance dec_eq_bool : DecidableRel (@eq bool). exact _. Defined. -Global Instance dec_eq_Empty_set : DecidableRel (@eq Empty_set). exact _. Defined. -Global Instance dec_eq_nat : DecidableRel (@eq nat). exact _. Defined. -Global Instance dec_eq_prod {A B} `{DecidableRel (@eq A), DecidableRel (@eq B)} : DecidableRel (@eq (A * B)). exact _. Defined. -Global Instance dec_eq_sum {A B} `{DecidableRel (@eq A), DecidableRel (@eq B)} : DecidableRel (@eq (A + B)). exact _. Defined. +Global Instance dec_eq_unit : DecidableRel (@eq unit) | 10. exact _. Defined. +Global Instance dec_eq_bool : DecidableRel (@eq bool) | 10. exact _. Defined. +Global Instance dec_eq_Empty_set : DecidableRel (@eq Empty_set) | 10. exact _. Defined. +Global Instance dec_eq_nat : DecidableRel (@eq nat) | 10. exact _. Defined. +Global Instance dec_eq_prod {A B} `{DecidableRel (@eq A), DecidableRel (@eq B)} : DecidableRel (@eq (A * B)) | 10. exact _. Defined. +Global Instance dec_eq_sum {A B} `{DecidableRel (@eq A), DecidableRel (@eq B)} : DecidableRel (@eq (A + B)) | 10. exact _. Defined. Lemma Decidable_respects_iff A B (H : A <-> B) : (Decidable A -> Decidable B) * (Decidable B -> Decidable A). Proof. solve_decidable_transparent. Defined. @@ -59,3 +59,6 @@ Proof. solve_decidable_transparent. Defined. Lemma Decidable_iff_to_flip_impl A B (H : A <-> B) : Decidable B -> Decidable A. Proof. solve_decidable_transparent. Defined. + +(** For dubious compatibility with [eauto using]. *) +Hint Extern 2 (Decidable _) => progress unfold Decidable : typeclass_instances core. |