diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/Classes/RelationClasses.v | 5 | ||||
| -rw-r--r-- | theories/Lists/List.v | 10 |
2 files changed, 10 insertions, 5 deletions
diff --git a/theories/Classes/RelationClasses.v b/theories/Classes/RelationClasses.v index 1a40e5d599..15cb02d37f 100644 --- a/theories/Classes/RelationClasses.v +++ b/theories/Classes/RelationClasses.v @@ -89,6 +89,11 @@ Section Defs. Global Instance Equivalence_PER {R} `(E:Equivalence R) : PER R | 10 := { }. + (** An Equivalence is a PreOrder plus symmetry. *) + + Global Instance Equivalence_PreOrder {R} `(E:Equivalence R) : PreOrder R | 10 := + { }. + (** We can now define antisymmetry w.r.t. an equivalence relation on the carrier. *) Class Antisymmetric eqA `{equ : Equivalence eqA} (R : relation A) := diff --git a/theories/Lists/List.v b/theories/Lists/List.v index c34bbd56e4..2437184a93 100644 --- a/theories/Lists/List.v +++ b/theories/Lists/List.v @@ -45,8 +45,8 @@ Section Lists. Definition hd_error (l:list A) := match l with - | [] => error - | x :: _ => value x + | [] => None + | x :: _ => Some x end. Definition tl (l:list A) := @@ -393,11 +393,11 @@ Section Elts. simpl; auto. Qed. - Fixpoint nth_error (l:list A) (n:nat) {struct n} : Exc A := + Fixpoint nth_error (l:list A) (n:nat) {struct n} : option A := match n, l with - | O, x :: _ => value x + | O, x :: _ => Some x | S n, _ :: l => nth_error l n - | _, _ => error + | _, _ => None end. Definition nth_default (default:A) (l:list A) (n:nat) : A := |