diff options
Diffstat (limited to 'theories/Classes/EquivDec.v')
| -rw-r--r-- | theories/Classes/EquivDec.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v index 6ce34535e..4b9b26384 100644 --- a/theories/Classes/EquivDec.v +++ b/theories/Classes/EquivDec.v @@ -18,7 +18,7 @@ Require Export Coq.Classes.Equivalence. -(** The [DecidableSetoid] class asserts decidability of a [Setoid]. It can be useful in proofs to reason more +(** The [DecidableSetoid] class asserts decidability of a [Setoid]. It can be useful in proofs to reason more classically. *) Require Import Coq.Logic.Decidable. @@ -43,8 +43,8 @@ Notation " x == y " := (equiv_dec (x :>) (y :>)) (no associativity, at level 70) Definition swap_sumbool {A B} (x : { A } + { B }) : { B } + { A } := match x with - | left H => @right _ _ H - | right H => @left _ _ H + | left H => @right _ _ H + | right H => @left _ _ H end. Open Local Scope program_scope. @@ -89,34 +89,34 @@ Obligation Tactic := unfold complement, equiv ; program_simpl. Program Instance prod_eqdec `(EqDec A eq, EqDec B eq) : ! EqDec (prod A B) eq := { equiv_dec x y := - let '(x1, x2) := x in - let '(y1, y2) := y in - if x1 == y1 then + let '(x1, x2) := x in + let '(y1, y2) := y in + if x1 == y1 then if x2 == y2 then in_left else in_right else in_right }. Program Instance sum_eqdec `(EqDec A eq, EqDec B eq) : EqDec (sum A B) eq := { - equiv_dec x y := + equiv_dec x y := match x, y with | inl a, inl b => if a == b then in_left else in_right | inr a, inr b => if a == b then in_left else in_right | inl _, inr _ | inr _, inl _ => in_right end }. -(** Objects of function spaces with countable domains like bool have decidable equality. +(** Objects of function spaces with countable domains like bool have decidable equality. Proving the reflection requires functional extensionality though. *) Program Instance bool_function_eqdec `(EqDec A eq) : ! EqDec (bool -> A) eq := - { equiv_dec f g := + { equiv_dec f g := if f true == g true then if f false == g false then in_left else in_right else in_right }. Next Obligation. - Proof. + Proof. extensionality x. destruct x ; auto. Qed. @@ -124,11 +124,11 @@ Program Instance bool_function_eqdec `(EqDec A eq) : ! EqDec (bool -> A) eq := Require Import List. Program Instance list_eqdec `(eqa : EqDec A eq) : ! EqDec (list A) eq := - { equiv_dec := + { equiv_dec := fix aux (x : list A) y { struct x } := match x, y with | nil, nil => in_left - | cons hd tl, cons hd' tl' => + | cons hd tl, cons hd' tl' => if hd == hd' then if aux tl tl' then in_left else in_right else in_right |