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Diffstat (limited to 'src/Data/Setoid/Either.idr')
-rw-r--r-- | src/Data/Setoid/Either.idr | 37 |
1 files changed, 0 insertions, 37 deletions
diff --git a/src/Data/Setoid/Either.idr b/src/Data/Setoid/Either.idr deleted file mode 100644 index 682ac5a..0000000 --- a/src/Data/Setoid/Either.idr +++ /dev/null @@ -1,37 +0,0 @@ -module Data.Setoid.Either - -import public Data.Setoid - -public export -data Either : (0 r : Rel a) -> (0 s : Rel b) -> Rel (Either a b) where - Left : forall r, s . r x y -> Either r s (Left x) (Left y) - Right : forall r, s . s x y -> Either r s (Right x) (Right y) - -public export -[eitherRefl] Reflexive a rel => Reflexive b rel' => Reflexive (Either a b) (Either rel rel') where - reflexive {x = (Left x)} = Left reflexive - reflexive {x = (Right x)} = Right reflexive - -public export -[eitherSym] Symmetric a rel => Symmetric b rel' => Symmetric (Either a b) (Either rel rel') where - symmetric (Left eq) = Left $ symmetric eq - symmetric (Right eq) = Right $ symmetric eq - -public export -[eitherTrans] Transitive a rel => Transitive b rel' - => Transitive (Either a b) (Either rel rel') where - transitive (Left eq) (Left eq') = Left $ transitive eq eq' - transitive (Right eq) (Right eq') = Right $ transitive eq eq' - -public export -EitherEquivalence : Setoid.Equivalence a rel -> Setoid.Equivalence b rel' - -> Setoid.Equivalence (Either a b) (Either rel rel') -EitherEquivalence eq eq' = MkEquivalence - { refl = MkReflexive $ reflexive @{eitherRefl @{eq.refl} @{eq'.refl}} - , sym = MkSymmetric $ symmetric @{eitherSym @{eq.sym} @{eq'.sym}} - , trans = MkTransitive $ transitive @{eitherTrans @{eq.trans} @{eq'.trans}} - } - -public export -EitherSetoid : Setoid -> Setoid -> Setoid -EitherSetoid x y = MkSetoid _ _ $ EitherEquivalence x.equivalence y.equivalence |