Add instances for Dual categories.

Control/Category/Structures.hs

@@ -1,4 +1,5 @@
 {-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE ConstraintKinds #-}
 {- |
 Module      :  Control.Category.Structures
@@ -20,6 +21,7 @@ import           Control.Arrow (Kleisli(..))
 import qualified Control.Arrow as BadArrow
 import           Control.Category
 import           Control.Monad
+import           Data.Semigroupoid.Dual
 import           Prelude hiding (id, (.))
 
 infixl 3 ***
@@ -50,6 +52,9 @@ class Category cat => Products cat where
 instance Monad m => Products (Kleisli m) where
     (***) = (BadArrow.***)
 
+instance Products cat => Products (Dual cat) where
+    Dual f *** Dual g = Dual $ f *** g
+
 instance Products (->) where
     (***) = (BadArrow.***)
 
@@ -77,6 +82,9 @@ class Category cat => Coproducts cat where
 instance Monad m => Coproducts (Kleisli m) where
     (+++) = (BadArrow.+++)
 
+instance Coproducts cat => Coproducts (Dual cat) where
+    Dual f +++ Dual g = Dual $ f +++ g
+
 instance Coproducts (->) where
     (+++) = (BadArrow.+++)
 
@@ -93,6 +101,10 @@ instance MonadPlus m => CatPlus (Kleisli m) where
     cempty = BadArrow.zeroArrow
     (/+/)  = (BadArrow.<+>)
 
+instance CatPlus cat => CatPlus (Dual cat) where
+    cempty = Dual cempty
+    Dual f /+/ Dual g = Dual $ f /+/ g
+
 -- | A category transformer.
 class CatTrans t where
     -- | Lift an arrow from the base category.

Control/SIArrow.hs

@@ -39,8 +39,10 @@ import Control.Category
 import Control.Category.Structures
 import Control.Lens.Cons
 import Control.Lens.Empty
+import Control.Lens.Iso
 import Control.Lens.SemiIso
 import Control.Monad
+import Data.Semigroupoid.Dual
 import Data.Tuple.Morph
 import Prelude hiding (id, (.))
 
@@ -94,6 +96,10 @@ instance MonadPlus m => SIArrow (Kleisli m) where
     siarr ai = Kleisli $ either fail return . apply ai
     sibind ai = Kleisli $ \a -> either fail (($ a) . runKleisli) $ apply ai a
 
+instance SIArrow cat => SIArrow (Dual cat) where
+    siarr = Dual . sipure
+    sibind ai = Dual $ sibind (iso id getDual . rev ai . iso getDual id)
+
 instance SIArrow ReifiedSemiIso' where
     siarr = reifySemiIso
     sibind ai = ReifiedSemiIso' $

semi-iso.cabal

@@ -66,6 +66,6 @@ library
                        Control.Category.Reader
                        Control.Category.Structures
                        Data.Profunctor.Exposed
-  build-depends:       base >= 4 && < 5, profunctors, transformers, lens, tuple-morph
+  build-depends:       base >= 4 && < 5, profunctors, transformers, lens, tuple-morph, semigroupoids
   default-language:    Haskell2010
   ghc-options:         -Wall