From b77e869f239b551f17e9c6927ea38e1c2bc781ae Mon Sep 17 00:00:00 2001
From: Sjoerd Visscher <sjoerd@w3future.com>
Date: Sun, 19 May 2019 15:59:40 +0200
Subject: [PATCH 1/2] Divisible and Adjunction instances for Contravariant Day

---
 src/Data/Functor/Contravariant/Day.hs | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/src/Data/Functor/Contravariant/Day.hs b/src/Data/Functor/Contravariant/Day.hs
index 625595e..749abb6 100644
--- a/src/Data/Functor/Contravariant/Day.hs
+++ b/src/Data/Functor/Contravariant/Day.hs
@@ -2,6 +2,8 @@
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE ExistentialQuantification #-}
 {-# LANGUAGE Rank2Types #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE UndecidableInstances #-}
 #if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707
 {-# LANGUAGE DeriveDataTypeable #-}
 #endif
@@ -41,8 +43,11 @@ module Data.Functor.Contravariant.Day
 #if __GLASGOW_HASKELL__ < 710
 import Control.Applicative
 #endif
+import Control.Arrow ((***))
 import Data.Functor.Contravariant
 import Data.Functor.Contravariant.Rep
+import Data.Functor.Contravariant.Adjunction
+import Data.Functor.Contravariant.Divisible
 import Data.Proxy
 import Data.Tuple (swap)
 #ifdef __GLASGOW_HASKELL__
@@ -84,6 +89,11 @@ dayTyCon = mkTyCon "Data.Functor.Contravariant.Day.Day"
 instance Contravariant (Day f g) where
   contramap f (Day fb gc abc) = Day fb gc (abc . f)
 
+instance (Divisible f, Divisible g) => Divisible (Day f g) where
+  divide h (Day f g l) (Day f' g' r) = Day (divided f f') (divided g g') (intertwine . (l *** r) . h)
+    where intertwine ((a, b), (c, d)) = ((a, c), (b, d))
+  conquer = Day conquer conquer (\a -> (a, a))
+  
 instance (Representable f, Representable g) => Representable (Day f g) where
   type Rep (Day f g) = (Rep f, Rep g)
 
@@ -99,6 +109,9 @@ instance (Representable f, Representable g) => Representable (Day f g) where
     Right (vf, vg) -> (Right vf, Right vg)
   {-# INLINE tabulate #-}
 
+instance (Adjunction f u, Adjunction f' u') => Adjunction (Day f f') (Day u u') where
+  unit a = Day (unit a) (unit a) (\(Day f f' g) -> (contramap (fst . g) f, contramap (snd . g) f'))
+  counit a = Day (counit a) (counit a) (\(Day u u' g) -> (contramap (fst . g) u, contramap (snd . g) u'))
 
 -- | Break apart the Day convolution of two contravariant functors.
 runDay :: (Contravariant f, Contravariant g) => Day f g a -> (f a, g a)

From 6c4e7ce698a39636b43a9f910b0abeb95f00a60a Mon Sep 17 00:00:00 2001
From: Sjoerd Visscher <sjoerd@w3future.com>
Date: Sun, 19 May 2019 15:59:52 +0200
Subject: [PATCH 2/2] Adjunction instance for Day

---
 src/Data/Functor/Day.hs | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/src/Data/Functor/Day.hs b/src/Data/Functor/Day.hs
index 6d8f60b..710e0fd 100644
--- a/src/Data/Functor/Day.hs
+++ b/src/Data/Functor/Day.hs
@@ -4,6 +4,8 @@
 {-# LANGUAGE KindSignatures #-}
 {-# LANGUAGE DeriveDataTypeable #-}
 {-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE UndecidableInstances #-}
 -----------------------------------------------------------------------------
 -- |
 -- Copyright   :  (C) 2014-2016 Edward Kmett
@@ -45,6 +47,7 @@ import Control.Comonad.Trans.Class
 import Data.Distributive
 import Data.Profunctor.Cayley (Cayley(..))
 import Data.Profunctor.Composition (Procompose(..))
+import Data.Functor.Adjunction
 import Data.Functor.Identity
 import Data.Functor.Rep
 #ifdef __GLASGOW_HASKELL__
@@ -100,6 +103,13 @@ instance (Representable f, Representable g) => Representable (Day f g) where
   tabulate f = Day (tabulate id) (tabulate id) (curry f)
   index (Day m n o) (x,y) = o (index m x) (index n y)
 
+instance (Adjunction f u, Adjunction f' u') => Adjunction (Day f f') (Day u u') where
+  unit a = Day (unit ()) (unit ()) (\f f' -> Day f f' (\() () -> a))
+  counit (Day f f' h) = case h a a' of Day u u' g -> g (indexAdjunction u f_) (indexAdjunction u' f_')
+    where
+      (a, f_) = splitL f
+      (a', f_') = splitL f'
+  
 instance (Comonad f, Comonad g) => Comonad (Day f g) where
   extract (Day fb gc bca) = bca (extract fb) (extract gc)
   duplicate (Day fb gc bca) = Day (duplicate fb) (duplicate gc) (\fb' gc' -> Day fb' gc' bca)