Implement transitivity instance, extract a part of modifyAt as a convenient 'edit' function useful elsewhere and present a right-infix version of (,) to allow writing the nested tuple indexes more conveniently

src/PDF/Box.hs

@@ -5,19 +5,28 @@
 {-# LANGUAGE UndecidableInstances #-}
 module PDF.Box (
       Box(..)
+    , (.@)
+    , edit
     , modifyAt
   ) where
 
 import Control.Monad.State (MonadState(..))
 
-class Box m i a b | m a i -> b where
+class Monad m => Box m i a b | m a i -> b where
   r :: i -> a -> m b
   w :: i -> a -> b -> m a
 
+edit :: Box m i a b => i -> (b -> m b) -> a -> m a
+edit i f a =
+  r i a >>= f >>= w i a
 
 modifyAt :: (MonadState a m, Box m i a b) => i -> (b -> m b) -> m ()
-modifyAt i f = do
+modifyAt i f = get >>= edit i f >>= put
-  a <- get
-  r i a >>= f >>= w i a >>= put
 
-instance (Box m i a b, Box m j b c) => Box m (i, j) a c
+instance (Box m i a b, Box m j b c) => Box m (i, j) a c where
+  r (i, j) a = r i a >>= r j
+  w (i, j) a c = r i a >>= flip (w j) c >>= w i a
+
+infixr 6 .@
+(.@) :: a -> b -> (a, b)
+(.@) = (,)