Added 'morphed' semi-iso and /$~, ~$/, ~$~ operators.

Control/Lens/SemiIso.hs

@@ -1,3 +1,4 @@
+{-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE Rank2Types #-}
 {-# LANGUAGE TupleSections #-}
 {-# LANGUAGE ViewPatterns #-}
@@ -58,6 +59,7 @@ module Control.Lens.SemiIso (
     unit,
     swapped,
     associated,
+    morphed,
     constant,
     exact,
 
@@ -99,6 +101,7 @@ import Data.Foldable
 import Data.Functor.Identity
 import Data.Profunctor.Exposed
 import Data.Traversable
+import Data.Tuple.Morph
 
 -- | A semi-isomorphism is a partial isomorphism with weakened laws.
 -- 
@@ -157,6 +160,14 @@ unit = iso (, ()) fst
 associated :: Iso' (a, (b, c)) ((a, b), c)
 associated = iso (\(a, (b, c)) -> ((a, b), c)) (\((a, b), c) -> (a, (b, c)))
 
+-- | An isomorphism between two arbitrary nested tuples, as long the contained
+-- types (ignoring units!) read from left to right are the same.
+--
+-- This is implemented using 'Data.Tuple.Morph.morph' from 'tuple-morph'.
+morphed :: (HFoldable a, HUnfoldable a, HFoldable b, HUnfoldable b, Rep a ~ Rep b)
+        => Iso' a b
+morphed = iso morph morph
+
 -- | \-> Always returns the argument.
 --
 -- \<- Maps everything to a @()@.

Data/SemiIsoFunctor.hs

@@ -1,3 +1,5 @@
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE PatternSynonyms #-}
 {- |
 Module      :  Data.SemiIsoFunctor
 Description :  Functors from the category of semi-isomoprihsms to Hask.
@@ -18,10 +20,13 @@ module Data.SemiIsoFunctor where
 
 import Control.Lens.Cons
 import Control.Lens.Empty
+import Control.Lens.Internal.SemiIso
 import Control.Lens.SemiIso
+import Data.Functor.Identity
+import Data.Tuple.Morph
 
 infixl 3 /|/
-infixl 4 /$/
+infixl 4 /$/, ~$/, /$~, ~$~
 infixl 5 /*/, /*, */
 infixl 1 //=
 infixr 1 =//
@@ -54,6 +59,30 @@ class SemiIsoFunctor f where
 (/$/) :: SemiIsoFunctor f => ASemiIso' a b -> f b -> f a
 (/$/) = simap
 
+-- | @ai /$~ f@ is equal to @ai . morphed /$/ f@.
+--
+-- This operator handles all the hairy stuff with uncurried application:
+-- it reassociates the argument tuple and removes unnecessary (or adds necessary)
+-- units to match the function type. You don't have to use /* and */ with this
+-- operator.
+(/$~) :: (SemiIsoFunctor f, HFoldable b', HFoldable b,
+          HUnfoldable b', HUnfoldable b, Rep b' ~ Rep b)
+      => ASemiIso' a b' -> f b -> f a
+(SemiIso f g) /$~ h = semiIso f g . morphed /$/ h
+
+-- | @ai ~$/ f@ is equal to @morphed . ai /$/ f@.
+(~$/) :: (SemiIsoFunctor f, HFoldable a', HFoldable a,
+          HUnfoldable a', HUnfoldable a, Rep a' ~ Rep a)
+      => ASemiIso' a' b -> f b -> f a
+(SemiIso f g) ~$/ h = morphed . semiIso f g /$/ h
+
+-- | @ai ~$~ f@ is equal to @morphed . ai . morphed /$/ f@.
+(~$~) :: (SemiIsoFunctor f, HFoldable b', HFoldable b', HFoldable b,
+          HFoldable a, HUnfoldable b', HUnfoldable b', HUnfoldable b,
+          HUnfoldable a, Rep b' ~ Rep b, Rep b' ~ Rep a)
+      => ASemiIso b' b' b' b' -> f b -> f a
+(SemiIso f g) ~$~ h = morphed . semiIso f g . morphed /$/ h
+
 -- | Equivalent of 'Applicative' for 'SemiIsoFunctor'.
 --
 -- However, this class implements uncurried application, unlike 

semi-iso.cabal

@@ -24,5 +24,6 @@ library
                        Control.Lens.Internal.SemiIso
                        Data.SemiIsoFunctor
                        Data.Profunctor.Exposed
-  build-depends:       base >= 4 && < 5, profunctors, transformers, lens
+  build-depends:       base >= 4 && < 5, profunctors, transformers, lens, tuple-morph
   default-language:    Haskell2010
+  ghc-options:         -Wall