injectivity problem

Nikolay.hs

{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE TypeFamilies #-}
module Nikolay where
import Control.Lens
-- superclass constraint here says that TtseT is the inverse to TestT,
-- without it, the example attached to test2 fails, since otherwise we
-- could be allowed to add a
-- 
-- type TestT Double = Char,
--
-- and then applying test2 to a Char doesn't determine the result type
class TtseT (TestT a) ~ a => Test a where
  type TestT a
  myiso :: Iso' a (TestT a)

{- |

>>> test1 (120 :: Int)
'x'

-}
test1 = view myiso

{- |

>>> test2 'x'
120

-}
test2 = view (from myiso)

instance Test Int where
  type TestT Int = Char
  myiso = enum

type family TtseT a
type instance TtseT Char = Int