Simple type family example errors about non injective type function

Question

I\'m trying to understand type families without much success. Here\'s a minimal example:

{-# LANGUAGE TypeFamilies #-}

class Object obj where
  type Unit ob         


        

Answer 1

Since associated types are not injective (defined below) you need an argument in order to type check. For instance, consider the following (incorrect) code.

class Valuable o where
  type Value o :: *
  value :: Value o

data Pearl
data Diamond

instance Valuable Pearl where
  type Value Pearl = Int
  value = 1000

instance Valuable Diamond where
  type Value Diamond = Int
  value = 10000

Note that Value a ~ Value b does not imply a ~ b as injectivity would have it. Thus it's now ambiguous as to what the value of value is. It doesn't even help if we constrict the type of value :: Int since Value Pearl ~ Value Diamond ~ Int.

---

That said, there's some very nice parallelism in the code.

import Control.Arrow

class Object obj where
  type Unit obj :: *
  unit :: obj -> Unit obj

instance (Object obj, Object obj') => Object (obj, obj') where
  type Unit (obj, obj') = (Unit obj, Unit obj')
  unit = unit *** unit