[Haskell-cafe] Excercise on tagless final interpreters

[matteo vezzola]

I'm playing with tagless final interpreters reading [1], using a very simple language:

>>> class Ints repr where
>>>     int :: Integer -> repr Integer
>>>     (.+.) :: repr Integer -> repr Integer -> repr Integer
>>>     (.*.) :: repr Integer -> repr Integer -> repr Integer
>>>     (.-.) :: repr Integer -> repr Integer
>>>     (.<=.) :: repr Integer -> repr Integer -> repr Bool

>>> newtype P repr t = P { unP :: Bool -> repr t }
>>> instance Ints repr => Ints (P repr) where
>>>     int n = P $ \ s -> if s then int n else (.-.) (int n)
>>>     (.-.) n = P $ unP n . not
>>>     n .+. m = P $ \ s -> unP n s .+. unP m s
>>>     n .*. m = P $ \ s -> unP n s .*. unP m s
>>>     n .<=. m = P $ \ s -> unP n s .<=. unP m s

After pushing down negations I'd like to distribute (.*.) over (.+.). [1] leaves it as an exercise, so it can't be that hard, but I don't get it...

Anyone knows how I could do it?

[1]: <http://okmij.org/ftp/tagless-final/course/lecture.pdf>


thanks,
-- 
matteo