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