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copied!<p>So this turns out to be wrong. I'll leave it here in case anybody wants to try to fix it.</p> <p>This implementation is the way @pigworker suggested I think. It compiles, but I haven't tested it. (I took the <code>cojoin1</code> implementation from <a href="http://blog.sigfpe.com/2006/12/evaluating-cellular-automata-is.html" rel="nofollow">http://blog.sigfpe.com/2006/12/evaluating-cellular-automata-is.html</a>)</p> <pre><code>{-# LANGUAGE KindSignatures #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE TypeFamilies #-} data Nat = Z | S Nat data U (n :: Nat) x where Point :: x -> U Z x Dimension :: [U n x] -> U n x -> [U n x] -> U (S n) x unPoint :: U Z x -> x unPoint (Point x) = x dmap :: (U n x -> U m r) -> U (S n) x -> U (S m) r dmap f (Dimension ls mid rs) = Dimension (map f ls) (f mid) (map f rs) right, left :: U (S n) x -> U (S n) x right (Dimension a b (c:cs)) = Dimension (b:a) c cs left (Dimension (a:as) b c) = Dimension as a (b:c) instance Functor (U n) where fmap f (Point x) = Point (f x) fmap f d@Dimension{} = dmap (fmap f) d class Functor w => Comonad w where (=>>) :: w a -> (w a -> b) -> w b coreturn :: w a -> a cojoin :: w a -> w (w a) x =>> f = fmap f (cojoin x) cojoin xx = xx =>> id instance Comonad (U n) where coreturn (Point x) = x coreturn (Dimension _ mid _) = coreturn mid cojoin (Point x) = Point (Point x) cojoin d@Dimension{} = fmap unlayer . unlayer . fmap dist . cojoin1 . fmap cojoin . layer $ d dist :: U (S Z) (U n x) -> U n (U (S Z) x) dist = layerUnder . unlayer layerUnder :: U (S n) x -> U n (U (S Z) x) layerUnder d@(Dimension _ Point{} _) = Point d layerUnder d@(Dimension _ Dimension{} _) = dmap layerUnder d unlayer :: U (S Z) (U n x) -> U (S n) x unlayer = dmap unPoint layer :: U (S n) x -> U (S Z) (U n x) layer = dmap Point cojoin1 :: U (S Z) x -> U (S Z) (U (S Z) x) cojoin1 a = layer $ Dimension (tail $ iterate left a) a (tail $ iterate right a) </code></pre>

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