Neil Mitchell wrote:
Hi
I'm starting to play with GADT's, and I was trying to write a safe
version of head and tail, on a safe version of lists. What I came up
with is:
data ConsT a
data NilT
data List a t where
Cons :: a -> List a b -> List a (ConsT b)
Nil :: List a NilT
instance Show a => Show (List a t) where
show (Cons a b) = show a ++ ":" ++ show b
show Nil = "[]"
safeHead :: List a (ConsT t) -> a
safeHead (Cons a b) = a
safeTail :: List a (ConsT t) -> List a t
safeTail (Cons a b) = b
safeMap :: (a -> b) -> List a t -> List b t
safeMap f Nil = Nil
safeMap f (Cons a b) = Cons (f a) (safeMap f b)
Defining safeMap was trivial, but one thing I couldn't figure out was
how to write something like fromList:
fromList [] = Nil
fromList (a:as) = Cons a (fromList as)
You need to use existentials.
The following code hides one in its definition:
fromList :: [a] -> (List a NilT -> r)
-> (forall b. List a (ConsT b) -> r) -> r
fromList [] nilk consk = nilk Nil
fromList (x:xs) nilk consk = fromList' xs (consk . Cons x)
where fromList' :: [a] -> (forall b. List a b -> r) -> r
fromList' [] k = k Nil
fromList' (x:xs) k = fromList' xs (k . Cons x)
Also it should be possible to arrange this to use a very simple library
for existentials I made, made possible by GHC 6.6's new support for
impredicativity.
-- exists a. F a
-- <=> exists a.not (not (F a))
-- <=> not (forall a.not (F a))
type Exists f = forall r.(forall a.(f a -> r)) -> r
open :: Exists f -> (forall a.(f a -> r)) -> r
open package k = package k
pack :: f a -> Exists f
pack a k = k a
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