Consider the following definition of lists with a statically determined minimum length. data Nat' = Z | S Nat' data NList (n::Nat') a where Rest :: [a] -> NList Z a (:>) :: a -> NList n a -> NList (S n) a uncons :: NList (S n) a -> (a, NList n a) uncons (x :> xs) = (x, xs) This works fine. Now consider an implementation using the new type literals in GHC: data NList (n::Nat) a where Rest :: NList 0 [a] (:>) :: a -> NList n a -> NList (n+1) a uncons :: NList (n+1) a -> NList n a uncons (x :> l) = l This gives a type error: /home/athas/code/nonempty_lists.hs:41:19: Could not deduce (n1 ~ n) from the context ((n + 1) ~ (n1 + 1)) bound by a pattern with constructor :> :: forall a (n :: Nat). a -> NList n a -> NList (n + 1) a, in an equation for `uncons' at /home/athas/code/nonempty_lists.hs:41:9-14 `n1' is a rigid type variable bound by a pattern with constructor :> :: forall a (n :: Nat). a -> NList n a -> NList (n + 1) a, in an equation for `uncons' at /home/athas/code/nonempty_lists.hs:41:9 `n' is a rigid type variable bound by the type signature for uncons :: NList (n + 1) a -> NList n a at /home/athas/code/nonempty_lists.hs:40:11 Expected type: NList n a Actual type: NList n1 a In the expression: l In an equation for `uncons': uncons (x :> l) = l I don't understand why GHC cannot infer that the two types are the same. My guess is that 'n+1' is not "structural" to GHC in the same way that 'S n' is. The page http://hackage.haskell.org/trac/ghc/wiki/TypeNats/MatchingOnNats mentions that "type level numbers of kind Nat have no structure", which seems to support my suspicion. What's the complete story, though? -- \ Troels /\ Henriksen