Hello Paul,
If you don't want to use the class system, you could write `repeat` with a type like this:
repeat :: Proxy n -> a -> Vector n a
(`Proxy` is the singleton family 'data Proxy n = Proxy`).
You can't really do it with a function of type `a -> Vector n a` because there is no way for the function to know how many elements to generate.
You cannot determine the length from the type `n` because polymorphism in Haskell is _parametric_, which means that the function needs to behave uniformly for all types.
This is nice because it makes reasoning about programs easier, but also, it allows for efficient implementation---there is no need to pass type-representations at run-time.
In contrast, overloaded values may behave differently depending on their type, just like your implementation of `repeat` below. This is perfectly OK, and it is clearly marked in the type.
I hope this helps,
-Iavor
On Thu, Oct 25, 2012 at 8:22 AM, Paul Visschers
<mail@paulvisschers.net> wrote:
Hello everyone,
I've been playing around with the data kinds extension to implement vectors that have a known length at compile time. Some simple code to illustrate:
> {-# LANGUAGE DataKinds, GADTs, KindSignatures #-}
>
> import Prelude hiding (repeat)
>
> data Nat = Zero | Succ Nat
> data Vector (n :: Nat) a where
> Nil :: Vector Zero a
> Cons :: a -> Vector n a -> Vector (Succ n) a
>
> class VectorRepeat (n :: Nat) where
> repeat :: a -> Vector n a
>
> instance VectorRepeat Zero where
> repeat _ = Nil
>
> instance VectorRepeat n => VectorRepeat (Succ n) where
> repeat x = Cons x (repeat x)
In this code I have defined a repeat function that works in a similar way to the one in the prelude, except that the length of the resulting vector is determined by the type of the result. I would have hoped that its type would become 'repeat :: a -> Vector n a', yet it is 'repeat :: VectorRepeat n => a -> Vector n a'. As far as I can tell, this class constraint should no longer be necessary, as all possible values for 'n' are an instance of this class. I actually really just want to define a closed type-directed function and would rather not (ab)use the type class system at all.
Is there a way to write the repeat function so that it has the type 'repeat :: a -> Vector n a' that I've missed? If not, is this just because it isn't implemented or are there conceptual caveats?
Paul Visschers
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe