[Haskell-cafe] Type-directed functions with data kinds

[Iavor Diatchki]

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 at 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
>
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