heres a version richard eisenburg helped me write https://gist.github.com/cartazio/9340008

see the linked gist for the full code but heres the meat of it 

data Shape (rank :: Nat) a where 
    Nil  :: Shape Z a
    (:*) ::  !(a) -> !(Shape r a ) -> Shape  (S r) a
    
    {-# INLINE reverseShape #-}
reverseShape :: Shape n a -> Shape n a 
reverseShape Nil = Nil
reverseShape list = go SZero Nil list
  where
    go :: SNat n1 -> Shape n1  a-> Shape n2 a -> Shape (n1 + n2) a
    go snat acc Nil = gcastWith (plus_id_r snat) acc
    go snat acc (h :* (t :: Shape n3 a)) =
      gcastWith (plus_succ_r snat (Proxy :: Proxy n3))
              (go (SSucc snat) (h :* acc) t)

On Tue, Sep 9, 2014 at 8:55 AM, Cristiano Paris <frodo@theshire.org> wrote:

Hi,

I'm playing around with Type Families so I decided to implement a simple fixed-length Vect of Integers.

Here is my straightforward implementation (ghc 7.8.3):

https://gist.github.com/anonymous/d838e68ce6a02412859f

As you can see, I'm trying to implement a reverse function for my vectors which guarantees that the output vector is the same size as the input one. I tried to express this constraint at the type level.

The problem is that I can't have ghc to type check the reverse function in the non-trivial case:

_________________
    Could not deduce (Plus n1 (S m) ~ S (Plus n1 m))
    from the context (n ~ S n1)
      bound by a pattern with constructor
                 CV :: forall n. Int -> Vect n -> Vect (S n),
               in an equation for ‘vecReverse’
      at vect3.hs:30:13-18
    Expected type: Vect (Plus n m)
      Actual type: Vect (Plus n1 (S m))
_________________

Iit has to do with the fact that the type checker can't deduce that:

Plus n1 (S m) ~ S (Plus n1 m) ~ Plus (S n1) m ~Plus n m

I tried to insert the following instance to the family:

Plus n (S m) = S (Plus n m)

but to no avail.

Any clue?

Thanks.

C.

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