[Haskell-cafe] Reversing a fixed-length vector

[Cristiano Paris]

I almost got there with Type Equalities, but I can't really understand the
"VecReverse n (S m)" constraint in the instance bit of "VecReverse (S n) m".

C.

On Tue, Sep 9, 2014 at 4:12 PM, adam vogt <vogt.adam at gmail.com> wrote:

> Hi Cristiano,
>
> You can also convince ghc about (Plus n1 (S m) ~ S (Plus n1 m)) by
> writing VecReverse as a class:
> https://gist.github.com/aavogt/15399cbdd5e74d0e9cd8
>
> Regards,
> Adam
>
> On Tue, Sep 9, 2014 at 10:07 AM, Cristiano Paris <frodo at theshire.org>
> wrote:
> > Gosh! I suspected I hit a non-trivial problem... cool!
> >
> > C.
> >
> > On Tue, Sep 9, 2014 at 3:56 PM, Carter Schonwald
> > <carter.schonwald at gmail.com> wrote:
> >>
> >> 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 at 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.
> >>>
> >>> --
> >>> GPG Key: 4096R/C17E53C6 2010-02-22
> >>> Fingerprint = 4575 4FB5 DC8E 7641 D3D8  8EBE DF59 B4E9 C17E 53C6
> >>>
> >>>
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> >>>
> >>
> >
> >
> >
> > --
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> >
> >
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>



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