[Haskell-cafe] to make a statically known sized non-empty list

Adam Gundry adam at well-typed.com
Fri Oct 25 07:43:21 UTC 2013

Hi Markus,

Rather than doing this...

On 24/10/13 21:35, Markus Läll wrote:
> data Nat = Zero | Succ Nat
> data family   NonEmpty (n :: Nat) a
> data instance NonEmpty Zero       a = Tail [a]
> data instance NonEmpty (Succ n)   a = Head a (NonEmpty n a)
> instance Functor (NonEmpty Zero) where
>    fmap f (Tail xs) = Tail (fmap f xs)
> instance Functor (NonEmpty (Succ a)) where
>    fmap f (Head x xs) = Head (f x) (fmap f xs)

...you are probably better off using a GADT like this:

    data NonEmpty2 (n :: Nat) a where
      Tail2 :: [a] -> NonEmpty2 Zero a
      Head2 :: a -> NonEmpty2 n a -> NonEmpty2 (Succ n) a

Now you can pattern-match on something of type `NonEmpty2 n a` in order
to learn more about the value of `n`, whereas with a data family, you
need to know the value of `n` in advance. This makes it harder to use.
For example, it is easy to convert in one direction:

    convert :: NonEmpty2 n a -> NonEmpty n a
    convert (Tail2 xs)   = Tail xs
    convert (Head2 x xs) = Head x (convert xs)

but going in the other direction is more complicated, and requires some
kind of dependent pi-type or singleton construction.

Hope this helps,


Adam Gundry, Haskell Consultant
Well-Typed LLP, http://www.well-typed.com/

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