[Haskell-beginners] Data type definition for a list of elements of alternating types?

[Tony Morris]

See the separated package on hackage.
On 03/04/2014 2:53 PM, "Jacek Dudek" <jzdudek at gmail.com> wrote:

> -- As an exercise I wanted to define a datatype that is an alternating
> list of elements of two different types. The best that I could do are
> the type definitions below:
>
> module BiList
>     ( BiList (..)
>     , AList (EmptyA)
>     , BList (EmptyB)
>     ) where
>
> data BiList a b
>     = Empty
>     | BA (AList a b)
>     | BB (BList a b)
>
> data AList a b
>     = EmptyA
>     | AL a (BList a b)
>
> data BList a b
>     = EmptyB
>     | BL b (AList a b)
>
> (<#) :: a -> (BList a b) -> (AList a b)
> a <# bs = AL a bs
>
> (<@) :: b -> (AList a b) -> (BList a b)
> b <@ as = BL b as
>
> infixr 5 <#
> infixr 5 <@
>
> example :: BiList Int Char
> example = BA $ 1 <# 'a' <@ 2 <# 'b' <@ 3 <# 'c' <@ 4 <# 'd' <@ EmptyA
>
> -- There are two things that I don't like about this implementation.
>
> -- (1) The BA and BB constructors that must be applied on top of
> instances of (AList a b) and (BList a b) to lift them to be of type
> (BiList a b).
>
> -- (2) Having three different constructors for an empty list: Empty,
> EmptyA, EmptyB, where ideally I would just have one.
>
> -- Is it possible to get around either of these annoyances with some
> type theory gymnastics? Maybe something like the function fromIntegral
> (the mechanics of which I don't really understand at this point)?
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