# [Haskell-cafe] number-parameterized types and heterogeneous lists

Anton Tayanovskyy anton.tayanovskyy at gmail.com
Fri Jun 20 09:19:01 EDT 2008

```Hi Harald,

Can you give a link to the paper? Interesting stuff. Thanks.

This is stretching my abilities a bit, but is this what you are after?

data Digit = forall b.(Digits (b Sz)) => Digit (Sz -> b Sz)

instance Digits [Digit] where
d2num []           acc = acc
d2num (Digit x:xs) acc = d2num xs (10*acc + d2num (x Sz) 0)

I assumed you only want D0..D9 as digits, maybe this is too narrow.

I've put this up on hpaste:

http://hpaste.org/8437#a1

Bests,

Anton

On Fri, Jun 20, 2008 at 3:01 PM, Harald ROTTER <harald.rotter at sagem.com> wrote:
>
>
> after reading Oleg Kiselyov's paper on number-parameterized types I started
> to play around with
> the class Digits that encodes decimal numbers in types. The "typed number"
> 10 would e.g. be defined as
>
>      D1 \$ D0 \$ Sz
>
> I wondered if it would be possible replace the expression above by a
> heterogeneous list like
>
>      [D1,D0]
>
> so I tried to define
>
>      data Digit = forall a b.(Digits a, Digits (b a)) => Digit (a -> b a)
>
>
> :t Digit D0
>
> <interactive>:1:0:
>    Ambiguous type variable `a' in the constraint:
>      `Digits a' arising from a use of `Digit' at <interactive>:1:0-7
>    Probable fix: add a type signature that fixes these type variable(s)
>
> Removing the type constraints in the definition of "Digit":
>
>      data Digit = forall a b.Digit (a -> b a)
>
> makes it work like this:
>
>      :t Digit D0
>      Digit D0 :: Digit
>
>      :t [Digit D0, Digit D1]
>      [Digit D0, Digit D1] :: [Digit]
>
> "Digit", however, is far too general (it also includes e.g. \x -> [x]), but
> I would like it to be restricted to the Digit class.
>
> Any help is appreciated.
>
> Thanks
>
> Harald.
>
>
> CODE:
>
> module Test where
>
> data D0 a = D0 a
> data D1 a = D1 a
> data D2 a = D2 a
> data D3 a = D3 a
> data D4 a = D4 a
> data D5 a = D5 a
> data D6 a = D6 a
> data D7 a = D7 a
> data D8 a = D8 a
> data D9 a = D9 a
>
> class Digits ds where
>    d2num :: Num a => ds -> a -> a
>
> data Sz = Sz    -- zero size
> instance Digits Sz where
>    d2num _ acc = acc
>
> instance Digits ds => Digits (D0 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc)
> instance Digits ds => Digits (D1 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+1)
> instance Digits ds => Digits (D2 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+2)
> instance Digits ds => Digits (D3 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+3)
> instance Digits ds => Digits (D4 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+4)
> instance Digits ds => Digits (D5 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+5)
> instance Digits ds => Digits (D6 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+6)
> instance Digits ds => Digits (D7 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+7)
> instance Digits ds => Digits (D8 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+8)
> instance Digits ds => Digits (D9 ds) where
>    d2num dds acc = d2num (t22 dds) (10*acc+9)
>
> t22 :: f x -> x
> t22 = undefined
>
> --data Digit = forall a b.(Digits a, Digits (b a)) => Digit (a -> b a)
> data Digit = forall a b.Digit (a -> b a)
>
> -------------------------------------------------------------------------------------------------
>
>
>
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