Re: [Haskell-cafe] Parsec and type level numerals

On Sun, Dec 14, 2008 at 6:54 AM, David Menendez wrote:

2008/12/13 Nathan Bloomfield :

...

I want to be able to parse a string of digits to a type level numeral as described in the Number parameterized types paper. After fiddling with the problem for a while, I'm not convinced it's possible- it seems as though one would need to know the type of the result before parsing, but then we wouldn't need to parse in the first place. :)

This can be done with existential types. I think Oleg Kiselyov has an example somewhere of a parser that determines the type of its output from its input, but here's the basic idea:

data SomeCard = forall a. (Card a) => SomeCard a

Now you can define parseP :: Parser SomeCard

Unfortunately, all you know about the value inside the SomeCard is that it's a member of the class Card, which may not be very helpful. Depending on how general you want to be, you can bundle more operations with SomeCard, or you can return a GADT that reflects the type-level natural at the value level.

-- Dave Menendez http://www.eyrie.org/~zednenem/ _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

Depending on what you actually want to do, you may be looking for Oleg Kiselyov's reifyIntegral function, which he defines in the paper "Functional Pearl: Implicit Configurations -- or Type Classes Reflect the Value of Types" (at http://www.cs.rutgers.edu/~ccshan/prepose/prepose.pdf ). It has type something like reifyIntegral :: forall a. Int -> (forall n. Numeral n => n -> a) -> a encoding n's existential type with continuation passing style. Cheers, Reiner