You're almost there, but you have correctly determined the problem;
you need to know the type of the parse result in order to parse.
However, it is possible to hide the type from the parser; try writing
this function instead:
{-# LANGUAGE ExistentialQuantification #-}
data AnyCard = forall t. Card t => AnyCard t
parseP :: Parser AnyCard
Now the type-level numeral is hidden in the "AnyCard" existential
type. In order to use it, you need to be able to use operations that
work on any instance of Card, which means the class/instance
declarations you have so far aren't that useful. Emulating dependent
types using existentials in Haskell is never pretty!
Another option is to use a GADT to hold the type:
{-# LANGUAGE GADTs, ExistentialQuantification #-}
data GADTNum t where
GZero :: GADTNum Zero
GSucc :: GADTNum a -> GADTNum (Succ a)
data AnyCard = forall t. AnyCard (GADTNum t)
Now, after the parse, you can use the structure of the GADT to
determine things about the existential type:
isTwo :: AnyCard -> Maybe (Succ (Succ Zero))
isTwo (AnyCard (GSucc (GSucc GZero))) = Succ (Succ Zero)
isTwo _ = Nothing
-- ryan
2008/12/13 Nathan Bloomfield
Hello all. I've got a puzzling Parsec problem. Perhaps the collective wisdom of haskell-cafe can point me in the right direction.
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. :) My first (simplified) approximation is as follows:
data Zero = Zero data Succ a = Succ a
class Card t instance Card Zero instance (Card a) => Card (Succ a)
parseP :: (Card a) => Parser a parseP = do { char '1' ; rest <- parseP ; return $ Succ rest } <|> return Zero
I'd like for this to parse, for example, "111" into Succ Succ Succ Zero. Of course this doesn't work because parseP is ill-typed, but I'm not sure how to fix it. It seems that what I'm asking for is a function whose type is forall a. (Card a) => String -> a, which is problematic.
Has anyone tried this before? I'm new to using Parsec and to parsing in general, so I apologize if this is a silly question. (Parsec is very impressive, by the way.)
Thanks-
Nathan Bloomfield University of Arkansas, Fayetteville
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