On Thu, Dec 20, 2007 at 11:39:42PM -0500, Ronald Guida wrote:
data PZero = PZero deriving (Show) data PSucc a = PSucc a deriving (Show)
type P1 = PSucc PZero type P2 = PSucc P1 type P3 = PSucc P2 -- etc
...
Now here's the puzzle. I want to create a function "vecLength" that accepts a vector and returns its length. The catch is that I want to calculate the length based on the /type/ of the vector, without looking at the number of elements in the list.
So I started by defining a class that allows me to convert a Peano number to an integer. I couldn't figure out how to define a function that converts the type directly to an integer, so I am using a two-step process. Given a Peano type /t/, I would use the expression "pToInt (pGetValue :: t)".
class Peano t where pGetValue :: t pToInt :: t -> Int
instance Peano PZero where pGetValue = PZero pToInt _ = 0
instance (Peano t) => Peano (PSucc t) where pGetValue = PSucc pGetValue pToInt (PSucc a) = 1 + pToInt a
Finally, I tried to define vecLength, but I am getting an error.
vecLength :: (Peano s) => Vec s t -> Int vecLength _ = pToInt (pGetValue :: s)
1. pGetValue is unneccessary, undefined :: s will work just as well. This is a fairly standard approach; the precision values in Floating, bitSize :: Bits a => a -> Int, and sizeOf :: Storable a => a -> Int all work this way. Some Haskeller, notably Alex Jacobson, prefer to use a 'proxy' type to make this value irrelevance explicit: data Proxy s -- for H98, data Proxy s = Proxy_ !(Proxy s) 2. The reason this doesn't work is that the scope of s in the type signature is the type signature, and the scope of s in the other type signature is the other type signature. They are very different type variables, and you cannot assign the type forall s. s to pGetValue - it has class constraints. The effect you are trying to achieve cannot be directly achieved in H98 (this is considered one of H98's few major flaws)... 2a: Use GHC extentions (ScopedTypeVariables). This extends the scope of type variables to include the definition. For backwards compatibility, it only applies to new-style explicit quantification: vecLength :: forall s. Peano s => Vec s t -> Int 2b: Use functions with type constraints to force relations between types: vecLength v = pToInt (vToPeano v) where vToPeano = undefined :: Vec s t -> s Figuring out why this works should be enlightening, and it seems hard to explain, so I'm leaving it as an excersize. :) Stefan