Levi Stephen schrieb:
Hi,
I have the following definitions
type Zero type Succ a
so that I can muck around with a Vector type that includes its length encoded in its type.
I was wondering whether it was possible to use SmallCheck (or QuickCheck) to generate random Peano numbers? Is there an issue here in that what I actually want to generate is a type rather than a value?
I do have
reifyInt :: Int -> (forall a. ReflectNum a => a -> b) -> b
but, I'm not sure if this can help me when I need to generate other values based upon that type (e.g., two vectors with the same size type)
Hi Levi, For QuickCheck, I know it is possible as long as you do not need to use type level functions in your tests. For example, using Alfonso's type-level and parametrized-data packages, one can write:
instance (Nat n, Arbitrary a) => Arbitrary (FSVec n a) where arbitrary = liftM (unsafeVector (undefined :: n)) $ mapM (const arbitrary) [1..toInt (undefined :: n)]
propLength :: forall n a. (Nat n) => FSVec n Integer -> Bool propLength (FSVec xs) = P.length xs == toInt (undefined :: n)
propLengthEqual :: forall n a. (Nat n) => FSVec n Integer -> FSVec n Integer -> Bool propLengthEqual v1 v2 = length v1 == length v2
tests1 = forM_ [0..100] $ \n -> reifyIntegral n $ \(t :: ty) -> quickCheck (propLength :: FSVec ty Integer -> Bool) tests2 = forM_ [0..100] $ \n -> reifyIntegral n $ \(t :: ty) -> quickCheck (uncurry propLengthEqual :: (FSVec ty Integer,FSVec ty Integer) -> Bool)
It is also possible to reify type-level numbers with more context; I managed to get as far as (iirc)
reifyPos :: Integer -> (forall n. (Pos n, Succ n n', DivMod10 n nd nm) => n -> r) -> r
This way you can test head, tail e.g., but I found it to be a lot of work to write additional reifications. I do not know if it is possible (I think it is not) to have a reification which allows you to use total type level functions such as Add, e.g.
tylvl = reifyIntegral? k $ \(n :: ty) -> toInt (m :: Add ty D9) -- (D9 is the type level number 9)
I'm really curious what exactly would make this possible. best regards, benedikt