Thanks for the link, it seems a lot more complicated than I thought, but understandable since the Peano arithmetic is fully recursive, it may has the same performance issue even at value level. This make type level Nat less attractive, I think. With TypeLits (assuming it doesn't have the slow performance issue) it is impossible to write something like: add :: a -> b -> a+b add a b = a+b ? Thanks Baojun On Mon, Apr 17, 2017 at 13:48 Will Yager wrote:

As I recall from the Idris paper, the compiler has special knowledge about types like Nat. As you have noticed, actually computing peano numbers is quite slow. Take a look at https://hackage.haskell.org/package/ghc-typelits-natnormalise for an example of "cheating" and embedding integers at the type level with special support.

Will

On Apr 17, 2017, at 3:34 PM, Baojun Wang wrote:

Hello cafe,

I tried to play with some type level natural numbers, and it seems type level function is quite slow, for instance:

(full source) https://gist.github.com/wangbj/5939aa7a30c3d756d98f5b5775e162a6

data Z data S n

class KnownNat n where natSing :: n -> Integer

instance KnownNat Z where natSing _ = 0 instance KnownNat n => KnownNat (S n) where natSing _ = 1 + natSing (undefined :: n)

natVal :: KnownNat n => n -> Integer natVal = natSing

natSing doesn't seems to know how to optimize when KnownNat is very big (i.e: 10000), I tried Peano Add/Mul, and they are very slow to be really useful. Is there any ways to improve this? How fully dependent typed language such as Adga/Idris handle this, do they have the same performance issue?

Thanks baojun

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