Hi Jake,

I think your problem is that the type signature for fromN lets the caller of fromN decide what n should be, when it has to be the other way around. Two ways to express that are:

1. make `fromN :: Integer -> SomeNatString`, making use of GADTs/ ExistentialQuantification (in the same way that SomeNat does):

data SomeNatString where

 SomeNatString :: KnownNat n => NatString n -> SomeNatString

2. use RankNTypes to express the same thing without adding a constructor, but at the cost of needing to write a type signature and continuation passing style code:

fromN :: Integer -> (forall n. KnownNat n => Proxy n -> r) -> r

fromN i f = case someNatVal i of Just n -> f n

Regards,

Adam

On Sun, Feb 28, 2016 at 4:40 PM, Jake <jake.waksbaum@gmail.com> wrote:

{-# LANGUAGE DataKinds, KindSignatures, ScopedTypeVariables, GADTs, AllowAmbiguousTypes #-}

import GHC.TypeLits

import Data.Proxy

import Data.Type.Equality

data NatString (n :: Nat) = NatString String deriving Show

showNS :: KnownNat n => NatString n -> (String, Integer)

showNS b@(NatString s) = (s, natVal b)

In this example, we use NatString like this:

> showNS (NatString "hey" :: NatString 4)

-- ("hey", 4)

We can then dynamically make NatStrings from Integers. For example, we can read an Integer from stdin and use it to create a NatString

main :: IO ()

main = do

  i <- readLn

  case someNatVal i of

    Just (SomeNat (p :: Proxy n)) ->

      let ns :: NatString n

          ns = NatString "hello!"

      in print $ showNS NatString

However, if I have trouble when I try to refactor out the middle part to create a function with type forall n. KnownNat n => Integer -> Bar n.

I use sameNat to convince the compiler that the Nat we get from the Integer is the same type as the the type n of the output.

fromN :: forall n. KnownNat n => Integer -> NatString n

fromN i =

 case someNatVal i of

   Just (SomeNat p) ->

     case sameNat p (Proxy :: Proxy n) of

       Just (Refl) ->

         let ns :: NatString n

             ns = NatString "hello!" in ns

This compiles, but if you try and use it the compiler complains.

> showNS (fromN 3)

-- No instance for (KnownNat n0) arising from a use of ‘showNS’

If we manually add the type annotation, everything is fine, but that kind of defeats the entire purpose.

> showNS (fromN 3 :: NatString 3)
-- ("hello!",3)

Strangely enough, when the NatString is immediately consumed instead of being returned, the compiler does its job and infers the correct type.

showFromN :: Integer -> (String, Integer)

showFromN i =

 case someNatVal i of

   Just (SomeNat (p :: Proxy n)) ->

     let ns :: NatString n

         ns = NatString "hello!" in showNS ns

> showFromN 3

-- ("hello!", 3)

Clearly the intermediate value of ns inside of showFromN has a type NatString 3 because showNS is using that fact.

How can I make the compiler infer that fromN 3 :: NatString 3 separately?

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