[Haskell-cafe] Infer Nat type from Integer argument

[adam vogt]

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 at 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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