[Haskell-cafe] Consistency issue with type level numeric literals

[Iavor Diatchki]

Hi Oleg,

yes, this is a bug, you are not supposed to define custom instances for the
built-in operators.  I just left it open until we hook in the solver.

Happy holidays,
-Iavor


On Sat, Dec 28, 2013 at 12:54 AM, <oleg at okmij.org> wrote:

>
> GHC 7.6.3 has quite convenient type-level numeric literals. We can use
> numbers like 1 and 2 in types. However, using the type level numeral
> has been quite a bit of a challenge, illustrated, for example, by
> the following SO question.
>
>
> http://stackoverflow.com/questions/20809998/type-level-nats-with-literals-and-an-injective-successor
>
> It seems the challenge has the reason: the type level numerals and
> their operations provided in GHC.TypeLits have a consistency
> issue. The following code demonstrates the issue: it constructs two
> distinct values of the type Sing 2. Singletons aren't singletons.
>
> {-# LANGUAGE KindSignatures #-}
> {-# LANGUAGE DataKinds #-}
> {-# LANGUAGE ScopedTypeVariables #-}
> {-# LANGUAGE TypeOperators #-}
> {-# LANGUAGE TypeFamilies #-}
> {-# LANGUAGE GADTs #-}
> {-# LANGUAGE PolyKinds #-}
>
> module NotSing where
>
> import GHC.TypeLits
>
> -- GHC strangely enough lets us define instances for (+)
> type instance 1 + 1 = 0
> type instance 0 + 1 = 2
>
> -- A singular representative of 1::Nat
> s1 :: Sing 1
> s1 = withSing id
>
> -- A singular representative of 2::Nat
> s2 :: Sing 2
> s2 = withSing id
>
> is2 :: IsZero 0
> is2 = IsSucc s1
>
> tran :: IsZero 0 -> Sing 2
> tran (IsSucc x) = case isZero x of
>                    IsSucc y -> case isZero y of
>                                 IsZero -> x
>
> -- Another singular representative of 2::Nat
> -- A singular representative of 2::Nat
> s2' :: Sing 2
> s2' = tran is2
>
>
> {-
> *NotSing> s2
> 2
> *NotSing> s2'
> 1
> -}
>
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