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

Simon Peyton-Jones simonpj at microsoft.com
Mon Dec 30 14:22:25 UTC 2013


Shouldn’t (+) be a closed type family (now that we have such things)?  Then the user couldn’t give new instances.


From: Haskell-Cafe [mailto:haskell-cafe-bounces at haskell.org] On Behalf Of Iavor Diatchki
Sent: 29 December 2013 18:30
To: oleg at okmij.org
Cc: Haskell Cafe
Subject: Re: [Haskell-cafe] Consistency issue with type level numeric literals

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,

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


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 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
*NotSing> s2'

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