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

1 Jan 2014

      Hello,

Yep, in 7.8 these are actually built-in constructors (which are not open
families) so if you try to define a custom instance you get an error about
an illegal instance for a closed type family.

Happy new year!
Iavor
On Dec 30, 2013 6:23 AM, "Simon Peyton-Jones"  wrote:
...
Iavor
Shouldn’t (+) be a closed type family (now that we have such things)?
Then the user couldn’t give new instances.
Simon
*From:* Haskell-Cafe [mailto:haskell-cafe-bounces@haskell.org] *On Behalf
Of *Iavor Diatchki
*Sent:* 29 December 2013 18:30
*To:* oleg@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,
-Iavor
On Sat, Dec 28, 2013 at 12:54 AM,  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-an...
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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