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,
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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