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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D;mso-fareast-language:EN-US">Iavor<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D;mso-fareast-language:EN-US">Shouldn’t (+) be a closed type family (now that we have such things)? Then the user couldn’t give new instances.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D;mso-fareast-language:EN-US">Simon<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif"">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif""> Haskell-Cafe [mailto:haskell-cafe-bounces@haskell.org]
<b>On Behalf Of </b>Iavor Diatchki<br>
<b>Sent:</b> 29 December 2013 18:30<br>
<b>To:</b> oleg@okmij.org<br>
<b>Cc:</b> Haskell Cafe<br>
<b>Subject:</b> Re: [Haskell-cafe] Consistency issue with type level numeric literals<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Hi Oleg,<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">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.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Happy holidays,<o:p></o:p></p>
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<p class="MsoNormal">-Iavor<o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><o:p> </o:p></p>
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<p class="MsoNormal">On Sat, Dec 28, 2013 at 12:54 AM, <<a href="mailto:oleg@okmij.org" target="_blank">oleg@okmij.org</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><br>
GHC 7.6.3 has quite convenient type-level numeric literals. We can use<br>
numbers like 1 and 2 in types. However, using the type level numeral<br>
has been quite a bit of a challenge, illustrated, for example, by<br>
the following SO question.<br>
<br>
<a href="http://stackoverflow.com/questions/20809998/type-level-nats-with-literals-and-an-injective-successor" target="_blank">http://stackoverflow.com/questions/20809998/type-level-nats-with-literals-and-an-injective-successor</a><br>
<br>
It seems the challenge has the reason: the type level numerals and<br>
their operations provided in GHC.TypeLits have a consistency<br>
issue. The following code demonstrates the issue: it constructs two<br>
distinct values of the type Sing 2. Singletons aren't singletons.<br>
<br>
{-# LANGUAGE KindSignatures #-}<br>
{-# LANGUAGE DataKinds #-}<br>
{-# LANGUAGE ScopedTypeVariables #-}<br>
{-# LANGUAGE TypeOperators #-}<br>
{-# LANGUAGE TypeFamilies #-}<br>
{-# LANGUAGE GADTs #-}<br>
{-# LANGUAGE PolyKinds #-}<br>
<br>
module NotSing where<br>
<br>
import GHC.TypeLits<br>
<br>
-- GHC strangely enough lets us define instances for (+)<br>
type instance 1 + 1 = 0<br>
type instance 0 + 1 = 2<br>
<br>
-- A singular representative of 1::Nat<br>
s1 :: Sing 1<br>
s1 = withSing id<br>
<br>
-- A singular representative of 2::Nat<br>
s2 :: Sing 2<br>
s2 = withSing id<br>
<br>
is2 :: IsZero 0<br>
is2 = IsSucc s1<br>
<br>
tran :: IsZero 0 -> Sing 2<br>
tran (IsSucc x) = case isZero x of<br>
IsSucc y -> case isZero y of<br>
IsZero -> x<br>
<br>
-- Another singular representative of 2::Nat<br>
-- A singular representative of 2::Nat<br>
s2' :: Sing 2<br>
s2' = tran is2<br>
<br>
<br>
{-<br>
*NotSing> s2<br>
2<br>
*NotSing> s2'<br>
1<br>
-}<br>
<br>
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<p class="MsoNormal"><o:p> </o:p></p>
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