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<p class="MsoNormal"><span style="mso-fareast-language:EN-US">I see this in GHC.TypeNats<o:p></o:p></span></p>
<p class="Code"><b><span style="mso-fareast-language:EN-US">sameNat ::</span></b><span style="mso-fareast-language:EN-US">
<b>(KnownNat a, KnownNat b) =><o:p></o:p></b></span></p>
<p class="Code"><b><span style="mso-fareast-language:EN-US"> Proxy a -> Proxy b -> Maybe (a :~: b)<o:p></o:p></span></b></p>
<p class="Code"><b><span style="mso-fareast-language:EN-US">sameNat x y<o:p></o:p></span></b></p>
<p class="Code"><b><span style="mso-fareast-language:EN-US"> | natVal x == natVal y = Just (unsafeCoerce Refl)<o:p></o:p></span></b></p>
<p class="Code"><b><span style="mso-fareast-language:EN-US"> | otherwise = Nothing<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">The unsafeCoerce says that sameNat is part of the trusted code base. And indeed, it’s only because SNat is a private newtype (i.e its data constructor is private to GHC.TypeNats) that you can’t
bogusly say (SNat 7 :: SNat 8)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">You want exactly the same thing, but for a comparison oriented data CompareEv, rather than its equality counterpart :~:. So the same approach seems legitimate.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">I always want code with unsafeCoerce to be clear about (a) why it’s necessary and (b) why it’s sound.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Simon<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Glasgow-haskell-users <glasgow-haskell-users-bounces@haskell.org>
<b>On Behalf Of </b>Conal Elliott<br>
<b>Sent:</b> 24 May 2018 00:39<br>
<b>To:</b> glasgow-haskell-users@haskell.org<br>
<b>Subject:</b> Natural number comparisons with evidence<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">When programming with GHC's type-level natural numbers and `KnownNat` constraints, how can one construct *evidence* of the result of comparisons to be used in further computations? For instance, we might define a type for augmenting the
results of `compare` with evidence:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> data CompareEv u v</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> = (u < v) => CompareLT</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> | (u ~ v) => CompareEQ</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> | (u > v) => CompareGT</span><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Then I'd like to define a comparison operation (to be used with `AllowAmbiguousTypes` and `TypeApplications`, alternatively taking proxy arguments):<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> compareEv :: (KnownNat m, KnownNat n) => CompareEv u v</span><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">With `compareEv`, we can bring evidence into scope in `case` expressions.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I don't know how to implement `compareEv`. The following attempt fails to type-check, since `compare` doesn't produce evidence (which is the motivation for `compareEv` over `compare`):<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> compareEv = case natVal (Proxy @ u) `compare` natVal (Proxy @ v) of</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> LT -> CompareLT</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> EQ -> CompareEQ</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Courier New"">> GT -> CompareGT</span><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Can `compareEv` be implemented in GHC Haskell? Is there already an implementation of something similar? Any other advice?<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Thanks, -- Conal<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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