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<p class="MsoNormal"><span style="mso-fareast-language:EN-US">I’m afraid I’ve lost sync with this conversation. At some point it’d be good to write up conclusions on a wiki page and/or a ticket, so we don’t lose them. Email threads are hard to parse later.<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>
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<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Libraries <libraries-bounces@haskell.org>
<b>On Behalf Of </b>Nicolas Frisby<br>
<b>Sent:</b> 21 May 2019 18:19<br>
<b>To:</b> Richard Eisenberg <rae@richarde.dev><br>
<b>Cc:</b> Haskell Libraries <libraries@haskell.org><br>
<b>Subject:</b> Re: request: a Nat ordering constraint that is not an equality constraint<o:p></o:p></span></p>
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Yep, agreed. Totally practical.<o:p></o:p></p>
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FYI: my code base at work seems quite happy with the IsTrue approach; a very happy simplification! Like so:<o:p></o:p></p>
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```<o:p></o:p></p>
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class IsTrue<o:p></o:p></p>
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(msg :: ErrorMessage) (b :: Bool) where<o:p></o:p></p>
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isTrue :: Proxy# msg -> b :~: 'True<o:p></o:p></p>
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instance IsTrue msg 'True where<o:p></o:p></p>
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isTrue = \_ -> Refl<o:p></o:p></p>
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instance TypeError msg => IsTrue msg 'False<o:p></o:p></p>
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isTrue = \_ -> error "impossible"<o:p></o:p></p>
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type (<=) n m = IsTrue (Msg n m) (n GHC.TypeLits.<=? m)<o:p></o:p></p>
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type Msg (n :: Nat) (m :: Nat) =<o:p></o:p></p>
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'ShowType n<o:p></o:p></p>
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':<>:<o:p></o:p></p>
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'Text " is not <= "<o:p></o:p></p>
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':<>:<o:p></o:p></p>
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'ShowType m<o:p></o:p></p>
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```<o:p></o:p></p>
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(An `absurd` for TypeError might be nice?<o:p></o:p></p>
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<span style="font-family:"Arial",sans-serif">Via isTrue, I can explicitly convert between the two <= constraints wherever I need to. Which I could use to explicitly manage those hypothetical hypotheticals we were discussing.</span><o:p></o:p></p>
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Just to spell it out: the SMT solver would indeed supercede TcTypeNats, but TcTypeNats in turn already supercedes the IsTrue-based encoding. So I've already lost some <= deductions. But my work code doesn't use any of them in this middle ground -- they're all
simple enough that IsTrue works as-is or complicated enough that TcTypeNats didn't work already (I'm grumpily writing and invoking Trusted Code Base "axia" in those cases -- I'm avoiding plugin dependencies at work for now.)<o:p></o:p></p>
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On Tue, May 21, 2019, 09:14 Richard Eisenberg <<a href="mailto:rae@richarde.dev">rae@richarde.dev</a>> wrote:<o:p></o:p></p>
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You're right that, without special support, the IsTrue approach won't work with any deductions from Givens. But -- short of strapping on an SMT solver -- we're always going to fall short there, so we should analyze a particular on-the-ground use case before
taking any drastic action. (It sounds like you agree with this.)<o:p></o:p></p>
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Richard<o:p></o:p></p>
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On May 21, 2019, at 5:52 PM, Nicolas Frisby <<a href="mailto:nicolas.frisby@gmail.com" target="_blank">nicolas.frisby@gmail.com</a>> wrote:<o:p></o:p></p>
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<o:p> </o:p></p>
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Yes, it seems possible that a user space declaration of <= via IsTrue as in my first email could get much of the desired behavior. I plan on trying it with the work code base soon, maybe even today -- it'll probably do better than my current workaround.<o:p></o:p></p>
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If, however, we want the Nat solver to do anything at all with a Given `IsTrue (n <=? m)`, then I think it will need changes. I don't know that machinery well, but it seems very likely it would ignore such Givens.<o:p></o:p></p>
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<o:p> </o:p></p>
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For example, I would naively expect the Nat solver should discharge a Wanted `IsTrue (n <=? m)` from two Givens `(IsTrue (n <=? x),IsTrue (x <=? m))`.<o:p></o:p></p>
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Simon's exploration of IsTrue/IsEqual might shed more light on what exactly the Nat solver should and should not do with such a Given. If it's in fact nothing at all, then yes, maybe a user space solution fully supplants the proposed Passive.<=. But I currently
anticipate that it should do something with such Givens.<o:p></o:p></p>
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Thanks. -Nick<o:p></o:p></p>
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On Tue, May 21, 2019, 00:29 Richard Eisenberg <<a href="mailto:rae@richarde.dev" target="_blank">rae@richarde.dev</a>> wrote:<o:p></o:p></p>
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This is an interesting proposal. When I started reading it, I wondered why anyone would want to avoid the current definition. But you motivate that part well. I would want a larger test of the IsTrue approach to make sure it does what you want before supporting
this. But wait: couldn't you write your GHC.TypeLits.Passive today, in a library, with no ill effect? If so, there isn't a strict reason GHC needs to adopt this. (Of course, if the new definition proves useful, then it might make sense to do so in time.)<br>
<br>
> On May 21, 2019, at 3:48 AM, Nicolas Frisby <<a href="mailto:nicolas.frisby@gmail.com" target="_blank">nicolas.frisby@gmail.com</a>> wrote:<br>
> <br>
> P.P.S. - Is there a standard place to find something like `IsTrue`? More generally: a test for type equality that does not drive unification? Thanks again.<br>
<br>
If something like this ends up in GHC, Data.Type.Bool seems like the right place.<br>
<br>
Richard<o:p></o:p></p>
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