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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hmm, no I don’t think that Flattening is a very serious problem:
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Firstly, we can somehow get around that if we use implication constraints and higher-order flattening<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">variables. We have discussed that (but not implemented). For example.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">forall a. F [a] ~ G Int
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">becomes:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">forall a. fsk a ~ G Int
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">forall a. true => fsk a ~ F [a]
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Secondly: flattening under a Forall is not terribly important, unless you have type families that dispatch on
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">polymorphic types, which is admittedly a rather rare case. We lose some completeness but that’s ok.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">For me, a more serious problem are polymorphic RHS, which give rise to exactly the same problems for type<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">inference as impredicative polymorphism. For instance:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">type instance F Int = forall a. a -> [a]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">g :: F Int<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">g = undefined<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">main = g 3<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Should this type check or not? And then all our discussions about impredicativity, explicit type applications etc become<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">relevant again.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Thanks!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">d-<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> Simon Peyton-Jones
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<b>Sent:</b> Friday, April 05, 2013 8:24 AM<br>
<b>To:</b> Manuel M T Chakravarty<br>
<b>Cc:</b> Iavor Diatchki; ghc-devs; Dimitrios Vytiniotis<br>
<b>Subject:</b> RE: Restrictions on polytypes with type families<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">Manuel has an excellent point. See the Note below in TcCanonical! I have no clue how to deal with this<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">Simon<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">Note [Flattening under a forall]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">Under a forall, we<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> (a) MUST apply the inert subsitution<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> (b) MUST NOT flatten type family applications<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">Hence FMSubstOnly.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">For (a) consider c ~ a, a ~ T (forall b. (b, [c])<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">If we don't apply the c~a substitution to the second constraint<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">we won't see the occurs-check error.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">For (b) consider (a ~ forall b. F a b), we don't want to flatten<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">to (a ~ forall b.fsk, F a b ~ fsk)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">because now the 'b' has escaped its scope. We'd have to flatten to<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> (a ~ forall b. fsk b, forall b. F a b ~ fsk b)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">and we have not begun to think about how to make that work!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> Manuel M T Chakravarty [<a href="mailto:chak@cse.unsw.edu.au">mailto:chak@cse.unsw.edu.au</a>]
<br>
<b>Sent:</b> 04 April 2013 02:01<br>
<b>To:</b> Simon Peyton-Jones<br>
<b>Cc:</b> Iavor Diatchki; ghc-devs<br>
<b>Subject:</b> Re: Restrictions on polytypes with type families<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">Simon Peyton-Jones <<a href="mailto:simonpj@microsoft.com">simonpj@microsoft.com</a>>:<o:p></o:p></p>
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<p class="MsoNormal">isn't this moving directly into the territory of impredicative types? <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-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">Ahem, maybe you are right. Impredicativity means that you can</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> <span class="apple-converted-space"> </span><b>instantiate a type variable with a polytype</b></span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">So if we allow, say (Eq (forall a.a->a)) then we’ve instantiated Eq’s type variable with a polytype. Ditto Maybe (forall a. a->a).</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">But this is only bad from an inference point of view, especially for implicit instantiation. Eg if we had</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> class C a where</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> op :: Int -> a</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">then if we have</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> f :: C (forall a. a->a) =>...</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> f = ...op...</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">do we expect op to be polymorphic??</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">For type families maybe things are easier because there is no implicit instantiation. </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Verdana","sans-serif";color:#1F497D">But I’m not sure</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">These kinds of issues are the reason that my conclusion at the time was (as Richard put it)<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Or, are<br>
| there any that are restricted because someone needs to think hard before<br>
| lifting it, and no one has yet done that thinking?<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">At the time, there were also problems with what the type equality solver was supposed to do with foralls.<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">I know, for example,<br>
| that the unify function in types/Unify.lhs will have to be completed to<br>
| work with foralls, but this doesn't seem hard.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">The solver changed quite a bit since I rewrote Tom's original prototype. So, maybe it is easy now, but maybe it is more tricky than you think. The idea of rewriting complex terms into equalities at the point of each application of a type
synonym family (aka type function) assumes that you can pull subterms out of a term into a separate equality, but how is this going to work if a forall is in the way? E.g., given<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> type family F a :: *<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">the equality<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> Maybe (forall a. F [a]) ~ G b<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">would need to be broken down to<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> x ~ F [a], Maybe (forall a. x) ~ G b<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">but you cannot do that, because you just moved 'a' out of its scope. Maybe you can move the forall out as well?<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Manuel<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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