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<pre style="margin-left:36.0pt"><span style="font-family:"Arial",sans-serif">I'm wondering about the claim "and that can float out of the implication". The Note does go on to mention #15009 --- and I understand how that Wanted floats *with* #15009 --- but as written, it sounds like the Wanted could float even without #15009.<o:p></o:p></span></pre>
<pre style="margin-left:36.0pt"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">Consider our example<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> forall a[2]. b[1] ~ a[2] => beta[1] ~ a[2]<o:p></o:p></span></pre>
<pre><span class="gmail-cm"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">If we leave the Given oriented as it is, the (beta~a) constraint cannot float, because it mentions a, which is bound by the forall<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">If we swizzle the Given we get this:<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> forall a[2]. a[2] ~ b[1] => beta[1] ~ a[2]<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">Now we’ll use that Given to rewrite the Wanted, to get this:<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> forall a[2]. a[2] ~ b[1] => beta[1] ~ b[1]<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">Now the Wanted can float – it no longer mentions a.<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">But wait! There’s a second thing that prevents floating: we never float out of an implication that binds Given equalities. But not quite: the Note [Let-bound skolems] explains that we don’t treat as “binding a Given equality” an equality whose LHS is one of the skolems bound by this very implication. And lo! in the implication<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> forall a[2]. a[2] ~ b[1] => beta[1] ~ b[1]<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">the a[2] on the LHS is indeed bound by this implication. So we do not disable floating (despite the apparent Given equality), and can float to give<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> beta[1] ~ b[1], (forall a[2]. a[2] ~ b[1] => <empty>)<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">Does that help explain? If so, might you update the Note(s) so they are clearer?<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">Thanks<o:p></o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
<pre><span style="font-family:"Arial",sans-serif">Simon<o:p></o:p></span></pre>
<pre><span class="gmail-cm"><o:p> </o:p></span></pre>
<pre><o:p> </o:p></pre>
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<p class="MsoNormal"><b><span lang="EN-US">rom:</span></b><span lang="EN-US"> Nicolas Frisby <nicolas.frisby@gmail.com>
<br>
<b>Sent:</b> 16 May 2019 06:03<br>
<b>To:</b> ghc-devs@haskell.org<br>
<b>Cc:</b> Richard Eisenberg <rae@cs.brynmawr.edu>; Simon Peyton Jones <simonpj@microsoft.com><br>
<b>Subject:</b> clarification re Note [Deeper level on the left]<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<a href="https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.haskell.org%2Fghc%2Fghc%2Fblob%2Fmaster%2Fcompiler%2Ftypecheck%2FTcUnify.hs%23L1754&data=02%7C01%7Csimonpj%40microsoft.com%7Cfd5cf759668242dc797f08d6d9bbddb8%7C72f988bf86f141af91ab2d7cd011db47%7C1%7C0%7C636935798235607415&sdata=cRksGeyxgGtNkWOf7nuF42BruMVyK8JyqbbAZC02DJM%3D&reserved=0">https://gitlab.haskell.org/ghc/ghc/blob/master/compiler/typecheck/TcUnify.hs#L1754</a>
contains<o:p></o:p></p>
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<o:p> </o:p></p>
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<pre><span class="gmail-cm">```<o:p></o:p></span></pre>
<pre><span class="gmail-cm">Note [Deeper level on the left]</span><o:p></o:p></pre>
<pre><span class="gmail-cm">~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</span><o:p></o:p></pre>
<pre><span class="gmail-cm">The most important thing is that we want to put tyvars with</span><o:p></o:p></pre>
<pre><span class="gmail-cm">the deepest level on the left. The reason to do so differs for</span><o:p></o:p></pre>
<pre><span class="gmail-cm">Wanteds and Givens, but either way, deepest wins! Simple.</span><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><span class="gmail-cm">* Wanteds. Putting the deepest variable on the left maximise the</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> chances that it's a touchable meta-tyvar which can be solved.</span><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><span class="gmail-cm">* Givens. Suppose we have something like</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> forall a[2]. b[1] ~ a[2] => beta[1] ~ a[2]</span><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><span class="gmail-cm"> If we orient the Given a[2] on the left, we'll rewrite the Wanted to</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> (beta[1] ~ b[1]), and that can float out of the implication.</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> Otherwise it can't. By putting the deepest variable on the left</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> we maximise our changes of eliminating skolem capture.<o:p></o:p></span></pre>
<pre><span class="gmail-cm"><o:p> </o:p></span></pre>
<pre><span class="gmail-cm"> See also TcSMonad Note [Let-bound skolems] for another reason<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> to orient with the deepest skolem on the left.<o:p></o:p></span></pre>
<pre><span class="gmail-cm"> IMPORTANT NOTE: this test does a level-number comparison on</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> skolems, so it's important that skolems have (accurate) level</span><o:p></o:p></pre>
<pre><span class="gmail-cm"> numbers.</span><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><span class="gmail-cm">See #15009 for an further analysis of why "deepest on the left"</span><o:p></o:p></pre>
<pre><span class="gmail-cm">is a good plan.<o:p></o:p></span></pre>
<pre>```<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
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<pre><span style="font-family:"Arial",sans-serif">I'm wondering about the claim "and that can float out of the implication". The Note does go on to mention #15009 --- and I understand how that Wanted floats *with* #15009 --- but as written, it sounds like the Wanted could float even without #15009.<o:p></o:p></span></pre>
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<pre><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></pre>
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<pre><span style="font-family:"Arial",sans-serif">Am I missing something? Roughly: I'm asking because I need to decide if there's a reason for my typechecker plugin to bother with "eliminating skolem capture" when #15009 does *not* apply.<br><br>Thanks. -Nick<o:p></o:p></span></pre>
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