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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D">On further reflection I have a question.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D">Under the limited design below, which Edward says will do all he wants:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-family:Symbol;color:#1F497D"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-family:"Calibri","sans-serif";color:#1F497D">The mutually recursive classes (call them A, B, C) must be defined all together. Like<br>
class B a => A a; class C a => B a; class A a => C a<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-family:Symbol;color:#1F497D"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-family:"Calibri","sans-serif";color:#1F497D">If a type T is an instance of any of those classes, it must be a member of all of them<o:p></o:p></span></p>
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</span></span></span><![endif]><span style="font-family:"Calibri","sans-serif";color:#1F497D">If a function f has type f :: A a => blah, then the signature f :: B a => blah and f :: C a => blah would work equally well<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D">In short, I see no advantage to making A,B,C separate classes compared to simply unioning them into a single class.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D">Bottom line: adding recursive superclasses with the restrictions I describe below would add no useful expressive power. But it would cost effort to implement. So why do it?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D">Maybe I’m missing something.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#1F497D"><br>
Simon<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""> Edward Kmett [mailto:ekmett@gmail.com]
<br>
<b>Sent:</b> 22 July 2011 20:07<br>
<b>To:</b> Simon Peyton-Jones<br>
<b>Cc:</b> Gábor Lehel; glasgow-haskell-users@haskell.org<br>
<b>Subject:</b> Re: Superclass Cycle via Associated Type<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">2011/7/22 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">I talked to Dimitrios. Fundamentally we think we should be able to handle recursive superclasses, albeit we have a bit more work to do on the type inference engine first.<br>
<br>
The situation we think we can handle ok is stuff like Edward wants (I've removed all the methods):<o:p></o:p></p>
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class LeftModule Whole m => Additive m<o:p></o:p></p>
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<p class="MsoNormal">class Additive m => Abelian m<br>
class (Semiring r, Additive m) => LeftModule r m<o:p></o:p></p>
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<p class="MsoNormal">class Multiplicative m where (*) :: m -> m -> m<br>
class LeftModule Natural m => Monoidal m<o:p></o:p></p>
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<p class="MsoNormal">class (Abelian m, Multiplicative m, LeftModule m m) => Semiring m<br>
class (LeftModule Integer m, Monoidal m) => Group m<o:p></o:p></p>
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<p class="MsoNormal">class Multiplicative m => Unital m<o:p></o:p></p>
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<p class="MsoNormal">class (Monoidal r, Unital r, Semiring r) => Rig<span style="color:#1F497D"> r</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">class (Rig r, Group r) => Ring r<o:p></o:p></p>
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<p class="MsoNormal">The superclasses are recursive but<br>
a) They constrain only type variables<br>
b) The variables in the superclass context are all<br>
mentioned in the head. In class Q => C a b c<br>
fv(Q) is subset of {a,b,c}<br>
<br>
Question to all: is that enough?<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">This would perfectly address all of the needs that I have had!<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">-Edward<o:p></o:p></p>
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