<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:x="urn:schemas-microsoft-com:office:excel" xmlns:p="urn:schemas-microsoft-com:office:powerpoint" xmlns:a="urn:schemas-microsoft-com:office:access" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:s="uuid:BDC6E3F0-6DA3-11d1-A2A3-00AA00C14882" xmlns:rs="urn:schemas-microsoft-com:rowset" xmlns:z="#RowsetSchema" xmlns:b="urn:schemas-microsoft-com:office:publisher" xmlns:ss="urn:schemas-microsoft-com:office:spreadsheet" xmlns:c="urn:schemas-microsoft-com:office:component:spreadsheet" xmlns:oa="urn:schemas-microsoft-com:office:activation" xmlns:html="http://www.w3.org/TR/REC-html40" xmlns:q="http://schemas.xmlsoap.org/soap/envelope/" xmlns:D="DAV:" xmlns:x2="http://schemas.microsoft.com/office/excel/2003/xml" xmlns:ois="http://schemas.microsoft.com/sharepoint/soap/ois/" xmlns:dir="http://schemas.microsoft.com/sharepoint/soap/directory/" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:dsp="http://schemas.microsoft.com/sharepoint/dsp" xmlns:udc="http://schemas.microsoft.com/data/udc" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:sps="http://schemas.microsoft.com/sharepoint/soap/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:udcxf="http://schemas.microsoft.com/data/udc/xmlfile" xmlns:wf="http://schemas.microsoft.com/sharepoint/soap/workflow/" xmlns:mver="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns:mrels="http://schemas.openxmlformats.org/package/2006/relationships" xmlns:ex12t="http://schemas.microsoft.com/exchange/services/2006/types" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=Content-Type content="text/html; charset=us-ascii">
<meta name=Generator content="Microsoft Word 12 (filtered medium)">
<style>
<!--
/* Font Definitions */
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;}
@page Section1
{size:612.0pt 792.0pt;
margin:72.0pt 72.0pt 72.0pt 72.0pt;}
div.Section1
{page:Section1;}
-->
</style>
<!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang=EN-GB link=blue vlink=purple>
<div class=Section1>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>See also the paper that Ralf and I wrote about “Derivable
type classes” (on my pubs page) which uses quantified constraints. <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'>Quantified constraints would be another perfectly sensible
extension. GHC does not support them at the moment though. I’m
really not too sure how much work it’d be to add them; quite significant
I suspect.<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'>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>
<div style='border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt'>
<div>
<div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'>
<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"'> haskell-bounces@haskell.org
[mailto:haskell-bounces@haskell.org] <b>On Behalf Of </b>Conal Elliott<br>
<b>Sent:</b> 02 August 2007 01:29<br>
<b>To:</b> haskell@haskell.org<br>
<b>Subject:</b> [Haskell] Quantified class constraints (& back-chaining)<o:p></o:p></span></p>
</div>
</div>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal style='margin-bottom:12.0pt'>I'm developing a type
constructor class and want the constraint <span style='font-family:"Courier New"'>forall
a. Monoid (m a)</span> (where <span style='font-family:"Courier New"'>m :: *
-> *</span> ), which is neither legal Haskell, nor supported by GHC.<br>
<br>
As a work-around, I used the first encoding suggested in "Simulating
Quantified Class Constraints" (Valery Trifonov, Haskell Workshop
'03). Add a type class <br>
<br>
<span style='font-family:"Courier New"'> class Monoid_f m
where<br>
mempty_f :: forall a. m a <br>
mappend_f :: forall a. m a -> m a -> m a</span><br>
<br>
and an instance *schema*<br>
<br>
<span style='font-family:"Courier New"'> -- instance Monoid_f
f where { mempty_f = mempty ; mappend_f = mappend }</span><br>
<br>
to instantiate manually wherever necessary. For instance,<br>
<br>
<span style='font-family:"Courier New"'> instance Monoid_f []
where { mempty_f = mempty ; mappend_f = mappend } </span><br>
<br>
<br>
The paper's second approach is to replace the schema and multiple
instantiations with a single instance.<br>
<br>
<span style='font-family:"Courier New"'> instance Monoid_f f
=> Monoid (f a) where <br>
{ mempty = mempty_f ; mappend = mappend_f }</span><br>
<br>
As the paper points out,<o:p></o:p></p>
<p class=MsoNormal>Unfortunately, due to the type variable f in the head of the
instance type, this declaration is not in Haskell 98; however, at least two
implementations support extensions allowing such declarations.<o:p></o:p></p>
<p class=MsoNormal style='margin-bottom:12.0pt'><br>
Sadly, this solution runs into the problem of instance selection based only on
head-matching, not back-chaining into constraints. For instance, I'd like
also to use the following "conflicting" declaration. <br>
<br>
<span style='font-family:"Courier New"'> instance
(Applicative f, Monoid a) => Monoid (f a) where <br>
mempty = pure mempty<br>
mappend = liftA2 mappend</span><br>
<br>
What's the state of thinking & doing with regard to universally quantified
class constraints? <br>
<br>
Note that hereditary Harrop formulas do include universally quantified
goals. Less ambitiously, I think GHC's type-checker already deals with
universally-quantified variables, so perhaps quantified constraints are not a
great reach (just guessing). <br>
<br>
Cheers, - Conal<o:p></o:p></p>
</div>
</div>
</body>
</html>