<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:m="http://schemas.microsoft.com/office/2004/12/omml" 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:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-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.E-MailFormatvorlage17
{mso-style-type:personal-compose;
font-family:"Calibri","sans-serif";
color:windowtext;}
..MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page Section1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
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=DE link=blue vlink=purple>
<div class=Section1>
<p class=MsoNormal>Hello,<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal><span lang=EN-US>this is maybe a simple question:<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>cbinary :: a -> b -> (a -> b ->
b) -> (b -> c) -> c<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- Version 1 works:<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>cbinary x y f g = g (f x y)<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- Version 2 should be exactly the same
according<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- to my understanding of the "."
operator definition,<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- but fails with: <o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- Occurs check: cannot construct the
infinite type: b = b -> b<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- When generalising the type(s) for
`cbinary'<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>-- cbinary x y f g = (g . f) x y<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>Can anybody explain why this happens and
how I can compose f and g?<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US>Hint: It works fine if f is defined as an
unary function.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>Thank you very much!<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US>Axel<o:p></o:p></span></p>
</div>
</body>
</html>