Disclaimer: I don't really know all about category theory, so some definitions might not be absolutely correct.<br><br>Monoid is the category of all types that have a empty value and an append operation.<br><br>The best example is a list.<br>
<br><pre><font size="4"><span class="keyword">instance</span> <span class="conid">Monoid</span> <span class="keyglyph">[</span><span class="varid">a</span><span class="keyglyph">]</span> <span class="keyword">where</span><br>
<a name="(line68)"></a> <span class="varid">mempty</span> <span class="keyglyph">=</span> <span class="conid">[]</span><br><a name="(line69)"></a> <span class="varid">mappend</span> <span class="keyglyph">=</span> <span class="layout">(</span><span class="varop">++</span><span class="layout">)</span></font><br>
<br></pre><br>Why do I need it? Well, you can think of a function where you need to incrementally store data. <br><br>Storing them to a Monoid, you can start with a list and then change to a Set, without changing the function itself, because it would be defined based on the Monoid operations.<br>
<br><pre><font size="4"><span class="keyword">instance</span> <span class="conid">Ord</span> <span class="varid">a</span> <span class="keyglyph">=></span> <span class="conid">Monoid</span> <span class="layout">(</span><span class="conid">Set</span> <span class="varid">a</span><span class="layout">)</span> <span class="keyword">where</span><br>
<a name="(line143)"></a> <span class="varid">mempty</span> <span class="keyglyph">=</span> <span class="varid">empty</span><br><a name="(line144)"></a> <span class="varid">mappend</span> <span class="keyglyph">=</span> <span class="varid">union</span><br>
<a name="(line145)"></a> <span class="varid">mconcat</span> <span class="keyglyph">=</span> <span class="varid">unions</span><br><br></font></pre>Hope I have helped!<br><br>Regards,<br><br>Rafael<br><br><br><br><div class="gmail_quote">
On Fri, Nov 13, 2009 at 14:14, Magicloud Magiclouds <span dir="ltr"><<a href="mailto:magicloud.magiclouds@gmail.com">magicloud.magiclouds@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
Hi,<br>
I have looked the concept of monoid and something related, but<br>
still, I do not know why we use it?<br>
<font color="#888888"><br>
--<br>
竹密岂妨流水过<br>
山高哪阻野云飞<br>
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<br></blockquote></div><br><br clear="all"><br>-- <br>Rafael Gustavo da Cunha Pereira Pinto<br><br>