<br><br><div class="gmail_quote">On Mon, May 5, 2008 at 9:53 AM, Wouter Swierstra <<a href="mailto:wss@cs.nott.ac.uk" target="_blank">wss@cs.nott.ac.uk</a>> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div><br>
On 1 May 2008, at 16:58, Michael Karcher wrote:<br>
<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
Wouter Swierstra <<a href="mailto:wss@cs.nott.ac.uk" target="_blank">wss@cs.nott.ac.uk</a>> wrote:<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
Hi Creighton,<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
Where could I find a proof that the initial algebras & final<br>
coalgebras of CPO coincide? I saw this referenced in the<br>
"Bananas.." paper as a fact, but am not sure where this comes from.<br>
</blockquote>
I couldn't find the statement you are referring to in "Functional<br>
Programming with Bananas, Lenses, Envelopes, and Barbed Wire" - but<br>
I'm not sure if this holds for every CPO.<br>
</blockquote>
<br>
Probably he was referring to the last paragraph of the introduction:<br>
<br>
Working in CPO has the advantage that the carriers of intial algebras<br>
and final co-algebras coincide, thus there is a single data type that<br>
comprises both finite and infinite elements.<br>
</blockquote>
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Ah - thanks for pointing that out. According to my more categorically inclined office mates, Marcelo Fiore's thesis is a good reference:<br>
<br>
<a href="https://www.lfcs.inf.ed.ac.uk/reports/94/ECS-LFCS-94-307/" target="_blank">https://www.lfcs.inf.ed.ac.uk/reports/94/ECS-LFCS-94-307/</a><br>
<br>
Hope that answers your question,<br><font color="#888888">
<br>
Wouter<br>
</font></blockquote></div><br>I've had a lot of good reading material from this thread, and I greatly appreciate it:<br>As a more background reading on this, I think Meijer & Fokkinga's "Program Calculation Properties of Continuous Algebras" is good, though the notation is a little idiosyncratic.<br>
<a href="http://citeseer.ist.psu.edu/717129.html">http://citeseer.ist.psu.edu/717129.html</a><br><br>I've also liked Baez et al's Rosetta Stone paper as food for thought <br><a href="http://math.ucr.edu/home/baez/rosetta.pdf" target="_blank">http://math.ucr.edu/home/baez/rosetta.pdf</a><br>
<br>Creighton Hogg<br>