On Mon, May 5, 2008 at 9:53 AM, Wouter Swierstra <[EMAIL PROTECTED]> wrote:
> > On 1 May 2008, at 16:58, Michael Karcher wrote: > > Wouter Swierstra <[EMAIL PROTECTED]> wrote: > > > > > Hi Creighton, > > > > > > > Where could I find a proof that the initial algebras & final > > > > coalgebras of CPO coincide? I saw this referenced in the > > > > "Bananas.." paper as a fact, but am not sure where this comes from. > > > > > > > I couldn't find the statement you are referring to in "Functional > > > Programming with Bananas, Lenses, Envelopes, and Barbed Wire" - but > > > I'm not sure if this holds for every CPO. > > > > > > > Probably he was referring to the last paragraph of the introduction: > > > > Working in CPO has the advantage that the carriers of intial algebras > > and final co-algebras coincide, thus there is a single data type that > > comprises both finite and infinite elements. > > > > Ah - thanks for pointing that out. According to my more categorically > inclined office mates, Marcelo Fiore's thesis is a good reference: > > https://www.lfcs.inf.ed.ac.uk/reports/94/ECS-LFCS-94-307/ > > Hope that answers your question, > > Wouter > I've had a lot of good reading material from this thread, and I greatly appreciate it: 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. http://citeseer.ist.psu.edu/717129.html I've also liked Baez et al's Rosetta Stone paper as food for thought http://math.ucr.edu/home/baez/rosetta.pdf Creighton Hogg
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