Re: [Haskell-cafe] Re: Couple of formal questions

On Mon, May 5, 2008 at 9:53 AM, Wouter Swierstra wrote:

On 1 May 2008, at 16:58, Michael Karcher wrote:

Wouter Swierstra wrote:

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Hi Creighton,

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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