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

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