[Haskell-cafe] Re: Couple of formal questions

[Wouter Swierstra]

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

> Wouter Swierstra <wss at cs.nott.ac.uk> 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