On Mon, May 5, 2008 at 9:53 AM, Wouter Swierstra <wss@cs.nott.ac.uk> wrote:

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

Wouter Swierstra <wss@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