[Haskell-cafe] Re: Couple of formal questions

[Creighton Hogg]

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

>
> 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
>

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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