[Haskell-cafe] Re: Couple of formal questions
wchogg at gmail.com
Sun May 11 11:35:46 EDT 2008
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:
> Hope that answers your question,
I've had a lot of good reading material from this thread, and I greatly
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.
I've also liked Baez et al's Rosetta Stone paper as food for thought
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