On Tue, Sep 30, 2008 at 12:51 AM, apfelmus <apfelmus@quantentunnel.de> wrote:

Jason Dagit wrote:
> Hello,
>
> I recently had someone point me to this thread on LtU:
> http://lambda-the-ultimate.org/node/2003
>
> The main paper in the article is this one:
> http://www.jucs.org/jucs_10_7/total_functional_programming/jucs_10_07_0751_0768_turner.pdf
>
> It leaves me with several questions:
> 1) Are there are existing Haskell-ish implementations of the total
> functional paradigm?

Agda?

http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php?n=Main.HomePage

It seems to me that dependent types are best for ensuring totality.

Bear with me, as I know virtual nothing about dependent types yet. In the total functional paradigm the language lacks a value for bottom. This means general recursion is out and in the paper I cited it was replaced with structural recursion on the inputs. How do dependent types remove bottom from the language?

> 2) Could we restructure Haskell so that it comes in 3 layers, total
> functional core, lazy pure partial functional middle, and IO outer layer?

The IO layer can be interpreted as "co-total", i.e. as codata.
Basically, this means that it's guaranteed that the program prints or
reads something after a finite amount of time and does not loop forever
without doing anything.

I was asserting that Haskell is currently 2 layered. Purely functional vs. IO. They integrate nicely and play well together, but I still think of them as distinct layers. Perhaps this is not fair or confusing though. The paper I cited did indeed use codata to define streams so that something, such as an OS, that needs to process infinite streams of requests can still do so.

Thanks,
Jason