[Haskell-cafe] Stream fusion and span/break/group/init/tails

[Dan Doel]

On Mon, Apr 29, 2013 at 10:05 AM, Duncan Coutts <
duncan.coutts at googlemail.com> wrote:

> On Thu, 2013-04-25 at 00:52 +0200, Gábor Lehel wrote:
> > On Wed, Apr 24, 2013 at 7:56 PM, Bryan O'Sullivan <bos at serpentine.com
> >wrote:
> >
> > > On Wed, Apr 24, 2013 at 10:47 AM, Duncan Coutts <
> > > duncan.coutts at googlemail.com> wrote:
> > >
> > >> I address it briefly in my thesis [1], Section 4.8.2. I think it's a
> > >> fundamental limitation of stream fusion.
> > >>
> > >
> > > See also concat, where the naive fusion-based implementation has
> quadratic
> > > performance:
> > >
> > > concat :: [Text] -> Text
> > > concat txts = unstream (Stream.concat (List.map stream txts))
> > >
> > > I've never figured out how to implement this with sensible
> characteristics
> > > within the fusion framework.
> > >
> >
> > If you could "solve" concat, might that also lead to be being able to do
> > without the Skip constructor?
>
> Dan is right, we still need Skip. My suggested "solution" to the
> concatmap problem is also mostly independent of the skip issue.
>
> You shouldn't think of skip as being a hack. It's not. It's how we
> express a more general class of producers in a way that is productive.


 To further this, note that in a total language, with the type:

    codata Stream a = End | Yield a (Stream a)

filter is not definable; it is not a total function. At least, barring an
extra proof of some sort that the predicate will yield true after a finite
amount of time. concat is similar.

Also, adding Skip (Stream a) is a relatively standard way of explicitly
representing lazy, partial values. (This is opposed to the partiality
monad, which is like an encoding of strict general recursion). That is, if
νF is the type of total values, then ν(F + Id) is the type of partial
values. I don't know how easy it is to delete from a more complex tree
using just that extension, but in theory you could productively represent
arbitrary manipulations with just that, I believe.

-- Dan
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