Joachim Breitner wrote:

Am Samstag, den 13.09.2014, 00:01 -0400 schrieb David Feuer:
> On Sep 12, 2014 2:35 PM, "Joachim Breitner" <mail@joachim-breitner.de>
> wrote:
> > Interesting. I assumed that some wrap.unwrap=id law would hold, or
> at
> > least some moral approximation (e.g. disregarding bottoms in an
> > acceptable manner). But if the wrappers have to do arbitrary stuff
> that
> > can arbitrarily interact with how the producer calls them, this
> becomes
> > a bit less appealing.
>
> No, nothing pleasant like that, I'm afraid. isoSimple is like that of
> course, but once it gets to foldl, the fusion rule is handing the
> builder a wrap/unwrap pair that isn't even close to that.

and parametricity doesn't help here? Note that due to the forall in the
type of buildW, you can probably reason about what kind of values buildW
can produce, as it can only use whatever the consumer handed to it.
Maybe there is an invariant for that type, and the worker/wrapper pair
is the identity for values that fulfill that invariant.

That seems reasonable, and I suspect without any proof that Takano Akio's wrapper for foldl and Dan Doel's wrapper for reverse probably satisfy it. Scans seem to be more of a challenge. It appears to me that Dan's scanl wrapper probably does *not* satisfy that requirement, and I don't know enough to have much chance of finding one that does.

David