Your scanl wrapper might be right for scanl, but it does not satisfy the condition Joachim proposed. In particular, if we define (!!) :: [a] -> Int -> a xs !! n | n < 0 = error "Negative index." | otherwise = foldrW indexWrap indexCons (error "Large index.") xs n where indexCons x _ 0 = x indexCons _ r n = r (n-1) indexWrap = isoSimple then the simple test print $ (reverse $ eft 1 1000) !! 50 works just fine. If we replace isoSimple with scanlWrap isoSimple, then the test fails. That is, this produces wrap and unwrap so that wrap . unwrap is not much like the identity; it needs to interact with scanlCons in some fashion to work properly. This does not seem to be at all unusual for worker/wrapper pairs, but i believe it means we need to find a more general local correctness criterion than Joachim proposed, if I understood him correctly. David On Sun, Sep 14, 2014 at 2:08 PM, Dan Doel wrote:

Which scanl wrapper are you referring to?

The first one I figured out was quite wrong in certain ways. But I think the new one is less controversial; it's a lot like the reverse one.

On Sun, Sep 14, 2014 at 1:03 PM, David Feuer wrote:

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Joachim Breitner wrote:

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Am Samstag, den 13.09.2014, 00:01 -0400 schrieb David Feuer:

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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

On Sep 12, 2014 2:35 PM, "Joachim Breitner" wrote: that

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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

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