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Paolo Perrone (Jul 02 2020 at 02:26):Hello all! This is the thread of discussion for the talk of Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore and Mario Román, "Profunctor Optics, a Categorical Update".
Date and time: Tuesday July 7, 11:00 UTC.
Zoom meeting: https://mit.zoom.us/j/7055345747
YouTube live stream: https://www.youtube.com/watch?v=MIfh-LndWv8&list=PLCOXjXDLt3pZDHGYOIqtg1m1lLOURjl1Q
Bryce Clarke (Jul 07 2020 at 10:48):Mario Román will be delivering this talk. The results grew out of his thesis, and a collaboration with the other authors during the ACT2019 school.
The extended abstract can be found here: https://www.ioc.ee/~mroman/publications/profunctoropticsacategoricalupdateAbstract.pdf
And the full arXiv paper may be found here: https://arxiv.org/abs/2001.07488
Paolo Perrone (Jul 07 2020 at 10:48):Hi all! We start in 12 minutes.
Mario Román (Jul 07 2020 at 13:10):On a question by Piotr Paradzinski: I have been using the term Tambara to cover Strong/Choice and so on. As you observe, that would require a parameter on the code. This is the complete definition one could end up using: https://github.com/mroman42/vitrea/blob/8aed32a88dfc1df28460896a1a7f51166ed67dc7/source/Tambara.hs#L74 I tried to simplify it on the slides, but, as you observe, the complete definition only makes sense when the parameters are passed to the Tambara. Thank you for the question!
Mario Román (Jul 07 2020 at 13:11):There was a second question on the order of composition. I cannot access the zoom chat again but I think this was answered by Jeremy Gibbons.
Esa Pulkkinen (Jul 07 2020 at 13:29):Yes about the order of composition. I was thinking "top-down" in the sense of projections, and was thinking of lenses as extensions of the projections. But the lenses were composed "bottom-up" so first part was always smallest, and it's somewhat confusing how the compositions look if you're accustomed to thinking size-hierarchy as starting in order of large-to-small.
Mario Román (Jul 07 2020 at 14:55):Esa Pulkkinen said:
Yes about the order of composition. I was thinking "top-down" in the sense of projections, and was thinking of lenses as extensions of the projections. But the lenses were composed "bottom-up" so first part was always smallest, and it's somewhat confusing how the compositions look if you're accustomed to thinking size-hierarchy as starting in order of large-to-small.
Yes, that is right, thank you for the question. I have changed over time the direction in which I write the category. I think the argument on the other side was to match the order p(a,b) -> p(s,t); but as you say, it is a bit counterintuitive (I guess one needs to make some choice there).
Esa Pulkkinen (Jul 07 2020 at 15:31):Perhaps this is related to separation of the "abstract view" of the lens (=no internal details visible) and the "concrete view" (=scary details of proofs visible). I mean in Haskell, newtype Lens a b s t = Lens (forall p. (...) => p a b -> p s t). The constructor would force separating the two views. Then you know what is "internal to lens" (anything that pattern matches or invokes Lens constructor) and what is "interface" (e.g. composing two lenses is interface). At least I felt I had to open the definition of Lens "abstraction" in order to understand what was happening in the composition.
Paolo Perrone (Jul 07 2020 at 17:58):Here's the video!
https://www.youtube.com/watch?v=SsS7ZBYRcw4&list=PLCOXjXDLt3pYot9VNdLlZqGajHyZUywdI
