Profunctor Optics, a Categorical Update · HackerPapers discussions

Profunctor Optics, a Categorical Update — mentioned by rssoconnor

Wed, 30 Nov 2022 19:08:27 GMT

Apologies for the jargon, but there isn't room in a comment box for a detailed explanation. "The Essence of the Iterator Pattern"[0] posed an open problem in type theory as to whether or not "lawful traversals", of type `∀ F:Applicative. (X -> F X) -> (B -> F B)` could appear for anything other than what is called a "finitary container"[1], B := ∃S. X^(P S) where the (P S) is a natural number (or equivalently a polynomial functor B := ∃n. C_n * X^n). Or rather, there was an open question as to what laws are needed so that "lawful traversals" would imply that B is a finitary container.…

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Profunctor Optics, a Categorical Update — mentioned by hither_shores

Mon, 27 Jun 2022 09:30:34 GMT

There are infinitely many, so all is out, but the standard ones are covered here: https://oleg.fi/gists/posts/2017-04-18-glassery.html Page 10 of this paper has a table with references to some more exotic optics, though it's going to be hard to parse without some category theory: https://arxiv.org/pdf/2001.07488.pdf

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Profunctor Optics, a Categorical Update — mentioned by dddbbb

Mon, 24 Feb 2020 21:10:24 GMT

Plenty of serious researchers in top universities are studying the intersection of mathematics and functional programming, and I don't think that they're somehow not 'real mathematicians'. Here's a paper by the author of this post, formalising a popular Haskell pattern in category theory: https://arxiv.org/abs/2001.07488 EDIT: switched to non-PDF link.

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Profunctor Optics, a Categorical Update — HN submission

Fri, 31 Jan 2020 19:34:55 GMT

Profunctor Optics, a Categorical Update

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.