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Category TheorySeven Sketches in Compositionality: An Invitation to Applied Category Theory
Seven Sketches in Compositionality: An Invitation to Applied Category Theory
2018 by Brendan Fong and David I. Spivak Category theory is becoming a central hub for all of pure mathematics. It is unmatched in its ability to organize and layer abstractions, to find commonalities between structures of all sorts, and to facilitate communication between different mathematical communities. But it has also been branching out into science, informatics, and industry. We believe that it has the potential to be a major cohesive force in the world, building rigorous bridges between disparate worlds, both theoretical and practical. The motto at MIT is mens et manus, Latin for mind and hand. We believe that category theory—and pure math in general—has stayed in the realm of mind for too long; it is ripe to be brought to hand.A very approachable but useful introduction to category theory. It avoids the Scylla and Charybdis of becoming incomprehensible after page 2 (as many academic texts do), and barely scratching the surface (as many popular texts do). By Andris Birkmanis at 20190428 03:53  Category Theory  Teaching & Learning  2 comments  other blogs  17973 reads
Comprehending Ringads
Comprehending Ringads
2016 by Jeremy Gibbons Ringad comprehensions represent a convenient notation for expressing database queries. The ringad structure alone does not provide a good explanation or an efficient implementation of relational joins; but by allowing heterogeneous comprehensions, involving both bag and indexed table ringads, we show how to accommodate these too.Indexed/parametric/graded monads are the key (read the paper to understand the pun). By Andris Birkmanis at 20180505 02:59  Category Theory  Semantics  Type Theory  login or register to post comments  other blogs  35125 reads
Databases from finite categoriesSpivak and Kent (2011). Ologs: A categorical framework for knowledge representation:
Ologs are essentially RDFs extended to encompass commuting diagrams, so a visual little language. The paper talks about how database schema can automatically be extracted from ologs. By Charles Stewart at 20170524 06:43  Category Theory  login or register to post comments  other blogs  23335 reads
Philip Wadler: Category Theory for the Working HackerNothing you don't already know, if you are inteo this sort of thing (and many if not most LtUers are), but a quick way to get the basic idea if you are not. Wadler has papers that explain CurryHoward better, and the category theory content here is very basic  but it's an easy listen that will give you the fundamental points if you still wonder what this category thing is all about. To make this a bit more fun for those already in the know: what is totally missing from the talk (understandable given time constraints) is why this should interest the "working hacker". So how about pointing out a few cool uses/ideas that discerning hackers will appreciate? Go for it! By Ehud Lamm at 20160807 17:26  Category Theory  Lambda Calculus  Semantics  106 comments  other blogs  53001 reads
Cakes, Custard, and Category TheoryEugenia Cheng's new popular coscience book is out, in the U.K. under the title Cakes, Custard and Category Theory: Easy recipes for understanding complex maths, and in the U.S. under the title How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics:
Cheng, one of the Catsters, gives a guided tour of mathematical thinking and research activities, and through the core philosophy underlying category theory. This is the kind of book you can give to your grandma and grandpa so they can boast to their friends what her grandchildren are doing (and bake you a nice dessert when you come and visit :) ). A pleasant weekend reading. By Ohad Kammar at 20150717 16:47  Category Theory  Critiques  Fun  General  Semantics  Theory  login or register to post comments  other blogs  9132 reads
Conservation laws for free!In this year's POPL, Bob Atkey made a splash by showing how to get from parametricity to conservation laws, via Noether's theorem:
By Ohad Kammar at 20141028 07:52  Category Theory  Fun  Functional  Lambda Calculus  Scientific Programming  Semantics  Theory  Type Theory  5 comments  other blogs  17269 reads
Seemingly impossible programsIn case this one went under the radar, at POPL'12, Martín Escardó gave a tutorial on seemingly impossible functional programs:
A shorter version (coded in Haskell) appears in Andrej Bauer's blog. By Ohad Kammar at 20141022 09:57  Category Theory  Fun  Functional  Paradigms  Semantics  Theory  36 comments  other blogs  18062 reads
Luca Cardelli FestschriftEarlier this week Microsoft Research Cambridge organised a Festschrift for Luca Cardelli. The preface from the book:
Hopefully the videos will be posted soon. By Ohad Kammar at 20140912 10:10  Category Theory  Lambda Calculus  Misc Books  Semantics  Theory  Type Theory  4 comments  other blogs  7989 reads
DependentlyTyped Metaprogramming (in Agda)Conor McBride gave an 8lecture summer course on Dependently typed metaprogramming (in Agda) at the Cambridge University Computer Laboratory:
The lecture notes, code, and video captures are available online. As with his previous course, the notes contain many(!) mind expanding exploratory exercises, some of which quite challenging. By Ohad Kammar at 20130830 07:34  Category Theory  Functional  Lambda Calculus  MetaProgramming  Paradigms  Semantics  Teaching & Learning  Theory  Type Theory  5 comments  other blogs  16285 reads
Lightweight Monadic Programming in MLLightweight Monadic Programming in ML
This is an intriguing paper, with an implementation in about 2,000 lines of OCaml. I'm especially interested in its application to probabilistic computing, yielding a result related to Kiselyov and Shan's Hansei effort, but without requiring delimited continuations (not that there's anything wrong with delimited continuations). On a theoretical level, it's nice to see such a compelling example of what can be done once types are freed from the shackle of "describing how bits are laid out in memory" (another such compelling example, IMHO, is typedirected partial evaluation, but that's literally another story). By Paul Snively at 20110728 18:11  Category Theory  Functional  Implementation  Semantics  Type Theory  35 comments  other blogs  23490 reads

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