Forwarded from Brett G.
Interested in enhancing type theory, theoretical mathematics, and functional programming for industry-grade software?
Symode is a company developed on the principle that elegant design and logical rigor must coexist in the intersection of mathematics and programming. Symode is looking for contributors to our mutual project to enhance software with safety and fault-tolerant design.
Stay tuned for more information!
Symode is a company developed on the principle that elegant design and logical rigor must coexist in the intersection of mathematics and programming. Symode is looking for contributors to our mutual project to enhance software with safety and fault-tolerant design.
Stay tuned for more information!
EventML: A functional programmming language with high level combinators that works with the Nuprl theorem prover
http://www.nuprl.org/software/
http://www.nuprl.org/software/
www.nuprl.org
EventML
implementing computational mathematics and providing logic-based tools that help automate programming
Logic, Languages, Compilation, and Verification
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html
Seemingly impossible functional programs
http://math.andrej.com/2007/09/28/seemingly-impossible-functional-programs/
http://math.andrej.com/2007/09/28/seemingly-impossible-functional-programs/
Category Theory with Bartosz Milewski: podcast
https://corecursive.com/035-bartosz-milewski-category-theory/
https://corecursive.com/035-bartosz-milewski-category-theory/
CoRecursive Podcast
Category Theory - CoRecursive Podcast
Today Adam talks to Bartosz Milewski. He is the author of a popular blog series, lecture series, and now book on Category Theory for programmers.The world of functional programming is rife with terminology imported from abstract algebra and Category Theory.…
The Type Theory Podcast
http://typetheorypodcast.com/
http://typetheorypodcast.com/
Homotopy Patch Theory
http://dlicata.web.wesleyan.edu/pubs/amlh14patch/amlh14patch.pdf
http://dlicata.web.wesleyan.edu/pubs/amlh14patch/amlh14patch.pdf
Kerodon - an online resource for homotopy-coherent mathematics
https://kerodon.net/kerodon.pdf
WIP book, requires basic knowledge of topology.
[Thanks to H]
https://kerodon.net/kerodon.pdf
WIP book, requires basic knowledge of topology.
[Thanks to H]
Forwarded from Cab
Also, a little disclamer. We have small meetings each Wednesday evening, chatting about category theory, Coq, ssreflect, HoTT, FP in general, NixOS — and all that good stuff. We are gathering in Kocherga (Moscow).
If you want to participate — PM me) (usually comes from 4 to 6 people)
If you want to participate — PM me) (usually comes from 4 to 6 people)
The Five Stages of Accepting Constructive Mathematics: Andrej Bauer
https://www.youtube.com/watch?v=21qPOReu4FI
https://www.youtube.com/watch?v=21qPOReu4FI
YouTube
Five Stages of Accepting Constructive Mathematics - Andrej Bauer
Andrej Bauer
University of Ljubljana, Slovenia; Member, School of Mathematics
March 18, 2013
Discussions about constructive mathematics are usually derailed by philosophical opinions and meta-mathematics. But how does it actually feel to do constructive mathematics?…
University of Ljubljana, Slovenia; Member, School of Mathematics
March 18, 2013
Discussions about constructive mathematics are usually derailed by philosophical opinions and meta-mathematics. But how does it actually feel to do constructive mathematics?…
1029786.1029818.pdf
644.2 KB
Logicians who reason about themselves
[Thanks to (a)]
[Thanks to (a)]
Forwarded from HH
Pointwise Kan extensions
I'm going to post again one of Bartosz's ingeniously simple written articles on category theory, this time it will be an introduction to pointwise Kan extensions. Although MacLane covers nearly everything you need to know about pointwise Kan extensions I think there's a huge benefit from approaching it from a slighty different angle, also Bartosz provides a Haskell implementation of Kan extensions (Kmetts library) in the end so programmers might also want to look into it.
https://bartoszmilewski.com/2018/01/23/pointwise-kan-extensions/
I'm going to post again one of Bartosz's ingeniously simple written articles on category theory, this time it will be an introduction to pointwise Kan extensions. Although MacLane covers nearly everything you need to know about pointwise Kan extensions I think there's a huge benefit from approaching it from a slighty different angle, also Bartosz provides a Haskell implementation of Kan extensions (Kmetts library) in the end so programmers might also want to look into it.
https://bartoszmilewski.com/2018/01/23/pointwise-kan-extensions/
Bartosz Milewski's Programming Cafe
Pointwise Kan Extensions
In my category theory blog posts, I stated many theorems, but I didn’t provide many proofs. In most cases, it’s enough to know that the proof exists. We trust mathematicians to do their…
Category Theory for Computing Science
http://www.tac.mta.ca/tac/reprints/articles/22/tr22.pdf
http://www.tac.mta.ca/tac/reprints/articles/22/tr22.pdf
seL4: Formal Verification of an OS Kernel
https://ts.data61.csiro.au/publications/nicta_full_text/1852.pdf
https://ts.data61.csiro.au/publications/nicta_full_text/1852.pdf
Linear Logic for Constructive Mathematics
https://arxiv.org/abs/1805.07518
https://arxiv.org/abs/1805.07518
arXiv.org
Affine logic for constructive mathematics
We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine logic into intuitionistic logic via a Chu/Dialectica...
Would aliens understand lambda calculus?
http://tomasp.net/blog/2018/alien-lambda-calculus/
[Thanks to Charlie Brown]
http://tomasp.net/blog/2018/alien-lambda-calculus/
[Thanks to Charlie Brown]
tomasp.net
Would aliens understand lambda calculus?
The question whether aliens would understand lambda calculus
is intriguing because it vividly formulates a fundamental question about our formal mathematical
knowledge. Are mathematical theories and results about them invented, i.e. constructed by
humans…
is intriguing because it vividly formulates a fundamental question about our formal mathematical
knowledge. Are mathematical theories and results about them invented, i.e. constructed by
humans…