Summary of Truth about Types, a talk by Bartosz Milewski
https://rakhim.org/summary-of-truth-about-types-a-talk-by-bartosz-milewski/
https://rakhim.org/summary-of-truth-about-types-a-talk-by-bartosz-milewski/
Graph Representations for Higher-Order Logic and Theorem Proving
https://arxiv.org/abs/1905.10006
https://arxiv.org/abs/1905.10006
Generative Language Modeling for Automated Theorem Proving
https://arxiv.org/pdf/2009.03393.pdf
https://arxiv.org/pdf/2009.03393.pdf
Towards Finding Longer Proofs
https://arxiv.org/pdf/1905.13100.pdf
https://arxiv.org/pdf/1905.13100.pdf
HoTT-I, the underlying type theory of Arend
https://arxiv.org/abs/2004.14195
https://arxiv.org/abs/2004.14195
An illustration of Hopf fibration
https://twitter.com/vi_ne_te/status/1302273506055516161
https://twitter.com/vi_ne_te/status/1302273506055516161
Twitter
Vignette
https://t.co/6XnX9C6xRr
Codependent types
https://twitter.com/shlevy/status/1302668614353539074
https://twitter.com/shlevy/status/1302668614353539074
Twitter
Shea Levy
@tizusa233 @cronokirby No full example I can convey in a tweet yet. One intuition: With a dependent function, the codomain varies based on elements of (i.e. functions into) the domain. With a codependent function, the domain varies based on destructors of…
Pure & constructive mathematics in theory and use
Codependent types https://twitter.com/shlevy/status/1302668614353539074
There's also cosigma types that we can explore
Kreisel's "Unwinding" Program
https://math.stanford.edu/~feferman/papers/unwind.pdf
https://math.stanford.edu/~feferman/papers/unwind.pdf
Intutionistic Sets and Ordinals
http://www.paultaylor.eu/ordinals/intso.pdf
http://www.paultaylor.eu/ordinals/intso.pdf
Practical Foundations of Mathematics
http://www.paultaylor.eu/prafm/
http://www.paultaylor.eu/prafm/
Relating first-order set theories, toposes and categories of classes
http://www.phil.cmu.edu/projects/ast/Papers/Awodey-Butz-Simpson-Streicher-APAL-2013.pdf
http://www.phil.cmu.edu/projects/ast/Papers/Awodey-Butz-Simpson-Streicher-APAL-2013.pdf
Infinite Time Turing Machines
https://arxiv.org/pdf/math/9808093.pdf
https://arxiv.org/pdf/math/9808093.pdf
An introduction to locally finitely presentable categories
https://pi.math.cornell.edu/~maru/documents/locally_finitely_presentable_cats.pdf
https://pi.math.cornell.edu/~maru/documents/locally_finitely_presentable_cats.pdf
1460059215690.pdf
3.7 MB
Conceptual Mathematics
A new pass at the NF consistency proof
https://randall-holmes.github.io/Nfproof/newattempt.pdf
https://randall-holmes.github.io/Nfproof/newattempt.pdf
A suite of cool logic programs
https://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/
https://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/
XOR's Hammer
A Suite of Cool Logic Programs
You may have heard about the Tarski-Seidenberg theorem, which says that the first-order theory of the reals is decidable, that the first-order theory of the complex numbers is similarly decidable, …
The relative efficiency of propositional proof systems
https://www.cs.toronto.edu/~sacook/homepage/cook_reckhow.pdf
https://www.cs.toronto.edu/~sacook/homepage/cook_reckhow.pdf