Math, Logic - vpatryshev/wowiki GitHub Wiki
Federico Aschieri, Francesco A. Genco, ⅋ means Parallel: Multiplicative Linear Logic Proofs as
Concurrent Functional Programs
Bernardy, Proofs for Free Uli Furbach, Logic for Computer Scientists Valeria de Paiva, Encyclopedia Valeria de Paiva, Dialectica Categories Intro to Indian Philosophy Paul Downen and Zena. M. Ariola, "A Tutorial on Computational Classical Logic and
the Sequent Calculus" Anel, "Ambiguity in Math" (video) John Alan Robinson, Computational Logic: Memories of the Past and Challenges for the Future principle of equivalence (nlab) P.N. Benton G.M. Biermany V.C.V. de Paiva, Computational Types from a Logical Perspective I Michael Stay, L.G. Meredith, Logic as a distributive law Kleene's T predicate Informally, the T predicate tells whether a particular computer program will halt when run with a particular input, and the corresponding U function is used to obtain the results of the computation if the program does halt.Rice's theorem all non-trivial, semantic properties of programs are undecidable.Tobias Ganzow and Lukasz Kaiser, New Algorithm for Weak Monadic Second-Order Logic on Inductive Structures De Bruijn Monads The technical part of Godel’s proof Lutz Straßburger, What is a logic, and what is a proof? Jacobs, Categorical Logic and Type Theory (pdf) , [also](https://pages.jh.edu/rrynasi1/NewFoundations4Math/Literature/Logic/Jacobs1999CategoricalLogic+TypeTheory.pdf ]David Spivak - A summary of categorical structures in Poly Gödel's proof of god's existence A Formal Logic for Formal Category Theory Polynomials for Enumerable Sets... and Turing machines automating mathematics Wolfram, Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel Probability Theory as Extended Logic
A.Joyal, Topos Theory, youtube Topos Colloquium online Barr, Wells, "Toposes, Triples and Theories" Topos Semantics for Higher-Order Modal Logic nLab, Subobject Classifier A.Joyal, Crash Course in Topos Theory, 1-4, youtube Olivia Caramello, Topos-theoretic background locales Adamek, Locally Presentable and Accessible Categories Topos Semantics for Higher-Order Modal Logic Laurent Lafforgue
Britannica article Barr, Wells, "Toposes, Triples and Theories" list of first order theories Lawvere Theories and Monads Vladimir Voevodsky, Lawvere theories and Jf-relative monads Chu. Operations and Lawvere Theories F.W.Lawvere page at Buffalo F. WILLIAM LAWVERE, FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES AND SOME ALGEBRAIC PROBLEMS IN THE CONTEXT OF FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES Martin Hyland, John Power, The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads algebraic data types, categorically [Z.L. Low, Algebraic Theories](Z.L. Low)
J. McCarthy, On the Model Theory of Knowledge Neil GhaniFredrik Nordvall ForsbergEmail authorAlex Simpson, Comprehensive Parametric Polymorphism: Categorical Models and Type Theory Finite Model Theory and its Applications D B MacQueen, G D Plotkin, R Sethi, An ideal model for recursive polymorphic types Nortström, Petersson, Smith, Programming in Martin-Löf's Type Theory Is there a known natural model of Peano Arithmetic where Goodstein's theorem fails? Geometric Model Theory Model Theory and Category Theory Theory of Objects
Geometric Model Theory - hard reading, manifolds, algebraic geometry
Model Theory and Category Theory - high level, but easy reading
Joseph Goguen, Tossing the Algebraic Flowers Down the Great Divide Riehl, Categories in Context Riehl, ∞-categories for undergraduates François Métayer, Fixed points of functors Adamek, Fixed points of functors Lawvere's fixed point theorem Pierce’s Basic Category Theory for Computer Scientists – The Good Parts Dan Marsden, Category Theory Using String Diagrams Awesome #categorytheory, κζ-calculus vault Zeit Raffer: agda cats , idris cats
Cat Theory for Scientists Free Applicative Functors me, Monad Genome wildcats
Knowledge base of 29 standard categories and several standard functors
User-definable categories, functors, natural transformations, universal properties, cones and other categorical constructions
State-of-the-art palette interface. Easily input all defined objects and operators (coming soon)
Automatic publish-quality generation of commutative and non-commutative diagrams
Visual functorial computations: apply a functor to a diagram and see the resulting diagram
Visual diagram evaluation: apply a diagram to an object and see the resulting diagram
Fully integrated documentation with 16 tutorial notebooks
Requires Mathematica® 8.x
Oleksandr Manzyuk, Calculating monad transformers with category theory Reprints in Theory and Applications of Categories (list of works) Francis Borceux, Gilberte Van den Bossche, Categories of algebraic sheaves CMCS 2016, Fixed Points of Functors Joachim Kock, Notes on Polynomial Functors A Type-Theoretical Definition of Weak ω-Categories M.Stay, Category Theory in JavaScript C.Williams, M.Stay, Native Type Theory Chasing diagrams in cryptography Steven Lack, On the monadicity of finitary monads - that's about when a free monad may exist for a functorFinster, Reutter, A Type Theory for Strictly Unital ∞-Categories Introduction to Turing Categories Ian Stark, Free-Algebra Models for the π-Calculus Gershom Bazerman on "Homological Computations for Term Rewriting Systems" VARMO VENE, CATEGORICAL PROGRAMMING WITH INDUCTIVE AND COINDUCTIVE TYPES Marina Christina Lehner, All Concepts are Kan Extensions” Adámek, Fixed Points of Functors strong monads in cartesian-closed categories are applicative functors Giri monad Niles Johnson, Donald Yau, 2-Dimensional Categories Categorical programming language with effects (github) Visual Category Theory Applied Category Theory Yuri I. Manin, FORGOTTEN MOTIVES: THE VARIETIES OF SCIENTIFIC EXPERIENCE Riehl, Categories in Context Paranatural Category Theory Fixpoint in Computer Science (including Uustalo's paper on fixpoints and Yoneda Lemma for dinaturals
Theorems for free! The Girard-Reynolds Isomorphism (second edition) Idioms are oblivious, arrows are meticulous, monads are promiscuous GRAMATICAS MATRICIALES DE GRAFOS Hinze, Wu, Gibbons, "Conjugate Hylomorphisms" Admissible numbering Rogers' equivalence theorem shows that all acceptable programming systems are equivalent to each other in the formal sense of numbering theory.Partial Commutative Monoids Jean-Yves Girard Mona: decidable arithmetic in practice Вавилов, Алгебры Клиффорда и Спинорные Группы, серия видео Exequiel Rivas, Mauro Jaskelioff, Notions of Computation as Monoids The Impact of seq on Free Theorems-Based Program Transformations Explicit Substitutions and Higher-Order Syntax Shut up and let me think! Or why you should work on the foundations of quantum mechanics as much as you please A THEORY OF TRANSFORMATION MONOIDS: COMBINATORICS AND REPRESENTATION THEORY Bukatin's essay on Penrose reflections on relativity Multi-scale Structural Complexity , code Reversible dynamics with closed time-like curves and freedom of choice Infinite Monkey Theorem Chaitin's Constant Normal Number Cantor Space Algorithmically Random Sequence Compositional Game Theory Gert Smolka, Confluence We study confluence of abstract relations and an abstract λβ-calculus parameterized with a function for β-reductionmy other shit Dmitri Pavlov M.Bukatin, Generalized Distances and Generalized Equalities M.Bukatin, Partial Metrics and Quantale-valued Sets M.Bukatin, On Duality between Metric and Logical Viewpoints Quantale (nCatLab) Guillaume Lample, François Charton, "Deep Learning for Symbolic Mathematics" Buzzard, The Future of Math Counterexamples in Topology А.Ю. Пирковский, Спектральная теория и функциональные исчисления для линейных операторов Seven Trees in One My adventures with categories
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