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Articles on mathematics, physics, and computer science.
Bourbaki Notes
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A local Ollama benchmark checks whether language models can identify the shrinking state variable in a recursive integer-square-root complexity analysis.
Part four extends LifetimeCheck through store and load operations, structured control flow, scope cleanup, coroutine tasks, return safety, and implementation patterns.
Part two follows the LifetimeCheck pass architecture, its type categories, points-to sets, allocation classification, and operation dispatch.
Part one introduces ClangIR as an MLIR-based representation for C++ static analysis and uses LifetimeCheck to motivate the series.
Part three shows how ClangIR AST attributes, move detection, smart pointer handling, and moved-from state tracking detect use-after-move bugs.
Base Definitions Category Theory by Example
Objects, morphisms, composition, identity morphisms, categories, and the category of sets provide the base language for the series.
Curry-Howard-Lambek Correspondence Category Theory by Example
The Curry-Howard-Lambek correspondence relates propositions, proofs, programs, and categorical structure.
Limits Category Theory by Example
Limits and colimits express universal constructions through cones, cocones, terminal objects, products, sums, and equalizers.
Monads Category Theory by Example
Monads arise from monoids in the category of endofunctors and model structured computation in programming languages.
Objects and Morphisms Category Theory by Example
Universal constructions describe initial and terminal objects, products, sums, monoids, exponential objects, and type algebra.
Notes on strict weak ordering and why violating std::sort comparator requirements can corrupt results.
Introduction Category Theory by Example
The series introduces category theory as a connected collection of definitions, examples, and applications in sets, programming languages, and physics.
Abstract Algebra Category Theory by Example
Groups, rings, fields, and vector spaces provide algebraic background used by the categorical examples.
A quantum teleportation protocol based on entangled photon pairs and Bell-state measurement, followed by the Mermin-Peres pseudo-telepathy game as a second application of entanglement.
Topos Category Theory by Example
Topos theory studies categories that behave like generalized universes of sets.
Yoneda's Lemma Category Theory by Example
Yoneda's lemma explains how an object of a locally small category is determined by the morphisms into or out of it.
Natural Transformations Category Theory by Example
Natural transformations compare functors component by component and organize functors into their own categories.
Functors Category Theory by Example
Functors map objects and morphisms between categories while preserving composition and identity.
Kleisli Category Category Theory by Example
Kleisli categories describe composition for computations with effects such as partiality, exceptions, and nondeterminism.
Part three of a three-post series on Shor's algorithm and its cryptographic applications, focused on elliptic curves and ECDH.
Part two of a three-post series on Shor's algorithm and its cryptographic applications, focused on the quantum Fourier transform and discrete logarithms.
A derivation of Grover's algorithm for unstructured search, including phase inversion, inversion about the mean, and square-root query complexity.
Part one of a three-post series on Shor's algorithm and its cryptographic applications, focused on period finding and RSA.
A derivation of the second-order coherence criterion for nonclassical light, explaining photon bunching, antibunching, sub-Poissonian statistics, and the Hanbury Brown-Twiss measurement.
A quantum cryptography protocol based on entangled photon pairs, using Bell-inequality tests to distribute a shared key and detect interception attempts.