https://bourbaki.co.uk Articles on mathematics, physics, and computer science. en https://bourbaki.co.uk/posts/computer-science-ai-local-llm-complexity-benchmark/ https://bourbaki.co.uk/posts/computer-science-ai-local-llm-complexity-benchmark/ Thu, 21 May 2026 12:00:00 +0000 A local Ollama benchmark checks whether language models can identify the shrinking state variable in a recursive integer-square-root complexity analysis. https://bourbaki.co.uk/posts/computer-science-compilers-cir-control-flow-lifetime/ https://bourbaki.co.uk/posts/computer-science-compilers-cir-control-flow-lifetime/ Wed, 11 Feb 2026 12:00:00 +0000 Part four extends LifetimeCheck through store and load operations, structured control flow, scope cleanup, coroutine tasks, return safety, and implementation patterns. https://bourbaki.co.uk/posts/computer-science-compilers-cir-lifetimecheck-pass/ https://bourbaki.co.uk/posts/computer-science-compilers-cir-lifetimecheck-pass/ Wed, 11 Feb 2026 12:00:00 +0000 Part two follows the LifetimeCheck pass architecture, its type categories, points-to sets, allocation classification, and operation dispatch. https://bourbaki.co.uk/posts/computer-science-compilers-cir-static-analysis/ https://bourbaki.co.uk/posts/computer-science-compilers-cir-static-analysis/ Wed, 11 Feb 2026 12:00:00 +0000 Part one introduces ClangIR as an MLIR-based representation for C++ static analysis and uses LifetimeCheck to motivate the series. https://bourbaki.co.uk/posts/computer-science-compilers-cir-use-after-move/ https://bourbaki.co.uk/posts/computer-science-compilers-cir-use-after-move/ Wed, 11 Feb 2026 12:00:00 +0000 Part three shows how ClangIR AST attributes, move detection, smart pointer handling, and moved-from state tracking detect use-after-move bugs. https://bourbaki.co.uk/posts/math-cattheory-base-definitions/ https://bourbaki.co.uk/posts/math-cattheory-base-definitions/ Fri, 03 Sep 2021 12:00:00 +0000 Objects, morphisms, composition, identity morphisms, categories, and the category of sets provide the base language for the series. https://bourbaki.co.uk/posts/math-cattheory-curry-howard-lambek/ https://bourbaki.co.uk/posts/math-cattheory-curry-howard-lambek/ Sun, 06 Sep 2020 12:00:00 +0000 The Curry-Howard-Lambek correspondence relates propositions, proofs, programs, and categorical structure. https://bourbaki.co.uk/posts/math-cattheory-limits/ https://bourbaki.co.uk/posts/math-cattheory-limits/ Mon, 03 Feb 2020 12:00:00 +0000 Limits and colimits express universal constructions through cones, cocones, terminal objects, products, sums, and equalizers. https://bourbaki.co.uk/posts/math-cattheory-monads/ https://bourbaki.co.uk/posts/math-cattheory-monads/ Thu, 26 Dec 2019 12:00:00 +0000 Monads arise from monoids in the category of endofunctors and model structured computation in programming languages. https://bourbaki.co.uk/posts/math-cattheory-objects-and-morphisms/ https://bourbaki.co.uk/posts/math-cattheory-objects-and-morphisms/ Wed, 25 Dec 2019 12:00:00 +0000 Universal constructions describe initial and terminal objects, products, sums, monoids, exponential objects, and type algebra. https://bourbaki.co.uk/posts/computer-science-algorithms-cppsort/ https://bourbaki.co.uk/posts/computer-science-algorithms-cppsort/ Mon, 23 Sep 2019 12:00:00 +0000 Notes on strict weak ordering and why violating std::sort comparator requirements can corrupt results. https://bourbaki.co.uk/posts/math-cattheory-introduction/ https://bourbaki.co.uk/posts/math-cattheory-introduction/ Wed, 24 Apr 2019 12:00:00 +0000 The series introduces category theory as a connected collection of definitions, examples, and applications in sets, programming languages, and physics. https://bourbaki.co.uk/posts/math-cattheory-abstract-algebra/ https://bourbaki.co.uk/posts/math-cattheory-abstract-algebra/ Wed, 24 Apr 2019 12:00:00 +0000 Groups, rings, fields, and vector spaces provide algebraic background used by the categorical examples. https://bourbaki.co.uk/posts/physics-quantum-information-quantum-teleportation-games/ https://bourbaki.co.uk/posts/physics-quantum-information-quantum-teleportation-games/ Sat, 23 Mar 2019 12:00:00 +0000 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. https://bourbaki.co.uk/posts/math-cattheory-topos/ https://bourbaki.co.uk/posts/math-cattheory-topos/ Thu, 28 Feb 2019 12:00:00 +0000 Topos theory studies categories that behave like generalized universes of sets. https://bourbaki.co.uk/posts/math-cattheory-yoneda/ https://bourbaki.co.uk/posts/math-cattheory-yoneda/ Mon, 18 Feb 2019 12:00:00 +0000 Yoneda's lemma explains how an object of a locally small category is determined by the morphisms into or out of it. https://bourbaki.co.uk/posts/math-cattheory-natural-transformations/ https://bourbaki.co.uk/posts/math-cattheory-natural-transformations/ Thu, 07 Feb 2019 12:00:00 +0000 Natural transformations compare functors component by component and organize functors into their own categories. https://bourbaki.co.uk/posts/math-cattheory-functors/ https://bourbaki.co.uk/posts/math-cattheory-functors/ Fri, 01 Feb 2019 12:00:00 +0000 Functors map objects and morphisms between categories while preserving composition and identity. https://bourbaki.co.uk/posts/math-cattheory-kleisli-category/ https://bourbaki.co.uk/posts/math-cattheory-kleisli-category/ Sun, 04 Nov 2018 12:00:00 +0000 Kleisli categories describe composition for computations with effects such as partiality, exceptions, and nondeterminism. https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-shor-cryptography-shor-elliptic-curves/ https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-shor-cryptography-shor-elliptic-curves/ Fri, 09 Feb 2018 12:00:00 +0000 Part three of a three-post series on Shor's algorithm and its cryptographic applications, focused on elliptic curves and ECDH. https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-shor-cryptography-quantum-fourier-discrete-logarithms/ https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-shor-cryptography-quantum-fourier-discrete-logarithms/ Wed, 20 Dec 2017 12:00:00 +0000 Part two of a three-post series on Shor's algorithm and its cryptographic applications, focused on the quantum Fourier transform and discrete logarithms. https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-grover-algorithm/ https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-grover-algorithm/ Sat, 30 Nov 2013 12:00:00 +0000 A derivation of Grover's algorithm for unstructured search, including phase inversion, inversion about the mean, and square-root query complexity. https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-shor-cryptography-shor-algorithm/ https://bourbaki.co.uk/posts/computer-science-quantum-algorithms-shor-cryptography-shor-algorithm/ Sat, 30 Nov 2013 12:00:00 +0000 Part one of a three-post series on Shor's algorithm and its cryptographic applications, focused on period finding and RSA. https://bourbaki.co.uk/posts/physics-quantum-information-nonclassical-light/ https://bourbaki.co.uk/posts/physics-quantum-information-nonclassical-light/ Sat, 30 Nov 2013 12:00:00 +0000 A derivation of the second-order coherence criterion for nonclassical light, explaining photon bunching, antibunching, sub-Poissonian statistics, and the Hanbury Brown-Twiss measurement. https://bourbaki.co.uk/posts/physics-quantum-information-quantum-cryptography-entanglement/ https://bourbaki.co.uk/posts/physics-quantum-information-quantum-cryptography-entanglement/ Sat, 30 Nov 2013 12:00:00 +0000 A quantum cryptography protocol based on entangled photon pairs, using Bell-inequality tests to distribute a shared key and detect interception attempts.