Mechanized Metasemantics of Modal Necessity YD Kim We factorize Kripke-style valuation as V = I o delta, where delta maps object-language formulas to syntactic distinctions and I maps such distinctions to possible-worlds truth-conditions. So modal evaluation is done over interpreted distinctions.

A Reusable Isabelle/HOL Framework for Propositional Labelled Natural Deduction A Ramos et al A reusable framework showing that labelled ND can be treated as a conservative refinement of ordinary ND, with generic structural metatheory and concrete label interpretations. isa-afp.org/entries/Gabb...

Type Annotations with Roundtrip Property K Kappelmann et al Type annotations are essential when printing terms to keep their meaning under reparsing and type inference. Building on prior work, we show that a reverse-greedy approach leads to a locally minimal and complete set of annotations.

The Gelfand–Naimark–Segal Construction R Schmoetten, J Fleuriot Complete normed algebras equipped with an involution are called C*-algebras. The GNS construction starts with a single suitable functional on a C*-algebra to obtain both a Hilbert space and a representation of the algebra.

Announcing IsabelleBlueprint: a new project-layer tool for Isabelle/HOL formalizations. Inspired by Lean Blueprint but built specifically for Isabelle. Many thanks to Arthur Freitas Ramos! github.com/Arthur742Ram...

Busy Beaver Function A Ramos et al Formalizes the BB upper-bound principle and its computability consequences for Turing machines. The abstract layer works over ™ models: it defines the time BB function and proves any total upper bound for this function decides halting. isa-afp.org/entries/Busy...

Erdős-Ginzburg-Ziv A Ramos et al. We formalize the Erdős–Ginzburg–Ziv theorem for multisets: every multiset of at least 2n−1 integers contains a submultiset of cardinality n whose sum is divisible by n. isa-afp.org/entries/Erdo...

The Classical Seifert–van Kampen Theorem A Ramos et al For open subsets U and V of a topological space with x0 ∈ U∩V and path-connected intersection, the fundamental group of U ∪ V at x0 is in bijection with the free product of the fundamental groups of U and V over U ∩ V isa-afp.org/entries/Seif...

The Mostowski Collapse Theorem (in Isabelle/ZF) A Ramos et al For a set equipped with a well-founded extensional relation R, the collapsing map is given by wf recursion. Its range is transitive, and the map is an order isomorphism between R and membership. isa-afp.org/entries/Most...

14 May 1925 | A Polish boy, Karol Kobyłecki, was born in Krakow. In #Auschwitz from 3 April 1942. No. 28797 In 1944 he was transferred to KL Mauthausen and liberated there. --- 📖 "Poles at KL Auschwitz”: http://lekcja.auschwitz.org/en_2020_06_polacy/

Andrew's Monotone Chain Convex Hull Algorithm A Ramos et al. The algorithm sorts planar points lexicographically, removes duplicates, computes lower and upper hull chains by a stack scan that removes non-left turns, etc. The formalization proves all key properties. isa-afp.org/entries/Andr...

Alon’s Combinatorial Nullstellensatz A Ramos et al ... for sparse multivariate polynomials over fields. The proof derives the coefficient formula from univariate Lagrange interpolation and uses it to obtain the standard nonvanishing conclusion over finite grids. isa-afp.org/entries/Comb...

Nash Equilibria for Finite Games A Ramos et al Nash equilibria for finite strategic form games: proves existence for finite ordinal potential games and games with dominant strategies. Prisoner’s Dilemma, a coordination game, matching pennies, rock-paper-scissors. isa-afp.org/entries/Nash...

The Banach–Tarski Paradox in Isabelle/HOL A Ramos et al ... for the closed unit ball in R^3: the free-group paradox, the free subgroup of SO(3), Hausdorff paradox, the absorption arguments for the sphere and the origin, and the finite-partition theorem for the ball. isa-afp.org/entries/Bana...

I just noticed that the Wikipedia page on AUTOMATH is not very good at all. It's too short, often wrong and has no examples. I could contribute to a proper page but I would not want to be the sole author. Anyone else want to help?

New on my blog: Mizar: the first usable proof assistant for mathematics lawrencecpaulson.github.io/2026/05/07/M...

Aho-Corasick String Matching A Ramos et al We formalize the Aho-Corasick multi-pattern matching algorithm as a verified executable reference automaton. After reading a text prefix, the state is the longest suffix of that prefix that is also a pattern prefix. isa-afp.org/entries/Aho_...

I absolutely don't understand this. Of course "infinity" does not exist. But neither does 3, or the unit circle. Mathematics is about ideas. It is not about real things. www.quantamagazine.org/what-can-we-...

Nagata Factoriality A Ramos et al A prime-generated version of Nagata's factoriality theorem in Isabelle/HOL: the theory of prime-generated multiplicative sets, it proves descent theorems showing that factoriality descends from a localization to the base ring. www.isa-afp.org/entries/Naga...

The Algebra of Iterative Constructions K Batz et al. The AIC is an algebraic approach to reasoning about iterations of continuous maps on complete lattices. AIC allows derivations of fixed point theorems via equational logic and avoids computations with indices. www.isa-afp.org/entries/Iter...

Archimedes' Cattle Problem M Eberl Archimedes challenged mathematicians of his day with a puzzle about the cattle herd of the sun god. We give a formal description of the problem and use continued fractions to compute a solution having 266,454 digits. www.isa-afp.org/entries/Arch...

Nominal Unification GB Brandão et al. Nominal unification generalises first-order unification to terms with binding. A possibly capturing substitution solves such equations if it makes the equated terms α-equivalent. Here we improve on a previous treatment. www.isa-afp.org/entries/Nomi...

New on my blog: "Why not use Lean?" lawrencecpaulson.github.io/2026/04/23/W...

Abstract Consistency Properties AH From, A Schlichtkrull Smullyan used abstract consistency properties to unify metatheoretical results in FOL, getting a model existence result implying completeness, compactness, etc. We generalise his work using locales. www.isa-afp.org/entries/Abst...

SAT is Not Solvable in Constant Time D Shea The SAT Problem cannot be decided by a deterministic Turing machine in constant time. The core of the argument is that a Turing machine bounded by constant time can only ever read the first C+1 cells of its input tape. www.isa-afp.org/entries/SAT_...

Sorted Rewriting A Yamada Provides various materials for sorted term rewrite systems, conditional TRSs. etc. We formalize the fundamental result that the rewrite steps induced by a CTRS is the least rewrite relation that models it. www.isa-afp.org/entries/Sort...

Lebesgue–Stieltjes Integral Yosuke Ito Formalizes basic facts and lemmas relating to integration wrt the Lebesgue–Stieltjes measure (interval measure). It includes the well-known formula to calculate the L–S integral: \int g(x) dF(x) = \int g(x) F'(x) dx www.isa-afp.org/entries/Lebe...

… and worse

Formal Verification of Axiom-Free Gödelian Ontological Argument and Trinity Necessity Proof in Isabelle HOL Kim, Yong-Dock 📧 We reconstruct metaphysical arguments and ontological claims within a framework of computational formalization and machine verification. www.isa-afp.org/entries/Axio...

Isabelle/Solidity - A shallow Embedding of Solidity D Marmsoler et al Smart contracts execute on the blockchain to automate financial transactions, where bugs can be costly. Our Solidity verification framework facilitates contract specification and verification. www.isa-afp.org/entries/Isab...

Actually, this on a banknote

The competition is incredibly fierce

I am not even going to attempt to add context to this headline. The tache doesn’t deserve it.

Vows never to return KLAXON, with supplementary “There’s probably more to this than they’re letting on” buzzer.

Announcing the Seventh Biennial Dr. Henry Armitage Memorial Scholarship Symposium of New Weird Fiction and Lovecraft-Related Research NecronomiCon Providence convention in Providence, RI 13-16 August, 2026 necronomicon-providence.com/the-armitage...

New on my blog: "Memories: doing my PhD at Stanford, under John L Hennessy" lawrencecpaulson.github.io/2026/02/13/J...

Workflow Net Fitness Measures M Manke Workflow nets are a specialization of Petri nets, for modelling business processes. It defines measures for the fitness of these nets, namely trace fitness and causal footprint fitness. These measure how well a model covers all the traces in an event log.

Arbitrage Opportunities Correspond to Probability Inequality Identities M Doty For a gambling market over boolean propositions, we show a correspondence between feasibility of trading strategies, validity of probability inequalities and solutions to MaxSAT problems. www.isa-afp.org/entries/Arbi...

Concentrated Liquidity Market Making Operations M Echenim Automated Market Makers are key to decentralized finance. They let users exchange tokens without needing order books. We formalize related notions and operations on pools, with an optimality result. www.isa-afp.org/entries/Conc...

A Bridge between CSP Processes and Functional Automata B Ballenghien B Wolff In HOL-CSP, defines Proc-Omata from functional automata, in four variants: whether deterministic/terminating or not. We do the Dining Philosophers for any number finite of diners. www.isa-afp.org/entries/HOL-...

Parameterized Termination for Sequential Composition and Synchronization Product B Ballenghien Building on HOL-CSP we introduce versions of these operators that with parameterized termination. We establish algebraic and operational laws, and fundamental properties. www.isa-afp.org/entries/HOL-...

'Sets' Revisited: Working with a Large Category in Isabelle/HOL EW Stark We formalise the category of sets and functions and prove standard properties. Key is an axiom that allows us to obtain objects internal to the category corresponding to externally given sets. www.isa-afp.org/entries/Sets...