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...

The Impossibility of Strategyproof Rank Aggregation M Eberl, P Lederer In Social Choice Theory, a social welfare function (SWF) maps a collection of individual preferences to an aggregated preference relation. This entry contains two impossibility results for SWFs. www.isa-afp.org/entries/SWF_...

A modern-day tragedy, BUT YOU CAN HELP. 1 Like = 1 Pray 1 Share = 10,000 Prays

Linear orders as rankings M Eberl Formalises the isomorphism between finite linear orders and lists, where the list is interpreted as a ranking: it lists the elements in strictly descending order. It also provides an algorithm to compute topological sortings. www.isa-afp.org/entries/Rank...

Swap Distance M Eberl The swap distance between 2 lists is the minimum # of swaps of adjacent elements needed to make the two lists the same. An O(n log n) algorithm for it is given via the connection to the number of inversions of a list, already available in the AFP www.isa-afp.org/entries/Swap...

PV solar panels produce about 20x more usable energy per hectare of land than growing biofuels ourworldindata.org/biofuel-land...

New in the AFP: Abel's Limit Theorem Kangfeng Ye This mechanises Abel's limit theorem on power series with real coefficients. An application of this theorem extends the generalised binomial theorem for a specific example from (-1,1) to its boundary cases –1 and 1. www.isa-afp.org/entries/Abel...

Isn't this a telling aspiration? To want robots to look after your kids, so you can do stuff, rather than robots to do stuff, so you can spend time with your kids? The darkness inside these shrivelled men must be like a gaping unfillable void.

@gilesyb.bsky.social this is what the inflection point looks like - chinas emissions will be tanking very soon e360.yale.edu/digest/china...

Compressed Oracles D Unruh We formalize the compressed quantum random oracle methodology by Zhandry (Crypto 2019). This is a formalism for modeling quantum random oracles to make quantum cryptographic proofs feasible. See Unruh (arXiv 2021). www.isa-afp.org/entries/Comp...

Nice to see it in real life

New on my blog: Broken proofs and broken provers lawrencecpaulson.github.io/2026/01/15/B...

Set Reconciliation P Hofmeier, E Karayel This entry verifies the set reconciliation algorithm with nearly optimal communication complexity, due to Minsky et al. Two partners who have a similar pair of sets can reconcile them using messages of nearly optimal size. www.isa-afp.org/entries/Set_...

Dynamic Pushdown Networks P Lammich A formalization of Dynamic Pushdown Networks (DPNs) and the automata-based algorithm for computing backward reachability sets using Isabelle/HOL. DPNs are an abstract model for interprocedural programs with dynamic thread creation. www.isa-afp.org/entries/Dyna...

The Partition Function and the Pentagonal Number Theorem Manuel Eberl The partition function gives the number of ways to write an integer as a sum of positive integers, not taking order into account. I use the Jacobi Triple Product to prove Pentagonal Number Theorem. www.isa-afp.org/entries/Pent...

Typed Ordered Resolution by A A Ahmed, B Toth Ordered Resolution is a refutationally complete calculus for first-order logic, used in many automatic theorem provers, which works by saturating a set of clauses. This entry includes a clean completeness proof. www.isa-afp.org/entries/Type...

New in the AFP: Dedekind Sums by Manuel Eberl, Anthony Bordg, Lawrence C Paulson and Wenda Li The formalisation follows Chapter 3 of Apostol's Modular Functions and Dirichlet Series in Number Theory and contains all facts related to Dedekind sums from it. www.isa-afp.org/entries/Dede...

From a focus group of Gen Z Republicans. (www.city-journal.org/article/manh...) Tell me again about how Zohran Mamdani is the big threat to Jewish thriving in the US today.