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Lawrence Paulson

@lawrpaulson.bsky.social
649 followers 281 following 875 posts

Computer scientist with a background in mathematics and logic. Academic researching formal verification technologies and applications. Also in the cesspit

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Lawrence Paulson @lawrpaulson.bsky.social · 31m
The Steiner Deltoid as the Tangent Envelope of Wallace–Simson Lines A Ramos et al In unit-circumcircle coordinates, the deltoid has an explicit complex parametrisation. We prove its derivative formula and an equality of sets between the appropriate Wallace–Simson line and the tangent line.
isa-afp.org
The Steiner Deltoid as the Tangent Envelope of Wallace--Simson Lines in Isabelle/HOL
The Steiner Deltoid as the Tangent Envelope of Wallace--Simson Lines in Isabelle/HOL in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 01/10/2026
EA hits the cover of the Economist. Why are so many philosophers bonkers?
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Lawrence Paulson @lawrpaulson.bsky.social · 01/10/2026
General Weierstrass Equations AF Ramos et al. This entry develops the general Weierstrass equation over commutative rings and fields. The definitions and invariant formulas follow the standard treatment in Silverman. isa-afp.org/entries/Gene...
isa-afp.org
General Weierstrass Equations
General Weierstrass Equations in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 25/09/2026
arstechnica.com/culture/2026...
arstechnica.com
We have a trailer for Musk documentary Elon called a "hit piece"
Oscar-winning documentarian Alex Gibney focuses on the world's wealthiest man.
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Lawrence Paulson @lawrpaulson.bsky.social · 25/09/2026
Work Bounds for Strongly Joinable Balanced Binary Search Trees M Haucke The complexity analysis of set operations on strongly joinable trees by Blelloch, Ferizovic and Sun: union, intersection, and difference run in time O(m log (n/m +1)) for input sets of size n and m where m≤n.
isa-afp.org
Work Bounds for Strongly Joinable Balanced Binary Search Trees
Work Bounds for Strongly Joinable Balanced Binary Search Trees in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 24/09/2026
Deterministic Context-Free Languages are Closed Under Complementation K Taskin, T Nipkow A deterministic context-free language (DCFL) is a language accepted by a deterministic pushdown automaton This entry proves that they are closed under complementation, following Hopcroft and Ullman (1979).
isa-afp.org
Deterministic Context-Free Languages are Closed Under Complementation (Hopcroft and Ullman)
Deterministic Context-Free Languages are Closed Under Complementation (Hopcroft and Ullman) in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 23/09/2026
The Teichmüller-Tukey Lemma V Kraisch, L Cordeiro This entry formalizes the Teichmüller-Tukey lemma: every nonempty family of sets of finite character contains a member that is maximal under inclusion. The development follows the direct choice-function construction of Sun and Yu.
isa-afp.org
The Teichmüller-Tukey Lemma
The Teichmüller-Tukey Lemma in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 18/09/2026
Strong Normalization for Church-Style System F AF Ramos et al. Every well-typed System F term is strongly normalizing. The reduction relation contains both term-beta and type-beta steps and is closed under all term contexts. The proof uses Girard-style reducibility candidates.
isa-afp.org
Strong Normalization for Church-Style System F
Strong Normalization for Church-Style System F in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 17/09/2026
Greibach's Hardest Context-Free Language by Tobias Nipkow A formalization of Greibach’s hardest context-free language theorem: There is a “hardest” context-free language L_0 such that every context-free language is an inverse homomorphic image of L_0. isa-afp.org/entries/Grei...
isa-afp.org
Greibach’s Hardest Context-Free Language
Greibach’s Hardest Context-Free Language in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 12/09/2026
The Földes–Hammer Characterization of Split Graphs  by AF Ramos et al This entry formalizes the classical Földes–Hammer theorem characterizing finite split graphs  as exactly the graphs with no induced copy of 2 K_2, C_4, or C_5.  isa-afp.org/entries/Fold...
isa-afp.org
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Lawrence Paulson @lawrpaulson.bsky.social · 11/09/2026
The Five Platonic Solids E Finken There are exactly five Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. A Platonic solid is a convex polyhedron whose faces are congruent regular polygons, with the same number of edges meeting at each vertex.
isa-afp.org
The Five Platonic Solids
The Five Platonic Solids in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 26/08/2026
A Z Salamon and M Wehar have given us a large chunk of multitape Turing machine theory: isa-afp.org/entries/Mult... isa-afp.org/entries/Mult... isa-afp.org/entries/Mult... isa-afp.org/entries/Mult... If you ever wondered how some TM construction in Hopcroft and Ullman really works, look no further
isa-afp.org
Multitape Turing Machine Substrate
Multitape Turing Machine Substrate in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 24/08/2026
Miquel's Theorem A Ramos Let ABC be a triangle in the Euclidean plane and let P, Q, R be points on the side lines BC, CA, AB respectively. Then the circumcircles of the three triangles AQR, BRP, CPQ pass through a common point, the Miquel point of the configuration. isa-afp.org/entries/Miqu...
isa-afp.org
Miquel's Theorem in Isabelle/HOL
Miquel's Theorem in Isabelle/HOL in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 23/08/2026
Laurent Series Expansions on an Annulus M Eberl A complex-valued function holomorphic on an open annulus has a (generalised) Laurent series expansion, which is valid on the entire annulus. An important special case is r=0, i.e. the local behaviour of a function around an isolated singularity.
isa-afp.org
Laurent Series Expansions on an Annulus
Laurent Series Expansions on an Annulus in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 21/08/2026
New on my blog: lawrencecpaulson.github.io/2026/08/21/L...
lawrencecpaulson.github.io
How I came to write THAT paper with Leslie Lamport
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Lawrence Paulson @lawrpaulson.bsky.social · 13/08/2026
First-Order Methods for Smooth Convex Optimization Feier Lyu General-purpose interfaces for gradients, first-order convexity certificates, smooth quadratic upper bounds, descent and telescoping arguments, projection geometry, projected-gradient mappings, residual certificates, etc.
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Reposted by Lawrence Paulson
Veerender Singh Jubbal @veerenderjubbal.bsky.social · 01/08/2026
Sam Altman
@sama •7h
cool use case of chatgpt work i heard last night:
connect your family calendars and explain your kids' interests.
every morning for the drive to school, have it make a podcast that talks about one kid's soccer game that afternoon, one kid's upcoming birthday, some news, etc.
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What if you just talked to your children
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Lawrence Paulson @lawrpaulson.bsky.social · 07/08/2026
Counterexample to Cost-Preserving Single-Source Unsplittable Flow A Ramos et al Dinitz, Garg, and Goemans proved that a feasible fractional single-source flow can be rounded to an unsplittable flow with additive congestion bounded. Goemans conjectured that the rounding can also preserve cost.
isa-afp.org
A Formal Counterexample to the Cost-Preserving Single-Source Unsplittable Flow Conjecture
A Formal Counterexample to the Cost-Preserving Single-Source Unsplittable Flow Conjecture in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 06/08/2026
Completeness of the Q0 Higher-Order Logic AH From et al Our work builds on Díaz's formalization of Q0's syntax, semantics, soundness and consistency. We prove completeness using the framework for abstract consistency properties by From and Schlichtkrull to get a model existence theorem for Q0.
isa-afp.org
Completeness of the Q0 Higher-Order Logic
Completeness of the Q0 Higher-Order Logic in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 06/08/2026
I've uploaded a new video on 40 Years of Isabelle. Apologies for the lousy thumbnail. youtu.be/nEf-WVtpEek
youtu.be
Isabelle 40 Years
YouTube video by Lawrence Paulson
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Lawrence Paulson @lawrpaulson.bsky.social · 05/08/2026
The Wallace–Simson Line Theorem AF Ramos et al Let ABC be a triangle and M a point on its circumcircle. Dropping the perpendiculars from M to the three side lines gives feet P, Q, R; then P,Q,R are collinear. Conversely if the three feet are collinear then M lies on the circumcircle of ABC.
isa-afp.org
The Wallace--Simson Line Theorem in Isabelle/HOL
The Wallace--Simson Line Theorem in Isabelle/HOL in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 30/07/2026
New on my blog: "Why is it all in the kernel?" lawrencecpaulson.github.io/2026/07/30/C...
lawrencecpaulson.github.io
Why is it all in the kernel?
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Lawrence Paulson @lawrpaulson.bsky.social · 21/07/2026
Counterexample to the Jacobian Conjecture AF Ramos et al The conjecture asks whether a polynomial self-map of affine space has a polynomial inverse whenever its Jacobian determinant is a nonzero constant. This entry gives an Isabelle/HOL verification of the 3-d map announced by Levent Alpöge.
isa-afp.org
Formal Verification of an Explicit Counterexample to the Jacobian Conjecture
Formal Verification of an Explicit Counterexample to the Jacobian Conjecture in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 21/07/2026
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Lawrence Paulson @lawrpaulson.bsky.social · 18/07/2026
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Lawrence Paulson @lawrpaulson.bsky.social · 18/07/2026
Termination Restricted to Right-Forward Closures R Thiemann et al We formalize Dershowitz' theorem that termination of a term rewrite system (TRS) is equivalent to termination starting from terms in the right-forward closures of right-hand sides, provided the TRS is right-linear or orthogonal.
isa-afp.org
Termination Restricted to Right-Forward Closures
Termination Restricted to Right-Forward Closures in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 17/07/2026
Checking Equality-Saturation Merge and Extraction Certificates AF Ramos et al Equality-saturation engines maintain equalities in an e-graph and later extract a representative from an e-class. We verify an executable checker. For extraction a finite e-graph is represented as an ordered e-class DAG.
isa-afp.org
Checking Equality-Saturation Merge and Extraction Certificates
Checking Equality-Saturation Merge and Extraction Certificates in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 17/07/2026
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Lawrence Paulson @lawrpaulson.bsky.social · 16/07/2026
Chevalley–Warning Theorem AF Ramos et al If finitely many multivariate polynomials over a finite field have total degree sum < the number of variables, then the number of their common zeros is divisible by the characteristic. The proof follows the standard finite-field power-sum argument.
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Lawrence Paulson @lawrpaulson.bsky.social · 15/07/2026
Conway's Circle Theorem A Ramos et al If the sides of a triangle are extended in a certain way, one obtains six points that lie on a circle. The result is given in three forms: as six explicit equations, as a subset of a sphere, and as a single claim over the six-point set.
isa-afp.org
Conway's Circle Theorem in Isabelle/HOL
Conway's Circle Theorem in Isabelle/HOL in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 14/07/2026
Monadic Second-Order Logic in HOL C Benzmüller. Kirchner We develop three embeddings of monadic second-order logic into classical higher-order logic side by side: a deep embedding, a maximal-shallow embedding, and a minimal-shallow embedding — the last a locale parametrised by an interpretation.
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Lawrence Paulson @lawrpaulson.bsky.social · 13/07/2026
Polynomial Commitment Schemes by Tobias Rothmann This entry formalizes PCSs and security proofs of two variants of the Kate–Zaverucha–Goldberg construction. We define an abstract PCS interface and games for correctness, polynomial binding, evaluation binding, hiding, and knowledge soundness.
isa-afp.org
Polynomial Commitment Schemes
Polynomial Commitment Schemes in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 13/07/2026
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Lawrence Paulson @lawrpaulson.bsky.social · 11/07/2026
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Lawrence Paulson @lawrpaulson.bsky.social · 09/07/2026
The AFP has just passed its 1000th contribution! M Eberl, Complete Elliptic Integrals –, Bessel Functions of the First Kind –, The Exponential and Logarithmic Integral –, Generalised Hypergeometric Series –, The Incomplete Gamma Function M Eberl, L Paulson, Rademacher's Series
isa-afp.org
Complete Elliptic Integrals and the Arithmetic–Geometric Mean
Complete Elliptic Integrals and the Arithmetic–Geometric Mean in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 08/07/2026
Height Bounds for Height-Balanced Trees Manuel Eberl In height-balanced binary trees, for each node, the height difference between the left and right subtree is bounded by some fixed d > 0. How bad can the imbalance get? The worst-case size of a tree of height h is roughly B_d * C_d^h for large h.
isa-afp.org
Height Bounds for Height-Balanced Trees
Height Bounds for Height-Balanced Trees in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 07/07/2026
Freiman's 3k - 4 Theorem AF Ramos et al This entry formalizes Freiman's 3k-4 theorem for finite sets of integers: small doubling, in the range |A+A| ≤ 3|A|-4, forces containment in a short arithmetic progression. isa-afp.org/entries/Frei...
isa-afp.org
Freiman's 3k - 4 Theorem
Freiman's 3k - 4 Theorem in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 06/07/2026
Certified Infinite Descent Criteria J Wright et al. Infinite Descent underpins the soundness of cyclic reasoning and, in program analysis, size-change termination. Many procedures for Infinite Descent are known: automata-based, relation-based and effective heuristics. isa-afp.org/entries/Infi...
isa-afp.org
Certified Infinite Descent Criteria
Certified Infinite Descent Criteria in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 05/07/2026
Axiomatic theory of hereditarily finite sets Š Holub, Z Haniková Our axioms for HF sets include the usual ones ZF set theory and alternatives. The strongest theory considered is ZFfin, obtained from ZF by negating the axiom of infinity and adding the axiom of transitive closure.
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Lawrence Paulson @lawrpaulson.bsky.social · 04/07/2026
Formalization of 3-independence of simple tabulation hashing Wei De Leong et al. Simple tabulation hashing is a computationally-efficient hashing algorithm to get values that behave independently and are uniformly distributed for any 3 distinct keys. We show 3-independence and non-4-independence.
isa-afp.org
Formalization of 3-independence of simple tabulation hashing
Formalization of 3-independence of simple tabulation hashing in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 29/06/2026
Greedy Algorithms for Cardinality-Constrained Submodular Maximization F Lyu The main result is the classical Nemhauser–Wolsey–Fisher approximation guarantee for deterministic greedy: after k-steps, the greedy solution satisfies the finite-step bound and hence the standard approximation ratio.
isa-afp.org
Greedy Algorithms for Cardinality-Constrained Submodular Maximization
Greedy Algorithms for Cardinality-Constrained Submodular Maximization in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 28/06/2026
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Lawrence Paulson @lawrpaulson.bsky.social · 28/06/2026
Optimal Classical Planning D Traytel We formalize the framework of pseudo-Boolean lower-bound certificates for classical planning introduced by Dold et al. The main results state that a suitable snapshot of a terminated A* run yields a valid certificate and therefore proves optimality.
isa-afp.org
Formalization of Lower-Bound Certificates for Optimal Classical Planning
Formalization of Lower-Bound Certificates for Optimal Classical Planning in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 26/06/2026
New on my blog: the Dottie number lawrencecpaulson.github.io/2026/06/26/D...
lawrencecpaulson.github.io
The Dottie Number
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Lawrence Paulson @lawrpaulson.bsky.social · 26/06/2026
Perron's Formula Manuel Eberl This entry provides a proof of Perron's Formula for a Dirichlet series. The proofs mainly follow Tenenbaum's Introduction to Analytic and Probabilistic Number Theory and Titchmarsh's Theory of Functions. isa-afp.org/entries/Perr...
isa-afp.org
Perron's Formula
Perron's Formula in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 25/06/2026
ML-Lex and ML-Yacc A Brucker, B Wolff Developing parsers within interactive theorem provers is a common task. We integrate standard ML-Lex and ML-Yacc into Isabelle/HOL with an Isar-level interface that allows users to write lexical and grammatical specifications directly within theory files.
isa-afp.org
ML-Lex and ML-Yacc for Isabelle
ML-Lex and ML-Yacc for Isabelle in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 18/06/2026
Formalization of Weighted Sets M Rabing et al A generalization of finite multisets where multiplicities are replaced by weights from a semigroup, weighted sets are equivalently represented as functions from elements to optional weights or as quotients of element-weight lists modulo permutation.
isa-afp.org
Formalization of Weighted Sets
Formalization of Weighted Sets in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 17/06/2026
New on my blog: Nullius in verba: the motto of the Royal Society lawrencecpaulson.github.io/2026/06/17/N...
lawrencecpaulson.github.io
Nullius in verba: the motto of the Royal Society
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Lawrence Paulson @lawrpaulson.bsky.social · 17/06/2026
A Formalization of the Exponential Blowup in the Transformations between CNF and DNF L Schulz et al A well-known result about propositional logic is that transforming a formula into disjunctive or conjunctive normal form can lead to an exponential blowup of the formula size.
isa-afp.org
A Formalization of the Exponential Blowup in the Transformations between CNF and DNF
A Formalization of the Exponential Blowup in the Transformations between CNF and DNF in the Archive of Formal Proofs
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Lawrence Paulson @lawrpaulson.bsky.social · 16/06/2026
The Dottie Number The Dottie number is the unique d such that cos d = d. It is approximately 0.739085133215 and has no known closed form. This theory shows d exists and is unique. Its value to 12 decimal places is proved. Also that it is transcendental and a universal attractor.
isa-afp.org
The Dottie Number
The Dottie Number in the Archive of Formal Proofs
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