Tootfinder

I'm very good at integral and differential calculus,
I know the scientific names of beings animalculous;
In short, in matters vegetable, animal, and mineral,
I am the very model of a modern Major-General.
-- Gilbert & Sullivan, "Pirates of Penzance"

Mathematician Karen Keskulla Uhlenbeck was born #OTD in 1942.
She is known for her work on PDEs, calculus of variations, topology, and gauge theory, and was the second woman (after Emmy Noether!) to give the plenary lecture to the International Congress of Mathematicians.

Robert McNees (@mcnees.bsky.social)
Mathematician Karen Keskulla Uhlenbeck was born #OTD in 1942. She is known for her work on PDEs, calculus of variations, topology, and gauge theory, and was the second woman (after Emmy Noether!) to give the plenary lecture to the International Congress of Mathematicians. 👩‍🔬 🧪

from my link log —
Lecture notes on the π-calculus and Concurrent ML.
https://www.cs.cmu.edu/~fp/courses/15312-f04/handouts/26-picalc.pdf
saved 2025-07-26

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
Sebastian Angermund
https://arxiv.org/abs/2506.19115 https://

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
A recast of the standard residue-class analysis of the 3x+1 (Collatz) map in terms of two elementary operators on arithmetic progressions. The resulting calculus (i) splits any progression into its even and odd subsequences in a single step, (ii) gives a closed formula for every set of seeds that realises a prescribed parity word, (iii) yields a one line affine invariant that forbids trajectories consisting of infinitely many odd moves, and (iv) reduces the non-trivial-cycle problem to a pair o…

A Quantum-Control Lambda-Calculus with Multiple Measurement Bases
Alejandro D\'iaz-Caro, Nicolas A. Monzon
https://arxiv.org/abs/2506.16244 https://

A Quantum-Control Lambda-Calculus with Multiple Measurement Bases
We introduce Lambda-SX, a typed quantum lambda-calculus that supports multiple measurement bases. By tracking duplicability relative to arbitrary bases within the type system, Lambda-SX enables more flexible control and compositional reasoning about measurements. We formalise its syntax, typing rules, subtyping, and operational semantics, and establish its key meta-theoretical properties. This proof-of-concept shows that support for multiple bases can be coherently integrated into the type disc…

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
Davide Addona, Vincenzo Leone, Luca Lorenzi, Abdelaziz Rhandi
https://arxiv.org/abs/2507.16368

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for every $p\in (1,\infty)$. We apply this result to the elliptic operator $-{\rm div}(Q\nabla)+V$, where the potential term V is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb R^d)$ and, for almost every $x\in \mathbb R^d$, $V(x)$ is a symm…

Homomorphism Calculus for User-Defined Aggregations
Ziteng Wang, Ruijie Fang, Linus Zheng, Dixin Tang, Isil Dillig
https://arxiv.org/abs/2508.15109 https://

Homomorphism Calculus for User-Defined Aggregations
Data processing frameworks like Apache Spark and Flink provide built-in support for user-defined aggregation functions (UDAFs), enabling the integration of domain-specific logic. However, for these frameworks to support \emph{efficient} UDAF execution, the function needs to satisfy a \emph{homomorphism property}, which ensures that partial results from independent computations can be merged correctly. Motivated by this problem, this paper introduces a novel \emph{homomorphism calculus} that can…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- On the chain rule in Goodwillie calculus
Max Blans, Thomas Blom

Optimization of centroidal Voronoi tessellations
Ernesto G. Birgin, Juan S. C. Franco, Antoine Laurain
https://arxiv.org/abs/2508.17721 https://arxiv.org/p…

Optimization of centroidal Voronoi tessellations
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric attributes such as area and perimeter. The derivative of the objective functional with respect to the position of the generators is computed using techniques of shape calculus and sensitivity analysis of minimization diagrams. Several numerical experiments are …

Analytical transit light curves for power-law limb darkening: a comprehensive framework via fractional calculus and differential equations
Farrukh A. Chishtie, Mohammad I. Saeed, Shaukat N. Goderya
https://arxiv.org/abs/2506.18860

Analytical transit light curves for power-law limb darkening: a comprehensive framework via fractional calculus and differential equations
We present the first complete analytical framework for computing exoplanetary transit light curves with arbitrary power-law limb darkening profiles $I(μ) \propto μ^α$, where $α$ can be any real number greater than $-1/2$, including the physically important non-integer cases. While the groundbreaking work of Agol et al. (2020) provided exact analytical solutions for polynomial limb darkening through recursion relations, stellar atmosphere models often favor power-law forms with fractional ex…

Quadratic estimates for the $H^\infty$-functional calculus of bisectorial Clifford operators
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
https://arxiv.org/abs/2506.16783

Quadratic estimates for the $H^\infty$-functional calculus of bisectorial Clifford operators
The $H^\infty$-functional calculus is a two-step procedure, introduced by A. McIntosh, that allows the definition of functions of sectorial operators in Banach spaces. It plays a crucial role in the spectral theory of differential operators, as well as in their applications to evolution equations and various other fields of science. An extension of the $H^\infty$-functional calculus also exists in the hypercomplex setting, where it is based on the notion of $S$-spectrum. Originally this was don…

This https://arxiv.org/abs/2306.17541 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csMS_…

Rigorous Function Calculi in Ariadne
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne, which provides a rigorous calculus for working with Euclidean functions. We first introduce the Ariadne framework, which is based on a clean separation of objects as providing exact, effective, validated and approximate information. We then discuss the function c…

Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations
Tom Mestdag, Kenzo Yasaka
https://arxiv.org/abs/2507.14678

Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations
We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our developments with several examples, including an application to dynamical systems with a symmetry group and to the invariant inverse problem of the calculus of variations.

Replaced article(s) found for math.OA. https://arxiv.org/list/math.OA/new
[1/1]:
- Divided Differences and Multivariate Holomorphic Calculus
Luiz Hartmann, Matthias Lesch

Generalized Multiple Operator Integrals for Operators with Finite Dimensions
Shih-Yu Chang
https://arxiv.org/abs/2506.19971 https://a…

Generalized Multiple Operator Integrals for Operators with Finite Dimensions
Multiple Operator Integrals (MOIs) have played a foundational role in operator theory and functional calculus, particularly for analyzing Hermitian matrices via spectral decomposition. Conventional MOIs rely on the assumption of self-adjointness, making them analytically tractable for computing Frechet derivatives, establishing trace formulas, and deriving commutator estimates. However, many problems in mathematics, science, and engineering involve matrices that are fundamentally non-Hermitian,…

from my link log —
Dana Scott on the lambda calculus, then and now.
https://www.cis.upenn.edu/~cis5110/lambda_calculus_timeline-Scott.pdf
saved 2025-07-18

Malliavin Calculus and Stochastic Differential Equations
Shizan Fang, Rongrong Tian
https://arxiv.org/abs/2507.13747 https://arxiv.or…

Malliavin Calculus and Stochastic Differential Equations
This paper is devoted to a study on SDEs with a bounded Borel drift b. We first remark that the original integration by parts formula due to P. Malliavin can be used to deal with derivatives with respect to space variables, then we obtain a link between the product of heat kernels and iterated divergences in Malliavin calculus. An explicit estimate for the derivative of solutions to SDE is obtained in terms of the L-infinity norm of b; as a result, we prove that the SDE defines a continuous flo…

On tested Bousfield-Friedlander localizations
Niall Taggart
https://arxiv.org/abs/2507.17321 https://arxiv.org/pdf/2507.17321

On tested Bousfield-Friedlander localizations
We demonstrate that a Bousfield-Friedlander localization with a set of test morphisms in the sense introduced by Bandklayder, Bergner, Griffiths, Johnson, and Santhanam can also be characterized as a left Bousfield localization at the set of test morphisms. This viewpoint enables us to establish a homogeneous model structure associated with any calculus arising from a Bousfield-Friedlander localization of this form. As a corollary, we show that homogeneous functors in discrete calculus coincide…

The decohered ZX-calculus
Titouan Carette, Daniela Cojocaru, Renaud Vilmart
https://arxiv.org/abs/2508.04296 https://arxiv.org/pdf/2508.04296

The decohered ZX-calculus
The discard ZX-calculus is known to be complete and universal for mixed-state quantum mechanics, allowing for both quantum and classical processes. However, if the quantum aspects of ZX-calculus have been explored in depth, little work has been done on the classical side. In this paper, we investigate a fragment of discard ZX-calculus obtained by decohering the usual generators of ZX-calculus. We show that this calculus is universal and complete for affinely supported probability distributions …

Bicategories of Lax Fractions
Graham Manuell, Lurdes Sousa
https://arxiv.org/abs/2507.12044 https://arxiv.org/pdf/2507.12044

Bicategories of Lax Fractions
The well-known calculus of fractions of Gabriel and Zisman provides a convenient way to formally invert morphisms in a category. This was extended to bicategories by Pronk. On the other hand, the second author has developed a calculus of lax fractions for order-enriched categories that formally turns a given class of morphisms into left adjoint right inverses. We extend these constructions by presenting a calculus of lax fractions for 2-categories that formally turns a class of morphisms and ps…

Quantum ergodicity for contact metric structures
Lino Benedetto
https://arxiv.org/abs/2507.18216 https://arxiv.org/pdf/2507.18216

Quantum ergodicity for contact metric structures
This paper is dedicated to the proof of a Quantum Ergodicity (QE) theorem for the eigenfunctions of subLaplacians on contact metric manifolds, under the assumption that the Reeb flow is ergodic. To do so, we rely on a semiclassical pseudodifferential calculus developed for general filtered manifolds that we specialize to the setting of contact manifolds. Our strategy is then reminiscent of an implementation of the Born-Oppenheimer approximation as we rely on the construction of microlocal proje…

Proofs that Modify Proofs, 1/2
Henry Towsner
https://arxiv.org/abs/2506.16491 https://arxiv.org/pdf/2506.16491

Proofs that Modify Proofs, 1/2
This paper is a prelude and elaboration on Proofs that Modify Proofs. Here we present an ordinal analysis of a fragment of the $μ$-calculus around the strength of parameter-free $Π^1_2$-comprehension using the same approach as that paper, interpreting functions on proofs as proofs in an expanded system. We build up the ordinal analysis in several stages, beginning by illustrating the method systems at the strength of paremeter-free $Π^1_1$-comprehension and full $Π^1_1$-comprehension.

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga
Gabriele Cecilia (Augusta University)
https://arxiv.org/abs/2508.13612 https://arxiv.…

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga
Reversible concurrent calculi are abstract models for concurrent systems in which any action can potentially be undone. Over the last few decades, different formalisms have been developed and their mathematical properties have been explored; however, none have been machine-checked within a proof assistant. This paper presents the first Beluga formalization of the Calculus of Communicating Systems with Keys and Proof labels (CCSKP), a reversible extension of CCS. Beyond the syntax and semantic…

Guaranteeing and Explaining Stability across Heterogeneous Load Balancing using Calculus Network Dynamics
Mengbang Zou, Yun Tang, Adolfo Perrusqu\'ia, Weisi Guo
https://arxiv.org/abs/2507.12892

Guaranteeing and Explaining Stability across Heterogeneous Load Balancing using Calculus Network Dynamics
Load balancing between base stations (BSs) allows BS capacity to be efficiently utilised and avoid outages. Currently, data-driven mechanisms strive to balance inter-BS load and reduce unnecessary handovers. The challenge is that over a large number of BSs, networks observe an oscillatory effect of load evolution that causes high inter-BS messaging. Without a calculus function that integrates network topology to describe the evolution of load states, current data-driven algorithms cannot explai…

New Insights into Integrals Involving Gaussian Sums
Jesus Retamozo
https://arxiv.org/abs/2507.17945 https://arxiv.org/pdf/2507.17945

New Insights into Integrals Involving Gaussian Sums
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals that emerge naturally in this context. The approach is mostly elementary, avoiding the need for advanced machinery, and aims to shed light on the rich interplay between analysis and arithmetic structures arising from these integrals.

Minimal Per-Flow Backlog Bounds at an Aggregate FIFO Server under Piecewise-Linear Arrival Curves
Lukas Wildberger, Anja Hamscher, Jens B. Schmitt
https://arxiv.org/abs/2506.16914

Minimal Per-Flow Backlog Bounds at an Aggregate FIFO Server under Piecewise-Linear Arrival Curves
Network Calculus (NC) is a versatile methodology based on min-plus algebra to derive worst-case per-flow performance bounds in networked systems with many concurrent flows. In particular, NC can analyze many scheduling disciplines; yet, somewhat surprisingly, an aggregate FIFO server is a notoriously hard case due to its min-plus non-linearity. A resort is to represent the FIFO residual service by a family of functions with a free parameter instead of just a single curve. For simple token-bucke…

Khovanov-Rozansky cycle calculus for bipartite links
A. Anokhina, E. Lanina, A. Morozov
https://arxiv.org/abs/2506.08721 https://arxi…

Khovanov-Rozansky cycle calculus for bipartite links
Bipartite calculus is a direct generalization of Kauffman planar expansion from $N=2$ to arbitrary $N$, applicable to the restricted class of knots which are entirely made of antiparallel lock tangles. Whenever applicable, it allows a straightforward generalization of the Khovanov calculus without a need of the technically complicated matrix factorization used for arbitrary $N$ in the Khovanov-Rozansky (KR) approach. The main object here is the $3^{n}$-dimensional hypercube with $n$ being the n…

Type-Driven Prompt Programming: From Typed Interfaces to a Calculus of Constraints
Abhijit Paul
https://arxiv.org/abs/2508.12475 https://arxiv.org/pdf/2508…

Type-Driven Prompt Programming: From Typed Interfaces to a Calculus of Constraints
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging prompt programming frameworks. However, there are gaps in constraint expressiveness and in supporting algorithms. To address these issues, we introduce the notion of Lambda Prompt, a dependently typed calculus with probabilistic refinements for syntactic and sema…

Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids
Niels Kowalzig, Thomas Weber
https://arxiv.org/abs/2507.16455 https://…

Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids
We develop a notion of covariant differential calculus for Hopf algebroids. As a byproduct, we prove analogues of the fundamental theorem of Hopf modules and a Takeuchi-Schneider equivalence in the realm of Hopf algebroids. The resulting categorical equivalences enable us to classify covariant calculi on Hopf algebroids and, more in general, covariant calculi on quantum homogeneous spaces in this context, in terms of substructures of the augmentation ideal. This generalises the well-known class…

Pseudodifferential Weyl calculus on vector bundles
Lars Andersson, Benjamin Moser, Marius A. Oancea, Claudio F. Paganini, Gabriel Schmid
https://arxiv.org/abs/2507.11965

Pseudodifferential Weyl calculus on vector bundles
We develop a geometric framework for Weyl quantization on pseudo-Riemannian manifolds, in which pseudodifferential operators act on sections of vector bundles equipped with arbitrary connections. We construct the associated star product and compute its semiclassical expansion up to third order in the expansion parameter. A central feature of our approach is a one-to-one correspondence between formally self-adjoint symbols and formally self-adjoint operators, extending known results from flat sp…

Discontinuity calculus and applications to two-body coupled-channel scattering
Hao-Jie Jing, Xiong-Hui Cao, Feng-Kun Guo
https://arxiv.org/abs/2507.06175 h…

Discontinuity calculus and applications to two-body coupled-channel scattering
We present a novel method, termed discontinuity calculus, for computing discontinuities of complex functions. This framework enables a systematic investigation of both analytic continuation and the topological structure of Riemann surfaces. We apply this calculus to analyze the analytic continuation of partial-wave amplitudes in two-body coupled-channel scattering problems and discuss their uniformization of the corresponding Riemann surfaces. This methodology offers new perspectives and tools …

String Diagrams for Defect-Based Surface Code Computing
Mateusz Kupper (Department of Informatics, University of Sussex), Dominic Horsman (Department of Computer Science, University of Oxford), Chris Heunen (School of Informatics, University of Edinburgh), Niel de Beaudrap (Department of Informatics, University of Sussex)
https://arxiv.org…

String Diagrams for Defect-Based Surface Code Computing
Surface codes are a popular choice for implementing fault-tolerant quantum computing. Two-qubit gates may be realised in these codes using only nearest-neighbour interactions, either by lattice surgery or by braiding defects around each other. The effect of lattice surgery operations may be simply described using the ZX-calculus: a graphical language that has proven effective for program design and optimisation. In this work, we formalise a similar description via the ZX-calculus of defect brai…

Encoding call-by-push-value in the pi-calculus
Benjamin Bennetzen, Nikolaj Rossander Kristensen, Peter Buus Steffensen
https://arxiv.org/abs/2506.10584 htt…

Encoding call-by-push-value in the pi-calculus
In this report we define an encoding of Levys call-by-push-value lambda-calculus (CBPV) in the pi-calculus, and prove that our encoding is both sound and complete. We present informal (by-hand) proofs of soundness, completeness, and all required lemmas. The encoding is specialized to the internal pi-calculus (pi-i-calculus) to circumvent certain challenges associated with using de Bruijn index in a formalization, and it also helps with bisimulation as early-, late- and open-bisimulation coincid…

Homogeneous Linear Calculus of Order 1 and a $\lambda$-Taylor Formula
Ronald Orozco L\'opez
https://arxiv.org/abs/2506.22976 https://

Homogeneous Linear Calculus of Order 1 and a $λ$-Taylor Formula
In this paper, a new calculus on sequences is defined. Also, the $λ$-derivative and the $λ$-integration are investigated. The fundamental theorem of $λ$-calculus is included. A suitable function basis for the $λ$-derivative and the $λ$-integral is provided, and various properties of this basis are given. A $λ$-Taylor formula for functions is given.

Some functor calculus on semirings
Pronay Biswas, Amartya Goswami, Sujit Kumar Sardar
https://arxiv.org/abs/2506.13378 https://arxiv.…

Some functor calculus on semirings
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent frames, with the latter forming a dense sublocale of the former. We define a natural transformation between these functors and analyze their categorical and topological properties. Further, we introduce a notion of support that assigns to each semiring a bound…

from my link log —
A tutorial implementation of a dependently typed lambda calculus.
https://webspace.science.uu.nl/~swier004/publications/2010-fundamentae-informatica.pdf
saved 2025-06-06

A Diagrammatic Calculus for a Functional Model of Natural Language Semantics
Matthieu Pierre Boyer
https://arxiv.org/abs/2507.00782 https://

A Diagrammatic Calculus for a Functional Model of Natural Language Semantics
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressivity of a more traditional denotation style. We will formalize a category based type and effect system, and construct a diagrammatic calculus to model parsing and handling of effects, and use it to efficiently compute the denotations for sentences.

Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains
Nick Lindemulder, Emiel Lorist, Floris Roodenburg, Mark Veraar
https://arxiv.org/abs/2507.13478

Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains
We study the Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the distance to the boundary. Our analysis applies to bounded $C^{1,λ}$-domains with $λ\in[0,1]$, revealing a crucial trade-off: lower domain regularity can be compensated by enlarging the weight exponent. As a primary consequence, we establish maximal regularity f…

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Shakir Sh. Yusubov, Shikhi Sh. Yusubov, Elimhan N. Mahmudov
https://arxiv.org/abs/2506.12926

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Summary]{In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<α\leq 1$ and the fractional Riemann- Liouville integral of order $β> 0$ at fixed endpoints. A fractional analogue of the Du Bois-Reymond lemma is proved, and the Euler-Lagrange conditions are proved for the simplest problem of fractional variational calculus with fixed ends and for the fractional isoperimetric problem. An approach is proposed to obtain the necess…

A Malliavin calculus approach to score functions in diffusion generative models
Ehsan Mirafzali, Frank Proske, Utkarsh Gupta, Daniele Venturi, Razvan Marinescu
https://arxiv.org/abs/2507.05550

A Malliavin calculus approach to score functions in diffusion generative models
Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the target data distribution via deterministic or stochastic differential equations (SDEs). The score function is typically estimated from data using a variety of approximation techniques, such as denoising or sliced score matching, Hyvärien's method, or Schröding…

Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes
Luis Wirth
https://arxiv.org/abs/2506.02429 https://…

Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes
This thesis presents the development of a novel finite element library in Rust based on the principles of Finite Element Exterior Calculus (FEEC). The library solves partial differential equations formulated using differential forms on abstract, coordinate-free simplicial complexes in arbitrary dimensions, employing an intrinsic Riemannian metric derived from edge lengths via Regge Calculus. We focus on solving elliptic Hodge-Laplace eigenvalue and source problems on the nD de Rham complex. We …

Doing calculus and checking my results with o3 feels a lot like Jernau Gurgeh talking to the ship about the progress of his game in Player of Games.

Short mollifiers of the Riemann zeta-function
J. Brian Conrey, David W. Farmer, Chung-Hang Kwan, Yongxiao Lin, Caroline L. Turnage-Butterbaugh
https://arxiv.org/abs/2508.11108 h…

Short mollifiers of the Riemann zeta-function
We apply the calculus of variations to construct a new sequence of linear combinations of derivatives of the Riemann $ζ$-function adapted to Levinson's method, which yield a positive proportion of zeros of the $ζ$-function on the critical line, regardless of how short the mollifier is. Our construction extends readily to modular $L$-functions. Even with Levinson's original choice of mollifier, our method more than doubles the proportions of zeros on the critical line for modular $L$-functions…

On the cut-elimination of the modal $\mu$-calculus: Linear Logic to the rescue
Esa\"ie Bauer, Alexis Saurin
https://arxiv.org/abs/2506.09791 https://

On the cut-elimination of the modal $μ$-calculus: Linear Logic to the rescue
This paper presents a proof-theoretic analysis of the modal $μ$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $μ$-calculus, using methods from linear logic and its exponential modalities. To achieve this, we introduce a new system, \muLLmodinf{}, which is a linear version of the modal $μ$-calculus, intertwining the modalities from the modal $μ$-calculus with the exponential modalities from linear logic. Our strategy for proving cut-elimination …

The S-functional calculus for the Clifford adjoint operator
F. Colombo, F. Mantovani, P. Schlosser
https://arxiv.org/abs/2508.12958 https://arxiv.org/pdf/2…

The S-functional calculus for the Clifford adjoint operator
In this paper, we work within the framework of modules over the Clifford algebra $\mathbb{R}_d$. Our investigation focuses on the S-spectrum and the S-functional calculus in its various forms for the adjoint T* of a Clifford operator T. One of the key results we present is that the bisectoriality of T can be transferred to T*. This is grounded in the fact that, for Clifford operators, the S-spectrum of the adjoint operator T* is identical to that of T. Furthermore, we demonstrate that for the e…

Crosslisted article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- Type-Driven Prompt Programming: From Typed Interfaces to a Calculus of Constraints
Abhijit Paul

from my link log —
The Epic Verse calculus: a core calculus for functional logic programming.
https://simon.peytonjones.org/verse-calculus/
saved 2025-06-12

Stochastic Calculus Approach to Thermodynamics of Jump Processes
Lars Torbj{\o}rn Stutzer
https://arxiv.org/abs/2508.00940 https://arxiv.org/pdf/2508.00940…

Stochastic Calculus Approach to Thermodynamics of Jump Processes
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems manifestly all have non-zero EP and therefore impose an "arrow of time". Thermodynamic inequalities are lower bounds on the total EP and are especially useful when only parts of systems are operationally accessible. We use a stochastic calculus approach to dir…

A Deep-Inference Sequent Calculus for Basic Propositional Team Logic (Without Delving Too Deep)
Aleksi Anttila, Rosalie Iemhoff, Fan Yang
https://arxiv.org/abs/2508.07509 https:…

A Deep-Inference Sequent Calculus for Basic Propositional Team Logic (Without Delving Too Deep)
We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two deep-inference rules for the inquisitive disjunction. We show that the system satisfies various desirable properties: it admits height-preserving weakening, contraction and inversion; it supports a procedure for constructing cutfree proofs and countermodels similar to th…

Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus
Ahmed Abdalmuhsin Abdalsahib
https://arxiv.org/abs/2507.13402 https://…

Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps, including linear, quadratic, cubic, and higher-order forms. Using elementary techniques from differentiation and integration, the approach produces polynomial expressions that represent total sums, even when each term is raised to a positive integer power. As a resu…

Underprepared for Physics: Reframing the narrative on readiness and instruction in calculus-based, introductory physics courses
Suzanne White Brahmia, Geraldine L. Cochran
https://arxiv.org/abs/2508.00257

Underprepared for Physics: Reframing the narrative on readiness and instruction in calculus-based, introductory physics courses
In the U.S., introductory calculus-based courses often acts as a gatekeeper to STEM degrees. But access to the prerequisite math is far from equal--students from low-income and racially marginalized communities are far less likely to have the chance to take calculus before college. These disparities are then compounded by rigid placement systems that reward procedural fluency in algebra and trigonometry, while overlooking the conceptual quantitative reasoning that physics truly demands. Labelin…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- An Algebraic Extension of Intuitionistic Linear Logic: The $L_!^S$-Calculus and Its Categorical M...
Alejandro D\'iaz-Caro, Malena Ivnisky, Octavio Malherbe

Pontryagin Maximum Principle for McKean-Vlasov Reaction-Diffusion Equations
Johan Benedikt Spille, Wilhelm Stannat
https://arxiv.org/abs/2507.16288 https:/…

Pontryagin Maximum Principle for McKean-Vlasov Reaction-Diffusion Equations
We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux differentiability of the control to state map and, using adjoint calculus, we derive explicit representations of the gradient of the cost functional and a Pontryagin maximum principle. On the way, we also prove a novel existence and uniqueness result for linear …

Replaced article(s) found for cs.DC. https://arxiv.org/list/cs.DC/new
[1/1]:
- Programming Distributed Collective Processes in the eXchange Calculus
Giorgio Audrito, Roberto Casadei, Ferruccio Damiani, Gianluca Torta, Mirko Viroli

A Non-Wellfounded and Labelled Sequent Calculus for Bimodal Provability Logic
Justus Becker
https://arxiv.org/abs/2506.14307 https://…

A Non-Wellfounded and Labelled Sequent Calculus for Bimodal Provability Logic
We present a labelled and non-wellfounded calculus for the bimodal provability logic CS. The system is obtained by modelling the Kripke-like semantics of this logic. As in arXiv:2309.00532, we enforce the second-order property of converse wellfoundedness by using techniques from cyclic proof theory. We will prove soundness and completeness of this system with respect to the semantics and provide a primitive decision procedure together with a way to extract countermodels.

Fair Termination for Resource-Aware Active Objects
Francesco Dagnino, Paola Giannini, Violet Ka I Pun, Ulises Torrella
https://arxiv.org/abs/2508.15333 https://

Fair Termination for Resource-Aware Active Objects
Active object systems are a model of distributed computation that has been adopted for modelling distributed systems and business process workflows. This field of modelling is, in essence, concurrent and resource-aware, motivating the development of resource-aware formalisations on the active object model. The contributions of this work are the development of a core calculus for resource-aware active objects together with a type system ensuring that well-typed programs are fairly terminating, i…

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[1/2]:
Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II:...

Evolution Equations on Manifolds with Conical Singularities
Elmar Schrohe
https://arxiv.org/abs/2506.17481 https://arxiv.org/pdf/2506…

Evolution Equations on Manifolds with Conical Singularities
This is an introduction to the analysis of nonlinear evolution equations on manifolds with conical singularities via maximal regularity techniques. We address the specific difficulties due to the singularities, in particular the choice of extensions of the conic Laplacian that guarantee the existence of a bounded $H_\infty$-calculus. We introduce the relevant technical tools and survey, as main examples, applications to the porous medium equation, the fractional porous medium equation, the Yama…

Graham positivity of triple Schubert calculus
Yibo Gao, Rui Xiong
https://arxiv.org/abs/2506.09421 https://arxiv.org/pdf/2506.09421…

Graham positivity of triple Schubert calculus
We prove Samuel's conjecture on certain Graham positivity of the expansion coefficient of two double Schubert polynomials in three sets of variables by establishing a refined version of Graham's positivity theorem. As a corollary, we prove Kirillov's conjecture on the positivity of skew divided difference operators applied to Schubert polynomials.

This https://arxiv.org/abs/2501.02556 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spatial Network Calculus: Toward Deterministic Wireless Networking
This paper extends the classical network calculus to spatial scenarios, focusing on wireless networks with differentiated services and varying transmit power levels. Building on a spatial network calculus, a prior extension of network calculus to spatial settings, we propose a generalized framework by introducing regulations for stationary marked point processes. The regulations correspond to two key constraints: the total transmit power of all transmitters within a spatial region and the cumul…

Positive Sharing and Abstract Machines
Beniamino Accattoli, Claudio Sacerdoti Coen, Jui-Hsuan Wu
https://arxiv.org/abs/2506.14131 https://

Positive Sharing and Abstract Machines
Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quad…

Quantum variational calculus on a lattice
Shahn Majid, Francisco Sim\~ao
https://arxiv.org/abs/2508.02628 https://arxiv.org/pdf/2508.02628

Quantum variational calculus on a lattice
We solve the long-standing problem of variational calculus on a noncommutative space or spacetime for a significant class of models with trivial jet bundle. Our approach entails a quantum version of the Anderson variational double complex $Ω(J^\infty)$ and includes Euler-Lagrange equations and a partial Noether's theorem. We show in detail how this works for a free field on a $\Bbb Z^m$ lattice regarded as a discrete noncommutative geometry, obtaining the Klein-Gordon equation for a scalar fie…

Rate estimates for weighted total variation norm in terms of Wasserstein distances
Iv\'an Ivkovic, Mikl\'os R\'asonyi
https://arxiv.org/abs/2506.16088

Rate estimates for weighted total variation norm in terms of Wasserstein distances
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment conditions. We apply our results to convergence of functionals in Malliavin calculus.

A Dwyer-Rezk classification for polynomial functors in Weiss calculus
David Barnes, Magdalena K\k{e}dziorek, Niall Taggart
https://arxiv.org/abs/2508.03808 https://

A Dwyer-Rezk classification for polynomial functors in Weiss calculus
In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving $d$-excisive functors from pointed spaces to spectra as spectrum-valued functors on the category of finite sets of cardinality at most $d$ and epimorphisms. We prove through different methods the analogous result in Weiss calculus: $d$-polynomial functors are equivalent to spectrum-valued functors on the category of finite-dimensional inner product spaces of dimension at m…

Closure Conversion, Flat Environments, and the Complexity of Abstract Machines
Beniamino Accattoli (Inria & LIX, \'Ecole Polytechnique), Dan Ghica (Huawei Central Software Institute, University of Birmingham), Giulio Guerrieri (University of Sussex), Cl\'audio Belo Louren\c{c}o (Huawei Central Software Institute), Claudio Sacerdoti Coen (Universit\`a di Bologna)

Closure Conversion, Flat Environments, and the Complexity of Abstract Machines
Closure conversion is a program transformation at work in compilers for functional languages to turn inner functions into global ones, by building closures pairing the transformed functions with the environment of their free variables. Abstract machines rely on similar and yet different concepts of closures and environments. In this paper, we study the relationship between the two approaches. We adopt a very simple λ-calculus with tuples as source language and study abstract machines for bot…

Generalized Clapeyron's theorem
Yury Grabovsky, Lev Truskinovsky
https://arxiv.org/abs/2508.12441 https://arxiv.org/pdf/2508.12441

Generalized Clapeyron's theorem
Clapeyron's Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations which can be viewed as nonlinear analogs of this classical result, reinterpreting them as rather general statements within Calculus of Variations. In the framework of nonlinear elasticity these relations reflect various partial symmetries of the material respo…

Intrinsic and Extrinsic Organized Attention: Softmax Invariance and Network Sparsity
Oluwadamilola Fasina, Ruben V. C. Pohle, Pei-Chun Su, Ronald R. Coifman
https://arxiv.org/abs/2506.15541

Intrinsic and Extrinsic Organized Attention: Softmax Invariance and Network Sparsity
We examine the intrinsic (within the attention head) and extrinsic (amongst the attention heads) structure of the self-attention mechanism in transformers. Theoretical evidence for invariance of the self-attention mechanism to softmax activation is obtained by appealing to paradifferential calculus, (and is supported by computational examples), which relies on the intrinsic organization of the attention heads. Furthermore, we use an existing methodology for hierarchical organization of tensors …

Whereas Leibniz’s task was to find the sum of infinitely many known terms, Hounsfield wondered:
Could the process be run in reverse?
With enough total dimmings, from enough directions, could we work backward to deduce the unknown absorption at each point along the many beams
— and use that to see inside the brain?
Most radiologists thought the idea was crazy. -- But one doctor was willing to listen.
He handed Hounsfield a jar containing a human brain with a t…

How a Puzzle About Fractions Got Brain Scans Rolling
A story of bowling pins, patterns and medical miracles.

Don't exhaust, don't waste
Riccardo Bianchini, Francesco Dagnino, Paola Giannini, Elena Zucca
https://arxiv.org/abs/2507.13792 https://

Don't exhaust, don't waste
We extend the semantics and type system of a lambda calculus equipped with common constructs to be resource-aware. That is, the semantics keep tracks of the usage of resources, and is stuck, besides in case of type errors, if either a needed resource is exhausted, or a provided resource would be wasted. In such way, the type system guarantees, besides standard soundness, that for well-typed programs there is a computation where no resource gets either exhausted or wasted. The no-waste extensi…

Stochastic Calculus for Pathwise Observables of Markov-Jump Processes: Unification of Diffusion and Jump Dynamics
Lars Torbj{\o}rn Stutzer, Cai Dieball, Alja\v{z} Godec
https://arxiv.org/abs/2508.04647

Stochastic Calculus for Pathwise Observables of Markov-Jump Processes: Unification of Diffusion and Jump Dynamics
Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They provide a means of thermodynamic inference in the typical situation, when not all dissipative degrees of freedom in a system are experimentally accessible. So far, theories focusing on path-wise observables have been developing in two major directions, diffusio…

Unstable $1$-semiadditivity as classifying Goodwillie towers
Connor Malin
https://arxiv.org/abs/2506.11245 https://arxiv.org/pdf/2506…

Unstable $1$-semiadditivity as classifying Goodwillie towers
A stable $\infty$-category is $1$-semiadditive if all norms for finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two unstable analogs of $1$-semiadditivity for an $\infty$-category $C$ and study their relation to the Goodwillie calculus of functors $C \rightarrow \s(C)$. We demonstrate these qualities are complete obstructions to the problem of endowing $\partial_\ast F$ with either a right module or a divided…

A Proof System with Causal Labels (Part II): checking Counterfactual Fairness
Leonardo Ceragioli, Giuseppe Primiero
https://arxiv.org/abs/2507.14655 https:…

A Proof System with Causal Labels (Part II): checking Counterfactual Fairness
In this article we propose an extension to the typed natural deduction calculus TNDPQ to model verification of counterfactual fairness in probabilistic classifiers. This is obtained formulating specific structural conditions for causal labels and checking that evaluation is robust under their variation.

The Free Functional Calculus in General
Julian Bushelli
https://arxiv.org/abs/2506.00170 https://arxiv.org/pdf/2506.00170

The Free Functional Calculus in General
The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important functions, such as the Schur complement. This paper presents a generalization of free functions, viewing them as a natural categorial structure: functors between functor categories that commute with natural transformation. We study this construction on genera…

A Proof System with Causal Labels (Part I): checking Individual Fairness and Intersectionality
Leonardo Ceragioli, Giuseppe Primiero
https://arxiv.org/abs/2507.14650

A Proof System with Causal Labels (Part I): checking Individual Fairness and Intersectionality
In this article we propose an extension to the typed natural deduction calculus TNDPQ to model verification of individual fairness and intersectionality in probabilistic classifiers. Their interpretation is obtained by formulating specific conditions for the application of the structural rule of Weakening. Such restrictions are given by causal labels used to check for conditional independence between protected and target variables.

Term Assignment and Categorical Models for Intuitionistic Linear Logic with Subexponentials
Daniel Rogozin
https://arxiv.org/abs/2507.12360 https://arxiv.o…

Term Assignment and Categorical Models for Intuitionistic Linear Logic with Subexponentials
In this paper, we present a typed lambda calculus ${\bf SILL}(λ)_Σ$, a type-theoretic version of intuitionistic linear logic with subexponentials, that is, we have many resource comonadic modalities with some interconnections between them given by a subexponential signature. We also give proof normalisation rules and prove the strong normalisation and Church-Rosser properties for $β$-reduction by adapting the Tait-Girard method to subexponential modalities. Further, we analyse subexponential…

Anomalous diffusion for mass transport phenomena I: Analytic solutions to time fractional diffusion
Nathaniel G. Hermann, M. Shane Hutson
https://arxiv.org/abs/2506.14043

Anomalous diffusion for mass transport phenomena I: Analytic solutions to time fractional diffusion
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or through complex mathematical structures (e.g. Fox-H functions). Here, we present a set of analytic solutions to common time fractional diffusion problems, written in terms of Mittag-Leffler and M-Wright functions, as well as generalized fractional error and compl…

Global Lipschitz regularity in anisotropic elliptic problems with natural gradient growth
Carlo Alberto Antonini, Andrea Cianchi
https://arxiv.org/abs/2507.14606

Global Lipschitz regularity in anisotropic elliptic problems with natural gradient growth
We deal with homogeneous Dirichlet and Neumann boundary-value problems for anisotropic elliptic operators of p-Laplace type. They emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of the gradient of trial functions. We establish global Lipschitz regularity of solutions under the weakest possible assumption on right-hand side of the equation, which may also include the gradient term with natural growth exponent. The res…

A Grammatical Calculus for the Ramanujan Polynomials
William Y. C. Chen, Amy M. Fu, Elena L. Wang
https://arxiv.org/abs/2506.01649 https://

A Grammatical Calculus for the Ramanujan Polynomials
As remarked by Berndt, no combinatorial perspective seems to be alluded in the original definition of the Ramanujan polynomials. On a different scene, a recursive algorithm to generate rooted trees has been devised independently by Shor and Dumont-Ramamonjisoa. Zeng discovered the connection between the Ramanujan polynomials and the enumeration of rooted trees by number of improper edges. We present a proper labeling scheme for rooted trees by employing an extra label. H…

This https://arxiv.org/abs/2410.06952 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Generalized Wigner-Weyl calculus for gauge theory and non-dissipative transport
We consider a theory of fermions interacting with a (in general, non-Abelian) gauge field. The theory is assumed to be essentially inhomogeneous, which might be provided by non-trivial background fields interacting with both fermions and gauge bosons. For this theory, a version of Wigner-Weyl calculus is developed, in which the Wigner transformation of the fermion Green function belongs to a matrix representation of gauge group. We demonstrate the power of the proposed formalism through the rep…

Proof Analysis of A Foundational Classical Singlesuccedent Sequent Calculus
Khashayar Irani
https://arxiv.org/abs/2507.04449 https://…

Proof Analysis of A Foundational Classical Singlesuccedent Sequent Calculus
In this paper we investigate the question: 'How can A Foundational Classical Singlesuccedent Sequent Calculus be formulated?' The choice of this particular area of proof-theoretic study is based on a particular ground that is, to formulate a robust and foundational classical singlesuccedent sequent calculus that includes a number of novel rules with the ultimate aim of deriving the singlesuccedent sequent Γ sequent arrow C. To this end, we argue that among all standard sequent calculi (at leas…

Analysis of Langevin midpoint methods using an anticipative Girsanov theorem
Matthew S. Zhang
https://arxiv.org/abs/2507.12791 https://

Analysis of Langevin midpoint methods using an anticipative Girsanov theorem
We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods for sampling from a target measure $π\propto \exp(-V)$. Borrowing techniques from Malliavin calculus, we compute estimates for the Radon-Nikodym derivative for processes on $L^2([0, T); \mathbb{R}^d)$ which may anticipate the Brownian motion, in the sense that they may not be adapted to the filtration at the same time…

This https://arxiv.org/abs/2504.09748 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Level-set topology optimisation with unfitted finite elements and automatic shape differentiation
In this paper we develop automatic shape differentiation techniques for unfitted discretisations and link these to recent advances in shape calculus for unfitted methods. We extend existing analytic shape calculus results to the case where the domain boundary intersects with the boundary of the background domain. We further show that we can recover these analytic derivatives to machine precision regardless of the mesh size using the developed automatic shape differentiation techniques, drastica…

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus
Julie Cailler, Simon Guilloud
https://arxiv.org/abs/2507.11349 https://

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-order logic: SC-TPTP. To avoid multiplication of standards, our proposed format over-specifies the TPTP derivation format by focusing on sequent formalisms. By doing so, it provides a high level of detail, is faithful to mathematical tradition, a…

Controlling Copatterns: There and Back Again (Extended Version)
Paul Downen
https://arxiv.org/abs/2508.12427 https://arxiv.org/pdf/2508.12427

Controlling Copatterns: There and Back Again (Extended Version)
Copatterns give functional programs a flexible mechanism for responding to their context, and composition can greatly enhance their expressiveness. However, that same expressive power makes it harder to precisely specify the behavior of programs. Using Danvy's functional and syntactic correspondence between different semantic artifacts, we derive a full suite of semantics for copatterns, twice. First, a calculus of monolithic copatterns is taken on a journey from small-step operational semantic…

from my link log —
Lambda calculus cooked N ways: Benchmarks for capture-avoiding substitution.
https://github.com/sweirich/lambda-n-ways
saved 2025-06-14

GitHub - sweirich/lambda-n-ways: Benchmarks for capture-avoiding substitution
Benchmarks for capture-avoiding substitution. Contribute to sweirich/lambda-n-ways development by creating an account on GitHub.

Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator
Radovan Dabeti\'c, Ralf Hiptmair
https://arxiv.org/abs/2507.19405 https://arxiv.…

Convergence of Discrete Exterior Calculus for the Hodge-Dirac Operator
A short proof of convergence for the discretization of the Hodge-Dirac operator in the framework of discrete exterior calculus (DEC) is provided using the techniques established in [Johnny Guzmán and Pratyush Potu, A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms, arXiv:2505.08934, 2025]

This https://arxiv.org/abs/2404.04218 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Simplifying explicit subtyping coercions in a polymorphic calculus with effects
Algebraic effect handlers are becoming an increasingly popular way of structuring effectful computations, and their performance is often a concern. One of the proposed approaches towards efficient compilation is tracking effect information through explicit subtyping coercions. However, in the presence of polymorphism, these coercions are compiled into additional arguments of compiled functions, incurring significant overhead. In this paper, we present a polymorphic effectful calculus, identify …

Monitorability for the Modal mu-Calculus over Systems with Data: From Practice to Theory
Luca Aceto, Antonis Achilleos, Duncan Paul Attard, L\'eo Exibard, Adrian Francalanza, Anna Ing\'olfsd\'ottir, Karoliina Lehtinen
https://arxiv.org/abs/2506.06172

Monitorability for the Modal mu-Calculus over Systems with Data: From Practice to Theory
Runtime verification, also known as runtime monitoring, consists of checking whether a system satisfies a given specification by observing the trace it produces during its execution. It is used as a lightweight verification technique to complement or substitute costlier methods such as model-checking. In the regular setting, Hennessy-Milner logic with recursion, a variant of the modal mu-calculus, provides a versatile formalism for expressing linear- and branching-time specifications of the c…

Replaced article(s) found for cs.PL. https://arxiv.org/list/cs.PL/new
[1/1]:
Opportunistically Parallel Lambda Calculus
https://

On a Second-Order Version of Russellian Theory of Definite Descriptions
Yaroslav Petrukhin
https://arxiv.org/abs/2508.13928 https://arxiv.org/pdf/2508.1392…

On a Second-Order Version of Russellian Theory of Definite Descriptions
Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of Russell's theory of definite descriptions. While full second-order logic is incomplete, its fragment defined by Henkin's general models admits completeness. We develop our theory within this fragment and formalize it using a cut-free sequent calculus.

Reachability is Decidable for ATM-Typable Finitary PCF with Effect Handlers
Ryunosuke Endo, Tachio Terauchi
https://arxiv.org/abs/2508.12572 https://arxiv.…

Reachability is Decidable for ATM-Typable Finitary PCF with Effect Handlers
It is well known that the reachability problem for simply-typed lambda calculus with recursive definitions and finite base-type values (finitary PCF) is decidable. A recent paper by Dal Lago and Ghyselen has shown that the same problem becomes undecidable when the language is extended with algebraic effect and handlers (effect handlers). We show that, perhaps surprisingly, the problem becomes decidable even with effect handlers when the type system is extended with answer type modification (ATM…

Efficient Model Checking for the Alternating-Time {\mu}-Calculus via Effectivity Frames
Daniel Hausmann, Merlin Humml, Simon Prucker, Lutz Schr\"oder
https://arxiv.org/abs/2506.01010

Efficient Model Checking for the Alternating-Time μ-Calculus via Effectivity Frames
The semantics of alternating-time temporal logic (ATL) and the more expressive alternating-time μ-calculus (AMC) is standardly given in terms of concurrent game frames (CGF). The information required to interpret AMC formulas is equivalently represented in terms of effectivity frames in the sense of Pauly; in many cases, this representation is more compact than the corresponding CGF, and in principle allows for faster evaluation of coalitional modalities. In the present work, we investigate wh…

Spegion: Implicit and Non-Lexical Regions with Sized Allocations
Jack Hughes, Michael Vollmer, Mark Batty
https://arxiv.org/abs/2506.02182 https://

Spegion: Implicit and Non-Lexical Regions with Sized Allocations
Region based memory management is a powerful tool designed with the goal of ensuring memory safety statically. The region calculus of Tofte and Talpin is a well known example of a region based system, which uses regions to manage memory in a stack-like fashion. However, the region calculus is lexically scoped and requires explicit annotation of memory regions, which can be cumbersome for the programmer. Other systems have addressed non-lexical regions, but these approaches typically require the…

This https://arxiv.org/abs/2505.12899 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Interpolation for the two-way modal mu-calculus
The two-way modal mu-calculus is the extension of the (standard) one-way mu-calculus with converse (backward-looking) modalities. For this logic we introduce two new sequent-style proof calculi: a non-wellfounded system admitting infinite branches and a finitary, cyclic version of this that employs annotations. As is common in sequent systems for two-way modal logics, our calculi feature an analytic cut rule. What distinguishes our approach is the use of so-called trace atoms, which serve to ap…

Cyclic proof theory of positive inductive definitions
Gianluca Curzi, Lukas Melgaard
https://arxiv.org/abs/2507.13057 https://arxiv.o…

Cyclic proof theory of positive inductive definitions
We study cyclic proof systems for $μ\mathsf{PA}$, an extension of Peano arithmetic by positive inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic $Π^1_2$-$\mathsf{CA}_0$ by Möllefeld. The main result of this paper is that cyclic and inductive $μ\mathsf{PA}$ have the same proof-theoretic strength. First, we translate cyclic proofs into an annotated variant based on Sprenger and Dam's systems for first-order $μ$-calculus, whose…

A simple formalization of alpha-equivalence
Kalmer Apinis, Danel Ahman
https://arxiv.org/abs/2507.10181 https://arxiv.org/pdf/2507.10…

A simple formalization of alpha-equivalence
While teaching untyped $λ$-calculus to undergraduate students, we were wondering why $α$-equivalence is not directly inductively defined. In this paper, we demonstrate that this is indeed feasible. Specifically, we provide a grounded, inductive definition for $α$-equivalence and show that it conforms to the specification provided in the literature. The work presented in this paper is fully formalized in the Rocq Prover.

Pebble Games and Algebraic Proof Systems
Lisa-Marie Jaser, Jacobo Toran
https://arxiv.org/abs/2506.21149 https://arxiv.org/pdf/2506.2…

Pebble Games and Algebraic Proof Systems
Analyzing refutations of the well known 0pebbling formulas Peb$(G)$ we prove some new strong connections between pebble games and algebraic proof system, showing that there is a parallelism between the reversible, black and black-white pebbling games on one side, and the three algebraic proof systems Nullstellensatz, Monomial Calculus and Polynomial Calculus on the other side. In particular we prove that for any DAG $G$ with a single sink, if there is a Monomial Calculus refutation for Peb$(G)$…

From Partial to Monadic: Combinatory Algebra with Effects
Liron Cohen (BGU), Ariel Grunfeld (BGU), Dominik Kirst (PICUBE), \'Etienne Miquey (I2M)
https://arxiv.org/abs/2506.09453

From Partial to Monadic: Combinatory Algebra with Effects
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $λ$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of computation by only incorporating non-termination as a computational effect. To provide a framework that better internalizes a wide range of computational effects, this paper puts forward the notion of Monadic Combinatory Algebras (MCAs). MCAs generalize the notion of P…

This https://arxiv.org/abs/2405.03536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Extensional and Non-extensional Functions as Processes
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $λ$-calculus, the process representations yield (at best) non-extensional $λ$-theories (i.e., $β$ rule holds, whereas $η$ does not). In the paper, we study how to obtain extensional representations, and how to move between extensional and non-extensional representations. Using Internal $π$, $\mathrm{I}π$ (a subset of the $π$-calculus in which all outputs are boun…