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In this paper we model discontinuous extended real functions in pointfree topology following a lattice-theoretic approach, in such a way that, if $L$ is a subfit frame, arbitrary extended real functions on $L$ are the elements of the…
Refactoring tools are central to modern development, with extract-function refactorings used heavily in day-to-day work. For Rust, however, ownership, borrowing, and advanced type features make automated extract-function refactoring…
Higher-order recursion schemes are a higher-order analogue of Boolean Programs; they form a natural class of abstractions for functional programs. We present a new, efficient algorithm for checking CTL properties of the trees generated by…
We implement extraction of Coq programs to functional languages based on MetaCoq's certified erasure. We extend the MetaCoq erasure output language with typing information and use it as an intermediate representation, which we call…
We propose the first steps in the development of a tool to automate the translation of Redex models into a (hopefully) semantically equivalent model in Coq, and to provide tactics to help in the certification of fundamental properties of…
Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from…
We report the current status of RBCK calculations on nucleon structure with both quenched and unquenched lattice QCD. The combination of domain wall fermions and DBW2 gauge action works well for isovector vector and axial charges, and…
For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y, where special attention is paid to spaces of vector-valued bounded continuous…
Motivated by experience in programming and in the teaching of programming, we make another assault on the longstanding problem of debugging. Having explored why debuggers are not used as widely as one might expect, especially in functional…
The proliferation of decentralized financial (DeFi) systems and smart contracts has underscored the critical need for software correctness. Bugs in such systems can lead to catastrophic financial losses. Formal verification offers a path to…
We consider the refined topological vertex of Iqbal et al, as a function of two parameters (x, y), and deform it by introducing Macdonald parameters (q, t), as in the work of Vuletic on plane partitions, to obtain 'a Macdonald refined…
We give a controllable energy-preserving and an observable co-energy-preserving de Branges-Rovnyak functional model realization of an arbitrary given operator Schur function defined on the complex right-half plane. We work the theory out…
Real-time execution is essential for cyber-physical systems such as robots. These systems operate in dynamic real-world environments where even small delays can undermine responsiveness and compromise performance. Asynchronous inference has…
The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of…
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau…
We present a solution of the operator-valued Schur-function realization problem on the right-half plane by developing the corresponding de Branges-Rovnyak canonical conservative simple functional model. This model corresponds to the closely…
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the…
In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of…
We initiate and study the theory of ``real decomposable maps" between real operator systems. Formally, this is new even in the complex case, which hitherto has restricted itself to the case where the systems are complex C*-algebras. We…