Related papers: Safe, Fast, Concurrent Proof Checking for the lamb…
Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
Notebooks provide an author-friendly environment for iterative development, modular execution, and easy sharing. Distributed workflows are increasingly being authored and executed in notebooks, yet sharing and reproducing them remains…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
Static code analysis tools are designed to aid software developers to build better quality software in less time, by detecting defects early in the software development life cycle. Even the most experienced developer regularly introduces…
We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the insertion of double negations. Recently, Brown and Rizkallah extended this translation to higher-order logic. In this paper, we adapt it for…
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
The complexity and size increase of software has extended the delay for developers as they wait for code analysis and code merge. With the larger and more complex software, more developers nowadays are developing software with large source…
Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…
A Learning Model Predictive Controller (LMPC) for linear system in presented. The proposed controller is an extension of the LMPC [1] and it aims to decrease the computational burden. The control scheme is reference-free and is able to…
Cycle-accurate software simulation of multicores with complex microarchitectures is often excruciatingly slow. People use simplified core models to gain simulation speed. However, a persistent question is to what extent the results derived…
New trends towards multiple core processors imply using standard programming models to develop efficient, reliable and portable programs for distributed memory multiprocessors and workstation PC clusters. Message passing using MPI is widely…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
Parallel decoding methods such as Jacobi decoding show promise for more efficient LLM inference as it breaks the sequential nature of the LLM decoding process and transforms it into parallelizable computation. However, in practice, it…
Parametricity allows the transfer of proofs between different implementations of the same data structure. The lambdaPi-calculus modulo theory is an extension of the lambda-calculus with dependent types and user-defined rewrite rules. It is…
Making threaded programs safe and easy to reason about is one of the chief difficulties in modern programming. This work provides an efficient execution model for SCOOP, a concurrency approach that provides not only data race freedom but…