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Search-based testing is widely used to find bugs in models of complex Cyber-Physical Systems. Latest research efforts have improved this approach by casting it as a falsification procedure of formally specified temporal properties,…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
Cminor is a mid-level imperative programming language; there are proved-correct optimizing compilers from C to Cminor and from Cminor to machine language. We have redesigned Cminor so that it is suitable for Hoare Logic reasoning and we…
Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision…
This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism…
We present a new soundness proof of Concurrent Separation Logic (CSL) based on a structural operational semantics (SOS). We build on two previous proofs and develop new auxiliary notions to achieve the goal. One uses a denotational…
Refinement type checkers are a powerful way to reason about functional programs. For example, one can prove properties of a slow, specification implementation, porting the proofs to an optimized implementation that behaves the same. Without…
Robust modules guarantee to do only what they are supposed to do - even in the presence of untrusted, malicious clients, and considering not just the direct behaviour of individual methods, but also the emergent behaviour from calls to more…
Large Reasoning Models (LRMs) excel at complex tasks using Chain-of-Thought (CoT) reasoning. However, their tendency to overthinking leads to unnecessarily lengthy reasoning chains, dramatically increasing inference costs. To mitigate this…
Summarization refinement faces challenges when extending to multi-dimension. In this paper, we introduce ReFeed, a powerful summarization refinement pipeline that enhances multiple dimensions through reflective reasoning on feedback. To…
Separation logic adds two connectives to assertion languages: separating conjunction * ("star") and its adjoint, separating implication -* ("magic wand"). Comparatively, separating implication is less widely used. This paper demonstrates…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
Expert-level scientific reasoning remains challenging for large language models, particularly on benchmarks such as Humanity's Last Exam (HLE), where rigid tool pipelines, brittle multi-agent coordination, and inefficient test-time scaling…
This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested)…
We report on using an agentic coding assistant (Claude Code, powered by Claude Opus 4.6) to mechanize a substantial Rocq correctness proof from scratch, with human guidance but without human proof writing. The proof establishes semantic…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
The last decade has sparked several valiant efforts in deductive verification of distributed agreement protocols such as consensus and leader election. Oddly, there have been far fewer verification efforts that go beyond the core protocols…
An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure…