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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…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Large language models (LLMs) can potentially help with verification using proof assistants by automating proofs. However, it is unclear how effective LLMs are in this task. In this paper, we perform a case study based on two mature Rocq…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
We present a novel characterization of stable mergesort functions using relational parametricity, and show that it implies the functional correctness of mergesort. As a result, one can prove the correctness of several variations of…
Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…
One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
Choreographic programming is a paradigm for writing coordination plans for distributed systems from a global point of view, from which correct-by-construction decentralised implementations can be generated automatically. Theory of…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Applying Gr\"obner basis theory to concrete problems in Lean 4 remains difficult since the current formalization of multivariate polynomials is based on a non-computable representation and is therefore not suitable for efficient symbolic…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…