Related papers: A bi-directional extensible interface between Lean…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Mathematical formulae carry complex and essential semantic information in a variety of formats. Accessing this information with different systems requires a standardized machine-readable format that is capable of encoding presentational and…
The Edinburgh Logical Framework (LF) is a dependently type lambda calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof…
The interactive theorem prover Lean enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the…
The rapid development of artificial intelligence (AI), marked by breakthroughs like 'AlphaEvolve' and 'Gemini Deep Think', is beginning to offer powerful new tools that have the potential to significantly alter the research practice in many…
Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…
We introduce a new software toolbox for agent-based simulation. Facilitating rapid prototyping by offering a user-friendly Python API, its core rests on an efficient C++ implementation to support simulation of large-scale multi-agent…
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
Optimization is used extensively in engineering, industry, and finance, and various methods are used to transform problems to the point where they are amenable to solution by numerical methods. We describe progress towards developing a…
A multitude of agent-oriented software engineering frameworks exist, most of which are developed by the academic multi-agent systems community. However, these frameworks often impose programming paradigms on their users that are challenging…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Proof engineering is notoriously labor-intensive: proofs that are straightforward on paper often require lengthy scripts in theorem provers. Recent advances in large language models (LLMs) create new opportunities for proof automation:…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
This work presents the system ANITA (Analytic Tableau Proof Assistant) developed for teaching analytic tableaux to computer science students. The tool is written in Python and can be used as a desktop application, or in a web platform. This…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…