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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…

Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…

Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…

It is well known in the Constraint Programming community that any non-binary constraint satisfaction problem (with finite domains) can be transformed into an equivalent binary one. One of the most well-known translations is the Hidden…

This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…

We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…

Immediate feedback has been shown to improve student learning. In programming courses, immediate, automated feedback is typically provided in the form of pre-defined test cases run by a submission platform. While these are excellent for…

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…

Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of…

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…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…

Automatically generated code is gaining traction recently, owing to the prevalence of Large Language Models (LLMs). Further, the AlphaProof initiative has demonstrated the possibility of using AI for general mathematical reasoning.…

In a previous work De Luca and Luna presented formal specifications of idealized formulations of the permission model of Android in the Coq proof assistant. This formal development is about 23 KLOC of Coq code, including proofs. This work…

We show how to extract a monotonic learning algorithm from a classical proof of a geometric statement by interpreting the proof by means of interactive realizability, a realizability sematics for classical logic. The statement is about the…

We aim to increase the flexibility at which a data worker can choose the right tool for the job, regardless of whether the tool is a code library or an interactive graphical user interface (GUI). To achieve this flexibility, we extend…

Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy…

Program verifiers for imperative languages such as C may be annotation-based, in which assertions and invariants are put into source files and then checked, or tactic-based, where proof scripts separate from programs are interactively…

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…