Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in
various fields, including science, engineering, finance, and everyday life. The development …

Advanced knowledge engineering (KE), represented by knowledge graph (KG), drives the
development of various fields and engineering technologies and provides various …

Proof-carrying code (PCC) is a framework for mechanically verifying the safety of machine
language programs. A program that is successfully verified by a PCC system is guaranteed …

We present a model of recursive and impredicatively quantified types with mutable
references. We interpret in this model all of the type constructors needed for typed …

In learning-assisted theorem proving, one of the most critical challenges is to generalize to
theorems unlike those seen at training time. In this paper, we introduce INT, an INequality …

Intel is applying formal verification to various pieces of mathematical software used in
Merced, the first implementation of the new IA-64 architecture. This paper discusses the …

Autoformalization is the task of translating natural language materials into machine-
verifiable formalisations. Progress in autoformalization research is hindered by the lack of a …

Generative AI has shown its values for many software engineering tasks. Still in its infancy,
large language model (LLM)-based proof generation lags behind LLM-based code …

We introduce a language based upon lambda calculus with products, coproducts and strictly
positive inductive types that allows the definition of recursive terms. We present the …

A formalisation of π-calculus in the Coq system is presented. Based on a de Bruijn notation
for names, our implementation exploits the mechanisation of some proof techniques …