Related papers: The Lean mathematical library
Graph representations of programs are commonly a central element of machine learning for code research. We introduce an open source Python library python_graphs that applies static analysis to construct graph representations of Python…
We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices,…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…
Almost all applications stop scaling at some point; those that don't are seldom performant when considering time to solution on anything but aspirational/unicorn resources. Recognizing these tradeoffs as well as greater user functionality…
Formalization of mathematics is the process of digitizing mathematical knowledge, which allows for formal proof verification as well as efficient semantic searches. Given the large and ever-increasing gap between the set of formalized and…
This document defines the mathematical backbone of the Statebox programming language. In the simplest way possible, Statebox can be seen as a clever way to tie together different theoretical structures to maximize their benefits and limit…
Scalar actions are ubiquitous in mathematics, and therefore it is valuable to be able to write them succinctly when formalizing. In this paper we explore how Lean 3's typeclasses are used by mathlib for scalar actions with examples,…
Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
While frontier formal mathematics systems now routinely develop repository-scale proof engineering artifacts requiring multi-file coordination and semantic correctness beyond compilation, existing evaluation benchmarks remain focused on…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
Creating fair AI systems is a complex problem that involves the assessment of context-dependent bias concerns. Existing research and programming libraries express specific concerns as measures of bias that they aim to constrain or mitigate.…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…