Computer Science as Infrastructure: the Spine of the Lean Computer Science Library (CSLib)

2026-02-16

AI Summary

This work addresses the absence of a centralized, reusable formal knowledge base in computer science, which hinders the development and verification of reliable systems. To this end, we propose CSLib—a modular formal library built on the Lean theorem prover—that enables systematic formalization of programming languages and computational models. CSLib is grounded in a unified semantic framework encompassing reduction systems and labeled transition systems, employs composable abstractions, and integrates engineering infrastructure compatible with Mathlib. The project incorporates automated proof support, continuous integration, and testing mechanisms. We have successfully established the core architecture of CSLib and completed the first formalizations of representative languages and models, thereby laying a scalable and maintainable foundation for formal computer science.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Following in the footsteps of the success of Mathlib - the centralised library of formalised mathematics in Lean - CSLib is a rapidly-growing centralised library of formalised computer science and software. In this paper, we present its founding technical principles, operation, abstractions, and semantic framework. We contribute reusable semantic interfaces (reduction and labelled transition systems), proof automation, CI/testing support for maintaining automation and compatibility with Mathlib, and the first substantial developments of languages and models.

Problem

• formalized computer science
• centralized library
• semantic framework
• proof automation
• compatibility with Mathlib

Innovation

• semantic interfaces
• proof automation
• CI/testing support
• formalized computer science
• Lean library