DSLean: A Framework for Type-Correct Interoperability Between Lean 4 and External DSLs

2026-02-20

AI Summary

This work addresses the challenges of integrating external domain-specific languages (DSLs) into interactive proof assistants—namely, the tedious, type-unsafe, and error-prone nature of expression translation. We propose DSLean, a framework built on Lean 4’s metaprogramming system that enables type-safe, bidirectional translation between external DSLs and their Lean equivalents through declarative syntax definitions. DSLean introduces a lightweight, syntax-directed bidirectional transformation mechanism coupled with type-driven semantic alignment, substantially reducing the integration overhead for external automated reasoning tools. We demonstrate the framework’s generality and practicality by successfully connecting solvers for interval arithmetic, ordinary differential equations, and ideal membership in polynomial rings, showcasing its effectiveness across diverse domains.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Domain-specific languages (DSLs) mediate interactions between interactive proof assistants and external automation, but translating between the prover's internal representation and such DSLs is a tedious engineering chore. To simplify this task, we present DSLean, a framework for bidirectional translation between expressions in the Lean proof assistant and external syntax. DSLean requires only a specification of an external language and its Lean equivalents, abstracting away meta-level implementation details. We demonstrate DSLean's capabilities by implementing three new automation tactics, providing access to external solvers for interval arithmetic, ordinary differential equations, and ring ideal membership.

Problem

• interoperability
• domain-specific languages
• proof assistants
• type correctness
• translation

Innovation

• DSLean
• bidirectional translation
• type-correct interoperability
• external DSLs
• Lean 4