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[2602.18844] When Agda met Vampire
Summary
The paper discusses integrating proof assistants like Agda with automated theorem provers (ATPs) to enhance automation in mechanized mathematics while preserving correctness.
Why It Matters
This research addresses the challenges of automating proof assistants, which are crucial for verified software development. By simplifying the integration with ATPs, the authors propose a method that could significantly enhance the efficiency of formal verification processes, making them more accessible to developers.
Key Takeaways
- Integration of Agda with ATP Vampire improves automation in proof assistance.
- The approach maintains correctness guarantees while simplifying implementation.
- Prototype successfully derives complex proofs, reducing development time significantly.
- Methodology is expected to extend to other ATPs and proof assistants.
- Addresses a key gap in the automation of dependently-typed proof systems.
Computer Science > Logic in Computer Science arXiv:2602.18844 (cs) [Submitted on 21 Feb 2026] Title:When Agda met Vampire Authors:Artjoms Šinkarovs, Michael Rawson View a PDF of the paper titled When Agda met Vampire, by Artjoms \v{S}inkarovs and 1 other authors View PDF Abstract:Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the situation by integrating proof assistants with automated theorem provers (ATPs) in a simple way, while preserving the correctness guarantees of the former. A central difficulty arises from the fact that most ATPs operate in classical first-order logic, whereas these proof assistants are grounded in constructive dependent type theory. We identify an expressive fragment of both languages -- essentially equational Horn -- that admits sound, straightforward translations in both directions. The approach produces a prototype system for Agda forwarding proof obligations to the ATP Vampire, then transforming the resulting classical proof into a constructive proof term that Agda can type-check. The prototype automatically derives proofs concerning the properties of a complex field equipped with roots of unity, which took professional Agda developers two full days to complete. The required engineering effort is modest, and we anticipate that the methodology will extend read...
