arXiv:2602.18767v3 Announce Type: replace-cross Abstract: In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a statement in a proof assistant. In this work, we introduce several novel concepts and capabilities to address obstacles faced by machine-assisted theorem proving. We first present a set of \textbf{atomic tactics}, a small finite set of tactics capable of proving any provable statement in Lean. We then introduce a \textbf{transposing atomization} algorithm which turns arbitrary proof expressions into a series o
The accelerating pace of AI research in theorem proving and formal verification makes this development timely, as researchers seek more efficient and robust methods for proof automation.
This work introduces atomic tactics and automation algorithms that could significantly enhance the capabilities of machine-assisted theorem proving, expanding the scope and reliability of formal verification.
The ability to atomize proofs into smaller, universal components and automatically construct proofs from them could lead to more scalable and generalizable AI-driven theorem provers.
- · Formal verification software developers
- · AI research in theorem proving
- · Lean 4 ecosystem
- · High-assurance software engineering
- · Manual theorem proving tasks
- · Less efficient proof automation methods
More complex software and hardware systems could be formally verified with greater ease and speed.
Increased adoption of formal methods could lead to higher standards of reliability and security in critical infrastructure.
The abstraction of proofs into atomic tactics might inspire similar breakthroughs in other AI reasoning domains, accelerating general AI capabilities.
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Read at arXiv cs.LG