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arXiv · 2605.20054

Automating proof search when equality is a logical connective

Kaustuv Chaudhuri·Arunava Gantait·Dale Miller
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Abstract

Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the derivation of core mathematical principles, such as Peano's axioms (excluding induction), and serves as a foundation for the Abella interactive proof assistant. However, integrating this equality into automated proof search remains challenging. We present a proof search procedure that extends unification to handle the complexities of quantifier alternation and equations that occur in both positive and negative occurrences. While established logical frameworks such as $λ$Prolog and LF lack direct support for this kind of equality, our procedure enables a lightweight logical framework that addresses this gap. Our system enables unification-aware proof search across a diverse range of first-order sequent calculi that can directly use this form of equality.

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Kaustuv Chaudhuri, Arunava Gantait, Dale Miller. 2026-05-19. Automating proof search when equality is a logical connective. https://arxiv.org/abs/2605.20054

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