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arXiv · 2605.00295

Polymorphism Meets DHOL

Rhea Ranalter·Florian Rabe·Cezary Kaliszyk
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Abstract

DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory. Automation support is obtained by translating DHOL to HOL, for which powerful modern automated theorem provers are available. However, a critically missing feature of DHOL is polymorphism. We develop the syntax and semantics of polymorphic DHOL and extend the translation accordingly. We implement the translation in the logic-embedding tool and evaluate it on a range of TPTP formalizations. The logic-embedding tool, together with an off-the-shelf HOL theorem prover easily creates a PDHOL theorem prover for experimenting.

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Rhea Ranalter, Florian Rabe, Cezary Kaliszyk. 2026-04-30. Polymorphism Meets DHOL. https://arxiv.org/abs/2605.00295

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