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Conversion of HOL Light proofs into Metamath

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arxiv 1412.8091 v2 pith:VZREWTUN submitted 2014-12-27 cs.LO math.LO

classification cs.LOmath.LO
keywords metamathlightproofsformalizationfoundationsmainmathttopentheory
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abstract

We present an algorithm for converting proofs from the OpenTheory interchange format, which can be translated to and from any of the HOL family of proof languages (HOL4, HOL Light, ProofPower, and Isabelle), into the ZFC-based Metamath language. This task is divided into two steps: the translation of an OpenTheory proof into a Metamath HOL formalization, $\mathtt{\text{hol.mm}}$, followed by the embedding of the HOL formalization into the main ZFC foundations of the main Metamath library, $\mathtt{\text{set.mm}}$. This process provides a means to link the simplicity of the Metamath foundations to the intense automation efforts which have borne fruit in HOL Light, allowing the production of complete Metamath proofs of theorems in HOL Light, while also proving that HOL Light is consistent, relative to Metamath's ZFC axiomatization.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mathematical Knowledge Bases as Grammar-Compressed Proof Terms: Exploring Metamath Proof Structures

    cs.LO 2025-05 conditional novelty 6.0 of 10

    Metamath knowledge bases can be represented as grammar-compressed proof terms, a view that supports automated lemma discovery and analysis of human versus machine proof structuring.

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