Conversion of HOL Light proofs into Metamath

Journal of Formalized Reasoning

Mario M Carneiro

关键词: metamath;    opentheory;    hol light;    proof translation;    formalization;    algorithms;   

DOI  :  10.6092/issn.1972-5787/4596

学科分类：计算机科学（综合）

来源: Universita degli Studi di Bologna

【 摘 要 】

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, hol.mm, followed by the embedding of the HOL formalization into the main ZFC foundations of the main Metamath library, 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.

【 授权许可】

CC BY