Proof-Producing Reflection for HOL

With an Application to Model Polymorphism
  • Benja Fallenstein
  • Ramana Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9236)


We present a reflection principle of the form “If \(\ulcorner \varphi \urcorner \) is provable, then \(\varphi \)” implemented in the HOL4 theorem prover, assuming the existence of a large cardinal. We use the large-cardinal assumption to construct a model of HOL within HOL, and show how to ensure \(\varphi \) has the same meaning both inside and outside of this model. Soundness of HOL implies that if \(\ulcorner \varphi \urcorner \) is provable, then it is true in this model, and hence \(\varphi \) holds. We additionally show how this reflection principle can be extended, assuming an infinite hierarchy of large cardinals, to implement model polymorphism, a technique designed for verifying systems with self-replacement functionality.



We thank Magnus Myreen for feedback on a draft of this paper. We also thank the anonymous reviewers for their helpful criticism.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Machine Intelligence Research InstituteBerkeleyUSA
  2. 2.Computer LaboratoryUniversity of CambridgeCambridgeUK

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