Proof-Producing Reflection for HOL - With an Application to Model Polymorphism

We present a reflection principle of the form “If pφq is provable, then φ” 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 φ has the same meaning both inside and outside of this model. Soundness of HOL implies that if pφq is provable, then it is true in this model, and hence φ 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.