A verified runtime for a verified theorem prover

Abstract

Theorem provers, such as ACL2, HOL, Isabelle and Coq, rely on the correctness of runtime systems for programming languages like ML, OCaml or Common Lisp. These runtime systems are complex and critical to the integrity of the theorem provers. In this paper, we present a new Lisp runtime which has been formally verified and can run the Milawa theorem prover. Our runtime consists of 7,500 lines of machine code and is able to complete a 4 gigabyte Milawa proof effort. When our runtime is used to carry out Milawa proofs, less unverified code must be trusted than with any other theorem prover. Our runtime includes a just-in-time compiler, a copying garbage collector, a parser and a printer, all of which are HOL4-verified down to the concrete x86 code. We make heavy use of our previously developed tools for machine-code verification. This work demonstrates that our approach to machine-code verification scales to non-trivial applications. © 2011 Springer-Verlag.