Prototyping a Scalable Proof Engine

Abstract

Formal verification is an exciting development in software engineering, enabling implementations of programs to be rigorously checked against mathematical specifications. Assuming the specification is well-defined, formal verification provides guarantees of a program’s correctness and freedom from bugs that are simply not possible with test-based methods. There’s just one catch: the process of verifying large programs in popular theorem provers such as Coq (now known as Rocq) or Lean is painfully slow. These proof assistants rely on proof engines to construct proofs of correctness for given properties, but to our knowledge, there is no widely available proof engine that offers strong performance guarantees. Even more frustrating is the lack of consensus on what “good” performance should even mean in this context. This thesis lays the groundwork for addressing that gap by presenting a proof engine design that achieves asymptotically linear-time performance with respect to several important variables. We illustrate the design and its performance characteristics with examples from an implementation of the design and outline directions for future work.