Certified compilers are complex software systems. Like other large systems, they demand modular, extensible designs. While there has been progress in extensible metatheory mechanization, scaling extensibility and reuse to meet the demands of full compiler verification remains a major challenge. We respond to this challenge by introducing novel expressive power to a proof language. Our language design equips the Rocq prover with an extensibility mechanism inspired by the object-oriented ideas of late binding, mixin composition, and family polymorphism. We implement our design as a plugin for Rocq, called Rocqet. We identify strategies for using Rocqet’s new expressive power to modularize the monolithic design of large certified developments as complex as the CompCert compiler. The payoff is a high degree of modularity and reuse in the formalization of intermediate languages, ISAs, compiler transformations, and compiler extensions, with the ability to compose these reusable components—certified compilers à la carte. We report significantly improved proof-compilation performance compared to earlier work on extensible metatheory mechanization. We also report good performance of the extracted compiler.

With the growing practice of mechanizing language metatheories, it has become ever more pressing that interactive theorem provers make it easy to write reusable, extensible code and proofs. This paper presents a novel language design geared towards extensible metatheory mechanization in a proof assistant. The new design achieves reuse and extensibility via a form of family polymorphism, an object-oriented idea, that allows code and proofs to be polymorphic to their enclosing families. Our development addresses technical challenges that arise from the underlying language of a proof assistant being simultaneously functional, dependently typed, a logic, and an interactive tool. Our results include (1) a prototypical implementation of the language design as a Coq plugin, (2) a dependent type theory capturing the essence of the language mechanism and its consistency and canonicity results, and (3) case studies showing how the new expressiveness naturally addresses real programming challenges in metatheory mechanization.