Extensible Metatheory Mechanization via Family Polymorphism

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