Abstract

This paper presents GMETA: a generic framework for first-order representations of variable binding that provides once and for all many of the so-called infrastructure lemmas and definitions required in mechanizations of formal metatheory. The framework employs datatype-generic programming and modular programming techniques to provide a universe representing a family of datatypes. This universe is generic in two different ways: it is language-generic in the sense that several object languages can be represented within the universe; and it is representation-generic, meaning that it is parameterizable over the particular choice of firstorder representations for binders (for example, locally nameless or de Bruijn). Using this universe, several libraries providing generic infrastructure lemmas and definitions are implemented. These libraries are used in case studies based on the POPLmark challenge, showing that dealing with challenging binding constructs, like the ones found in System F<:, is possible with GMETA. All of GMETA’s generic infrastructure is implemented in the Coq theorem prover, ensuring the soundness of that infrastructure. Furthermore, due to GMETA’s modular design, the libraries can be easily used, extended and customized by end users. 1.

Citations