In this work, we formalize a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators.

This paper has been submitted to ITP 2017. A draft of the paper is available here.

A zip archive with the Isabelle formalization is available here.

Lorenzo Gheri and Andrei Popescu