Bindings as bounded natural functors

Blanchette, Jasmin Christian, Gheri, Lorenzo, Popescu, Andrei and Traytel, Dmitriy (2019) Bindings as bounded natural functors. Proceedings of the ACM on Programming Languages, Volume 3 Issue POPL. In: 46th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2019), 13-19 Jan 2019, Hotel Cascais Miragem, Cascais, Portugal. . ISSN 2475-1421 [Conference or Workshop Item] (doi:10.1145/3290335)

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Abstract

We present a general framework for specifying and reasoning about syntax with bindings. Abstract binder types are modeled using a universe of functors on sets, subject to a number of operations that can be used to construct complex binding patterns and binding-aware datatypes, including non-well-founded and infinitely branching types, in a modular fashion. Despite not committing to any syntactic format, the framework is “concrete” enough to provide definitions of the fundamental operators on terms (free variables, alpha-equivalence, and capture-avoiding substitution) and reasoning and definition principles. This work is compatible with classical higher-order logic and has been formalized in the proof assistant Isabelle/HOL.

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