Bindings as Bounded Natural Functors

Abstract : the Romanian Academy, Romania DMITRIY TRAYTEL, ETH Zürich, Switzerland 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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Proceedings of the ACM on Programming Languages, ACM, 2019, 3 (POPL), pp.1-34. 〈10.1145/3290335〉
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Jasmin Christian Blanchette, Lorenzo Gheri, Andrei Popescu, Dmitriy Traytel. Bindings as Bounded Natural Functors. Proceedings of the ACM on Programming Languages, ACM, 2019, 3 (POPL), pp.1-34. 〈10.1145/3290335〉. 〈hal-01989726〉

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