A type- and scope-safe universe of syntaxes with binding: their semantics and proofs

Guillaume Allais, Robert Atkey, James Chapman, Conor McBride, James McKinna

Research output: Contribution to journalArticlepeer-review


The syntax of almost every programming language includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of α-equivalence, capture-avoiding substitution, typing contexts, runtime environments, and so on. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. Modern programming languages include features that enable constraints like scope safety to be expressed in types. Nevertheless, the programmer is still forced to write the same boilerplate over again for each new implementation of a scope-safe operation (e.g., renaming, substitution, desugaring, printing), and then again for correctness proofs. We present an expressive universe of syntaxes with binding and demonstrate how to (1) implement scope-safe traversals once and for all by generic programming; and (2) how to derive properties of these traversals by generic proving. Our universe description, generic traversals and proofs, and our examples have all been formalised in Agda and are available in the accompanying material available online at https://github.com/gallais/generic-syntax.
Original languageEnglish
Article numbere22
Number of pages55
JournalJournal of Functional Programming
Early online date19 Oct 2021
Publication statusPublished - 19 Oct 2021


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