Title
A type- and scope-safe universe of syntaxes with binding: their semantics and proofs
Abstract
The syntax of almost every programming language includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of alpha-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.
Year
DOI
Venue
2021
10.1017/S0956796820000076
JOURNAL OF FUNCTIONAL PROGRAMMING
DocType
Volume
Issue
Journal
31
1
ISSN
Citations 
PageRank 
0956-7968
0
0.34
References 
Authors
0
5
Name
Order
Citations
PageRank
Guillaume Allais100.34
Robert Atkey228919.16
James Chapman300.34
Conor McBride475247.89
James Mckinna500.34