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

Part of: ICFP2018

Published online by Cambridge University Press:  19 October 2021

GUILLAUME ALLAIS Open the ORCID record for GUILLAUME ALLAIS [Opens in a new window] ,
ROBERT ATKEY Open the ORCID record for ROBERT ATKEY [Opens in a new window] ,
JAMES CHAPMAN Open the ORCID record for JAMES CHAPMAN [Opens in a new window] ,
CONOR MCBRIDE Open the ORCID record for CONOR MCBRIDE [Opens in a new window]  and
JAMES MCKINNA Open the ORCID record for JAMES MCKINNA [Opens in a new window]
GUILLAUME ALLAIS
Affiliation:
University of St Andrews, St Andrews KY16 9AJ, UK (e-mail: guillaume.allais@ens-lyon.org)
ROBERT ATKEY
Affiliation:
University of Strathclyde, Glasgow G1 1XQ, UK (e-mail: robert.atkey@strath.ac.uk)
JAMES CHAPMAN
Affiliation:
Input Output HK Ltd., Edinburgh EH8 9BT, UK (e-mail: james.chapman@iohk.io)
CONOR MCBRIDE
Affiliation:
University of Strathclyde, Glasgow G1 1XQ, UK (e-mail: conor.mcbride@strath.ac.uk)
JAMES MCKINNA
Affiliation:
Heriot-Watt University, Edinburgh EH14 4AS, UK (e-mail: J.McKinna@hw.ac.uk)
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Abstract

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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.

Type
Research Article
Information
Journal of Functional Programming , Volume 31 , 2021 , e22
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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