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European Conference on Object-Oriented Programming

ECOOP 2012: ECOOP 2012 – Object-Oriented Programming pp 459–483Cite as

Soundness of Object-Oriented Languages with Coinductive Big-Step Semantics

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7313))

Abstract

It is well known that big-step operational semantics are not suitable for proving soundness of type systems, because of their inability to distinguish stuck from non-terminating computations. We show how this problem can be solved by interpreting coinductively the rules for the standard big-step operational semantics of a Java-like language, thus making the claim of soundness more intuitive: whenever a program is well-typed, its coinductive operational semantics returns a value.

Indeed, coinduction allows non-terminating computations to return values; this is proved by showing that the set of proof trees defining the semantic judgment forms a complete metric space when equipped with a proper distance function.

In this way, we are able to prove soundness of a nominal type system w.r.t. the coinductive semantics. Since the coinductive semantics is sound w.r.t. the usual small-step operational semantics, the standard claim of soundness can be easily deduced.

This work has been partially supported by MIUR DISCO - Distribution, Interaction, Specification, Composition for Object Systems. I would like to thank Erik Ernst for his useful comments and suggestions; many thanks also to Sophia Drossopoulou, Atsushi Igarashi, Alan Mycroft and Elena Zucca for all their useful suggestions and questions.

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Author information

Authors and Affiliations

  1. DISI, Università di Genova, Italy

    Davide Ancona

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  1. Davide Ancona
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Editors and Affiliations

  1. School of Engineering and Computer Science, Victoria University of Wellington, 6140, Wellington, New Zealand

    James Noble

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Ancona, D. (2012). Soundness of Object-Oriented Languages with Coinductive Big-Step Semantics. In: Noble, J. (eds) ECOOP 2012 – Object-Oriented Programming. ECOOP 2012. Lecture Notes in Computer Science, vol 7313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31057-7_21

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  • DOI: https://doi.org/10.1007/978-3-642-31057-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31056-0

  • Online ISBN: 978-3-642-31057-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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