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How to prove type soundness of Java-like languages without forgoing big-step semantics

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Davide AnconaAuthors Info & Claims

FTfJP'14: Proceedings of 16th Workshop on Formal Techniques for Java-like Programs

Pages 1 - 6

https://doi.org/10.1145/2635631.2635846

Published: 28 July 2014 Publication History

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Abstract

Small-step operational semantics is the most commonly employed formalism for proving type soundness of statically typed programming languages, because of its ability to distinguish stuck from non-terminating computations, as opposed to big-step operational semantics.

Despite this, big-step operational semantics is more abstract, and more useful for specifying interpreters.

In previous work we have proposed a new proof technique to prove type soundness of a Java-like language expressed in terms of its big-step operational semantics. However the presented proof is rather involved, since it requires showing that the set of proof trees defining the semantic judgment forms a complete metric space when equipped with a specific distance function.

In this paper we propose a more direct and abstract approach that exploits a standard and general compactness property of the metric space of values, that allows approximation of the coinductive big-step semantics in terms of the small-step one; in this way type soundness can be proved by standard mathematical induction.

References

[1]

D. Ancona. Soundness of Object-Oriented Languages with Coinductive Big-Step Semantics. In J. Noble, editor, ECOOP 2012 - Object-Oriented Programming, volume 7313, pages 459--483. Springer, 2012.

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[2]

D. Ancona and A. Corradi. Sound and complete subtyping between coinductive types for object-oriented languages. In ECOOP 2014 - Object-Oriented Programming, 2014. To appear.

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[3]

A. Arnold and M. Nivat. The metric space of infinite trees. Algebraic and topological properties. Fundamenta Informaticae, 3:445--476, 1980.

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A. Igarashi, B. C. Pierce, and P. Wadler. Featherweight Java: a minimal core calculus for Java and GJ. ACM Transactions on Programming Languages and Systems, 23(3):396--450, 2001.

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X. Leroy and H. Grall. Coinductive big-step operational semantics. Information and Computation, 207:284--304, 2009.

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Cited By

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Dagnino F(2022)A Meta-theory for Big-step SemanticsACM Transactions on Computational Logic10.1145/352272923:3(1-50)Online publication date: 6-Apr-2022
https://dl.acm.org/doi/10.1145/3522729
Ancona DDagnino FRot JZucca E(2020)A Big Step from Finite to Infinite ComputationsScience of Computer Programming10.1016/j.scico.2020.102492(102492)Online publication date: Jun-2020
https://doi.org/10.1016/j.scico.2020.102492
Dagnino FBono VZucca EDezani-Ciancaglini M(2020)Soundness Conditions for Big-Step SemanticsProgramming Languages and Systems10.1007/978-3-030-44914-8_7(169-196)Online publication date: 18-Apr-2020
https://doi.org/10.1007/978-3-030-44914-8_7
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Index Terms

How to prove type soundness of Java-like languages without forgoing big-step semantics
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
2. Theory of computation
  1. Semantics and reasoning
    1. Program semantics

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Published In

FTfJP'14: Proceedings of 16th Workshop on Formal Techniques for Java-like Programs

July 2014

33 pages

ISBN:9781450328661

DOI:10.1145/2635631

Program Chair:
David J. Pearce
Victoria University of Wellington, New Zealand

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Published: 28 July 2014

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ECOOP '14

ECOOP '14: European Conference on Object-Oriented Programming

July 28 - August 1, 2014

Uppsala, Sweden

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FTfJP'14 Paper Acceptance Rate 5 of 8 submissions, 63%;

Overall Acceptance Rate 51 of 75 submissions, 68%

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Dagnino F(2022)A Meta-theory for Big-step SemanticsACM Transactions on Computational Logic10.1145/352272923:3(1-50)Online publication date: 6-Apr-2022
https://dl.acm.org/doi/10.1145/3522729
Ancona DDagnino FRot JZucca E(2020)A Big Step from Finite to Infinite ComputationsScience of Computer Programming10.1016/j.scico.2020.102492(102492)Online publication date: Jun-2020
https://doi.org/10.1016/j.scico.2020.102492
Dagnino FBono VZucca EDezani-Ciancaglini M(2020)Soundness Conditions for Big-Step SemanticsProgramming Languages and Systems10.1007/978-3-030-44914-8_7(169-196)Online publication date: 18-Apr-2020
https://doi.org/10.1007/978-3-030-44914-8_7
Ancona DDagnino FZucca E(2017)Reasoning on divergent computations with coaxiomsProceedings of the ACM on Programming Languages10.1145/31339051:OOPSLA(1-26)Online publication date: 12-Oct-2017
https://dl.acm.org/doi/10.1145/3133905
Ancona DDagnino FZucca E(2017)Generalizing Inference Systems by CoaxiomsProgramming Languages and Systems10.1007/978-3-662-54434-1_2(29-55)Online publication date: 19-Mar-2017
https://doi.org/10.1007/978-3-662-54434-1_2
Ancona DFrassetto FMonahan R(2015)A three-valued type system for true positives detection in Java-like languagesProceedings of the 17th Workshop on Formal Techniques for Java-like Programs10.1145/2786536.2786539(1-7)Online publication date: 7-Jul-2015
https://dl.acm.org/doi/10.1145/2786536.2786539

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Coinductive big-step operational semantics

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