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Type soundness proofs with definitional interpreters

Authors:

Tiark RompfAuthors Info & Claims

ACM SIGPLAN Notices, Volume 52, Issue 1

Pages 666 - 679

https://doi.org/10.1145/3093333.3009866

Published: 01 January 2017 Publication History

Abstract

While type soundness proofs are taught in every graduate PL class, the gap between realistic languages and what is accessible to formal proofs is large. In the case of Scala, it has been shown that its formal model, the Dependent Object Types (DOT) calculus, cannot simultaneously support key metatheoretic properties such as environment narrowing and subtyping transitivity, which are usually required for a type soundness proof. Moreover, Scala and many other realistic languages lack a general substitution property.

The first contribution of this paper is to demonstrate how type soundness proofs for advanced, polymorphic, type systems can be carried out with an operational semantics based on high-level, definitional interpreters, implemented in Coq. We present the first mechanized soundness proofs in this style for System F and several extensions, including mutable references. Our proofs use only straightforward induction, which is significant, as the combination of big-step semantics, mutable references, and polymorphism is commonly believed to require coinductive proof techniques.

The second main contribution of this paper is to show how DOT-like calculi emerge from straightforward generalizations of the operational aspects of F, exposing a rich design space of calculi with path-dependent types inbetween System F and DOT, which we dub the System D Square.

By working directly on the target language, definitional interpreters can focus the design space and expose the invariants that actually matter at runtime. Looking at such runtime invariants is an exciting new avenue for type system design.

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Cited By

Rajić GSruk V(2024)Definitions and Computational Properties of OCL: A Systematic ReviewIEEE Access10.1109/ACCESS.2024.342886512(99704-99738)Online publication date: 2024
https://doi.org/10.1109/ACCESS.2024.3428865
Zhou LZhou YOliveira B(2023)Recursive Subtyping for AllProceedings of the ACM on Programming Languages10.1145/35712417:POPL(1396-1425)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571241
Blaudeau CLiu F(2022)A conceptual framework for safe object initialization: a principled and mechanized soundness proof of the Celsius modelProceedings of the ACM on Programming Languages10.1145/35633146:OOPSLA2(729-757)Online publication date: 31-Oct-2022
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Index Terms

Type soundness proofs with definitional interpreters
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 52, Issue 1

POPL '17

January 2017

901 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/3093333

Editor:
Matthew Fluet

Issue’s Table of Contents

POPL '17: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages
January 2017
901 pages
ISBN:9781450346603
DOI:10.1145/3009837
General Chair:
Giuseppe Castagna
Paris Diderot University, France / CNRS, France
,
Program Chair:
Andrew D. Gordon
Microsoft Research, UK / University of Edinburgh, UK

Copyright © 2017 ACM.

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Published: 01 January 2017

Published in SIGPLAN Volume 52, Issue 1

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https://doi.org/10.1109/ACCESS.2024.3428865
Zhou LZhou YOliveira B(2023)Recursive Subtyping for AllProceedings of the ACM on Programming Languages10.1145/35712417:POPL(1396-1425)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571241
Blaudeau CLiu F(2022)A conceptual framework for safe object initialization: a principled and mechanized soundness proof of the Celsius modelProceedings of the ACM on Programming Languages10.1145/35633146:OOPSLA2(729-757)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563314
Liu FLhoták OXing EPham NRichard-Foy JDoeraene S(2021)Safe object initialization, abstractlyProceedings of the 12th ACM SIGPLAN International Symposium on Scala10.1145/3486610.3486895(33-43)Online publication date: 17-Oct-2021
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Feitosa SRibeiro RCavalcante EDantas FBatista T(2020)An Intrinsically-Typed Solution for the List-Machine BenchmarkProceedings of the 24th Brazilian Symposium on Context-Oriented Programming and Advanced Modularity10.1145/3427081.3427082(1-8)Online publication date: 19-Oct-2020
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Feitosa SMena ARibeiro RBois A(2019)An Inherently-Typed Formalization for Featherweight JavaProceedings of the XXIII Brazilian Symposium on Programming Languages10.1145/3355378.3355385(11-18)Online publication date: 23-Sep-2019
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