article

Occurrence typing modulo theories

Authors:

Andrew M. Kent,

Sam Tobin-HochstadtAuthors Info & Claims

ACM SIGPLAN Notices, Volume 51, Issue 6

Pages 296 - 309

https://doi.org/10.1145/2980983.2908091

Published: 02 June 2016 Publication History

Abstract

We present a new type system combining occurrence typing---a technique previously used to type check programs in dynamically-typed languages such as Racket, Clojure, and JavaScript---with dependent refinement types. We demonstrate that the addition of refinement types allows the integration of arbitrary solver-backed reasoning about logical propositions from external theories. By building on occurrence typing, we can add our enriched type system as a natural extension of Typed Racket, reusing its core while increasing its expressiveness. The result is a well-tested type system with a conservative, decidable core in which types may depend on a small but extensible set of program terms. In addition to describing our design, we present the following: a formal model and proof of correctness; a strategy for integrating new theories, with specific examples including linear arithmetic and bitvectors; and an evaluation in the context of the full Typed Racket implementation. Specifically, we take safe vector operations as a case study, examining all vector accesses in a 56,000 line corpus of Typed Racket programs. Our system is able to prove that 50% of these are safe with no new annotations, and with a few annotations and modifications we capture more than 70%.

References

[1]

Esteban Allende, Oscar Callau, Johan Fabry, Éric Tanter, and Marcus Denker. Gradual Typing for Smalltalk. Science of Computer Programming, 2014.

Digital Library

[2]

Ambrose Bonnaire-Sergeant, Rowan Davies, and Sam Tobin-Hochstadt. Practical Optional Types for Clojure. In Proc. ESOP, 2016.

[3]

Chiyan Chen and Hongwei Xi. Combining Programming with Theorem Proving. In Proc. ICFP, 2005.

Digital Library

[4]

Ravi Chugh, David Herman, and Ranjit Jhala. Dependent Types for Javascript. In Proc. OOPSLA, 2012.

Digital Library

[5]

Ravi Chugh, Patrick M. Rondon, and Ranjit Jhala. Nested Refinements: A Logic for Duck Typing. In Proc. POPL, 2012.

Digital Library

[6]

Microsoft Co. Typescript Language Specification. http: //www.typescriptlang.org, 2014.

[7]

George B. Dantzig and B. Curtis Eaves. Fourier-Motzkin Elimination and Its Dual. J. Combinatorial Theory Series A, 1973.

[8]

Leonardo De Moura and Nikolaj Bjorner. Z3: An Efficient SMT Solver. In Proc. TACAS, 2008.

Digital Library

[9]

Matthias Felleisen, Robert Bruce Findler, and Matthew Flatt. Semantics Engineering with PLT Redex. MIT Press, 2009.

Digital Library

[10]

Matthew Flatt and PLT. Reference: Racket. Technical Report PLT-TR-2010-1, PLT Design Inc., 2010.

[11]

https:// racket-lang.org/tr1.

[12]

Matthew Fluet and Riccardo Pucella. Practical Datatype Specializations with Phantom Types and Recursion Schemes. Electronic Notes in Theoretical Computer Science, 2006.

Digital Library

[13]

Michael Greenberg, Benjamin C. Pierce, and Stephanie Weirich. Contracts Made Manifest. In Proc. POPL, 2010.

Digital Library

[14]

Jessica Gronski, Kenneth Knowles, Aaron Tomb, Stephen N. Freund, and Cormac Flanagan. Sage: Hybrid Checking for Flexible Specifications. In Proc. Wksp. on Scheme and Functional Programming, 2006.

[15]

David Herman and Philippe Meunier. Improving the Static Analysis of Embedded Languages via Partial Evaluation. In Proc. ICFP, 2004.

Digital Library

[16]

Facebook Inc. Flow: A static type checker for JavaScript. http://flowtype.org, 2014.

[17]

Facebook Inc. Hack. http://hacklang.org, 2014.

[18]

Kenneth Knowles and Cormac Flanagan. Compositional Reasoning and Decidable Checking for Dependent Contract Types. In Proc. PLPV, 2009.

Digital Library

[19]

Kenneth Knowles and Cormac Flanagan. Hybrid Type Checking. ACM Trans. Program. Lang. Syst., 2010.

Digital Library

[20]

Frederic P. Miller, Agnes F. Vandome, and John McBrewster. Advanced Encryption Standard. Alpha Press, 2009.

[21]

Xinming Ou, Gang Tan, Yitzhak Mandelbaum, and David Walker. Dynamic Typing with Dependent Types. IFIP Intl. Conf. on Theoretical Computer Science, 2004.

[22]

Benjamin C. Pierce and David N. Turner. Local Type Inference. ACM Trans. Program. Lang. Syst., 2000.

Digital Library

[23]

Patrick M. Rondon, Ming Kawaguci, and Ranjit Jhala. Liquid Types. In Proc. PLDI, 2008.

Digital Library

[24]

Nikhil Swamy, Juan Chen, Cédric Fournet, Pierre-Yves Strub, Karthikeyan Bhargavan, and Jean Yang. Secure Distributed Programming with Value-dependent Types. In Proc. ICFP, 2011.

Digital Library

[25]

Nikhil Swamy, Cătălin Hriţcu, Chantal Keller, Aseem Rastogi, Antoine Delignat-Lavaud, Simon Forest, Karthikeyan Bhargavan, Cédric Fournet, Pierre-Yves Strub, Markulf Kohlweiss, Jean-Karim Zinzindohoue, and Santiago Zanella-Béguelin. Dependent Types and Multi-monadic Effects in F*. In Proc. POPL, 2016.

Digital Library

[26]

Sam Tobin-Hochstadt and Matthias Felleisen. Interlanguage Migration: From Scripts to Programs. In Proc. DLS, 2006.

[27]

Sam Tobin-Hochstadt and Matthias Felleisen. Logical Types for Untyped Languages. In Proc. ICFP, 2010.

Digital Library

[28]

Niki Vazou, Eric L. Seidel, Ranjit Jhala, Dimitrios Vytiniotis, and Simon Peyton-Jones. Refinement Types for Haskell. In Proc. ICFP, 2014.

Digital Library

[29]

Panagiotis Vekris, Benjamin Cosman, and Ranjit Jhala. Trust, but Verify: Two-Phase Typing for Dynamic Languages. In Proc. ECOOP, 2015.

[30]

Michael M. Vitousek, Andrew M. Kent, Jeremy G. Siek, and Jim Baker. Design and Evaluation of Gradual Typing for Python. In Proc. DLS, 2014.

Digital Library

[31]

Stephanie Weirich. Depending on Types. In Proc. ICFP, 2014.

Digital Library

[32]

Hongwei Xi. Dependent ML: An Approach to Practical Programming with Dependent Types. J. Functional Programming, 2007.

Digital Library

[33]

Hongwei Xi and Frank Pfenning. Eliminating Array Bound Checking Through Dependent Types. In Proc. PLDI, 1998.

Digital Library

Cited By

Webbers Rvon Gleissenthall KJhala R(2024)Refinement Type RefutationsProceedings of the ACM on Programming Languages10.1145/36897458:OOPSLA2(962-987)Online publication date: 8-Oct-2024
https://doi.org/10.1145/3689745
Rehman BTomb A(2023)Correctness-by-Construction Meets Refinement TypesProceedings of the 25th ACM International Workshop on Formal Techniques for Java-like Programs10.1145/3605156.3606449(8-10)Online publication date: 18-Jul-2023
https://dl.acm.org/doi/10.1145/3605156.3606449
Sun KChen SWang MHao D(2023)What Types Are Needed for Typing Dynamic Objects? A Python-Based Empirical StudyProgramming Languages and Systems10.1007/978-981-99-8311-7_2(24-45)Online publication date: 26-Nov-2023
https://dl.acm.org/doi/10.1007/978-981-99-8311-7_2
Show More Cited By

Index Terms

Occurrence typing modulo theories
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning

Recommendations

Occurrence typing modulo theories
PLDI '16: Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation

We present a new type system combining occurrence typing---a technique previously used to type check programs in dynamically-typed languages such as Racket, Clojure, and JavaScript---with dependent refinement types. We demonstrate that the addition of ...
Revisiting occurrence typing
Abstract
We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capture some programming patterns used in untyped languages. Although occurrence typing was tied from its inception to set-...
Sums of uncertainty: refinements go gradual
POPL '17

A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program annotated with ...

Comments

Information & Contributors

Information

Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 51, Issue 6

PLDI '16

June 2016

726 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/2980983

Editor:
Andy Gill
University of Kansas, Lawrence, KS

Issue’s Table of Contents

PLDI '16: Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation
June 2016
726 pages
ISBN:9781450342612
DOI:10.1145/2908080
General Chair:
Chandra Krintz
University of California at Santa Barbara, USA
,
Program Chair:
Emery Berger
University of Massachusetts at Amherst, USA

Copyright © 2016 ACM.

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].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 June 2016

Published in SIGPLAN Volume 51, Issue 6

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
393
Total Downloads

Downloads (Last 12 months)29
Downloads (Last 6 weeks)2

Reflects downloads up to 27 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Webbers Rvon Gleissenthall KJhala R(2024)Refinement Type RefutationsProceedings of the ACM on Programming Languages10.1145/36897458:OOPSLA2(962-987)Online publication date: 8-Oct-2024
https://doi.org/10.1145/3689745
Rehman BTomb A(2023)Correctness-by-Construction Meets Refinement TypesProceedings of the 25th ACM International Workshop on Formal Techniques for Java-like Programs10.1145/3605156.3606449(8-10)Online publication date: 18-Jul-2023
https://dl.acm.org/doi/10.1145/3605156.3606449
Sun KChen SWang MHao D(2023)What Types Are Needed for Typing Dynamic Objects? A Python-Based Empirical StudyProgramming Languages and Systems10.1007/978-981-99-8311-7_2(24-45)Online publication date: 26-Nov-2023
https://dl.acm.org/doi/10.1007/978-981-99-8311-7_2
Campora JChen S(2020)Taming type annotations in gradual typingProceedings of the ACM on Programming Languages10.1145/34282594:OOPSLA(1-30)Online publication date: 13-Nov-2020
https://doi.org/10.1145/3428259
Gilbert F(2019)Verifiable Certificates for Predicate SubtypingProgramming Languages and Systems10.1007/978-3-030-17184-1_16(440-466)Online publication date: 6-Apr-2019
https://doi.org/10.1007/978-3-030-17184-1_16
Borkowski MVazou NJhala R(2024)Mechanizing Refinement TypesProceedings of the ACM on Programming Languages10.1145/36329128:POPL(2099-2128)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632912
Castagna GLanvin VLaurent MNguyen K(2022)Revisiting occurrence typingScience of Computer Programming10.1016/j.scico.2022.102781217:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.scico.2022.102781
Jhala R(2022)Embedded Domain Specific VerifiersPrinciples of Systems Design10.1007/978-3-031-22337-2_26(535-553)Online publication date: 29-Dec-2022
https://doi.org/10.1007/978-3-031-22337-2_26
Campora JChen S(2020)Taming type annotations in gradual typingProceedings of the ACM on Programming Languages10.1145/34282594:OOPSLA(1-30)Online publication date: 13-Nov-2020
https://dl.acm.org/doi/10.1145/3428259
Serrano M(2020)JavaScript AOT compilationACM SIGPLAN Notices10.1145/3393673.327695053:8(50-63)Online publication date: 6-Apr-2020
https://dl.acm.org/doi/10.1145/3393673.3276950
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Issue’s Table of Contents