research-article

Really Natural Linear Indexed Type Checking

Authors:

Arthur Azevedo de Amorim,

Marco Gaboardi,

Emilio Jesús Gallego Arias,

Justin HsuAuthors Info & Claims

IFL '14: Proceedings of the 26nd 2014 International Symposium on Implementation and Application of Functional Languages

Article No.: 5, Pages 1 - 12

https://doi.org/10.1145/2746325.2746335

Published: 01 October 2014 Publication History

Abstract

Recent works have shown the power of linear indexed type systems for enforcing complex program properties. These systems combine linear types with a language of type-level indices, allowing more fine-grained analyses. Such systems have been fruitfully applied in diverse domains, including implicit complexity and differential privacy.

A natural way to enhance the expressiveness of this approach is by allowing the indices to depend on runtime information, in the spirit of dependent types. This approach is used in DFuzz, a language for differential privacy. The DFuzz type system relies on an index language supporting real and natural number arithmetic over constants and variables. Moreover, DFuzz uses a subtyping mechanism to make types more flexible. By themselves, linearity, dependency, and subtyping each require delicate handling when performing type checking or type inference; their combination increases this challenge substantially, as the features can interact in non-trivial ways.

In this paper, we study the type-checking problem for DFuzz. We show how we can reduce type checking for (a simple extension of) DFuzz to constraint solving over a first-order theory of naturals and real numbers which, although undecidable, can often be handled in practice by standard numeric solvers.

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Cited By

Lobo-Vesga ERusso AGaboardi MCortiñas C(2024)Sensitivity by ParametricityProceedings of the ACM on Programming Languages10.1145/36897268:OOPSLA2(415-441)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689726
Kellison AHsu J(2024)Numerical Fuzz: A Type System for Rounding Error AnalysisProceedings of the ACM on Programming Languages10.1145/36564568:PLDI(1954-1978)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656456
Toro MDarais DAbuah CNear JÁrquez DOlmedo FTanter É(2023)Contextual Linear Types for Differential PrivacyACM Transactions on Programming Languages and Systems10.1145/358920745:2(1-69)Online publication date: 17-May-2023
https://dl.acm.org/doi/10.1145/3589207
Show More Cited By

Index Terms

Really Natural Linear Indexed Type Checking
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs

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IFL '14: Proceedings of the 26nd 2014 International Symposium on Implementation and Application of Functional Languages

October 2014

124 pages

ISBN:9781450332842

DOI:10.1145/2746325

Editor:
Sam Tobin-Hochstadt

Copyright © 2014 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].

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SIGPLAN: ACM Special Interest Group on Programming Languages
Northeastern University

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Published: 01 October 2014

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IFL '14

IFL '14: International Symposium on Implementation and Application of Functional Languages

October 1 - 3, 2014

MA, Boston, USA

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IFL '14 Paper Acceptance Rate 10 of 20 submissions, 50%;

Overall Acceptance Rate 19 of 36 submissions, 53%

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Cited By

Lobo-Vesga ERusso AGaboardi MCortiñas C(2024)Sensitivity by ParametricityProceedings of the ACM on Programming Languages10.1145/36897268:OOPSLA2(415-441)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689726
Kellison AHsu J(2024)Numerical Fuzz: A Type System for Rounding Error AnalysisProceedings of the ACM on Programming Languages10.1145/36564568:PLDI(1954-1978)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656456
Toro MDarais DAbuah CNear JÁrquez DOlmedo FTanter É(2023)Contextual Linear Types for Differential PrivacyACM Transactions on Programming Languages and Systems10.1145/358920745:2(1-69)Online publication date: 17-May-2023
https://dl.acm.org/doi/10.1145/3589207
wunder jAmorim ABaillot PGaboardi M(2023)Bunched Fuzz: Sensitivity for Vector MetricsProgramming Languages and Systems10.1007/978-3-031-30044-8_17(451-478)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30044-8_17
Aguirre ABarthe GHsu JKaminski BKatoen JMatheja C(2021)A pre-expectation calculus for probabilistic sensitivityProceedings of the ACM on Programming Languages10.1145/34343335:POPL(1-28)Online publication date: 4-Jan-2021
https://dl.acm.org/doi/10.1145/3434333
Chadha RSistla AViswanathan MGorla D(2021)On linear time decidability of differential privacy for programs with unbounded inputsProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470708(1-13)Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1109/LICS52264.2021.9470708
Moon BEades III HOrchard D(2021)Graded Modal Dependent Type TheoryProgramming Languages and Systems10.1007/978-3-030-72019-3_17(462-490)Online publication date: 23-Mar-2021
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Roth EZhang HHaeberlen APierce BLu SHowell J(2020)OrchardProceedings of the 14th USENIX Conference on Operating Systems Design and Implementation10.5555/3488766.3488826(1065-1081)Online publication date: 4-Nov-2020
https://dl.acm.org/doi/10.5555/3488766.3488826
de Amorim AGaboardi MHsu JKatsumata SBouyer P(2019)Probabilistic relational reasoning via metricsProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470192(1-19)Online publication date: 24-Jun-2019
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Sato TBarthe GGaboardi MHsu JKatsumata SBouyer P(2019)Approximate span liftingsProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470166(1-14)Online publication date: 24-Jun-2019
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