research-article

A type theory for incremental computational complexity with control flow changes

Authors:

Zoe Paraskevopoulou,

Deepak GargAuthors Info & Claims

ICFP 2016: Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming

Pages 132 - 145

https://doi.org/10.1145/2951913.2951950

Published: 04 September 2016 Publication History

Abstract

Incremental computation aims to speed up re-runs of a program after its inputs have been modified slightly. It works by recording a trace of the program's first run and propagating changes through the trace in incremental runs, trying to re-use as much of the original trace as possible. The recent work CostIt is a type and effect system to establish the time complexity of incremental runs of a program, as a function of input changes. However, CostIt is limited in two ways. First, it prohibits input changes that influence control flow. This makes it impossible to type programs that, for instance, branch on inputs that may change. Second, the soundness of CostIt is proved relative to an abstract cost semantics, but it is unclear how the semantics can be realized.

In this paper, we address both these limitations. We present DuCostIt, a re-design of CostIt, that combines reasoning about costs of change propagation and costs of from-scratch evaluation. The latter lifts the restriction on control flow changes. To obtain the type system, we refine Flow Caml, a type system for information flow analysis, with cost effects. Additionally, we inherit from CostIt index refinements to track data structure sizes and a co-monadic type. Using a combination of binary and unary step-indexed logical relations, we prove DuCostIt's cost analysis sound relative to not only an abstract cost semantics, but also a concrete semantics, which is obtained by translation to an ML-like language.

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Cited By

QU WGABOARDI MGARG D(2021)Relational cost analysis in a functional-imperative settingJournal of Functional Programming10.1017/S095679682100007131Online publication date: 2-Nov-2021
https://doi.org/10.1017/S0956796821000071
Rajani VGarg D(2019)On the expressiveness and semantics of information flow typesJournal of Computer Security10.3233/JCS-191382(1-28)Online publication date: 6-Dec-2019
https://doi.org/10.3233/JCS-191382
Qu WGaboardi MGarg D(2019)Relational cost analysis for functional-imperative programsProceedings of the ACM on Programming Languages10.1145/33416963:ICFP(1-29)Online publication date: 26-Jul-2019
https://dl.acm.org/doi/10.1145/3341696
Show More Cited By

Index Terms

A type theory for incremental computational complexity with control flow changes
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning
    2. Program semantics

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cover image ACM Conferences

ICFP 2016: Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming

September 2016

501 pages

ISBN:9781450342193

DOI:10.1145/2951913

General Chairs:
Jacques Garrigue
Nagoya University, Japan
,
Gabriele Keller
University of New South Wales, Australia
,
Program Chair:
Eijiro Sumii
Tohoku University, Japan

ACM SIGPLAN Notices Volume 51, Issue 9
ICFP '16
September 2016
501 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/3022670
Editor:
Matthew Fluet
Issue’s Table of Contents

Copyright © 2016 Owner/Author.

Permission to make digital or hard copies of part or all 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 third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Published: 04 September 2016

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ICFP'16: ACM SIGPLAN International Conference on Functional Programming

September 18 - 24, 2016

Nara, Japan

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Overall Acceptance Rate 333 of 1,064 submissions, 31%

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Cited By

QU WGABOARDI MGARG D(2021)Relational cost analysis in a functional-imperative settingJournal of Functional Programming10.1017/S095679682100007131Online publication date: 2-Nov-2021
https://doi.org/10.1017/S0956796821000071
Rajani VGarg D(2019)On the expressiveness and semantics of information flow typesJournal of Computer Security10.3233/JCS-191382(1-28)Online publication date: 6-Dec-2019
https://doi.org/10.3233/JCS-191382
Qu WGaboardi MGarg D(2019)Relational cost analysis for functional-imperative programsProceedings of the ACM on Programming Languages10.1145/33416963:ICFP(1-29)Online publication date: 26-Jul-2019
https://dl.acm.org/doi/10.1145/3341696
Paraskevopoulou ZAppel A(2019)Closure conversion is safe for spaceProceedings of the ACM on Programming Languages10.1145/33416873:ICFP(1-29)Online publication date: 26-Jul-2019
https://dl.acm.org/doi/10.1145/3341687
Çiçek EQu WBarthe GGaboardi MGarg DMcKinley KFisher K(2019)Bidirectional type checking for relational propertiesProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314603(533-547)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314603
Giarrusso PRégis-Gianas YSchuster P(2019)Incremental $$\lambda $$ -Calculus in Cache-Transfer StyleProgramming Languages and Systems10.1007/978-3-030-17184-1_20(553-580)Online publication date: 6-Apr-2019
https://doi.org/10.1007/978-3-030-17184-1_20
Rajani VGarg D(2018)Types for Information Flow Control: Labeling Granularity and Semantic Models2018 IEEE 31st Computer Security Foundations Symposium (CSF)10.1109/CSF.2018.00024(233-246)Online publication date: Jul-2018
https://doi.org/10.1109/CSF.2018.00024
Wang PWang DChlipala A(2017)TiML: a functional language for practical complexity analysis with invariantsProceedings of the ACM on Programming Languages10.1145/31339031:OOPSLA(1-26)Online publication date: 12-Oct-2017
https://dl.acm.org/doi/10.1145/3133903
Çiçek EBarthe GGaboardi MGarg DHoffmann J(2017)Relational cost analysisACM SIGPLAN Notices10.1145/3093333.300985852:1(316-329)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009858
Çiçek EBarthe GGaboardi MGarg DHoffmann JCastagna GGordon A(2017)Relational cost analysisProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009858(316-329)Online publication date: 1-Jan-2017
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