research-article

Specifying and verifying sparse matrix codes

Authors:

Johannes Hölzl,

Ali Sinan Köksal,

Rastislav Bodík,

Mooly SagivAuthors Info & Claims

ICFP '10: Proceedings of the 15th ACM SIGPLAN international conference on Functional programming

Pages 249 - 260

https://doi.org/10.1145/1863543.1863581

Published: 27 September 2010 Publication History

Abstract

Sparse matrix formats are typically implemented with low-level imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variable-free functional language (LL) in which even advanced formats can be expressed naturally, as a pipeline-style composition of smaller construction steps. We translate LL programs to Isabelle/HOL and describe a proof system based on parametric predicates for tracking relationship between mathematical vectors and their concrete representations. This proof theory automatically verifies full functional correctness of many formats. We show that it is reusable and extensible to hierarchical sparse formats.

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Cited By

Laird ALiu BBjørner NDehnavi M(2024)SpEQ: Translation of Sparse Codes using EquivalencesProceedings of the ACM on Programming Languages10.1145/36564458:PLDI(1680-1703)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656445
Gladshtein VZhao QAhrens WAmarasinghe SSergey I(2024)Mechanised Hypersafety Proofs about Structured DataProceedings of the ACM on Programming Languages10.1145/36564038:PLDI(647-670)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656403
Liu JZhao ZDing ZBrock BRong HZhang Z(2024)UniSparse: An Intermediate Language for General Sparse Format CustomizationProceedings of the ACM on Programming Languages10.1145/36498168:OOPSLA1(137-165)Online publication date: 29-Apr-2024
https://doi.org/10.1145/3649816
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Index Terms

Specifying and verifying sparse matrix codes
1. Software and its engineering
  1. Software notations and tools
    1. Context specific languages
      1. Specialized application languages
2. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Program verification

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Published In

cover image ACM Conferences

ICFP '10: Proceedings of the 15th ACM SIGPLAN international conference on Functional programming

September 2010

398 pages

ISBN:9781605587943

DOI:10.1145/1863543

General Chair:
Paul Hudak
Yale University, USA
,
Program Chair:
Stephanie Weirich
University of Pennsylvania, USA

ACM SIGPLAN Notices Volume 45, Issue 9
ICFP '10
September 2010
382 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1932681
Issue’s Table of Contents

Copyright © 2010 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 ACM 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

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Publication History

Published: 27 September 2010

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ICFP '10

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SIGPLAN

ICFP '10: ACM SIGPLAN International Conference on Functional Programming

September 27 - 29, 2010

Maryland, Baltimore, USA

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

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Cited By

Laird ALiu BBjørner NDehnavi M(2024)SpEQ: Translation of Sparse Codes using EquivalencesProceedings of the ACM on Programming Languages10.1145/36564458:PLDI(1680-1703)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656445
Gladshtein VZhao QAhrens WAmarasinghe SSergey I(2024)Mechanised Hypersafety Proofs about Structured DataProceedings of the ACM on Programming Languages10.1145/36564038:PLDI(647-670)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656403
Liu JZhao ZDing ZBrock BRong HZhang Z(2024)UniSparse: An Intermediate Language for General Sparse Format CustomizationProceedings of the ACM on Programming Languages10.1145/36498168:OOPSLA1(137-165)Online publication date: 29-Apr-2024
https://doi.org/10.1145/3649816
Chou SAmarasinghe S(2022)Compilation of dynamic sparse tensor algebraProceedings of the ACM on Programming Languages10.1145/35633386:OOPSLA2(1408-1437)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563338
Chou SKjolstad FAmarasinghe SDonaldson ATorlak E(2020)Automatic generation of efficient sparse tensor format conversion routinesProceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3385412.3385963(823-838)Online publication date: 11-Jun-2020
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Cao HSankaranarayanan JFeng JLi YSamet H(2019)Understanding Metropolitan Crowd Mobility via Mobile Cellular Accessing DataACM Transactions on Spatial Algorithms and Systems10.1145/33233455:2(1-18)Online publication date: 25-Jul-2019
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Chou SKjolstad FAmarasinghe S(2018)Format abstraction for sparse tensor algebra compilersProceedings of the ACM on Programming Languages10.1145/32764932:OOPSLA(1-30)Online publication date: 24-Oct-2018
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Chowdhury RRamachandran V(2018)Cache-Oblivious Buffer Heap and Cache-Efficient Computation of Shortest Paths in GraphsACM Transactions on Algorithms10.1145/314717214:1(1-33)Online publication date: 3-Jan-2018
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Strout MHall MOlschanowsky C(2018)The Sparse Polyhedral Framework: Composing Compiler-Generated Inspector-Executor CodeProceedings of the IEEE10.1109/JPROC.2018.2857721106:11(1921-1934)Online publication date: Nov-2018
https://doi.org/10.1109/JPROC.2018.2857721
Eppstein D(2017)The Parametric Closure ProblemACM Transactions on Algorithms10.1145/314721214:1(1-22)Online publication date: 6-Dec-2017
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