research-article

Formal verification of SSA-based optimizations for LLVM

Authors:

Santosh Nagarakatte,

Milo M.K. Martin,

Steve ZdancewicAuthors Info & Claims

PLDI '13: Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation

Pages 175 - 186

https://doi.org/10.1145/2491956.2462164

Published: 16 June 2013 Publication History

Abstract

Modern compilers, such as LLVM and GCC, use a static single assignment(SSA) intermediate representation (IR) to simplify and enable many advanced optimizations. However, formally verifying the correctness of SSA-based optimizations is challenging because SSA properties depend on a function's entire control-flow graph.

This paper addresses this challenge by developing a proof technique for proving SSA-based program invariants and compiler optimizations. We use this technique in the Coq proof assistant to create mechanized correctness proofs of several "micro" transformations that form the building blocks for larger SSA optimizations. To demonstrate the utility of this approach, we formally verify a variant of LLVM's mem2reg transformation in Vellvm, a Coq-based formal semantics of the LLVM IR. The extracted implementation generates code with performance comparable to that of LLVM's unverified implementation.

References

[1]

Static Single Assignment Book, 2012. Working draft available at http://ssabook.gforge.inria.fr/latest/book.pdf.

[2]

A. W. Appel. SSA is functional programming. SIGPLAN Not., 33(4): 17--20, April 1998. ISSN 0362-1340.

Digital Library

[3]

J. Aycock and N. Horspool. Simple generation of static single assignment form. In CC, 2000.

Digital Library

[4]

G. Barthe, D. Demange, and D. Pichardie. A formally verified SSA-based middle-end - Static Single Assignment meets CompCert. In ESOP, 2012.

Digital Library

[5]

J. O. Blech, S. Glesner, J. Leitner, and S. Mülling. Optimizing code generation from SSA form: A comparison between two formal correctness proofs in Isabelle/HOL. Electron. Notes Theor. Comput. Sci., 141(2):33--51, 2005.

Digital Library

[6]

The Coq Proof Assistant Reference Manual (Version 8.3pl1). The Coq Development Team, 2011.

[7]

R. Cytron, J. Ferrante, B. K. Rosen, M. N.Wegman, and F. K. Zadeck. Efficiently computing static single assignment form and the control dependence graph. TOPLAS, 13:451--490, 1991.

Digital Library

[8]

R. A. Kelsey. A correspondence between continuation passing style and static single assignment form. In IR, number 3, 1995.

Digital Library

[9]

X. Leroy. A formally verified compiler back-end. Journal of Automated Reasoning, 43(4):363--446, December 2009. ISSN 0168-7433.

Digital Library

[10]

The LLVM Reference Manual (Version 3.0). The LLVM Development Team, 2011. http://llvm.org/releases/3.0/docs/LangRef.html.

[11]

W. Mansky and E. L. Gunter. A framework for formal verification of compiler optimizations. In ITP, 2010.

Digital Library

[12]

Y. Matsuno and A. Ohori. A type system equivalent to static single assignment. In PPDP, 2006.

Digital Library

[13]

V. S. Menon, N. Glew, B. R. Murphy, A. McCreight, T. Shpeisman, A. Adl-Tabatabai, and L. Petersen. A verifiable SSA program representation for aggressive compiler optimization. In POPL, 2006.

Digital Library

[14]

S. S. Muchnick. Advanced compiler design and implementation. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1997. ISBN 1-55860-320-4.

Digital Library

[15]

V. C. Sreedhar and G. R. Gao. A linear time algorithm for placing"-nodes. In POPL, 1995.

Digital Library

[16]

J.-B. Tristan and X. Leroy. Formal verification of translation validators: a case study on instruction scheduling optimizations. In POPL, 2008.

Digital Library

[17]

J.-B. Tristan and X. Leroy. Verified validation of lazy code motion. In PLDI, 2009.

Digital Library

[18]

J. B. Tristan and X. Leroy. A simple, verified validator for software pipelining. In POPL, 2010.

Digital Library

[19]

B. Yakobowski. Étude sémantique dun langage intermédiaire de type Static Single Assignment. Rapport de dea (Master's thesis), ENS Cachan and INRIA Rocquencourt, Sept. 2004.

[20]

X. Yang, Y. Chen, E. Eide, and J. Regehr. Finding and understanding bugs in C compilers. In PLDI, 2011.

Digital Library

[21]

J. Zhao and S. Zdancewic. Mechanized verification of computing dominators for formalizing compilers. In CPP, 2012.

Digital Library

[22]

J. Zhao, S. Nagarakatte, M. M. K. Martin, and S. Zdancewic. For-malizing the LLVM intermediate representation for verified program transformations. In POPL, 2012.

Digital Library

Cited By

Arora JLu SJain DXu THoushmand FPhothilimthana PLesani MNarayanan PMurthy KBodik RSabne AMendis C(2025)TensorRight: Automated Verification of Tensor Graph RewritesProceedings of the ACM on Programming Languages10.1145/37048659:POPL(832-863)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704865
Namjoshi KZuck L(2025)Program Correctness through Self-CertificationCommunications of the ACM10.1145/368962468:2(74-84)Online publication date: 13-Jan-2025
https://dl.acm.org/doi/10.1145/3689624
Yang YSun MWu JLi QZhou YEeckhout LSmaragdakis GLiang KSampson AKim MRossbach C(2025)Debugger Toolchain Validation via Cross-Level DebuggingProceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 110.1145/3669940.3707271(280-294)Online publication date: 30-Mar-2025
https://dl.acm.org/doi/10.1145/3669940.3707271
Show More Cited By

Index Terms

Formal verification of SSA-based optimizations for LLVM
1. Software and its engineering
  1. Software organization and properties
    1. Software functional properties
      1. Correctness
2. Theory of computation
  1. Logic
    1. Proof theory
  2. Semantics and reasoning
    1. Program reasoning
      1. Program verification

Recommendations

Formalizing the LLVM intermediate representation for verified program transformations
POPL '12: Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

This paper presents Vellvm (verified LLVM), a framework for reasoning about programs expressed in LLVM's intermediate representation and transformations that operate on it. Vellvm provides a mechanized formal semantics of LLVM's intermediate ...
Formal verification of SSA-based optimizations for LLVM
PLDI '13

Modern compilers, such as LLVM and GCC, use a static single assignment(SSA) intermediate representation (IR) to simplify and enable many advanced optimizations. However, formally verifying the correctness of SSA-based optimizations is challenging ...
Formal Verification of an SSA-Based Middle-End for CompCert

CompCert is a formally verified compiler that generates compact and efficient code for a large subset of the C language. However, CompCert foregoes using SSA, an intermediate representation employed by many compilers that enables writing simpler, faster ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

PLDI '13: Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation

June 2013

546 pages

ISBN:9781450320146

DOI:10.1145/2491956

General Chair:
Hans-J. Boehm
HP Labs
,
Program Chair:
Cormac Flanagan
University of California, Santa Cruz

ACM SIGPLAN Notices Volume 48, Issue 6
PLDI '13
June 2013
515 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2499370
Issue’s Table of Contents

Copyright © 2013 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]

Sponsors

SIGPLAN: ACM Special Interest Group on Programming Languages

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 June 2013

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

PLDI '13

Sponsor:

SIGPLAN

PLDI '13: ACM SIGPLAN Conference on Programming Language Design and Implementation

June 16 - 19, 2013

Washington, Seattle, USA

Acceptance Rates

PLDI '13 Paper Acceptance Rate 46 of 267 submissions, 17%;

Overall Acceptance Rate 406 of 2,067 submissions, 20%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

88
Total Citations
View Citations
791
Total Downloads

Downloads (Last 12 months)64
Downloads (Last 6 weeks)6

Reflects downloads up to 25 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Arora JLu SJain DXu THoushmand FPhothilimthana PLesani MNarayanan PMurthy KBodik RSabne AMendis C(2025)TensorRight: Automated Verification of Tensor Graph RewritesProceedings of the ACM on Programming Languages10.1145/37048659:POPL(832-863)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704865
Namjoshi KZuck L(2025)Program Correctness through Self-CertificationCommunications of the ACM10.1145/368962468:2(74-84)Online publication date: 13-Jan-2025
https://dl.acm.org/doi/10.1145/3689624
Yang YSun MWu JLi QZhou YEeckhout LSmaragdakis GLiang KSampson AKim MRossbach C(2025)Debugger Toolchain Validation via Cross-Level DebuggingProceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 110.1145/3669940.3707271(280-294)Online publication date: 30-Mar-2025
https://dl.acm.org/doi/10.1145/3669940.3707271
Lin JIkarashi YBernstein GMcCann J(2024)UFO Instruction Graphs Are Machine KnittableACM Transactions on Graphics10.1145/368794843:6(1-22)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687948
Rose ABansal S(2024)Modeling Dynamic (De)Allocations of Local Memory for Translation ValidationProceedings of the ACM on Programming Languages10.1145/36498638:OOPSLA1(1463-1492)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649863
Kim JGu RShao Z(2024) SimplMMJournal of Systems Architecture: the EUROMICRO Journal10.1016/j.sysarc.2023.103049147:COnline publication date: 17-Apr-2024
https://dl.acm.org/doi/10.1016/j.sysarc.2023.103049
Kim JKoenig JChen HGu RShao Z(2024) ThreadAbsJournal of Systems Architecture: the EUROMICRO Journal10.1016/j.sysarc.2023.103046147:COnline publication date: 17-Apr-2024
https://dl.acm.org/doi/10.1016/j.sysarc.2023.103046
van Oorschot DHuisman MŞakar Ö(2024)First Steps towards Deductive Verification of LLVM IRFundamental Approaches to Software Engineering10.1007/978-3-031-57259-3_15(290-303)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57259-3_15
Barrière ABlazy SPichardie D(2023)Formally Verified Native Code Generation in an Effectful JIT: Turning the CompCert Backend into a Formally Verified JIT CompilerProceedings of the ACM on Programming Languages10.1145/35712027:POPL(249-277)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571202
Shang JXu KHan LWang HChai YYang X(2023)Optimization of Access Address Calculation for LLVM2023 4th International Conference on Information Science, Parallel and Distributed Systems (ISPDS)10.1109/ISPDS58840.2023.10235678(458-464)Online publication date: 14-Jul-2023
https://doi.org/10.1109/ISPDS58840.2023.10235678
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 Table of Conten