research-article

From program verification to program synthesis

Authors:

Saurabh Srivastava,

Jeffrey S. FosterAuthors Info & Claims

ACM SIGPLAN Notices, Volume 45, Issue 1

Pages 313 - 326

https://doi.org/10.1145/1707801.1706337

Published: 17 January 2010 Publication History

Abstract

This paper describes a novel technique for the synthesis of imperative programs. Automated program synthesis has the potential to make programming and the design of systems easier by allowing programs to be specified at a higher-level than executable code. In our approach, which we call proof-theoretic synthesis, the user provides an input-output functional specification, a description of the atomic operations in the programming language, and a specification of the synthesized program's looping structure, allowed stack space, and bound on usage of certain operations. Our technique synthesizes a program, if there exists one, that meets the input-output specification and uses only the given resources.

The insight behind our approach is to interpret program synthesis as generalized program verification, which allows us to bring verification tools and techniques to program synthesis. Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions. It then generates constraints that relate the unknowns and enforces three kinds of requirements: partial correctness, loop termination, and well-formedness conditions on program guards. We formalize the requirements that program verification tools must meet to solve these constraint and use tools from prior work as our synthesizers.

We demonstrate the feasibility of the proposed approach by synthesizing programs in three different domains: arithmetic, sorting, and dynamic programming. Using verification tools that we previously built in the VS3 project we are able to synthesize programs for complicated arithmetic algorithms including Strassen's matrix multiplication and Bresenham's line drawing; several sorting algorithms; and several dynamic programming algorithms. For these programs, the median time for synthesis is 14 seconds, and the ratio of synthesis to verification time ranges between 1x to 92x (with an median of 7x), illustrating the potential of the approach.

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Cited By

Goharshady AHitarth SMohammadi FMotwani H(2023)Algebro-geometric Algorithms for Template-Based Synthesis of Polynomial ProgramsProceedings of the ACM on Programming Languages10.1145/35860527:OOPSLA1(727-756)Online publication date: 6-Apr-2023
https://dl.acm.org/doi/10.1145/3586052
Hozzová PKovács LNorman CVoronkov A(2023)Program Synthesis in SaturationAutomated Deduction – CADE 2910.1007/978-3-031-38499-8_18(307-324)Online publication date: 2-Sep-2023
https://doi.org/10.1007/978-3-031-38499-8_18
Wild APorter B(2022)Multi-donor Neural Transfer Learning for Genetic ProgrammingACM Transactions on Evolutionary Learning and Optimization10.1145/35630432:4(1-40)Online publication date: 24-Nov-2022
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Index Terms

From program verification to program synthesis
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning

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From program verification to program synthesis
POPL '10: Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 45, Issue 1

POPL '10

January 2010

500 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/1707801

Issue’s Table of Contents

POPL '10: Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
January 2010
520 pages
ISBN:9781605584799
DOI:10.1145/1706299
General Chair:
Manuel Hermenegildo
IMDEA-Software and T.U. of Madrid, Spain
,
Program Chair:
Jens Palsberg
UCLA, University of California, Los Angeles

Copyright © 2010 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 January 2010

Published in SIGPLAN Volume 45, Issue 1

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Cited By

Goharshady AHitarth SMohammadi FMotwani H(2023)Algebro-geometric Algorithms for Template-Based Synthesis of Polynomial ProgramsProceedings of the ACM on Programming Languages10.1145/35860527:OOPSLA1(727-756)Online publication date: 6-Apr-2023
https://dl.acm.org/doi/10.1145/3586052
Hozzová PKovács LNorman CVoronkov A(2023)Program Synthesis in SaturationAutomated Deduction – CADE 2910.1007/978-3-031-38499-8_18(307-324)Online publication date: 2-Sep-2023
https://doi.org/10.1007/978-3-031-38499-8_18
Wild APorter B(2022)Multi-donor Neural Transfer Learning for Genetic ProgrammingACM Transactions on Evolutionary Learning and Optimization10.1145/35630432:4(1-40)Online publication date: 24-Nov-2022
https://dl.acm.org/doi/10.1145/3563043
Steinhöfel D(2022)Ever Change a Running System: Structured Software Reengineering Using Automatically Proven-Correct Transformation RulesErnst Denert Award for Software Engineering 202010.1007/978-3-030-83128-8_10(197-226)Online publication date: 28-Feb-2022
https://doi.org/10.1007/978-3-030-83128-8_10
Rahmani KRaza MGulwani SLe VMorris DRadhakrishna ASoares GTiwari A(2021)Multi-modal program inference: a marriage of pre-trained language models and component-based synthesisProceedings of the ACM on Programming Languages10.1145/34855355:OOPSLA(1-29)Online publication date: 15-Oct-2021
https://dl.acm.org/doi/10.1145/3485535
Houshmand FLesani MVora K(2021)Grafs: declarative graph analyticsProceedings of the ACM on Programming Languages10.1145/34735885:ICFP(1-32)Online publication date: 19-Aug-2021
https://dl.acm.org/doi/10.1145/3473588
Krasanakis ESymeonidis A(2021)Defining behaviorizeable relations to enable inference in semi-automatic program synthesisJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2021.100714123(100714)Online publication date: Nov-2021
https://doi.org/10.1016/j.jlamp.2021.100714
Scott JSudula TRehman HMora FGanesh V(2021)BanditFuzz: Fuzzing SMT Solvers with Multi-agent Reinforcement LearningFormal Methods10.1007/978-3-030-90870-6_6(103-121)Online publication date: 10-Nov-2021
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Drămnesc IJebelean T(2021): Deductive Synthesis of Sorting Algorithms in Theorema Theoretical Aspects of Computing – ICTAC 202110.1007/978-3-030-85315-0_18(314-333)Online publication date: 6-Sep-2021
https://dl.acm.org/doi/10.1007/978-3-030-85315-0_18
Itzhaky SPeleg HPolikarpova NRowe RSergey I(2021)Deductive Synthesis of Programs with Pointers: Techniques, Challenges, OpportunitiesComputer Aided Verification10.1007/978-3-030-81685-8_5(110-134)Online publication date: 15-Jul-2021
https://doi.org/10.1007/978-3-030-81685-8_5
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