research-article

A devil's advocate against termination of direct recursion

Author:

Thom FrühwirthAuthors Info & Claims

PPDP '15: Proceedings of the 17th International Symposium on Principles and Practice of Declarative Programming

Pages 103 - 113

https://doi.org/10.1145/2790449.2790518

Published: 14 July 2015 Publication History

Abstract

A devil's advocate is one who argues against a claim, not as a committed opponent but in order to determine the validity of the claim. We are interested in a devil's advocate that argues against termination of a program. He does so by producing a maleficent program that can cause the non-termination of the original program. By inspecting and running the malicious program, one may gain insight into the potential reasons for non-termination and produce counterexamples for termination.

We introduce our method in the concurrent programming language Constraint Handling Rules (CHR). Like in other declarative languages, non-termination occurs through unbounded recursion. Given a self-recursive rule, we automatically generate one or more devil's rules from it. The construction of the devil's rules is straight-forward and involves no guessing. The devil's rules can be simple. For example, they are non-recursive for rules with single recursion.

We show that the devil's rules are maximally vicious in the following sense: For any program that contains the self-recursive rule and for any infinite computation through that rule in that program, there is a corresponding infinite computation with the recursive rule and the devil's rules alone. In that case, the malicious rules serve as a finite witness for non-termination. On the other hand, if the devil's rules do not exhibit an infinite computation, the recursive rule is unconditionally terminating. We also identify cases where the static analysis of the devil's rule decides termination or non-termination of the recursive rule.

References

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Cited By

Miura KPowell CMunetomo M(2022)Optimal answer generation by equivalent transformation incorporating multi-objective genetic algorithmSoft Computing10.1007/s00500-022-06923-126:19(10535-10546)Online publication date: 17-Mar-2022
https://doi.org/10.1007/s00500-022-06923-1
Roman DKifer M(2018)ServLogSemantic Web10.3233/SW-1702629:2(257-290)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.3233/SW-170262
Frühwirth T(2016)Why Can’t You Behave? Non-termination Analysis of Direct Recursive Rules with ConstraintsRule Technologies. Research, Tools, and Applications10.1007/978-3-319-42019-6_14(208-222)Online publication date: 28-Jun-2016
https://doi.org/10.1007/978-3-319-42019-6_14
Show More Cited By

Index Terms

A devil's advocate against termination of direct recursion
1. Software and its engineering
2. Theory of computation
  1. Logic
    1. Logic and verification

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Reviews

Reviewer: R. Clayton

A totally correct system terminates. Instead of establishing termination directly, this paper describes a technique based on non-termination. This technique is statically derivable from the program text and produces non-termination results that are informative relative to the system's failure to terminate. A logically adept reader may be feeling anxious: to show not non-terminating is not to show termination. The logically sophisticated reader may be anticipating restrictive table setting to support this technique. The technique is described relative to a rule-based constraint language. "Devil's rules," syntactically derived from a program's directly recursive rules, are added to the program, and are designed to drive the program into non-termination, called maximally vicious computations. The central theorem of the paper shows that non-terminating programs contains maximally vicious computations characterized by devil's rules. In the absence of devil's rules, a program terminates. Now for the fine print: a program with devil's rules may converge to failure, from which nothing can be concluded. In addition, the technique applies only to programs with rules satisfying various conditions needed by devil's-rule derivations. The technique is in its early days, however, and further work may broaden and strengthen the results it can achieve. The paper is a vigorous read, requiring knowledge of more advanced forms of logic programming as well as the usual first-order predicate logic. The simple even-predicate running example proved to be a surprisingly effective help when working through the paper carefully. Online Computing Reviews Service

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cover image ACM Other conferences

PPDP '15: Proceedings of the 17th International Symposium on Principles and Practice of Declarative Programming

July 2015

263 pages

ISBN:9781450335164

DOI:10.1145/2790449

Conference Chair:
Moreno Falaschi
University of Siena, Italy
,
Program Chair:
Elvira Albert
Complutense University of Madrid, Spain

Copyright © 2015 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

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Association for Computing Machinery

New York, NY, United States

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Published: 14 July 2015

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PPDP '15

PPDP '15: 17th International Symposium on Principles and Practice of Declarative Programming

July 14 - 16, 2015

Siena, Italy

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Cited By

Miura KPowell CMunetomo M(2022)Optimal answer generation by equivalent transformation incorporating multi-objective genetic algorithmSoft Computing10.1007/s00500-022-06923-126:19(10535-10546)Online publication date: 17-Mar-2022
https://doi.org/10.1007/s00500-022-06923-1
Roman DKifer M(2018)ServLogSemantic Web10.3233/SW-1702629:2(257-290)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.3233/SW-170262
Frühwirth T(2016)Why Can’t You Behave? Non-termination Analysis of Direct Recursive Rules with ConstraintsRule Technologies. Research, Tools, and Applications10.1007/978-3-319-42019-6_14(208-222)Online publication date: 28-Jun-2016
https://doi.org/10.1007/978-3-319-42019-6_14
Frühwirth T(2015)Constraint Handling Rules - What Else?Rule Technologies: Foundations, Tools, and Applications10.1007/978-3-319-21542-6_2(13-34)Online publication date: 12-Jul-2015
https://doi.org/10.1007/978-3-319-21542-6_2

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