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Verifying correctness of logic programs [chapter]

A. Bossi, N. Cocco
<span title="">1989</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Starting from Hogger's considerations on this topic, we supply a sufficient condition for completeness. Modularity and pre/post specifications of program modules are then discussed.  ...  We propose a sufficient condition for partial correctness with respect to a pre/post specification. Some small examples illustrate our technique. 1.  ...  The sufficient condition for partial correctness was given by Hogger, while we supply another one for completeness.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-50940-2_30">doi:10.1007/3-540-50940-2_30</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nhplvkuojvczdmbotplyuontle">fatcat:nhplvkuojvczdmbotplyuontle</a> </span>
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Proof method of partial correctness and weak completeness for normal logic programs

Gérard Ferrand, Pierre Deransart
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7qdabej4lbaczotmeg3ldn4ioy" style="color: black;">The Journal of Logic Programming</a> </i> &nbsp;
This research was supported in part by CNRS (Orltans and METHEOL project of the GRECO Programmation). Thanks are due to the anonymous referees for their comments and suggestions.  ...  Q.E.D. 4.3, About Proof Method of Completeness We have introduced the concepts of partial correctness and weak completeness which both correspond in fact to a notion of general partial correctness: Mp  ...  D We present a proof method for partial correctness and weak completeness for any normal programs, which coincides with the already known proof methods for partial correctness and completeness for definite  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0743-1066(93)90033-d">doi:10.1016/0743-1066(93)90033-d</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/azn34bec5vce3nihagl2ic4bgq">fatcat:azn34bec5vce3nihagl2ic4bgq</a> </span>
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A Mechanical Analysis of Program Verification Strategies

Sandip Ray, Warren A. Hunt, John Matthews, J. Strother Moore
<span title="2008-03-14">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2ewief65xnegfh2slwulpgsnba" style="color: black;">Journal of automated reasoning</a> </i> &nbsp;
The completeness result implies that given any proof of correctness of a sequential program one can derive a proof in each of the above strategies.  ...  Based on our formalization, we prove that each strategy is both sound and complete.  ...  Matt Kaufmann has provided numerous insights, including a comment that started us on track for the results of this paper in the first place.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10817-008-9098-1">doi:10.1007/s10817-008-9098-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/72r2bfbywranblss2zer22wuoy">fatcat:72r2bfbywranblss2zer22wuoy</a> </span>
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Page 263 of Mathematical Reviews Vol. , Issue 85a [page]

<span title="">1985</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Orthogonally, one may want to prove programs by induction on their data structure: the correctness of the program on complex data items is deduced from its correctness on simpler data items.  ...  The invariant assertion method is used to prove programs by in- duction on their control structure: The correctness of complex control structures is deduced from the correctness of their com- ponents,  ... 
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Page 4272 of Mathematical Reviews Vol. , Issue 86i [page]

<span title="">1986</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Author summary: “Our main result is a characterization of the space induced by the Scott topology on the set of total objects of a bounded-complete cpo.  ...  The correct- ness of a compiler for a small imperative language is proved as an illustration.”  ... 
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Page 581 of Mathematical Reviews Vol. 56, Issue 2 [page]

<span title="">1978</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A number of examples is given where subgoal induction is used to prove partial correctness.  ...  Partial correctness is then proved by introducing invariants which relate the auxiliary vari- ables to the actual ones (a simple significant example is given).  ... 
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Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Andrei-Sebastian Buruiană, Ştefan Ciobâcă
<span title="2019-02-21">2019</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
We give a language-parametric solution to the problem of total correctness, by automatically reducing it to the problem of partial correctness, under the assumption that an expression whose value decreases  ...  We implement a prototype on top of the RMT tool and we show that it works in practice on a number of examples.  ...  The proof system was shown in [14] to be sound (and also relatively complete) for the problem of partial correctness.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.289.1">doi:10.4204/eptcs.289.1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gnz25yvfbnasncjcyalig3kdcq">fatcat:gnz25yvfbnasncjcyalig3kdcq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191026021947/https://arxiv.org/pdf/1902.08419v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/5a/615ac7d39235a5bd9f614a4f9b41fca9a6aff261.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.289.1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Formal specification and prototyping of a program specializer [chapter]

Sandrine Blazy, Philippe Facon
<span title="">1995</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The tool is specified in terms of inference rules and operates by induction on the abstract syntax. The correctness of these rules is proved using rule induction.  ...  This paper reports on the use of formal specifications in the development of a software maintenance tool for specializing imperative programs, which have become very complex due to extensive modifications  ...  the R-completeness and soundness rules, we use rule induction on the partial evaluation, and on the dynamic semantics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-59293-8_227">doi:10.1007/3-540-59293-8_227</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tdf5jwnw45hmhhxfngaj2qzfbq">fatcat:tdf5jwnw45hmhhxfngaj2qzfbq</a> </span>
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Nondeterministic flowchart programs with recursive procedures: Semantics and correctness II

Jean H. Gallier
<span title="">1981</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Using results on unfolding proved in part 1, we prove that this method is sound and complete with a finite number of assertions.  ...  We study four notions of correctness: two notions of partial correctness (existential and universal) and the corresponding notions of total correctness.  ...  Finally, I thank the referee for scrutinizing the manuscript very carefully and suggesting many improvements.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(81)80001-1">doi:10.1016/s0304-3975(81)80001-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dprzzxib5jdejklgiybgnee4ne">fatcat:dprzzxib5jdejklgiybgnee4ne</a> </span>
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A complete axiomatic system for proving deductions about recursive programs

David Harel, Amir Puneli, Jonathan Stavi
<span title="">1977</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the ninth annual ACM symposium on Theory of computing - STOC &#39;77</a> </i> &nbsp;
Me wish to thank Nachum Oershowitz for suggestions following a detailed reading of a previous version of the paper. The first author benefited from many related discussions with Vaughan R. Pratt.  ...  , namely that of proving partial correctness of specific programs.  ...  D is shown to be a complete system (in Cook's sense) for proving deductions of the form e 1, .... r n ~ # over a language, the wff*n of which are assertions in some assertion language L and partial correctness  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706093130/http://www.wisdom.weizmann.ac.il/~dharel/SCANNED.PAPERS/AxiomaticSystem.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e3/e2/e3e2f95a592c7bc8879fe88b39d55c3fd2c6520b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/800105.803415"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

A correction

E. T. Bell
<span title="">1929</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
Complete isomorphism is possible, provided we attend in Halphen's theorem to the degenerate case of one period infinite. * A partial isomorphism between the functions of Lucas and Weierstrass, this Bulletin  ...  has kindly pointed out to me that the isomorphism established in my paper in the last issue of this Bulletin,* is not, as there stated, partial, but complete.  ...  Complete isomorphism is possible, provided we attend in Halphen's theorem to the degenerate case of one period infinite.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1929-04752-9">doi:10.1090/s0002-9904-1929-04752-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/btvchyogjrffbgqcanipezvjfu">fatcat:btvchyogjrffbgqcanipezvjfu</a> </span>
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Proving correctness of coroutines without history variables

EdmundMelson Clarke
<span title="">1980</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnqseeosvrf6tnj6sc3lbn2y4e" style="color: black;">Acta Informatica</a> </i> &nbsp;
We examine the question of whether history variables are necessary in formal proofs of correctness for coroutines.  ...  Examples are given to illustrate this technique of verifying coroutines and our axiom system is shown to be sound and relatively complete with respect to an ooerational semantics for eoroutines.  ...  In particular we investigate the question of whether history variables are necessary in proving partial correctness of coroutines.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829181332/http://www.cs.cmu.edu/~emc/papers/Technical%20Reports/80_emc_coroutines.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5e/07/5e078ef9f00e1d62b259e82dc6dd87105817c370.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf00263992"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 13 of Western Journal of Medicine and Surgery Vol. 1, Issue [page]

<span title="">1844</span> <i title="Open Court Publishing Co"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_western-journal-of-medicine-and-surgery" style="color: black;">Western Journal of Medicine and Surgery </a> </i> &nbsp;
‘Take now the Dr.’s definition, which is certainly the correct one, and his symptoms attending complete inver- sion, and if they do not show the case to have been*one of complete inversion, | shall utterly  ...  ~e any unfairness in his criticisms; yet I certainly do not see the correctness and sufficiency of some of his stric- tures in proving that the cases of Dr, White and Dr.  ... 
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Formal Verification of Quantum Algorithms Using Quantum Hoare Logic [chapter]

Junyi Liu, Bohua Zhan, Shuling Wang, Shenggang Ying, Tao Liu, Yangjia Li, Mingsheng Ying, Naijun Zhan
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
for partial correctness of quantum programs.  ...  In particular, we formalize the syntax and semantics of quantum programs in Isabelle/HOL, write down the rules of quantum Hoare logic, and verify the soundness and completeness of the deduction system  ...  QHL is proved to be (relatively) complete for both partial correctness and total correctness of quantum programs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-25543-5_12">doi:10.1007/978-3-030-25543-5_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kvxjv4o5pfbqblpvof6xcpb2d4">fatcat:kvxjv4o5pfbqblpvof6xcpb2d4</a> </span>
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Page 2362 of Mathematical Reviews Vol. , Issue 81F [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A sound and complete proof system for partial program correctness. Mathematical foundations of computer science, 1979 (Proc.  ...  From the introduction: “We investigate soundness and complete. ness of a proof system dealing with partial correctness of programs ' 81f:68019 structure, subscripted variables and (possibly recursive)  ... 
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