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Some results concerning proofs of statements about programs

1970
*
Journal of computer and system sciences (Print)
*

three concepts

doi:10.1016/s0022-0000(70)80013-7
fatcat:lwjolmjgnfdabfeujnsn7m52ai
*of*the equivalence*of*computations and*of**programs*, this system can be used to show that two computations or*programs*are or are not equivalent. (2) Given a*program*and a finite number ... That is, it is shown that certain relations*of*equivalence among*programs*and the relation*of*a*program*to the functions whose computation it specifies probably obey the law*of*excluded middle in this ... INTRODUCTION A number*of*writers have considered the problem*of*using various systems*of*logic to make and prove*statements**about*computations and*programs*. ...##
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Page 4105 of Mathematical Reviews Vol. , Issue 94g
[page]

1994
*
Mathematical Reviews
*

“We obtain two basic

*results*: one*concerns*the characterization*of*the well-founded model in terms*of*(generalized)*proof*trees and as the least fixed point*of**some*operator acting on*proof*tree roots. ... The second basic*result**concerns*an application: a sound and complete*proof*method*of*partial correctness and weak ...##
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A Note on the Decidability of the Necessity of Axioms
[article]

2014
*
arXiv
*
pre-print

A typical kind

arXiv:1408.5314v1
fatcat:tlkldohfvjccloe2kpyhq5ruzi
*of*question in mathematical logic is that for the necessity*of*a certain axiom: Given a*proof**of**some**statement*ϕ in*some*axiomatic system T, one looks for minimal subsystems*of*T that allow ... In particular, one asks whether, given*some*system T+ψ, T alone suffices to prove ϕ. We show that this problem is undecidable unless T+ψ is decidable. ... There are various places in mathematical logic where one is*concerned*with the necessity*of*certain axioms for the*proof**of*a theorem; in set theory, typical questions are*about*the necessity*of*the axiom ...##
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Why Do We Believe Theorems?
[article]

2014
*
arXiv
*
pre-print

Our argument is based on considerations

arXiv:1411.4857v1
fatcat:gtwibgx4nbd5jhjuiimqvyem2y
*concerning*length*of*formal derivations. We also discuss psychological and social factors that contribute to building belief in theorems. ... Opposing this opinion, the main claim*of*the present paper is that such a gain*of*confidence obtained from any link between*proofs*and formal derivations is, even in principle, impossible in the present ... Thanks are due to Jody Azzouni for enlightening discussions*concerning*the subject*of*this paper and to an anonymous referee whose important remarks permitted us to correct the arguments and improve presentation ...##
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Fifty years of Hoare's Logic
[article]

2019
*
arXiv
*
pre-print

We present a history

arXiv:1904.03917v2
fatcat:kfpjuntx35g4vhnkvsnetmkdnm
*of*Hoare's logic. ... The second one*concerns*reasoning*about*time complexity*of*the*programs*. ... Subsequently Hoare introduced an axiom to reason*about*the assignment*statement*and the*proof*rules to reason*about*the*program*composition and the while*statement*. ...##
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Page 42 of Journal of Research and Practice in Information Technology Vol. 14, Issue 2
[page]

1982
*
Journal of Research and Practice in Information Technology
*

The most important assertions

*concern*the initial and final values*of*variables. Assertions*about*their intermediate values are included to simplify the*proof*. ...*Some*methods*of**program*construction and*some*computer languages lead to easier*proofs*than others. These points are demonstrated convincingly in E.W. ...##
###
Mathematical Proofs at a Crossroad?
[chapter]

2004
*
Lecture Notes in Computer Science
*

In the last decades, the increasing length and complexity

doi:10.1007/978-3-540-27812-2_2
fatcat:5dzfdx5ppfghlkjglfgnbkq5gu
*of*many mathematical*proofs*led to the expansion*of**some*empirical, experimental, psychological and social aspects, yesterday only marginal, but ... now changing radically the very essence*of**proof*. ... For*some*a*proof*including computer*programs*is like a telephone directory, while a human*proof*may compete with a beautiful novel. ...##
###
Page 190 of American Society of Civil Engineers. Collected Journals Vol. 129, Issue 4
[page]

2003
*
American Society of Civil Engineers. Collected Journals
*

While part

*of*him wants to pursue the matter, he also realizes that exploring his doubts*about*the exist- ing room being explosion-*proof*will not only further stress out Dante, but could*result*in additional ...*Results*are tabulated at the end*of*the voting period and the statistical responses are reported, along with commentary and in*some*cases, the actual solution for the case. ...##
###
Didactical Issues at the Interface of Mathematics and Computer Science
[chapter]

2019
*
The Mathematics Teacher in the Digital Era
*

We will elaborate on the links between the concepts

doi:10.1007/978-3-030-28483-1_6
fatcat:cgtoxvtatfdipczdeyocpkav5y
*of*algorithm,*proof*, and*program*, and will argue for their significance in a general reflection on didactical issues in mathematics and computer science ... In view*of*this, addressing the question*of**proof*in mathematics and computer science is a central didactical issue, which we examine in this contribution. ...*about*the*statement*. ...##
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Computation, Proof, Machine: Mathematics Enters a New Age, Gilles Dowek, Cambridge University Press, 2015. Hardback, ISBN 978-0-521-11801-9, 152 pages

2017
*
Theory and Practice of Logic Programming
*

In a short Chapter 11 a convincing case for the

doi:10.1017/s1471068417000011
fatcat:yiexizomkbf4fjlgbt5lcdmzcy
*proof*-checking*programs*is made: one*of*such*programs*discovered an, admittedly small, mistake in one*of*Newton's*proofs**concerning*the motion*of*planets ... Paulson, Let me conclude with*some*minor complaints*about*the book under review. ...##
###
Fifty years of Hoare's logic

2019
*
Formal Aspects of Computing
*

Subsequently Hoare introduced an axiom to reason

doi:10.1007/s00165-019-00501-3
fatcat:vzxfucuz45fozhicmxzkxdpdjm
*about*the assignment*statement*and the*proof*rules to reason*about*the*program*composition and the while*statement*. ... Precursors Turing The*concern**about*correctness*of*computer*programs*is as old as computers themselves. ... The assertions used for partial correctness are similar to the ones used in the correctness*proof**of*[dB75]*of*a*program*corresponding to Turing's example that uses both a while and a repeat*statement*...##
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Reasoning about call-by-value: a missing result in the history of Hoare's logic
[article]

2019
*
arXiv
*
pre-print

, and in which the correctness

arXiv:1909.06215v1
fatcat:rrsfhxbsn5co5mlt7u7nb3zlsu
*proofs*are linear in the length*of*the*program*. ... We provide a sound and relatively complete Hoare-like*proof*system for reasoning*about*partial correctness*of*recursive procedures in presence*of*local variables and the call-by-value parameter mechanism ... Acknowledgement We thank Ernst-Rüdiger Olderog and Stijn de Gouw for helpful comments*about*the contributions*of*a number*of*relevant references. ...##
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Javalight is type-safe---definitely

1998
*
Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '98
*

*of*the machine-checked

*proof*

*of*type soundness. ... We emphasize that by 'machine-checked' we do not just mean th& it has passed

*some*type checker, but that

*some*non-trivial properties

*of*the language have been established with t.he help

*of*a (semiautomatic ... We thank Sophia Drossopoulou and Donald Syme for the very helpful discussions

*about*their work. ...

##
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Mathematics and the mind
[chapter]

2002
*
Advances in Consciousness Research
*

This is a modest question that

doi:10.1075/aicr.33.08nel
fatcat:jeh44nqfkfbztpsaanhyfrnl5e
*concerns*the functioning*of*the mind in one area, rather than the fundamental nature*of*consciousness, but I expect it to be more fruitful than speculations*about*Platonic ... Such a*program*requires no debugging since it is a by-product*of*a*proof*that the objects have the properties stated in the theorem whose constructive*proof*has been verified. ...##
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Gödel and the Limits of Logic

1999
*
Scientific American
*

:

doi:10.1038/scientificamerican0699-76
fatcat:nbdbeqxbrnbnto6x7lmyh3xj2y
*some*other true*statements**about*the natural numbers will remain unprovable. ... his refrigerator aroused continuing*concern**about*his mental stability. ... Further reading Read more*about*mathematical*proof*in past Plus articles, including our series on the origins*of**proof*from Euclid to Gödel to the*proof**of*Fermat's Last Theorem. ...
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