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	Hoare logic - Wikipedia, the free encyclopedia
		Hoare logic (also known as Floyd–Hoare logic) is a formal system developed by the British computer scientist C.
		The purpose of the system is to provide a set of logical rules in order to reason about the correctness of computer programs with the rigour of mathematical logic.
		Hoare logic has axioms and inference rules for all the constructs of a simple imperative programming language.
	en.wikipedia.org /wiki/Hoare_logic (461 words)

	Logika - Wikipédia
		For instance, propositional logic and predicate logic are a kind of formal logic, as well as temporal logic, modal logic, Hoare logic, the calculus of constructions etc. Higher order logics refer to logical systems based on a hierarchy of types.
		Aristotelian logic is sometimes referred to as formal logic because it specifically deals with forms of reasoning, but is not formal in the sense we use it here or as is common in current usage.
		Mathematical logic refers to two distinct areas of research: The first, primarily of historical interest, is the use of formal logic to study mathematical reasoning, and the second, in the other direction, the application of mathematics to the study of formal logic.
	su.wikipedia.org /wiki/Logika (1264 words)

	Hoare logic: Encyclopedia topic (Site not responding. Last check: 2007-08-19)
		Hoare logic is a formal system (formal system: in logic, mathematics, and computer science, a formal system is a formal grammar...
		Hoare acknowledges earlier contributions from Robert Floyd (Robert Floyd: more facts about this subject), who had published a similar system for flowchart (flowchart: A diagram of the sequence of operations in a computer program or an accounting system) s.
		Hoare logic has axiom (axiom: (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident) s and inference rule (inference rule: in logic, especially in mathematical logic, a rule of inference is a scheme for constructing...
	www.absoluteastronomy.com /reference/hoare_logic (628 words)

	COMP317: Logic and Computation (Site not responding. Last check: 2007-08-19)
		Axiomatic semantics is concerned with logical properties of programs: Hoare Logic describes the meaning of programs (more indirectly than either operational or denotational semantics) by saying what can be said about the states before and after a program is executed.
		Hoare Logic is an example of a formal logic; in order to explain formal logics in general, and Hoare logic in particular, we begin with a historical review of logic, biased towards a view of formal logics as games that have nothing whatsoever to do with Truth.
		This furthers a formal approach to logic, where the validity of an argument is abstracted from its content: in this case, validity is just a result of the algebraic properties of the logical connectives.
	www.csc.liv.ac.uk /~grant/Teaching/COMP317/logic.html (1648 words)

	Hoare logic (Site not responding. Last check: 2007-08-19)
		Hoare logic (also known as Floyd–Hoare logic) is a formal system developed by the British...
		Hoare Logic is a program logic introduced around thirty years ago that is used to...
		A New Deconstructive Logic: Linear Logic (1997) Article by V. Danos, J.-B. Joinet and H. Schellinx outlining how linear logic can function as a `mark-up logic' allowing the embedding of a large class of logics in a manner that respects their underlying proof semantics (cf.
	www.serebella.com /encyclopedia/article-Hoare_logic.html (1752 words)

	C. A. R. Hoare - Wikipedia, the free encyclopedia
		Sir Charles Antony Richard Hoare (Tony Hoare or C.A.R. Hoare, born January 11, 1934) is a British computer scientist, probably best known for the development of Quicksort, the world's most widely used sorting algorithm, in 1960.
		He also developed Hoare logic, and the formal language Communicating Sequential Processes (CSP) used to specify the interactions of concurrent processes and the inspiration for the Occam programming language.
		Born in Colombo (Sri Lanka) to British parents, he received his Bachelor's degree in Classics from the University of Oxford (Merton College) in 1956.
	en.wikipedia.org /wiki/C._A._R._Hoare (357 words)

	A Classical Mind: Microsoft Researcher Receives Kyoto Prize: Sir Antony Hoare helped solve some of computer science's ...
		Over the past four decades, Hoare's passion for precision and insights into how it may be achieved have served as beacons for the rest of the research community, leading to advances in the design of modern computer languages, increased software reliability and simplified computing with multiple computers.
		Hoare, 66, will be recognized for his "pioneering and fundamental contributions to software science" when he receives the Kyoto Prize in Advanced Technology later this week in Japan.
		Dijkstra credits Hoare's success to his "flexible and brilliant mind," as well as his good fortune to have attended British public schools -- which are considered by some to be the equivalent of American private schools -- and universities.
	www.microsoft.com /presspass/features/2000/nov00/11-06hoare.mspx (1925 words)

	Prof. David Harel - Books
		In Dynamic Logic, such programs are first-class objects on a par with formulas, complete with a collection of operators for forming compound programs inductively from a basis of primitive programs.
		Apart from the obvious heavy reliance on classical logic, computability theory and programming, the subject has its roots in the work of Thiele [198] and Engeler [42] in the late 1960's, who were the first to advance the idea of formulating and investigating formal systems dealing with properties of programs in an abstract setting.
		Dynamic Logic, which emphasizes the modal nature of the program/assertion interaction, was introduced by Pratt in 1976 [162].
	www.wisdom.weizmann.ac.il /~dharel/dynamic_logic.html#preface (848 words)

	ipedia.com: Logic Article
		In ordinary language, logic is the reasoning used to reach a conclusion from a set of assumptions.
		As such, of particular concern in logic is the structure of inference—the formal relations between the newly produced assertions and the previously established ones, where formal means relations are independent of the assertions themselves.
		As a byproduct, logic provides prescriptions for reasoning, that is, how people—as well as other intelligent beings, machines, and systems—ought to reason.
	www.ipedia.com /logic_1.html (1493 words)

	Kestrel Institute - Research Staff - Dusko Pavlovic - Security
		We present a specialized protocol logic that is built around a process language for describing the actions of a protocol.
		Like Floyd-Hoare logic, our logic contains axioms and inference rules for each of the main protocol actions and proofs are protocol-directed, meaning that the outline of a proof of correctness follows the sequence of actions in the protocol.
		We prove that the protocol logic is sound, in a specific sense: each provable assertion about an action or sequence of actions holds in any run of the protocol, under attack, in which the given actions occur.
	www.kestrel.edu /home/people/pavlovic/security.html (1149 words)

	teaching Hoare logic (Site not responding. Last check: 2007-08-19)
		It would be misleading to give students the impression that Hoare logic simply does not work with higher types.
		The results for L4 show that it is possible to use Hoare logic to reason about programs with higher types and infinite range.
		I interpret the results on L4 to show that the limitations of Hoare logic are due to the way the store can be accessed in some languages with higher types rather than the presence of higher types alone.
	www.cis.upenn.edu /~bcpierce/types/archives/1988/msg00143.html (193 words)

	[No title]
		The fact that P is both a pre- and post-condition for the while loop is reflected in the conclusion of the rule.
		Soundness is important because it says that Hoare logic doesn't allow us to derive triples that actually don't hold.
		This result is known as the relative completeness of Hoare logic and is due to Cook (1974); the proof is fairly complex and we will omit it (but you can find details in the Winskel book).
	www.cs.cornell.edu /courses/cs411/2004fa/lectures/lec11.txt (1251 words)

	Exercise 13: Hoare Logic
		Hoare's original approach was to describe a set of logical rules that should hold true of a programming language, this implies a meaning for programs in the language.
		However, the rules of Hoare logic are a natural way to reason about programs.
		introduction in Hoare logic is expressed in terms of syntactic substitution.
	cs.anu.edu.au /student/comp8033/ex13.html (1249 words)

	Hoare Logic and Auxiliary Variables - Kleymann (ResearchIndex) (Site not responding. Last check: 2007-08-19)
		However, the axioms and rules of Hoare Logic turn a blind eye to the rle of auxiliary variables.
		Courtesy of this new rule, Hoare Logic is adaptation complete, which benefits software re-use.
		14 A generalization of Owicki-Gries's Hoare Logic for a concurr..
	citeseer.ist.psu.edu /434676.html (783 words)

	Hoare logic and lambda calculus (Site not responding. Last check: 2007-08-19)
		Hoare logic can be presented as a quantifier-free fragment of multi-sorted predicate logic (with Hoare triples as atomic formulas).
		I am using this approach in my chapter on Denotational Semantics of Algol-like Languages in the Handbook of Logic in Computer Science.
		A preliminary draft of this is available from me in return for comments, corrections and suggestions for improvement.
	www.cis.upenn.edu /~bcpierce/types/archives/1988/msg00137.html (100 words)

	Information Flow Analysis. (Site not responding. Last check: 2007-08-19)
		The logic facilitates static checking of a larger class of programs than can be checked by extant type-based approaches in which a program is deemed insecure when it contains an insecure subprogram.
		The logic is based on an abstract interpretation of program traces that makes independence between program variables explicit.
		The logic enjoys ``small'' specifications, so as to facilitate modular reasoning; these can be combined by a frame rule.
	www.cis.ksu.edu /~tamtoft/CV/cv/node51.html (210 words)

	Ketul Patel
		The goal of this course is to study formal techniques for describing computation and compilation.
		This approach leads to a more general understanding of programming languages, specification, logic, mathematics, and proof theory.
		An overview of propositional logic and predicate calculus.
	www.iit.edu /~pateke12/CS589.html (833 words)

	C. A. R. Hoare - Iridis Encyclopedia (Site not responding. Last check: 2007-08-19)
		Sir Charles Antony Richard Hoare (Tony Hoare) is a British computer scientist, probably best known for the development of Quicksort, the world's most widely used sorting algorithm, and perhaps even the world's most widely used algorithm of any kind, in 1960.
		Born in Colombo (Sri Lanka) to British parents, he received his Bachelor's degree in Classics from the University of Oxford in 1956.
		The aphorism "Premature optimization is the root of all evil," often ascribed to Knuth, was actually coined by Hoare.
	www.iridis.com /Tony_Hoare (317 words)

	[No title]
		My treatment of Floyd-Hoare logic is done in the greatest detail for what I call the direct declarative language (with assignments but no conditionals or loops).
		This illustrates a subtlely in first order categorical logic: that the relevant structure consists of less than all finite (limits and) stable disjoint colimits.
		The categorical structure corresponding to first order logic is a (Heyting) pretopos, which need not have coequalisers of arbitrary parallel pairs.
	www.mta.ca /~cat-dist/catlist/1999/cat-while-floyd-hoare (1160 words)

	Crash in Program and Logic (Site not responding. Last check: 2007-08-19)
		With traditional Hoare logic it is possible to prove partial correctness of programs through statements of the kind "If the precondition holds and the program terminates, then the postcondition holds." In this work-in-progress we try to extend Hoare logic in a way that it can deal also with crashes (i.e., abrupt termination).
		We propose to extend the two-valued logic to a three-valued logic, in which the third truth value corresponds to "crash." In such an extension it would be possible to model partial functions in programs by partial functions in the extended Hoare logic.
		We aim to discuss choices about possible three-valued logic candidates, and to relate this approach to Kleene algebras, in the perspective of using algebraic expressions inside programs as effective tools to directly calculate partial correctness assertions.
	www.cs.bham.ac.uk /~mmk/papers/02-AVOCS.html (258 words)

	Analyzing Java in Isabelle/HOL: Formalization, Type Safety and Hoare Logic
		The second main contribution is a sound and complete Hoare logic, where the soundness proof for our Hoare logic gives new insights into the role of type safety.
		To our knowledge, this logic is the first one for an object-oriented language that has been proved complete.
		By-products of this work are a new general technique for handling side-effecting expressions and their results, the discovery of the strongest possible rule of consequence, and a new rule for flexible handling of mutual recursion.
	david.von-oheimb.de /cs/diss (677 words)

	The FLINT Project: Hoare Logic and Type Systems for FPCC (Site not responding. Last check: 2007-08-19)
		In the process, we are explicitly manipulating the interface between Hoare logic and a syntactic type system.
		To our knowledge, this is the first account of combining such certification proofs from languages at different levels of abstraction.
		Hoare logic-style reasoning, on the other hand, can handle low-level details very well but cannot account for embedded code pointers in data structures, a feature common to higher-order and object-oriented programming.
	flint.cs.yale.edu /flint/publications/rtpcc.html (210 words)

	Amazon.com: Mathematical Logic for Computer Science: Books: Mordechai Ben-Ari (Site not responding. Last check: 2007-08-19)
		Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students.
		The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates.
		The study of logic was begun by the ancient Greeks whose educational system stressed competence in philosophy and rhetoric.
	www.amazon.com /exec/obidos/tg/detail/-/1852333197?v=glance (727 words)

	Abstracts of papers by Torben Amtoft
		Thus the logic employs independence assertions to describe the noninterference property that formalizes confidentiality, and employs region assertions to describe possible aliasing.
		The logic is based on an abstract interpretation of a "prelude" semantics which makes independence between program variables explicit.
		The model resembles a logic language and is parametrized with respect to evaluation order, but it should not be too difficult to transfer the ideas to other languages.
	www.cis.ksu.edu /~tamtoft/Papers/abstracts.html (4415 words)

	COT 3420 Syllabus
		Master deriving formal proofs using the axioms and rules of inference of a logic.
		Be familiar with applications of logic to computer science, such as logic programming or program derivation using Hoare logic.
		Hoare Logic---we will define the meaning of a small programming language by giving logical rules for each construct.
	www.cs.fiu.edu /~smithg/cot3420/syllabus.html (541 words)

	The world's top hoare logic websites
		The purpose of the system is to provide a set of logical rules which one can use to reason about computer programs.
		Let C be a line, or sequence of lines, in a computer program, and let P and Q be logical predicates such that if P is true before C is executed then Q will necessarily be true after C is executed.
		is an expression in Hoare logic, also known as a Hoare triple.
	www.websbiggest.com /dir-wiki.cfm?cat=hoare_logic&tab=edit (218 words)

	Amazon.com: Dynamic Logic (Foundations of Computing): Books: David Harel,Dexter Kozen,Jerzy Tiuryn (Site not responding. Last check: 2007-08-19)
		For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events.
		Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value.
		Provides an introduction to Dynamic Logic, an approach to formal reasoning about programs which is strongly related to classical logic.
	www.amazon.com /exec/obidos/tg/detail/-/0262082896?v=glance (1025 words)

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