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Loop-invariant Code
In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes checked within the code by an assertion call. Knowing its invariant(s) is essential in understanding the effect of a loop. In formal program verification, particularly the Floyd-Hoare approach, loop invariants are expressed by formal predicate logic and used to prove properties of loops and by extension algorithms that employ loops (usually correctness properties). The loop invariants will be true on entry into a loop and following each iteration, so that on exit from the loop both the loop invariants and the loop termination condition can be guaranteed. From a programming methodology viewpoint, the loop invariant can be viewed as a more abstract specification of the loop, which characterizes the deeper purpose of the loop beyond the details of this implementation. A survey article covers fundamental algorithms from many a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Correctness
Partial may refer to: Mathematics * Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ** ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial dee" ** Partial differential equation, a differential equation that contains unknown multivariable functions and their partial derivatives Other uses *Partial application, in computer science the process of fixing a number of arguments to a function, producing another function *Partial charge or net atomic charge, in chemistry a charge value that is not an integer or whole number *Partial fingerprint, impression of human fingers used in criminology or forensic science *Partial seizure or focal seizure, a seizure that initially affects only one hemisphere of the brain * Partial or Part score, in contract bridge a trick score less than 100, as well as other meanings * Partial or Partial wave, one sound wave of which a complex tone is compose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floyd–Hoare Logic
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare, and subsequently refined by Hoare and other researchers. The original ideas were seeded by the work of Robert W. Floyd, who had published a similar system for flowcharts. Hoare triple The central feature of Hoare logic is the Hoare triple. A triple describes how the execution of a piece of code changes the state of the computation. A Hoare triple is of the form : \ C \ where P and Q are '' assertions'' and C is a ''command''.Hoare originally wrote "P\Q" rather than "\C\". P is named the ''precondition'' and Q the ''postcondition'': when the precondition is met, executing the command establishes the postcondition. Assertions are formulae in predicate logic. Hoare logic provides axioms and inference rules for all the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eiffel
Eiffel may refer to: Places * Eiffel Peak, a summit in Alberta, Canada * Champ de Mars – Tour Eiffel station, Paris, France; a transit station Structures * Eiffel Tower, in Paris, France, designed by Gustave Eiffel * Eiffel Bridge, Ungheni, Moldova, designed by Gustave Eiffel * Eiffel Bridge, Láchar, Spain, built by the studio of Gustave Eiffel * Eiffel Bridge, Zrenjanin, Serbia, built by Gustave Eiffel's company * Eiffel Building, Sao Paulo, Brazil; a mixed use building Education * Eiffel School of Management (est. 2007), Creteil, France * Gustave Eiffel French School of Budapest, Hungary * Gustave Eiffel University (est. 2020), Champs-sur-Marne, Marne la Vallée, France * Lycée Gustave Eiffel (other) Music * Eiffel 65, an Italian electronic music group, originally called Eiffel * Eiffel (band), a French rock group * '' 5 Eiffel'' (EP), a 1982 record by Kim Larsen * " Alec Eiffel", a song by the alternative rock band Pixies Other uses * Eiffel (company), succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assert
Assertion or assert may refer to: Computing * Assertion (software development), a computer programming technique * assert.h, a header file in the standard library of the C programming language * Assertion definition language, a specification language providing a formal grammar to specify behaviour and interfaces for computer software Logic and language * Logical assertion, a statement that asserts that a certain premise is true * Proof by assertion, an informal fallacy in which a proposition is repeatedly restated * Time of assertion, in linguistics a secondary temporal reference in establishing tense * Assertive, a speech act that commits a speaker to the truth of the expressed proposition Other uses * Assert (horse) Assert (17 April 1979 – 14 September 1995) was an Irish Thoroughbred racehorse and sire. As a two-year-old he was beaten by Golden Fleece on his debut but went on to win the Beresford Stakes. In the following year he won four Group One ... (1979–1995 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Informal Example
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to: Dress code and events * Formal wear, attire for formal events * Semi-formal attire, attire for semi-formal events * Informal attire, more controlled attire than casual but less than formal * Formal (university), official university dinner, ball or other event * School formal, official school dinner, ball or other event Logic and mathematics *Formal logic, or mathematical logic ** Informal logic, the complement, whose definition and scope is contentious *Formal fallacy, reasoning of invalid structure ** Informal fallacy, the complement *Informal mathematics, also called naïve mathematics *Formal cause, Aristotle's intrinsic, determining cause * Formal power series, a generalization of power series without requiring convergence, used in combinatorics *Formal calculation, a calculation which is systematic, but without a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Postconditions
In computer programming, a postcondition is a condition or predicate that must always be true just after the execution of some section of code or after an operation in a formal specification. Postconditions are sometimes tested using assertions within the code itself. Often, postconditions are simply included in the documentation of the affected section of code. For example: The result of a factorial is always an integer and greater than or equal to 1. So a program that calculates the factorial of an input number would have postconditions that the result after the calculation be an integer and that it be greater than or equal to 1. Another example: a program that calculates the square root of an input number might have the postconditions that the result be a number and that its square be equal to the input. Postconditions in object-oriented programming In some software design approaches, postconditions, along with preconditions and class invariants, are components of the softwar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whiley (programming Language)
Whiley is an experimental programming language that combines features from the functional and imperative paradigms, and supports formal specification through function preconditions, postconditions and loop invariants. The language uses flow-sensitive typing also known as "flow typing." The Whiley project began in 2009 in response to the "Verifying Compiler Grand Challenge" put forward by Tony Hoare in 2003. The first public release of Whiley was in June, 2010. Primarily developed by David Pearce, Whiley is an open source project with contributions from a small community. The system has been used for student research projects and in teaching undergraduate classes. It was supported between 2012 and 2014 by the Royal Society of New Zealand's Marsden Fund. The Whiley compiler generates code for the Java virtual machine and can inter-operate with Java and other JVM based languages. Overview The goal of Whiley is to provide a realistic programming language where verification i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Invariant
In computer programming, specifically object-oriented programming, a class invariant (or type invariant) is an invariant used for constraining objects of a class. Methods of the class should preserve the invariant. The class invariant constrains the state stored in the object. Class invariants are established during construction and constantly maintained between calls to public methods. Code within functions may break invariants as long as the invariants are restored before a public function ends. With concurrency, maintaining the invariant in methods typically requires a critical section to be established by locking the state using a mutex. An object invariant, or representation invariant, is a computer programming construct consisting of a set of invariant properties that remain uncompromised regardless of the state of the object. This ensures that the object will always meet predefined conditions, and that methods may, therefore, always reference the object without the risk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eiffel (programming Language)
Eiffel is an object-oriented programming, object-oriented programming language designed by Bertrand Meyer (an object-orientation proponent and author of ''Object-Oriented Software Construction'') and Eiffel Software. Meyer conceived the language in 1985 with the goal of increasing the reliability of commercial software development; the first version becoming available in 1986. In 2005, Eiffel became an International Organization for Standardization, ISO-standardized language. The design of the language is closely connected with the Eiffel programming method. Both are based on a set of principles, including design by contract, command–query separation, the uniform access principle, uniform-access principle, the Single choice principle, single-choice principle, the open–closed principle, and option–operand separation. Many concepts initially introduced by Eiffel later found their way into Java (programming language), Java, C Sharp (programming language), C#, and other langua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Logical equivalences In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these. General logical equivalences Logical equivalences involving conditional statements :#p \implies q \equiv \neg p \vee q :#p \implies q \equiv \neg q \implies \neg p :#p \vee q \equiv \neg p \implies q :#p \wedge q \equiv \neg (p \implies \neg q) :#\neg (p \implies q) \equiv p \wedge \neg q :#(p \implies q) \wedge (p \implie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
