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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive symbols (which collectively form an alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the primitive symbols—combinations that are formed fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pointer (computer Programming)
In computer science, a pointer is an object in many programming languages that stores a memory address. This can be that of another value located in computer memory, or in some cases, that of memory-mapped computer hardware. A pointer ''references'' a location in memory, and obtaining the value stored at that location is known as '' dereferencing'' the pointer. As an analogy, a page number in a book's index could be considered a pointer to the corresponding page; dereferencing such a pointer would be done by flipping to the page with the given page number and reading the text found on that page. The actual format and content of a pointer variable is dependent on the underlying computer architecture. Using pointers significantly improves performance for repetitive operations, like traversing iterable data structures (e.g. strings, lookup tables, control tables and tree structures). In particular, it is often much cheaper in time and space to copy and dereference pointers th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Correctness
Total may refer to: Mathematics * Total, the summation of a set of numbers * Total order, a partial order without incomparable pairs * Total relation, which may also mean ** connected relation (a binary relation in which any two elements are comparable). * Total function, a partial function that is also a total relation Business * TotalEnergies, a French petroleum company * Total (cereal), a food brand by General Mills * Total, a brand of strained yogurt made by Fage * Total, a database management system marketed by Cincom Systems * Total Linhas Aéreas - a brazilian airline * Total, a line of dental products by Colgate Music and culture * Total (group), an American R&B girl group * '' Total: From Joy Division to New Order'', a compilation album * ''Total'' (Sebastian album) * ''Total'' (Total album) * ''Total'' (Teenage Bottlerocket album) * ''Total'' (Seigmen album) * ''Total'' (Wanessa album) * ''Total'' (Belinda Peregrín album) * '' Total 1'', an annual compilati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
While Rule
''While'' is a word in the English language that functions both as a noun and as a subordinating conjunction. Its meaning varies largely based on its intended function, position in the phrase and even the writer or speaker's regional dialect. As a conjunction, it is synonymous with the word ''whilst'', a form often considered archaic in American English, as well as in some style guides on both sides of the Atlantic. Usage Noun ''A while'' and ''awhile'' are often confused due to the fact that ''while'' is often accompanied by the indefinite article. The main difference is that ''a while'' means "an amount of time" or "some duration" whereas ''awhile'' is an adverb meaning "''for'' some amount of time" or "''for'' some duration". :"I slept for a while before dinner." :"I slept awhile before dinner." Both of these sentences yield the same effective meaning. ''Whilst'' is only a conjunction, and so its use here would be incorrect. Conjunction The primary function of the wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Invariant
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] |
Program Transformation
A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and in fewer cases the transformations result in programs that semantically differ from the original in predictable ways. While the transformations can be performed manually, it is often more practical to use a program transformation system that applies specifications of the required transformations. Program transformations may be specified as automated procedures that modify compiler data structures (e.g. abstract syntax trees) representing the program text, or may be specified more conveniently using patterns or templates representing parameterized source code fragments. A practical requirement for source code transformation systems is that they be able to effectively process programs written in a programming language. This usually requir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consequence Rule
Consequence may refer to: * Logical consequence, also known as a ''consequence relation'', or ''entailment'' * In operant conditioning, a result of some behavior * Consequentialism, a theory in philosophy in which the morality of an act is determined by its effects * Unintended consequences * In logic, a consequent is the second half of a hypothetical proposition or consequences * Consequent (music), the second half of a period (music) Games * Consequences (game), a parlour game Fiction * ''Consequences'' (novel), a 1919 novel by E. M. Delafield * "Consequences" (Kipling story), an 1888 short story by Rudyard Kipling * "Consequences" (Cather story), a 1915 short story by Willa Cather Film and TV * ''Die Konsequenz'' (English: ''The Consequence''), a 1977 West German film * ''Anjaam'' (English: ''Consequence''), a 1994 Hindi film * '' Anjaam (1940 film)'', an earlier Hindi film of the same name * Consequence (film), a 2003 action thriller film starring Armand Assante * '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliasing (computing)
In computing, aliasing describes a situation in which a data location in memory can be accessed through different symbolic names in the program. Thus, modifying the data through one name implicitly modifies the values associated with all aliased names, which may not be expected by the programmer. As a result, aliasing makes it particularly difficult to understand, analyze and optimize programs. Aliasing analysers intend to make and compute useful information for understanding aliasing in programs. Examples Buffer overflow For example, most implementations of the C programming language do not perform array bounds checking. One can then exploit the implementation of the programming language by the compiler and the computer architecture's assembly language conventions, to achieve aliasing effects by writing outside of the array (a type of buffer overflow). This invokes undefined behaviour according to the C language specification; however many implementations of C will show th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitution (logic)
Substitution is a fundamental concept in logic. A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions. The resulting expression is called a substitution instance, or instance for short, of the original expression. Propositional logic Definition Where ''ψ'' and ''φ'' represent formulas of propositional logic, ''ψ'' is a substitution instance of ''φ'' if and only if ''ψ'' may be obtained from ''φ'' by substituting formulas for symbols in ''φ'', replacing each occurrence of the same symbol by an occurrence of the same formula. For example: ::(R → S) & (T → S) is a substitution instance of: ::P & Q and ::(A ↔ A) ↔ (A ↔ A) is a substitution instance of: ::(A ↔ A) In some deduction systems for propositional logic, a new expression (a proposition) may be entered on a line of a derivation if it is a substitution instan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Variables And Bound Variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context. A bound variable, in contrast, is a variable that has been ''bound'' to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Deduction
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasoning. Motivation Natural deduction grew out of a context of dissatisfaction with the axiomatizations of deductive reasoning common to the systems of Hilbert, Frege, and Russell (see, e.g., Hilbert system). Such axiomatizations were most famously used by Russell and Whitehead in their mathematical treatise ''Principia Mathematica''. Spurred on by a series of seminars in Poland in 1926 by Łukasiewicz that advocated a more natural treatment of logic, Jaśkowski made the earliest attempts at defining a more natural deduction, first in 1929 using a diagrammatic notation, and later updating his proposal in a sequence of papers in 1934 and 1935. His proposals led to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NOP (code)
In computer science, a NOP, no-op, or NOOP (pronounced "no op"; short for no operation) is a machine language instruction and its assembly language mnemonic, programming language statement, or computer protocol command that does nothing. Machine language instructions Some computer instruction sets include an instruction whose explicit purpose is to not change the state of any of the programmer-accessible registers, status flags, or memory. It often takes a well-defined number of clock cycles to execute. In other instruction sets, there is no explicit NOP instruction, but the assembly language mnemonic NOP represents an instruction which acts as a NOP; e.g., on the SPARC, sethi 0, %g0. A NOP must not access memory, as that could cause a memory fault or page fault. A NOP is most commonly used for timing purposes, to force memory alignment, to prevent hazards, to occupy a branch delay slot, to render void an existing instruction such as a jump, as a target of an execute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
