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Separation Logic
In computer science, separation logic is an extension of Hoare logic, a way of reasoning about programs. It was developed by John C. Reynolds, Peter O'Hearn, Samin Ishtiaq and Hongseok Yang, drawing upon early work by Rod Burstall. The assertion language of separation logic is a special case of the logic of bunched implications (BI). A CACM review article by O'Hearn charts developments in the subject to early 2019. Overview Separation logic facilitates reasoning about: * programs that manipulate pointer data structures—including information hiding in the presence of pointers; * ''"transfer of ownership"'' (avoidance of semantic frame axioms); and * virtual separation (modular reasoning) between concurrent modules. Separation logic supports the developing field of research described by Peter O'Hearn and others as ''local reasoning'', whereby specifications and proofs of a program component mention only the portion of memory used by the component, and not the entire global ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). 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 preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Memory Allocation
Memory management (also dynamic memory management, dynamic storage allocation, or dynamic memory allocation) is a form of resource management applied to computer memory. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single process might be underway at any time. Several methods have been devised that increase the effectiveness of memory management. Virtual memory systems separate the memory addresses used by a process from actual physical addresses, allowing separation of processes and increasing the size of the virtual address space beyond the available amount of RAM using paging or swapping to secondary storage. The quality of the virtual memory manager can have an extensive effect on overall system performance. The system allows a computer to appear as if it may have more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memory Management
Memory management (also dynamic memory management, dynamic storage allocation, or dynamic memory allocation) is a form of Resource management (computing), resource management applied to computer memory. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single Process (computing), process might be underway at any time. Several methods have been devised that increase the effectiveness of memory management. Virtual memory systems separate the memory addresses used by a process from actual physical addresses, allowing separation of processes and increasing the size of the virtual address space beyond the available amount of Random-access memory, RAM using paging or swapping to secondary storage. The quality of the virtual memory manager can have an extensive effect on overall system C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tony Hoare
Sir Charles Antony Richard Hoare (; born 11 January 1934), also known as C. A. R. Hoare, is a British computer scientist who has made foundational contributions to programming languages, algorithms, operating systems, formal verification, and concurrent computing. His work earned him the Turing Award, usually regarded as the highest distinction in computer science, in 1980. Hoare developed the sorting algorithm quicksort in 1959–1960. He developed Hoare logic, an axiomatic basis for verifying program correctness. In the semantics of concurrency, he introduced the formal language communicating sequential processes (CSP) to specify the interactions of concurrent processes, and along with Edsger Dijkstra, formulated the dining philosophers problem. Since 1977, he has held positions at the University of Oxford and Microsoft Research in Cambridge. Education and early life Tony Hoare was born in Colombo, Ceylon (now Sri Lanka) to British parents; his father was a colonial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relevance Logic
Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but not universally, called ''relevant logic'' by British and, especially, Australian logicians, and ''relevance logic'' by American logicians. Relevance logic aims to capture aspects of implication that are ignored by the " material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is not new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a donkey, then two and two is four" is true when translated as a material implication, yet it seems int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frame Problem
In artificial intelligence, with implications for cognitive science, the frame problem describes an issue with using first-order logic to express facts about a robot in the world. Representing the state of a robot with traditional first-order logic requires the use of many axioms that simply imply that things in the environment do not change arbitrarily. For example, Hayes describes a " block world" with rules about stacking blocks together. In a first-order logic system, additional axioms are required to make inferences about the environment (for example, that a block cannot change position unless it is physically moved). The frame problem is the problem of finding adequate collections of axioms for a viable description of a robot environment. John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, ''Some Philosophical Problems from the Standpoint of Artificial Intelligence''. In this paper, and many that came after, the formal mathematical problem was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjunction (category Theory)
In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of "optimal solutions" to certain problems (i.e., constructions of objects having a certain universal property), such as the construction of a free group on a set in algebra, or the construction of the Stone–Čech compactification of a topological space in topology. By definition, an adjunction between categories \mathcal and \mathcal is a pair of functors (assumed to be covariant) :F: \mathcal \rightarrow \mathcal and G: \mathcal \rightarrow \mathcal and, for all objects c in \mathcal and d in \mathcal, a bijection between the respective morphism sets :\mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Ponens
In propositional logic, (; MP), also known as (), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P'' implies ''Q.'' ''P'' is true. Therefore, ''Q'' must also be true." ''Modus ponens'' is a mixed hypothetical syllogism and is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of ''modus ponens''. The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. Explanation The form of a ''modus ponens'' argument is a mixed hypothetical syllogism, with two premises and a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entailment
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises?Beall, JC and Restall, Greg, Logical Consequence' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Conjunction
In logic, mathematics and linguistics, ''and'' (\wedge) is the Truth function, truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as \wedge or \& or K (prefix) or \times or \cdot in which \wedge is the most modern and widely used. The ''and'' of a set of operands is true if and only if ''all'' of its operands are true, i.e., A \land B is true if and only if A is true and B is true. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English language, English "Conjunction (grammar), and"; * In programming languages, the Short-circuit evaluation, short-circuit and Control flow, control structure; * In set theory, Intersection (set theory), intersection. * In Lattice (order), lattice theory, logical conjunction (Infimum and supremum, greatest lower bound). Notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Function
In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to . The subset , that is, the '' domain'' of viewed as a function, is called the domain of definition or natural domain of . If equals , that is, if is defined on every element in , then is said to be a total function. In other words, a partial function is a binary relation over two sets that associates to every element of the first set ''at most'' one element of the second set; it is thus a univalent relation. This generalizes the concept of a (total) function by not requiring ''every'' element of the first set to be associated to an element of the second set. A partial function is often used when its exact domain of definition is not known, or is difficult to specify. However, even when the exact domain of definition is known, partial functions are often used for simplicity or brevity. This is the case in calculus, where, for example, the quotien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
