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Krivine Machine
In theoretical computer science, the Krivine machine is an ''abstract machine'' (sometimes called ''virtual machine''). As an abstract machine, it shares features with Turing machines and the SECD machine. The Krivine machine explains how to compute a recursive function. More specifically it aims to define rigorously head normal form reduction of a Lambda calculus, lambda term using call-by-name reduction. Thanks to its formalism, it tells in details how a kind of reduction works and sets the theoretical foundation of the operational semantics of functional programming languages. On the other hand, Krivine machine implements call-by-name because it evaluates the body of a β-reducible expression, redex before it Function application, applies the body to its parameter. In other words, in an expression (''λ'' ''x''. ''t'') ''u'' it evaluates first ''λ'' ''x''. ''t'' before applying it to ''u''. In functional programming, this would mean that in order to evaluate a function appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine De Krivine
A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by Animal power, animals and Human power, people, by natural forces such as Wind power, wind and Water power, water, and by Chemical energy, chemical, Thermal energy, thermal, or electricity, electrical power, and include a system of mechanism (engineering), mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems. Renaissance natural philosophers identified six simple machines which were the elementary devices that put a load into motion, and calculated the ratio of output force to input fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence. Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Models Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Models Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite state machines * Post machines ( Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model Functional models Functional models include: * Abstract re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and parallel distributed processing were established. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Educational Abstract Machines
Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty. Various researchers emphasize the role of critical thinking in order to distinguish education from indoctrination. Some theorists require that education results in an improvement of the student while others prefer a value-neutral definition of the term. In a slightly different sense, education may also refer, not to the process, but to the product of this process: the mental states and dispositions possessed by educated people. Education originated as the transmission of cultural heritage from one generation to the next. Today, educational goals increasingly encompass new ideas such as the liberation of learners, skills needed for modern society, empathy, and complex vocational skills. Types of education are commonly divided into formal, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Olivier Danvy
Olivier Danvy is a French computer scientist specializing in programming languages, partial evaluation, and continuations. He is a professor at Yale-NUS College in Singapore. Danvy received his PhD degree from the Université Paris VI in 1986. He is notable for the number of scientific papers which acknowledge his help. Writing in ''Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...'', editor Declan Butler reports on an analysis of acknowledgments on nearly one third of a million scientific papers and reports that Danvy is "the most thanked person in computer science". Danvy himself is quoted as being "stunned to find my name at the top of the list", ascribing his position to a "series of coincidences": he is multidisciplinary, is well travelled, is part of an interna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics Of Programming Languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid string (computer science), strings in a programming language syntax. Semantics describes the processes a computer follows when Execution (computing), executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain computer platform, platform, hence creating a model of computation. History In 1967, Robert W. Floyd publishes the paper ''Assigning meanings to programs''; his chief aim is "a rigorous standard for proofs about computer programs, including formal verification, proofs of correctness, equivalence, and termination". Floyd further writes: A semantic definition of a programming language, in our approach, is founded on a Syntax (programming languages), syntactic defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operational Semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms (denotational semantics). Operational semantics are classified in two categories: structural operational semantics (or small-step semantics) formally describe how the ''individual steps'' of a computation take place in a computer-based system; by opposition natural semantics (or big-step semantics) describe how the ''overall results'' of the executions are obtained. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and denotational semantics. The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Explicit Substitution
In computer science, lambda calculus, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution of variables, substitution. This is in contrast to the standard lambda calculus where substitutions are performed by beta reductions in an implicit manner which is not expressed within the calculus; the "freshness" conditions in such implicit calculi are a notorious source of errors. The concept has appeared in a large number of published papers in quite different fields, such as in abstract machines, predicate logic, and symbolic computation. Overview A simple example of a lambda calculus with explicit substitution is "λx", which adds one new form of term to the lambda calculus, namely the form M⟨x:=N⟩, which reads "M where x will be substituted by N". (The meaning of the new term is the same as the common idiom let x:=N in M from many programming languages.) λx can be written with the followi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic Compilation
Reproducible builds, also known as deterministic compilation, is a process of compiling software which ensures the resulting binary code can be reproduced. Source code compiled using deterministic compilation will always output the same binary. Reproducible builds can act as part of a chain of trust; the source code can be signed, and deterministic compilation can prove that the binary was compiled from trusted source code. Methods For the compilation process to be deterministic, the input to the compiler must be the same, regardless of the build environment used. This typically involves normalizing variables that may change, such as order of input files, timestamps, locales, and paths. Additionally, the compilers must not introduce non-determinism themselves. This sometimes happens when using hash tables with a random hash seed value. It can also happen when using the address of variables because that varies from address space layout randomization (ASLR). Build systems, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambda Calculus Definition
Lambda calculus is a formal mathematical system based on lambda abstraction and function application. Two definitions of the language are given here: a standard definition, and a definition using mathematical formulas. Standard definition This formal definition was given by Alonzo Church. Definition Lambda expressions are composed of * variables v_, v_, ..., v_, ... * the abstraction symbols lambda '\lambda ' and dot '.' * parentheses ( ) The set of lambda expressions, \Lambda , can be defined inductively: #If x is a variable, then x \in \Lambda #If x is a variable and M \in \Lambda , then (\lambda x . M) \in \Lambda #If M, N \in \Lambda , then (M \ N) \in \Lambda Instances of rule 2 are known as abstractions and instances of rule 3 are known as applications. Notation To keep the notation of lambda expressions uncluttered, the following conventions are usually applied. * Outermost parentheses are dropped: M \ N instead of (M \ N) * Applications are assumed to be left- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
