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Futamura Projection
In computing, partial evaluation is a technique for several different types of program optimization by specialization. The most straightforward application is to produce new programs that run faster than the originals while being guaranteed to behave in the same way. A computer program ''prog'' is seen as a mapping of input data into output data: : prog : I_\text \times I_\text \to O, where I_\text, the ''static data'', is the part of the input data known at compile time. The partial evaluator transforms \langle prog, I_\text\rangle into prog^* : I_\text \to O by precomputing all static input at compile time. prog^* is called the "residual program" and should run more efficiently than the original program. The act of partial evaluation is said to "residualize" prog to prog^*. Futamura projections A particularly interesting example of the use of partial evaluation, first described in the 1970s by Yoshihiko Futamura, is when ''prog'' is an interpreter for a programming languag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, engineering, mathematical, technological and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology and software engineering. The term "computing" is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers. History The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. Computing is intimately tied to the representation of numbers, though mathematical conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (computer Science)
In computer science, program optimization, code optimization, or software optimization, is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less memory storage or other resources, or draw less power. General Although the word "optimization" shares the same root as "optimal", it is rare for the process of optimization to produce a truly optimal system. A system can generally be made optimal not in absolute terms, but only with respect to a given quality metric, which may be in contrast with other possible metrics. As a result, the optimized system will typically only be optimal in one application or for one audience. One might reduce the amount of time that a program takes to perform some task at the price of making it consume more memory. In an application where memory space is at a premium, on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specialization (logic)
Specialization or Specialized may refer to: Academia * Academic specialization, may be a course of study or major at an academic institution or may refer to the field in which a specialist practices * Specialty (medicine), a branch of medical practice Biology * Cellular differentiation, the process by which a less specialized cell becomes a more specialized cell type * Specialty (medicine), a branch of medical science * Generalist and specialist species, in biology and ecology * Specialization in multicellular organisms Computer science * Partial template specialization, a particular form of class template specialization * Template specialization, a style of computer programming which allows alternative implementations to be provided based on certain characteristics of the parameterized type that is being instantiated Economics and industry * Departmentalization, refers to the process of grouping activities into departments * Division of labour, the specialization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Program
A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer program in its human-readable form is called source code. Source code needs another computer program to execute because computers can only execute their native machine instructions. Therefore, source code may be translated to machine instructions using the language's compiler. ( Assembly language programs are translated using an assembler.) The resulting file is called an executable. Alternatively, source code may execute within the language's interpreter. If the executable is requested for execution, then the operating system loads it into memory and starts a process. The central processing unit will soon switch to this process so it can fetch, decode, and then execute each machine instruction. If the source code is requested for execution, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map (mathematics)
In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: ''mapping'' the Earth surface to a sheet of paper. The term ''map'' may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term ''transformation'' can be used interchangeably, but ''transformation'' often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. Maps as functions In many branches of mathematics, the term ''map'' is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a " continuous function" in topology, a "linear transformation" in linear algebra, etc. Some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compile-time Function Execution
In computing, compile-time function execution (or compile time function evaluation, or general constant expressions) is the ability of a compiler, that would normally compile a function to machine code and execute it at run time, to execute the function at compile time. This is possible if the arguments to the function are known at compile time, and the function does not make any reference to or attempt to modify any global state (i.e. it is a pure function). If the value of only some of the arguments are known, the compiler may still be able to perform some level of compile-time function execution ( partial evaluation), possibly producing more optimized code than if no arguments were known. Examples Lisp The Lisp macro system is an early example of the use of compile-time evaluation of user-defined functions in the same language. C++ The Metacode extension to C++ (Vandevoorde 2003) was an early experimental system to allow compile-time function evaluation (CTFE) and code inject ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoization
In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing. Although related to caching, memoization refers to a specific case of this optimization, distinguishing it from forms of caching such as buffering or page replacement. In the context of some logic programming languages, memoization is also known as tabling. Etymology The term "memoization" was coined by Donald Michie in 1968 and is derived from the Latin word "memorandum" ("to be remembered"), usually truncated as "memo" in American English, and thus carries the meaning of "turning he results ofa function into something to be remembered". While "memoization" might be confused with "memorization" (becaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Application
In computer science, partial application (or partial function application) refers to the process of fixing a number of arguments to a function, producing another function of smaller arity. Given a function f \colon (X \times Y \times Z) \to N , we might fix (or 'bind') the first argument, producing a function of type \text(f) \colon (Y \times Z) \to N . Evaluation of this function might be represented as f_(2, 3). Note that the result of partial function application in this case is a function that takes two arguments. Partial application is sometimes incorrectly called currying, which is a related, but distinct concept. Motivation Intuitively, partial function application says "if you fix the first parameter (computer science), arguments of the function, you get a function of the remaining arguments". For example, if function ''div''(''x'',''y'') = ''x''/''y'', then ''div'' with the parameter ''x'' fixed at 1 is another function: ''div''1(''y'') = ''div''(1,''y'') = 1/''y''. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Run-time Algorithm Specialisation
In computer science, run-time algorithm specialization is a methodology for creating efficient algorithms for costly computation tasks of certain kinds. The methodology originates in the field of automated theorem proving and, more specifically, in the Vampire theorem prover project. The idea is inspired by the use of partial evaluation in optimising program translation. Many core operations in theorem provers exhibit the following pattern. Suppose that we need to execute some algorithm \mathit(A,B) in a situation where a value of A ''is fixed for potentially many different values of'' B. In order to do this efficiently, we can try to find a specialization of \mathit for every fixed A, i.e., such an algorithm \mathit_A, that executing \mathit_A(B) is equivalent to executing \mathit(A,B). The specialized algorithm may be more efficient than the generic one, since it can ''exploit some particular properties'' of the fixed value A. Typically, \mathit_A(B) can avoid some operations tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smn Theorem
In computability theory the ' theorem, (also called the translation lemma, parameter theorem, and the parameterization theorem) is a basic result about programming languages (and, more generally, Gödel numberings of the computable functions) (Soare 1987, Rogers 1967). It was first proved by Stephen Cole Kleene (1943). The name ' comes from the occurrence of an ''S'' with subscript ''n'' and superscript ''m'' in the original formulation of the theorem (see below). In practical terms, the theorem says that for a given programming language and positive integers ''m'' and ''n'', there exists a particular algorithm that accepts as input the source code of a program with free variables, together with ''m'' values. This algorithm generates source code that effectively substitutes the values for the first ''m'' free variables, leaving the rest of the variables free. Details The basic form of the theorem applies to functions of two arguments (Nies 2009, p. 6). Given a Gödel numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strength Reduction
In compiler construction, strength reduction is a compiler optimization where expensive operations are replaced with equivalent but less expensive operations. The classic example of strength reduction converts "strong" multiplications inside a loop into "weaker" additions – something that frequently occurs in array addressing. Examples of strength reduction include: * replacing a multiplication within a loop with an addition * replacing an exponentiation within a loop with a multiplication Code analysis Most of a program's execution time is typically spent in a small section of code (called a hot spot), and that code is often inside a loop that is executed over and over. A compiler uses methods to identify loops and recognize the characteristics of register values within those loops. For strength reduction, the compiler is interested in: *Loop invariants: the values which do not change within the body of a loop. *Induction variables: the values which are being iterated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Template Metaprogramming
Template metaprogramming (TMP) is a metaprogramming technique in which templates are used by a compiler to generate temporary source code, which is merged by the compiler with the rest of the source code and then compiled. The output of these templates can include compile-time constants, data structures, and complete functions. The use of templates can be thought of as compile-time polymorphism. The technique is used by a number of languages, the best-known being C++, but also Curl, D, Nim, and XL. Template metaprogramming was, in a sense, discovered accidentally. Some other languages support similar, if not more powerful, compile-time facilities (such as Lisp macros), but those are outside the scope of this article. Components of template metaprogramming The use of templates as a metaprogramming technique requires two distinct operations: a template must be defined, and a defined template must be instantiated. The template definition describes the generic form of the gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
