Functional Language
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Functional Language
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner. Functional programming is sometimes treated as synonymous with purely functional programming, a subset of functional programming which treats all functions as deterministic mathematical functions, or pure functions. When a pure function is called with some ...
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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 ...
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Declarative Programming
In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow. Many languages that apply this style attempt to minimize or eliminate side effects by describing ''what'' the program must accomplish in terms of the problem domain, rather than describe ''how'' to accomplish it as a sequence of the programming language primitives (the ''how'' being left up to the language's implementation). This is in contrast with imperative programming, which implements algorithms in explicit steps. Declarative programming often considers programs as theories of a formal logic, and computations as deductions in that logic space. Declarative programming may greatly simplify writing parallel programs. Common declarative languages include those of database query languages (e.g., SQL, XQuery), regular expressions, logic programming, functio ...
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Formal Verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code. The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite-state machines, labelled transition systems, Petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, ...
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Software Testing
Software testing is the act of examining the artifacts and the behavior of the software under test by validation and verification. Software testing can also provide an objective, independent view of the software to allow the business to appreciate and understand the risks of software implementation. Test techniques include, but not necessarily limited to: * analyzing the product requirements for completeness and correctness in various contexts like industry perspective, business perspective, feasibility and viability of implementation, usability, performance, security, infrastructure considerations, etc. * reviewing the product architecture and the overall design of the product * working with product developers on improvement in coding techniques, design patterns, tests that can be written as part of code based on various techniques like boundary conditions, etc. * executing a program or application with the intent of examining behavior * reviewing the deployment infrastructure a ...
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Debugging
In computer programming and software development, debugging is the process of finding and resolving '' bugs'' (defects or problems that prevent correct operation) within computer programs, software, or systems. Debugging tactics can involve interactive debugging, control flow analysis, unit testing, integration testing, log file analysis, monitoring at the application or system level, memory dumps, and profiling. Many programming languages and software development tools also offer programs to aid in debugging, known as ''debuggers''. Etymology The terms "bug" and "debugging" are popularly attributed to Admiral Grace Hopper in the 1940s. While she was working on a Mark II computer at Harvard University, her associates discovered a moth stuck in a relay and thereby impeding operation, whereupon she remarked that they were "debugging" the system. However, the term "bug", in the sense of "technical error", dates back at least to 1878 and Thomas Edison who describes the "litt ...
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Software Bug
A software bug is an error, flaw or fault in the design, development, or operation of computer software that causes it to produce an incorrect or unexpected result, or to behave in unintended ways. The process of finding and correcting bugs is termed " debugging" and often uses formal techniques or tools to pinpoint bugs. Since the 1950s, some computer systems have been designed to deter, detect or auto-correct various computer bugs during operations. Bugs in software can arise from mistakes and errors made in interpreting and extracting users' requirements, planning a program's design, writing its source code, and from interaction with humans, hardware and programs, such as operating systems or libraries. A program with many, or serious, bugs is often described as ''buggy''. Bugs can trigger errors that may have ripple effects. The effects of bugs may be subtle, such as unintended text formatting, through to more obvious effects such as causing a program to crash, freezing th ...
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Imperative Programming
In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program consists of commands for the computer to perform. Imperative programming focuses on describing ''how'' a program operates step by step, rather than on high-level descriptions of its expected results. The term is often used in contrast to declarative programming, which focuses on ''what'' the program should accomplish without specifying all the details of ''how'' the program should achieve the result. Imperative and procedural programming Procedural programming is a type of imperative programming in which the program is built from one or more procedures (also termed subroutines or functions). The terms are often used as synonyms, but the use of procedures has a dramatic effect on how imperative programs appear and how they are constructed ...
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Procedure (computer Science)
In computer programming, a function or subroutine is a sequence of program instructions that performs a specific task, packaged as a unit. This unit can then be used in programs wherever that particular task should be performed. Functions may be defined within programs, or separately in libraries that can be used by many programs. In different programming languages, a function may be called a routine, subprogram, subroutine, method, or procedure. Technically, these terms all have different definitions, and the nomenclature varies from language to language. The generic umbrella term ''callable unit'' is sometimes used. A function is often coded so that it can be started several times and from several places during one execution of the program, including from other functions, and then branch back (''return'') to the next instruction after the ''call'', once the function's task is done. The idea of a subroutine was initially conceived by John Mauchly during his work on ENIAC, ...
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Side Effect (computer Science)
In computer science, an operation, function or expression is said to have a side effect if it modifies some state variable value(s) outside its local environment, which is to say if it has any observable effect other than its primary effect of returning a value to the invoker of the operation. Example side effects include modifying a non-local variable, modifying a static local variable, modifying a mutable argument passed by reference, performing I/O or calling other functions with side-effects. In the presence of side effects, a program's behaviour may depend on history; that is, the order of evaluation matters. Understanding and debugging a function with side effects requires knowledge about the context and its possible histories. Side effects play an important role in the design and analysis of programming languages. The degree to which side effects are used depends on the programming paradigm. For example, imperative programming is commonly used to produce side effects, to ...
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Pure Function
In computer programming, a pure function is a function that has the following properties: # the function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable reference arguments or input streams), and # the function has no side effects (no mutation of local static variables, non-local variables, mutable reference arguments or input/output streams). Thus a pure function is a computational analogue of a mathematical function. Some authors, particularly from the imperative language community, use the term "pure" for all functions that just have the above property 2 (discussed below). Examples Pure functions The following examples of C++ functions are pure: Impure functions The following C++ functions are impure as they lack the above property 1: The following C++ functions are impure as they lack the above property 2: The following C++ functions are impure as they lack both the above properties 1 and ...
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Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ...
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Deterministic System
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.Dynamical systems
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In physics

Physical laws that are described by represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly. In