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Bottom Type
In type theory, a theory within mathematical logic, the bottom type of a type system is the type that is a subtype of all other types. Where such a type exists, it is often represented with the up tack (⊥) symbol. When the bottom type is empty, a function whose return type is bottom cannot return any value, not even the lone value of a unit type. In such a language, the bottom type may therefore be known as the zero or never type. In the Curry–Howard correspondence, an empty type corresponds to falsity. Computer science applications In subtyping systems, the bottom type is a subtype of all types. It is dual to the top type, which spans all possible values in a system. If a type system is sound, the bottom type is uninhabited and a term of bottom type represents a logical contradiction. In such systems, typically no distinction is drawn between the bottom type and the empty type, and the terms may be used interchangeably. If the bottom type is inhabited, its terms typical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance And Contravariance (computer Science)
Many programming language type systems support subtyping. For instance, if the type is a subtype of , then an expression of type should be substitutable wherever an expression of type is used. Variance refers to how subtyping between more complex types relates to subtyping between their components. For example, how should a list of s relate to a list of s? Or how should a function that returns relate to a function that returns ? Depending on the variance of the type constructor, the subtyping relation of the simple types may be either preserved, reversed, or ignored for the respective complex types. In the OCaml programming language, for example, "list of Cat" is a subtype of "list of Animal" because the list type constructor is covariant. This means that the subtyping relation of the simple types are preserved for the complex types. On the other hand, "function from Animal to String" is a subtype of "function from Cat to String" because the function type constructor is cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fail-stop
{{Unreferenced, date=June 2019, bot=noref (GreenC bot) A fail-stop subset of a computer language is one that has the same semantics as the original, except in the case where an exceptional condition arises. The fail-stop subset must report an exceptional condition whenever the superset language reports one, but may additionally report an exceptional condition in other cases. Fail-stop languages are often used in computer systems where correctness is very important, since it is easier to make such systems fail-fast. For example, the "+" operator in many programming languages is not associative because of the possibility of floating-point overflow. Repairing these languages to fail fast when commonly assumed properties do not hold makes it much easier to write and verify correct code. Examples In many widely used programming languages the code below might reduce the bank account value if the deposited amount or old account value is very large, by causing an overflowed value to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contradiction
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." In modern formal logic and type theory, the term is mainly used instead for a ''single'' proposition, often denoted by the falsum symbol \bot; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History By creation of a paradox, Plato's '' Euthydemus'' dialogue demonstrates the need for the notion of ''contradiction''. In the ensuing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dart (programming Language)
Dart is a programming language designed for client development, such as for the web and mobile apps. It is developed by Google and can also be used to build server and desktop applications. It is an object-oriented, class-based, garbage-collected language with C-style syntax. It can compile to either machine code or JavaScript, and supports interfaces, mixins, abstract classes, reified generics and type inference. History Dart was unveiled at the GOTO conference in Aarhus, Denmark, October 10–12, 2011. The project was founded by Lars Bak and Kasper Lund. Dart 1.0 was released on November 14, 2013. Dart initially had a mixed reception and the Dart initiative has been criticized by some for fragmenting the web, due to the original plans to include a Dart VM in Chrome. Those plans were dropped in 2015 with the 1.9 release of Dart to focus instead on compiling Dart to JavaScript. Dart 2.0 was released in August 2018, with language changes including a type system. Dart 2. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D (programming Language)
D, also known as dlang, is a multi-paradigm system programming language created by Walter Bright at Digital Mars and released in 2001. Andrei Alexandrescu joined the design and development effort in 2007. Though it originated as a re-engineering of C++, D is a profoundly different language —features of D can be considered streamlined and expanded-upon ideas from C++, however D also draws inspiration from other high-level programming languages, notably Java, Python, Ruby, C#, and Eiffel. D combines the performance and safety of compiled languages with the expressive power of modern dynamic and functional programming languages. Idiomatic D code is commonly as fast as equivalent C++ code, while also being shorter. The language as a whole is not memory-safe but includes optional attributes designed to guarantee memory safety of either subsets of or the whole program. Type inference, automatic memory management and syntactic sugar for common types allow faster develo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kotlin (programming Language)
Kotlin () is a cross-platform, statically typed, general-purpose programming language with type inference. Kotlin is designed to interoperate fully with Java, and the JVM version of Kotlin's standard library depends on the Java Class Library, but type inference allows its syntax to be more concise. Kotlin mainly targets the JVM, but also compiles to JavaScript (e.g., for frontend web applications using React) or native code via LLVM (e.g., for native iOS apps sharing business logic with Android apps). Language development costs are borne by JetBrains, while the Kotlin Foundation protects the Kotlin trademark. On 7 May 2019, Google announced that the Kotlin programming language is now its preferred language for Android app developers. Since the release of Android Studio 3.0 in October 2017, Kotlin has been included as an alternative to the standard Java compiler. The Android Kotlin compiler produces Java 8 bytecode by default (which runs in any later JVM), but lets the pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Closure Tools
Google Closure Tools is a set of tools to help developers build rich web applications with JavaScript. It was developed by Google for use in their web applications such as Gmail, Google Docs and Google Maps. Closure Compiler The Closure Compiler is a tool for making JavaScript downloads run faster, at the expense of human readability. It does not compile from JavaScript to machine code, but rather compiles from JavaScript to more efficient JavaScript. It parses JavaScript, analyzes it, removes dead code and rewrites and minifies what is left. It also checks syntax, variable references, and types and warns about common JavaScript pitfalls. It supports transpiling modern ECMAScript code to ECMAScript 5, so that programmers can write JavaScript that uses those features, and run it in browsers or other environments that do not yet support them. (the Traceur Compiler is another Google project that supports transpiling ES6 to ES3.) CLI based tools Tool set provide a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JavaScript
JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of websites use JavaScript on the client side for webpage behavior, often incorporating third-party libraries. All major web browsers have a dedicated JavaScript engine to execute the code on users' devices. JavaScript is a high-level, often just-in-time compiled language that conforms to the ECMAScript standard. It has dynamic typing, prototype-based object-orientation, and first-class functions. It is multi-paradigm, supporting event-driven, functional, and imperative programming styles. It has application programming interfaces (APIs) for working with text, dates, regular expressions, standard data structures, and the Document Object Model (DOM). The ECMAScript standard does not include any input/output (I/O), such as networking, storage, or graphics facilities. In practice, the web bro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TypeScript
TypeScript is a free and open source programming language developed and maintained by Microsoft. It is a strict syntactical superset of JavaScript and adds optional static typing to the language. It is designed for the development of large applications and transpiles to JavaScript. As it is a superset of JavaScript, existing JavaScript programs are also valid TypeScript programs. TypeScript may be used to develop JavaScript applications for both client-side and server-side execution (as with Node.js or Deno). Multiple options are available for transpilation. The default TypeScript Compiler can be used, or the Babel compiler can be invoked to convert TypeScript to JavaScript. TypeScript supports definition files that can contain type information of existing JavaScript libraries, much like C++ header files can describe the structure of existing object files. This enables other programs to use the values defined in the files as if they were statically typed TypeScript entitie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia (programming Language)
Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programming language; with multiple dispatch as its core programming paradigm. Julia supports concurrent, (composable) parallel and distributed computing (with or without using MPI or the built-in corresponding to "OpenMP-style" threads), and direct calling of C and Fortran libraries without glue code. Julia uses a just-in-time (JIT) compiler that is referred to as "just- ahead-of-time" (JAOT) in the Julia community, as Julia compiles all code (by default) to machine code before running it. Julia is garbage-collected, uses eager evaluation, and includes efficient libraries for floating-point calculations, linear algebra, random number generation, and regular expression matching. Many libraries are available, including some (e.g., for fas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
