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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. Relation with the empty type When the bottom type is uninhabited, 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, never or empty type which, in the Curry–Howard correspondence, corresponds to falsity. However, when the bottom type is inhabited, it is then different from the empty type. 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. Computer science applications In subtyping systems, the bottom type is a subtype of all types. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. 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 have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf 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 paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scala (programming Language)
Scala ( ) is a strongly statically typed high-level general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are intended to address criticisms of Java. Scala source code can be compiled to Java bytecode and run on a Java virtual machine (JVM). Scala can also be transpiled to JavaScript to run in a browser, or compiled directly to a native executable. When running on the JVM, Scala provides language interoperability with Java so that libraries written in either language may be referenced directly in Scala or Java code. Like Java, Scala is object-oriented, and uses a syntax termed '' curly-brace'' which is similar to the language C. Since Scala 3, there is also an option to use the off-side rule (indenting) to structure blocks, and its use is advised. Martin Odersky has said that this turned out to be the most productive change introduced in Scala 3. Unlike J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contradiction
In traditional logic, a contradiction involves a proposition conflicting 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 by Lars Bak and Kasper Lund and developed by Google. It can be used to develop web and mobile apps as well as server and desktop applications. Dart is an object-oriented, class-based, garbage-collected language with C-style syntax. It can compile to machine code, JavaScript, or WebAssembly. It supports interfaces, mixins, abstract classes, reified generics and type inference. The latest version of Dart is . History Dart was unveiled at the GOTO conference in Aarhus, Denmark, October 10–12, 2011. Lars Bak and Kasper Lund founded the project. Dart 1.0 was released on November 14, 2013. Dart had a mixed reception at first. Some criticized the Dart initiative for fragmenting the web because of plans to include a Dart VM in Chrome. Those plans were dropped in 2015 with the Dart 1.9 release. Focus changed to compiling Dart code to JavaScript. Dart 2.0 was released in August 2018 with language changes including a type sy ... [...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 now a very different language. As it has developed, it has drawn inspiration from other high-level programming languages. Notably, it has been influenced by Java, Python, Ruby, C#, and Eiffel. The D language reference describes it as follows: Features D is not source-compatible with C and C++ source code in general. However, any code that is legal in both C/C++ and D should behave in the same way. Like C++, D has closures, anonymous functions, compile-time function execution, design by contract, ranges, built-in container iteration concepts, and type inference. D's declaration, statement and expression syntaxes also closely match those of C++. Unlike C++, D also implements garbage collection, first cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kotlin (programming Language)
Kotlin () is a Cross-platform software, cross-platform, static typing, statically typed, general-purpose programming language, general-purpose High-level programming language, high-level programming language with type inference. Kotlin is designed to interoperate fully with Java (programming language), Java, and the Java virtual machine, JVM version of Kotlin's standard library depends on the Java Class Library, but type inference allows its syntax (programming languages), syntax to be more concise. Kotlin mainly targets the JVM, but also compiles to JavaScript (e.g., for frontend web applications using React (software), React) or machine code, native code via LLVM (e.g., for native iOS apps sharing business logic with Android (operating system), 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 had become its preferred language for Andro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, 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), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Closure Tools
Google Closure Tools was a set of tools built with the goal of helping developers optimize rich web applications with JavaScript. It was developed by Google for use in their web applications such as Gmail, Google Docs and Google Maps. As of Aug 1, 2024 the Closure Library has been sunset, for not "meeting the needs of modern JavaScript development". Closure Compiler The Closure Compiler is a tool that attempts to compress and optimize JavaScript code, at the expense of human readability. Unlike an actual compiler, it does not compile from JavaScript to machine code but rather minifies JavaScript. The process executes the following steps: # Parses the submitted JavaScript # Analyzes the JavaScript # Removes any dead code # 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 to achieve a wider range of browser compatibility, si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JavaScript
JavaScript (), often abbreviated as JS, is a programming language and core technology of the World Wide Web, alongside HTML and CSS. Ninety-nine percent of websites use JavaScript on the client side for webpage behavior. Web browsers have a dedicated JavaScript engine that executes the client code. These engines are also utilized in some servers and a variety of apps. The most popular runtime system for non-browser usage is Node.js. 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 netwo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TypeScript
TypeScript (abbreviated as TS) is a high-level programming language that adds static typing with optional type annotations to JavaScript. It is designed for developing large applications and transpiles to JavaScript. It is developed by Microsoft as free and open-source software released under an Apache License 2.0. TypeScript may be used to develop JavaScript applications for both client-side and server-side execution (as with Node.js, Deno or Bun). Multiple options are available for transpiling. 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 entities. There are third-party header files for popular li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia (programming Language)
Julia is a high-level programming language, high-level, general-purpose programming language, general-purpose dynamic programming language, dynamic programming language, designed to be fast and productive, for e.g. data science, artificial intelligence, machine learning, modeling and simulation, most commonly used for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism and the use of multiple dispatch as a core programming paradigm, a default just-in-time compilation, just-in-time (JIT) compiler (with support for ahead-of-time compilation) and an tracing garbage collection, efficient (multi-threaded) garbage collection implementation. Notably Julia does not support classes with encapsulated methods and instead it relies on structs with generic methods/functions not tied to them. By default, Julia is run similarly to scripting languages, using its runtime, and allows for read–eval–print loop, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ceylon (programming Language)
Ceylon was an object-oriented, strongly statically typed programming language with an emphasis on immutability, created by Red Hat. Ceylon programs run on the Java virtual machine (JVM), and could be compiled to JavaScript. The language design focuses on source code readability, predictability, toolability, modularity, and metaprogrammability. Important features of Ceylon include: * A type system enforcing null safety and list element existence at compile time * Regular syntax and semantics, avoiding special cases and primitively-defined constructs in favor of syntactic sugar * Support for generic programming and metaprogramming, with reified generics * Modularity built into the language, based on JBoss modules, interoperable with OSGi and Maven * powerful tools, including an Eclipse-based IDE The name "Ceylon" is an oblique reference to Java, in that Java and Sri Lanka, formerly known as Ceylon, are islands known for growth and export of coffee and tea. In August 201 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
