|
Lean (proof Assistant)
Lean is a theorem prover and programming language. It is based on the calculus of constructions with inductive types. The Lean project is an open source project, hosted on GitHub. It was launched by Leonardo de Moura at Microsoft Research in 2013. Lean has an interface that differentiates it from other interactive theorem provers. Lean can be compiled to JavaScript and accessed in a web browser. It has native support for Unicode symbols. (These can be typed using LaTeX-like sequences, such as "\times" for "×".) Lean also has an extensive support for meta-programming. Lean has gotten attention from mathematicians Thomas Hales and Kevin Buzzard. Hales is using it for his project, Formal Abstracts. Buzzard uses it for the Xena project. One of the Xena Project's goals is to rewrite every theorem and proof in the undergraduate math curriculum of Imperial College London in Lean. Examples Here is how the natural numbers are defined in Lean. inductive nat : Type , zero : nat , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Programming
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 wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kevin Buzzard
Kevin Mark Buzzard (born 21 September 1968) is a British mathematician and currently a professor of pure mathematics at Imperial College London. He specialises in arithmetic geometry and the Langlands program. Biography While attending the Royal Grammar School, High Wycombe he competed in the International Mathematical Olympiad, where he won a bronze medal in 1986 and a gold medal with a perfect score in 1987. He obtained a B.A. degree ( Parts I & II) in Mathematics at Trinity College, Cambridge, where he was Senior Wrangler (achiever of the highest mark), and went on to complete the C.A.S.M. He then completed his dissertation, entitled ''The levels of modular representations'', under the supervision of Richard Taylor, for which he was awarded a Ph.D. degree. He took a lectureship at Imperial College London in 1998, a readership in 2002, and was appointed to a professorship in 2004. From October to December 2002 he held a visiting professorship at Harvard University, having ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Free Software
Microsoft Corporation is an American multinational technology corporation producing computer software, consumer electronics, personal computers, and related services headquartered at the Microsoft Redmond campus located in Redmond, Washington, United States. Its best-known software products are the Windows line of operating systems, the Microsoft Office suite, and the Internet Explorer and Edge web browsers. Its flagship hardware products are the Xbox video game consoles and the Microsoft Surface lineup of touchscreen personal computers. Microsoft ranked No. 21 in the 2020 Fortune 500 rankings of the largest United States corporations by total revenue; it was the world's largest software maker by revenue as of 2019. It is one of the Big Five American information technology companies, alongside Alphabet, Amazon, Apple, and Meta. Microsoft was founded by Bill Gates and Paul Allen on April 4, 1975, to develop and sell BASIC interpreters for the Altair 8800. It rose to domina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software Programmed In C++
Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure political rights, as for a disenfranchised group * Free will, control exercised by rational agents over their actions and decisions * Free of charge, also known as gratis. See Gratis vs libre. Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free format, a file format which can be used without restrictions * Free software, software usable and distributable with few restrictions and no payment * Freeware, a broader class of software available at no cost Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free And Open-source Software
Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source code is openly shared so that people are encouraged to voluntarily improve the design of the software. This is in contrast to proprietary software, where the software is under restrictive copyright licensing and the source code is usually hidden from the users. FOSS maintains the software user's civil liberty rights (see the Four Essential Freedoms, below). Other benefits of using FOSS can include decreased software costs, increased security and stability (especially in regard to malware), protecting privacy, education, and giving users more control over their own hardware. Free and open-source operating systems such as Linux and descendants of BSD are widely utilized today, powering millions of servers, desktops, smartphones (e.g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Languages
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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Educational Math Software
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] |
Proof Assistants
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. System comparison * ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. * Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification. * HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems the logical core is a library of their programming language. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Languages Created In 2013
Program, programme, programmer, or programming may refer to: Business and management * Program management, the process of managing several related projects * Time management * Program, a part of planning Arts and entertainment Audio * Programming (music), generating music electronically * Radio programming, act of scheduling content for radio * Synthesizer programmer, a person who develops the instrumentation for a piece of music Video or television * Broadcast programming, scheduling content for television * Program music, a type of art music that attempts to render musically an extra-musical narrative * Synthesizer patch or program, a synthesizer setting stored in memory * "Program", an instrumental song by Linkin Park from '' LP Underground Eleven'' * Programmer, a film on the lower half of a double feature bill; see B-movie Science and technology * Computer program, a set of instructions that describes how to perform a specific task to a computer. * Computer programmi ... [...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] |
Mimalloc
mimalloc (pronounced "me-malloc") is a free and open-source compact general-purpose memory allocator developed by Microsoft with focus on performance characteristics. The library is about 11000 lines of code and works as a drop-in replacement for malloc of the C standard library and requires no additional code changes. mimalloc was initially developed for the run-time systems of the Lean and Koka languages. Notable design aspects include free list sharding, eager page reset, first-class heaps. It can co-exist with other memory allocators linked to the same program. mimalloc is available on Windows, Mac OS X, Linux and *BSD. The source code is licensed under MIT License and available on GitHub. See also *C dynamic memory allocation *Manual memory management *Dynamic memory allocation Memory management is a form of resource management applied to computer memory. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
