Epigram (programming Language)
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Epigram (programming Language)
Epigram is a functional programming language with dependent types, and the integrated development environment (IDE) usually packaged with the language. Epigram's type system is strong enough to express program specifications. The goal is to support a smooth transition from ordinary programming to integrated programs and proofs whose correctness can be checked and certified by the compiler. Epigram exploits the ''Curry–Howard correspondence'', also termed the ''propositions as types principle'', and is based on intuitionistic type theory. The Epigram prototype was implemented by Conor McBride based on joint work with James McKinna. Its development is continued by the Epigram group in Nottingham, Durham, England, Durham, St Andrews, and Royal Holloway, University of London in the United Kingdom (UK). The current experimental implementation of the Epigram system is freely available together with a user manual, a tutorial and some background material. The system has been used under ...
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Functional Programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declarative programming paradigm in which function definitions are Tree (data structure), trees of Expression (computer science), expressions that map Value (computer science), values to other values, rather than a sequence of Imperative programming, imperative Statement (computer science), statements which update the State (computer science), 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 Identifier (computer languages), identifiers), passed as Parameter (computer programming), arguments, and Return value, returned from other functions, just as any other data type can. This allows programs to be written in a Declarative programming, ...
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Program Specification
In computer science, formal specifications are mathematically based techniques whose purpose are to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning tools. These specifications are ''formal'' in the sense that they have a syntax, their semantics fall within one domain, and they are able to be used to infer useful information. Motivation In each passing decade, computer systems have become increasingly more powerful and, as a result, they have become more impactful to society. Because of this, better techniques are needed to assist in the design and implementation of reliable software. Established engineering disciplines use mathematical analysis as the foundation of creating and validating product design. Formal specifications are one such way to achieve this in software engineering reliability as once predicted. ...
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Natural Numbers
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by success ...
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ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of technical limitations of computer systems at the time it was invented, ASCII has just 128 code points, of which only 95 are , which severely limited its scope. All modern computer systems instead use Unicode, which has millions of code points, but the first 128 of these are the same as the ASCII set. The Internet Assigned Numbers Authority (IANA) prefers the name US-ASCII for this character encoding. ASCII is one of the List of IEEE milestones, IEEE milestones. Overview ASCII was developed from telegraph code. Its first commercial use was as a seven-bit teleprinter code promoted by Bell data services. Work on the ASCII standard began in May 1961, with the first meeting of the American Standards Association's (ASA) (now the American Nat ...
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LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as defense against herbivorous insects. Latex is not to be confused with plant sap; it is a distinct substance, separately produced, and with different functions. The word latex is also used to refer to natural latex rubber, particularly non-vulcanized rubber. Such is the case in products like latex gloves, latex condoms ...
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Natural Deduction
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasoning. Motivation Natural deduction grew out of a context of dissatisfaction with the axiomatizations of deductive reasoning common to the systems of Hilbert, Frege, and Russell (see, e.g., Hilbert system). Such axiomatizations were most famously used by Russell and Whitehead in their mathematical treatise ''Principia Mathematica''. Spurred on by a series of seminars in Poland in 1926 by Łukasiewicz that advocated a more natural treatment of logic, Jaśkowski made the earliest attempts at defining a more natural deduction, first in 1929 using a diagrammatic notation, and later updating his proposal in a sequence of papers in 1934 and 1935. His proposals led to diffe ...
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GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, it has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. As of June 2022, GitHub reported having over 83 million developers and more than 200 million repositories, including at least 28 million public repositories. It is the largest source code host . History GitHub.com Development of the GitHub.com platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett and Scott Chacon after it had been made available for a few months prior as a beta release. GitHub has an annual keynote called GitHub Universe. Organizational ...
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United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and Northern Ireland. The United Kingdom includes the island of Great Britain, the north-eastern part of the island of Ireland, and many smaller islands within the British Isles. Northern Ireland shares a land border with the Republic of Ireland; otherwise, the United Kingdom is surrounded by the Atlantic Ocean, the North Sea, the English Channel, the Celtic Sea and the Irish Sea. The total area of the United Kingdom is , with an estimated 2020 population of more than 67 million people. The United Kingdom has evolved from a series of annexations, unions and separations of constituent countries over several hundred years. The Treaty of Union between the Kingdom of England (which included Wales, annexed in 1542) and the Kingdom of Scotland in 170 ...
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Royal Holloway, University Of London
Royal Holloway, University of London (RHUL), formally incorporated as Royal Holloway and Bedford New College, is a public research university and a constituent college of the federal University of London. It has six schools, 21 academic departments and approximately 10,500 undergraduate and postgraduate students from over 100 countries. The campus is located west of Egham, Surrey, from central London. The Egham campus was founded in 1879 by the Victorian entrepreneur and philanthropist Thomas Holloway. Royal Holloway College was officially opened in 1886 by Queen Victoria as an all-women college. It became a member of the University of London in 1900. In 1945, the college admitted male postgraduate students, and in 1965, around 100 of the first male undergraduates. In 1985, Royal Holloway merged with Bedford College (another former all-women's college in London). The merged college was named Royal Holloway and Bedford New College (RHBNC), this remaining the official registered ...
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St Andrews
St Andrews ( la, S. Andrea(s); sco, Saunt Aundraes; gd, Cill Rìmhinn) is a town on the east coast of Fife in Scotland, southeast of Dundee and northeast of Edinburgh. St Andrews had a recorded population of 16,800 , making it Fife's fourth-largest settlement and 45th most populous settlement in Scotland. The town is home to the University of St Andrews, the third oldest university in the English-speaking world and the oldest in Scotland. It was ranked as the best university in the UK by the 2022 Good University Guide, which is published by ''The Times'' and ''The Sunday Times''. According to other rankings, it is ranked as one of the best universities in the United Kingdom. The town is named after Saint Andrew the Apostle. The settlement grew to the west of St Andrews Cathedral, with the southern side of the Scores to the north and the Kinness Burn to the south. The burgh soon became the ecclesiastical capital of Scotland, a position which was held until the Scottish ...
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Durham, England
Durham ( , locally ), is a cathedral city and civil parish on the River Wear, County Durham, England. It is an administrative centre of the County Durham District, which is a successor to the historic County Palatine of Durham (which is different to both the ceremonial county and district of County Durham). The settlement was founded over the final resting place of St Cuthbert. Durham Cathedral was a centre of pilgrimage in medieval England while the Durham Castle has been the home of Durham University since 1832. Both built in 11th-century, the buildings were designated as a World Heritage Site by UNESCO in 1986. HM Prison Durham is also located close to the city centre and was built in 1816. Name The name "Durham" comes from the Brythonic element , signifying a hill fort and related to -ton, and the Old Norse , which translates to island.Surtees, R. (1816) ''History and Antiquities of the County Palatine of Durham'' (Classical County Histories) The Lord Bishop of Durh ...
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Nottingham
Nottingham ( , East Midlands English, locally ) is a city status in the United Kingdom, city and Unitary authorities of England, unitary authority area in Nottinghamshire, East Midlands, England. It is located north-west of London, south-east of Sheffield and north-east of Birmingham. Nottingham has links to the legend of Robin Hood and to the lace-making, bicycle and Tobacco industry, tobacco industries. The city is also the county town of Nottinghamshire and the settlement was granted its city charter in 1897, as part of Queen Victoria's Diamond Jubilee celebrations. Nottingham is a tourist destination; in 2018, the city received the second-highest number of overnight visitors in the Midlands and the highest number in the East Midlands. In 2020, Nottingham had an estimated population of 330,000. The wider conurbation, which includes many of the city's suburbs, has a population of 768,638. It is the largest urban area in the East Midlands and the second-largest in the Midland ...
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