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LEGO (proof Assistant)
LEGO is a proof assistant developed by Randy Pollack at the University of Edinburgh. It implements several type theories: the Edinburgh Logical Framework (LF), the Calculus of Constructions (CoC), the Generalized Calculus of Constructions A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common character ... (GCC) and the Unified Theory of Dependent Types (UTT). References External links * Proof assistants Dependently typed languages {{mathlogic-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Assistant
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 langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randy Pollack
Randy is a given name, popular in the United States and Canada. It is primarily a masculine name. It was originally derived from the names Randall, Randolf, Randolph, as well as Bertrand and Andrew, and may be a short form (hypocorism) of them. ''Randi'' is approximately the feminine equivalent of Randy. People with the given name A *Randy Abbey (born 1974), Ghanaian media personality * Randy Adler (??–2016), American bishop * Randy Albelda (born 1955), American economist *Randy Allen (other), multiple people * Randy Ambrosie (born 1963), Canadian sports executive * Randy Anderson (1959–2002), American wrestling referee * Randy Angst, American politician * Randy Armstrong (other), multiple people *Randy Arozarena (born 1995), Cuban baseball player * Randy Asadoor (born 1962), American baseball player * Randy Atcher (1918–2002), American television personality * Randy Avent, American electrical engineer * Randy Avon (born 1940), American politician * Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Edinburgh
The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1582 and officially opened in 1583, it is one of Scotland's four ancient universities and the sixth-oldest university in continuous operation in the English-speaking world. The university played an important role in Edinburgh becoming a chief intellectual centre during the Scottish Enlightenment and contributed to the city being nicknamed the "Athens of the North." Edinburgh is ranked among the top universities in the United Kingdom and the world. Edinburgh is a member of several associations of research-intensive universities, including the Coimbra Group, League of European Research Universities, Russell Group, Una Europa, and Universitas 21. In the fiscal year ending 31 July 2021, it had a total income of £1.176 billion, of w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edinburgh Logical Framework
In logic, a logical framework provides a means to define (or present) a logic as a signature in a higher-order type theory in such a way that provability of a formula in the original logic reduces to a type inhabitation problem in the framework type theory. This approach has been used successfully for (interactive) automated theorem proving. The first logical framework was Automath; however, the name of the idea comes from the more widely known Edinburgh Logical Framework, LF. Several more recent proof tools like Isabelle are based on this idea. Unlike a direct embedding, the logical framework approach allows many logics to be embedded in the same type system. Overview A logical framework is based on a general treatment of syntax, rules and proofs by means of a dependently typed lambda calculus. Syntax is treated in a style similar to, but more general than Per Martin-Löf's system of arities. To describe a logical framework, one must provide the following: # A characterization o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Constructions
In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. It can serve as both a typed programming language and as constructive foundation for mathematics. For this second reason, the CoC and its variants have been the basis for Coq and other proof assistants. Some of its variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive constructions (which adds coinduction), and the predicative calculus of inductive constructions (which removes some impredicativity). General traits The CoC is a higher-order typed lambda calculus, initially developed by Thierry Coquand. It is well known for being at the top of Barendregt's lambda cube. It is possible within CoC to define functions from terms to terms, as well as terms to types, types to types, and types to terms. The CoC is strongly normalizing, and hence consistent. Usage The CoC has been developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Calculus Of Constructions
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation. Generalization can also be used to refer to the process of identifying the parts of a whole, as belonging to the whole. The parts, which might be unrelated when left on their own, may be brought together as a group, hence belonging to the whole by establishing a common relation between them. However, the parts cannot be generalized into a whole—until a common relation is established among ''all'' parts. This does not mean that th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unified Theory Of Dependent Types
{{disambiguation ...
Unified may refer to: * The Unified, a wine symposium held in Sacramento, California, USA * ''Unified'', the official student newspaper of Canterbury Christ Church University * UNFD, an Australian record label * ''Unified'' (Sweet & Lynch album), 2017 * ''Unified'' (Super8 & Tab album), 2014 Unify may refer to: * ''Unify'', an album by Electric Universe * Unify Corporation, former name of Daegis Inc. * Unify Gathering, an Australian music festival * Unify GmbH & Co. KG, formerly Siemens Enterprise Communications See also * * * * Unification (other) * United (other) * Unity (other) Unity may refer to: Buildings * Unity Building, Oregon, Illinois, US; a historic building * Unity Building (Chicago), Illinois, US; a skyscraper * Unity Buildings, Liverpool, UK; two buildings in England * Unity Chapel, Wyoming, Wisconsin, US; a ... [...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 langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
