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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] |
Common Lisp
Common Lisp (CL) is a dialect of the Lisp programming language, published in ANSI standard document ''ANSI INCITS 226-1994 (S20018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard. The Common Lisp language was developed as a standardized and improved successor of Maclisp. By the early 1980s several groups were already at work on diverse successors to MacLisp: Lisp Machine Lisp (aka ZetaLisp), Spice Lisp, NIL and S-1 Lisp. Common Lisp sought to unify, standardise, and extend the features of these MacLisp dialects. Common Lisp is not an implementation, but rather a language specification. Several implementations of the Common Lisp standard are available, including free and open-source software and proprietary products. Common Lisp is a general-purpose, multi-paradigm programming language. It supports a combination of procedural, functional, and object-oriented programming paradigms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idris (programming Language)
Idris is a purely-functional programming language with dependent types, optional lazy evaluation, and features such as a totality checker. Idris may be used as a proof assistant, but it is designed to be a general-purpose programming language similar to Haskell. The Idris type system is similar to Agda's, and proofs are similar to Coq's, including tactics (theorem proving functions/procedures) via elaborator reflection. Compared to Agda and Coq, Idris prioritizes management of side effects and support for embedded domain-specific languages. Idris compiles to C (relying on a custom copying garbage collector using Cheney's algorithm) and JavaScript (both browser- and Node.js-based). There are third-party code generators for other platforms, including JVM, CIL, and LLVM. Idris is named after a singing dragon from the 1970s UK children's television program ''Ivor the Engine''. Features Idris combines a number of features from relatively mainstream functional programming lang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard ML
Standard ML (SML) is a general-purpose, modular, functional programming language with compile-time type checking and type inference. It is popular among compiler writers and programming language researchers, as well as in the development of theorem provers. Standard ML is a modern dialect of ML, the language used in the Logic for Computable Functions (LCF) theorem-proving project. It is distinctive among widely used languages in that it has a formal specification, given as typing rules and operational semantics in ''The Definition of Standard ML''. Language Standard ML is a functional programming language with some impure features. Programs written in Standard ML consist of expressions as opposed to statements or commands, although some expressions of type unit are only evaluated for their side-effects. Functions Like all functional languages, a key feature of Standard ML is the function, which is used for abstraction. The factorial function can be expressed as follows: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HOL4
HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems in this family follow the LCF approach as they are implemented as a library which defines an abstract data type of proven theorems such that new objects of this type can only be created using the functions in the library which correspond to inference rules in higher-order logic. As long as these functions are correctly implemented, all theorems proven in the system must be valid. As such, a large system can be built on top of a small trusted kernel. Systems in the HOL family use ML or its successors. ML was originally developed along with LCF as a meta-language for theorem proving systems; in fact, the name stands for "Meta-Language". Underlying logic HOL systems use variants of classical higher-order logic, which has simple axiomatic foundations with few axioms and well-understood semantics. The logic used in HOL prov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HOL Light
HOL Light is a member of the HOL theorem prover family. Like the other members, it is a proof assistant for classical higher order logic. Compared with other HOL systems, HOL Light is intended to have relatively simple foundations. HOL Light is authored and maintained by the mathematician and computer scientist John Harrison. HOL Light is released under the simplified BSD license. Logical foundations HOL Light is based on a formulation of type theory with equality as the only primitive notion. The primitive rules of inference are the following: This formulation of type theory is very close to the one described in section II.2 of . References * Further reading *{{Citation , author = Freek Wiedijk , title = Formal Proof — Getting Started , journal = Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Research
Microsoft Research (MSR) is the research subsidiary of Microsoft. It was created in 1991 by Richard Rashid, Bill Gates and Nathan Myhrvold with the intent to advance state-of-the-art computing and solve difficult world problems through technological innovation in collaboration with academic, government, and industry researchers. The Microsoft Research team has more than 1,000 computer scientists, physicists, engineers, and mathematicians, including Turing Award winners, Fields Medal winners, MacArthur Fellows, and Dijkstra Prize winners. Between 2010 and 2018, 154,000 AI patents were filed worldwide, with Microsoft having by far the largest percentage of those patents, at 20%.Louis Columbus, January 6, 201Microsoft Leads The AI Patent Race Going Into 2019 ''Forbes'' According to estimates in trade publications, Microsoft spent about $6 billion annually in research initiatives from 2002-2010 and has spent from $10–14 billion annually since 2010. Microsoft Research has made signi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F* (programming Language)
F* (pronounced ''F star'') is a functional programming language inspired by ML and aimed at program verification. Its type system includes dependent types, monadic effects, and refinement types. This allows expressing precise specifications for programs, including functional correctness and security properties. The F* type-checker aims to prove that programs meet their specifications using a combination of SMT solving and manual proofs. Programs written in F* can be translated to OCaml, F#, and C for execution. Previous versions of F* could also be translated to JavaScript. The latest version of F* is written entirely in a common subset of F* and F#, and bootstraps in both OCaml and F#. It is open source (under the Apache License 2.0) and is under active development on 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, soft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
INRIA
The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name ''Institut de recherche en informatique et en automatique'' (IRIA) in 1967 at Rocquencourt near Paris, part of Plan Calcul. Its first site was the historical premises of SHAPE (central command of NATO military forces), which is still used as Inria's main headquarters. In 1980, IRIA became INRIA. Since 2011, it has been styled ''Inria''. Inria is a Public Scientific and Technical Research Establishment (EPST) under the double supervision of the French Ministry of National Education, Advanced Instruction and Research and the Ministry of Economy, Finance and Industry. Administrative status Inria has 9 research centers distributed across France (in Bordeaux, Grenoble-Inovallée, Lille, Lyon, Nancy, Paris- Rocquencourt, Rennes, Saclay, and Sophia Antipolis) and one center ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OCaml
OCaml ( , formerly Objective Caml) is a general-purpose programming language, general-purpose, multi-paradigm programming language which extends the Caml dialect of ML (programming language), ML with object-oriented programming, object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez, and others. The OCaml toolchain includes an interactive top-level Interpreter (computing), interpreter, a bytecode compiler, an optimizing native code compiler, a reversible debugger, and a package manager (OPAM). OCaml was initially developed in the context of automated theorem proving, and has an outsize presence in static program analysis, static analysis and formal methods software. Beyond these areas, it has found serious use in systems programming, web development, and financial engineering, among other application domains. The acronym ''CAML'' originally stood for ''Categorical Abstract Machine Language'', but O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albatross (programming Language)
Albatrosses, of the biological family Diomedeidae, are large seabirds related to the procellariids, storm petrels, and diving petrels in the order Procellariiformes (the tubenoses). They range widely in the Southern Ocean and the North Pacific. They are absent from the North Atlantic, although fossil remains show they once occurred there and occasional vagrants are found. Albatrosses are among the largest of flying birds, and species of the genus ''Diomedea'' (great albatrosses) have the longest wingspans of any extant birds, reaching up to . The albatrosses are usually regarded as falling into four genera, but disagreement exists over the number of species. Albatrosses are highly efficient in the air, using dynamic soaring and slope soaring to cover great distances with little exertion. They feed on squid, fish, and krill by either scavenging, surface seizing, or diving. Albatrosses are colonial, nesting for the most part on remote oceanic islands, often with several spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
