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JAPE (software)
Jape is a configurable, graphical proof assistant, originally developed by Richard Bornat at Queen Mary, University of London and Bernard Sufrin the University of Oxford. It allows user to define a logic, decide how to view proofs, and much more. It works with variants of the sequent calculus and natural deduction. It is claimedC. Kaliszyk, F. Wiedijk, M. Hendriks and F. van Raamsdonk, Teaching logic using a state-of-the-art proof assistant" In: H. Geuvers and P. Courtieu (eds.), ''PATE'07, International Workshop on Proof Assistants and Types in Education,'' 37–50, 2007. that Jape is the most popular program for "computer-assisted logic teaching" that involves exercises in developing proofs in mathematical logic. The program is available for the Mac, Unix, and Windows operating systems. It is written in the Java programming language and released under the GNU GPL. See also * List of proof assistants References External links Jape Onlineofficial distribution website JapeSou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Bornat
Richard Bornat (born 1944), is a British author and researcher in the field of computer science. He is also professor of Computer programming at Middlesex University. Previously he was at Queen Mary, University of London. Research Bornat's research interests includes ''program proving'' in separation logic. His focus is on the proofs themselves; as opposed to any logical underpinnings. Much of the work involves discovering ways to state the properties of independent modules, in a manner that makes their composition into useful systems conducive. Bornat (in conjunction with Bernard Sufrin of the Oxford University Computing Laboratory) developed Jape, a proof calculator; he is involved in research on the usability of this tool for exploration of novel proofs. Richard Bornat's PhD students have included Samson Abramsky in the early 1980s. In 2004, one of Bornat's students developed an aptitude test to ''"divide people up into programmers and non-programmers before they ever co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macintosh
The Mac (known as Macintosh until 1999) is a family of personal computers designed and marketed by Apple Inc., Apple Inc. Macs are known for their ease of use and minimalist designs, and are popular among students, creative professionals, and software engineers. The current lineup includes the MacBook Air and MacBook Pro laptops, as well as the iMac, Mac Mini, Mac Studio and Mac Pro desktops. Macs run the macOS operating system. The Macintosh 128K, first Mac was released in 1984, and was advertised with the highly-acclaimed 1984 (advertisement), "1984" ad. After a period of initial success, the Mac languished in the 1990s, until co-founder Steve Jobs returned to Apple in 1997. Jobs oversaw the release of many successful products, unveiled the modern Mac OS X, completed the Mac transition to Intel processors, 2005-06 Intel transition, and brought features from the iPhone back to the Mac. During Tim Cook's tenure as CEO, the Mac underwent a period of neglect, but was later reinv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SourceForge
SourceForge is a web service that offers software consumers a centralized online location to control and manage open-source software projects and research business software. It provides source code repository hosting, bug tracking, mirroring of downloads for load balancing, a wiki for documentation, developer and user mailing lists, user-support forums, user-written reviews and ratings, a news bulletin, micro-blog for publishing project updates, and other features. SourceForge was one of the first to offer this service free of charge to open-source projects. Since 2012, the website has run on Apache Allura software. SourceForge offers free hosting and free access to tools for developers of free and open-source software. , the SourceForge repository claimed to host more than 502,000 projects and had more than 3.7 million registered users. Concept SourceForge is a web-based source code repository. It acts as a centralized location for free and open-source software pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of 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 User interface, 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 progra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU GPL
The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general use and was originally written by the founder of the Free Software Foundation (FSF), Richard Stallman, for the GNU Project. The license grants the recipients of a computer program the rights of the Free Software Definition. These GPL series are all copyleft licenses, which means that any derivative work must be distributed under the same or equivalent license terms. It is more restrictive than the Lesser General Public License and even further distinct from the more widely used permissive software licenses BSD, MIT, and Apache. Historically, the GPL license family has been one of the most popular software licenses in the free and open-source software domain. Prominent free software programs licensed under the GPL include the Linux kernel a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Windows
Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for servers, and Windows IoT for embedded systems. Defunct Windows families include Windows 9x, Windows Mobile, and Windows Phone. The first version of Windows was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs). Windows is the most popular desktop operating system in the world, with 75% market share , according to StatCounter. However, Windows is not the most used operating system when including both mobile and desktop OSes, due to Android's massive growth. , the most recent version of Windows is Windows 11 for consumer PCs and tablets, Windows 11 Enterprise for corporations, and Windows Server 2022 for servers. Genealogy By marketing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unix
Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, and others. Initially intended for use inside the Bell System, AT&T licensed Unix to outside parties in the late 1970s, leading to a variety of both academic and commercial Unix variants from vendors including University of California, Berkeley (Berkeley Software Distribution, BSD), Microsoft (Xenix), Sun Microsystems (SunOS/Solaris (operating system), Solaris), Hewlett-Packard, HP/Hewlett Packard Enterprise, HPE (HP-UX), and IBM (IBM AIX, AIX). In the early 1990s, AT&T sold its rights in Unix to Novell, which then sold the UNIX trademark to The Open Group, an industry consortium founded in 1996. The Open Group allows the use of the mark for certified operating systems that comply with the Single UNIX Specification (SUS). Unix systems are chara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...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 language. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequent Calculus
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the natural style of deduction used by mathematicians than to David Hilbert's earlier style of formal logic, in which every line was an unconditional tautology. More subtle distinctions may exist; for example, propositions may implicitly depend upon non-logical axioms. In that case, sequents signify conditional theorems in a first-order language rather than conditional tautologies. Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments. * Hilbert style. Every line is an unconditional tautology (or theorem). * Gentzen s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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