Traceability is the capability to trace something. In some cases, it is interpreted as the ability to verify the history, location, or application of an item by means of documented recorded identification. Other common definitions include the capability (and implementation) of keeping track of a given set or type of information to a given degree, or the ability to chronologically interrelate uniquely identifiable entities in a way that is verifiable. Traceability is applicable to measurement, supply chain, software development, healthcare and security. == Measurement == The term measurement traceability or metrological traceability is used to refer to an unbroken chain of comparisons relating an instrument's measurements to a known standard. Calibration to a traceable standard can be used to determine an instrument's bias, precision, and accuracy. It may also be used to show a chain of custody—from current interpretation of evidence to the actual evidence in a legal context, or history of handling of any information. In many countries, national standards for weights and measures are maintained by a National Metrological Institute (NMI) which provides the highest level of standards for the calibration / measurement traceability infrastructure in that country. Examples of government agencies include the National Physical Laboratory, UK (NPL) the National Institute of Standards and Technology (NIST) in the USA, the Physikalisch-Technische Bundesanstalt (PTB) in Germany, the Instituto Nazionale di Ricerca Metrologica (INRiM) in Italy, and the National Research Council of Canada (NRC). As defined by NIST, "Traceability of measurement requires the establishment of an unbroken chain of comparisons to stated references each with a stated uncertainty." A clock providing traceable time is traceable to a time standard such as Coordinated Universal Time or International Atomic Time. The Global Positioning System is a source of traceable time. === Food processing === In food processing (meat processing, fresh produce processing), the term traceability refers to the recording through means of barcodes or RFID tags and other tracking media, all movement of product and steps within the production process. One of the key reasons this is such a critical point is in instances where an issue of contamination arises, and a recall is required. Where traceability has been closely adhered to, it is possible to identify, by precise date/time and exact location which goods must be recalled, and which are safe, potentially saving millions of dollars in the recall process. Traceability within the food processing industry is also utilised to identify key high production and quality areas of a business, versus those of low return, and where points in the production process may be improved. In food processing software, traceability systems imply the use of a unique piece of data (e.g., order date/time or a serialized sequence number, generally through the use of a barcode / RFID) which can be traced through the entire production flow, linking all sections of the business, including suppliers and future sales through the supply chain. Messages and files at any point in the system can then be audited for correctness and completeness, using the traceability software to find the particular transaction and/or product within the supply chain. In food systems, ISO 22005, as part of the ISO 22000 family of standards, has been developed to define the principles for food traceability and specifies the basic requirements for the design and implementation of a feed and food traceability system. It can be applied by an organization operating at any step in the feed and food chain. The European Union's General Food Law came into force in 2002, making traceability compulsory for food and feed operators and requiring those businesses to implement traceability systems. The EU introduced its Trade Control and Expert System, or TRACES, in April 2004. The system provides a central database to track movement of animals within the EU and from third countries. Australia has its National Livestock Identification System to keep track of livestock from birth to slaughterhouse. India has started taking initiatives for setting up traceability systems at Government and Corporate levels. Grapenet, an initiative by Agriculture and Processed Food Products Export Development Authority (APEDA), Ministry of Commerce, Government of India is an example in this direction. GrapeNet is an internet based traceability software system for monitoring fresh grapes exported from India to the European Union. GrapeNet is a first of its kind initiative in India that has put in place an end-to-end system for monitoring pesticide residue, achieve product standardization and facilitate tracing back from pallets to the farm of the Indian grower, through the various stages of sampling, testing, certification and packing. Grapenet won the National Award (Gold), in the winners announced for the best e-Governance initiatives undertaken in India in 2007. The Directorate Generate Foreign Trade (DGFT), Government of India, through its notification dated 04.02.2009 relating to Amendment in Foreign Trade Policy (RE2008)has mandated that Export to the European Union is permitted subject to registration with APEDA, thereby making Grapenet mandatory for all exports of fresh grapes from India to Europe. Uruguay has also designed a system called "Traceability & Electronic Information System of the Beef Industry". Traceability in food supply can also refer to practices employed by individual companies, including Ritual and Amway's Nutrilite. In the case of Nutrilite's supplements, ingredients are documented and tested throughout farming, processing, and manufacturing to ensure traceability at each stage of production. == Systems and software development == In systems and software development, the term traceability (or requirements traceability) refers to the ability to link product requirements back to stakeholders' rationales and forward to corresponding design artifacts, code, and test cases. Traceability supports numerous software engineering activities such as change impact analysis, compliance verification or traceback of code, regression test selection, and requirements validation. It is usually accomplished in the form of a matrix created for the verification and validation of the project. Unfortunately, the practice of constructing and maintaining a requirements trace matrix (RTM) can be very arduous and over time the traces tend to erode into an inaccurate state unless date/time stamped. Alternate automated approaches for generating traces using information retrieval methods have been developed. The IEEE defines traceability as "(1)The degree to which a relationship can be established between two or more products of the development process, especially products having a predecessor, successor or master-subordinate relationship to one another. For example, the degree to which the requirements and design of a given software component match. See also: consistency. " and "(2) The degree to which each element in a software development product establishes its reason for existing; for example, the degree to which each element in a bubble chart references the requirement that it satisfies." In transaction processing software, traceability implies use of a unique piece of data (e.g., order date/time or a serialized sequence number) which can be traced through the entire software flow of all relevant application programs. Messages and files at any point in the system can then be audited for correctness and completeness, using the traceability key to find the particular transaction. This is also sometimes referred to as the transaction footprint. == Health care == Patient safety during healthcare service plays an important role in preventing delayed recovery or even mortality, by increasing and improving the quality of life of citizens, and is considered an indicator of the quality status of health services Maintaining patient safety is a complex task and involves factors inherent to the environment and human actions. New technologies facilitate the traceability tools of patients and medications. This is particularly relevant for drugs that are considered high risk and cost. Recent research in the healthcare industry emphasizes the significant impact of Blockchain Technology (BCT) on improving the performance of healthcare supply chain management. It highlights BCT's role in enhancing transparency, data immutability, and efficient management, leading to better cooperation among stakeholders and effective risk mitigation in healthcare services. The World Health Organization has recognized the importance of traceability for medical products of human origin (MPHO) and urged member states "to encourage the implementation of globally consistent coding systems to facilitate national and international traceability". == Security and cri
Ultra Hal
Ultra Hal is a chatbot intended to function as a virtual assistant. It was developed by Zabaware, Inc. Ultra Hal uses a natural language interface with animated characters using speech synthesis. Users can communicate with the chatterbot via typing or via a speech recognition engine. It utilizes the WordNet lexical dictionary. Its name is an allusion to HAL 9000, the artificial intelligence from the movie 2001: A Space Odyssey. Ultra Hal won the 2007 Loebner Prize for "most human" chatterbot.
Shadowrun
Shadowrun is a science fantasy tabletop role-playing game set in an alternate future in which cybernetics, magic and fantasy creatures co-exist. It combines genres of cyberpunk, urban fantasy, and crime, with occasional elements of conspiracy, horror, and detective fiction. From its inception in 1989, it has spawned a franchise that includes a series of novels, a collectible card game, two miniature-based tabletop wargames, and multiple video games. The title is taken from the game's main premise – a near-future world damaged by a massive magical event, where industrial espionage and corporate warfare runs rampant. A shadowrun – a successful data theft or physical break-in at a rival corporation or organization – is one of the main tools employed by both corporate rivals and underworld figures. Deckers (futuristic hackers) can tap into an immersive, three-dimensional cyberspace on such missions as they seek access, physical or remote, to the power structures of rival groups. They are opposed by rival deckers and lethal, potentially brain-destroying artificial intelligences called "Intrusion Countermeasures" (IC), while they are protected by street fighters and/or mercenaries, often with cyborg implants (called cyberware), magicians, and other exotic figures. Magic has also returned to the world after a series of plagues; dragons who can take human form have returned as well, and are commonly found in high positions of corporate power. == Publication history == Shadowrun was developed and published by FASA from 1989 until early 2001, when the company closed and Shadowrun was transferred to WizKids, a company founded by former FASA employees. Two years before its closure, FASA sold its videogame branch, FASA Interactive, to Microsoft corporation, keeping rights to publishing novels and pen and paper RPGs. Since then, digital rights to Shadowrun IP have belonged to Microsoft. WizKids licensed the RPG rights to Fantasy Productions, who were already publishing a German version, until WizKids was acquired by Topps in 2003. Catalyst Game Labs, a publishing imprint of InMediaRes Productions, licensed the rights from Topps to publish new products. WizKids itself produced an unsuccessful collectible action figure game based on the property, called Shadowrun Duels. A fifth edition of Shadowrun was announced in December 2012. A limited-edition softcover was sold at the Origins Game Fair in June 2013, and the PDF in July 2013. A hardcover was published in August 2013. Shadowrun Anarchy was published in October 2016 It is a simplified version of the ruleset which allows focus more on the narration than on the rules. The sixth edition, called Shadowrun, Sixth World, was announced on May 1, 2019 to coincide with the game's 30th anniversary, along with a new website at shadowrunsixthworld.com. The game was published on August 26, 2019. The mechanics for this new version are generally similar to those of fifth edition, with some rules reworked for what line developer Jason Hardy describes as streamlining. This new version also progressed the in-game year to 2080. Since 2004, Shadowrun Missions (SRM) has offered fans "living campaigns" that allow for persistent character advancement. SRM is broken down into seasons which are made up of up to 24 individual missions that can be played at home, with special missions available to play exclusively at conventions. Each SRM season develops an overarching plot focused on a specific city from the Shadowrun setting. Missions settings have included the divided city of Denver, the corporate city-state of Manhattan, the Seattle Metroplex city-state, the formerly walled-off wastelands of Chicago, and Neo-Tokyo. For Shadowrun, Sixth World missions returned to Seattle, with twenty-four missions set in 2081, right after Seattle declared independence from the UCAS. The current Shadowrun Missions setting is 2083 New Orleans. The Shadowrun role-playing game has spawned several properties, including Shadowrun: The Trading Card Game, eight video games, an action figure game (Shadowrun Duels), two magazines, an art book and more than 50 novels, starting with the Secrets of Power series which introduces some of the original characters of Shadowrun and provides an introduction to this fictional universe. In addition to the main rule book there have been over 100 published supplements including adventures and expansions to both the rules and the game settings. Catalyst Game Labs announced that 2013 would be "The Year of Shadowrun," and in addition to the release of Shadowrun fifth edition that it has collaborated with publishers on the following properties: Shadowrun: Crossfire, The Adventure Deck-building Game; Shadowrun: Sprawl Gangers, a tactical miniatures wargame; and Shadowrun: Hostile Takeover, a board game designed by Bryan C.P. Steele was planned for release in late 2014/early 2015. Catalyst had been in collaboration with Nordic Games and Cliffhanger Studios to create Shadowrun Chronicles: Boston Lockdown online RPG, however it was shuttered November 30, 2018, with the producers citing lack of funding and the end of the license terms for use of the IP. == Fictional universe == Shadowrun takes place several decades in the future (2050 in the first edition, currently 2088). The end of the Mesoamerican Long Count calendar ushered in the "Sixth World", with once-mythological beings (e.g. dragons) appearing and forms of magic suddenly emerging. Large numbers of humans have "Goblinized" into orks and trolls, while many human children are born as elves, dwarves, and even more exotic creatures. In North America, indigenous peoples discovered that their traditional ceremonies allow them to command powerful spirits, and rituals associated with a new Ghost Dance movement let them take control of much of the western U.S. and Canada, where they formed a federation of Native American Nations. Seattle remains under U.S. control by treaty as a city-state enclave, and most game materials are set there and assume campaigns will use it as their setting. In parallel with these magical developments, the setting's 21st century features technological and social developments associated with cyberpunk science fiction. Megacorporations control the lives of their employees and command their own armies; many of the largest have extraterritoriality, such as currently enjoyed by foreign heads of state. Technological advances make cyberware (mechanical replacement body parts) and bioware (augmented vat-grown body parts implanted in place of or in tandem with natural organs) common. The Computer Crash of 2029 led to the creation of the Matrix, a worldwide computer network that users interact with via direct neural interface. When conflicts arise, corporations, governments, organized crime syndicates, and even wealthy individuals subcontract their dirty work to specialists, who then perform "shadowruns" or missions undertaken by deniable assets without identities or those that wish to remain unknown. The most skilled of these specialists, called shadowrunners, have earned a reputation for getting the job done. They have developed a knack for staying alive, and prospering, in the world of Shadowrun. The Shadowrun world is cross-genre, incorporating elements of both cyberpunk and urban fantasy. Unlike in a purely cyberpunk game, in the Shadowrun world, magic exists and has "worked" since 2011. Among other things, this split humankind into subtypes, also known as metatypes/metahumans. Some of these metatypes take the form of common fantasy races. Likewise, some animals have turned into familiar monsters of past fantasy and lore and both monsters and human magicians have regained magical powers. By the second half of the 21st century, in the time the game is set, these events are accepted as commonplace. Man, machine, and magic exist in a world where the amazing is among the most common and technology has entered into every facet of human (and metahuman) life. === Races === Characters in Shadowrun can be humans, orks, trolls, elves, dwarves, as well as certain diverging subspecies (known as metavariants) such as gnomes, giants, dryads, etc. In the early days, when magic returned to the world, humans began to either change into, or give birth to, elf and dwarf infants, a phenomenon called Unexplained Genetic Expression (UGE). Later, some juvenile and adult humans "goblinized" into other races (mostly orks, but also some trolls). The term "metahuman" is used either to refer to humanity as a whole, including all races, or to refer specifically to non-human races, depending on context. The return of Halley's Comet brought even further variation in the form of changelings, who have variation atypical to their metatype or even species, such as electroreception. Two of the metahuman races, elves and orks, have fictional languages. Additionally, a virus known as the Human Meta-Human Vampiric Virus (HMHVV), with many variant strains, has been known to cause f
Orion's Arm
The Orion's Arm Universe Project (OA) is a multi-authored online hard science fiction world-building project, first established in 2000 by M. Alan Kazlev, Donna Malcolm Hirsekorn, Bernd Helfert and Anders Sandberg and further co-authored by many people since. Anyone can contribute articles, stories, artwork, or music to the website. The first published Orion's Arm book, a collection of five novellas set within the OA universe, called Against a Diamond Sky, was released in September 2009. == Canon == The fictional setting of Orion's Arm takes place about 10,000 years in the future, where an interstellar civilization spread across thousands of light-years, with inhabited planets and space habitats. Its inhabitants range from humans to extensively modified human beings, including superhumans with advanced augmentations and internal AI systems, while most people exist as softwares. Engineered wormholes are used for interstellar travel and transport, although not for time travel. The setting also includes several alien civilizations and evidence of more advanced alien societies in the past. At its highest levels, directed human evolution has produced vast godlike beings linked across interstellar distances, capable of understanding and creating technologies beyond ordinary minds. == Reception == Orion's Arm has been reviewed in the role-playing magazine Knights of the Dinner Table, as well as on Boing Boing by transhumanist science fiction author Cory Doctorow. References to the Encyclopaedia Galactica have been made in a book on overcoming Librarian stereotypes. The Orion's Arm website has also been recommended in a children's teaching guide.
Digital organism
A digital organism is a self-replicating computer program that mutates and evolves. Digital organisms are used as a tool to study the dynamics of Darwinian evolution, and to test or verify specific hypotheses or mathematical models of evolution. The study of digital organisms is closely related to the area of artificial life. == History == Digital organisms can be traced back to the game Darwin, developed in 1961 at Bell Labs, in which computer programs had to compete with each other by trying to stop others from executing . A similar implementation that followed this was the game Core War. In Core War, it turned out that one of the winning strategies was to replicate as fast as possible, which deprived the opponent of all computational resources. Programs in the Core War game were also able to mutate themselves and each other by overwriting instructions in the simulated "memory" in which the game took place. This allowed competing programs to embed damaging instructions in each other that caused errors (terminating the process that read it), "enslaved processes" (making an enemy program work for you), or even change strategies mid-game and heal themselves. Steen Rasmussen at Los Alamos National Laboratory took the idea from Core War one step further in his core world system by introducing a genetic algorithm that automatically wrote programs. However, Rasmussen did not observe the evolution of complex and stable programs. It turned out that the programming language in which core world programs were written was very brittle, and more often than not mutations would completely destroy the functionality of a program. The first to solve the issue of program brittleness was Thomas S. Ray with his Tierra system, which was similar to core world. Ray made some key changes to the programming language such that mutations were much less likely to destroy a program. With these modifications, he observed for the first time computer programs that did indeed evolve in a meaningful and complex way. Later, Chris Adami, Titus Brown, and Charles Ofria started developing their Avida system, which was inspired by Tierra but again had some crucial differences. In Tierra, all programs lived in the same address space and could potentially execute or otherwise interfere with each other's code. In Avida, on the other hand, each program lives in its own address space. Because of this modification, experiments with Avida became much cleaner and easier to interpret than those with Tierra. With Avida, digital organism research has begun to be accepted as a valid contribution to evolutionary biology by a growing number of evolutionary biologists. Evolutionary biologist Richard Lenski of Michigan State University has used Avida extensively in his work. Lenski, Adami, and their colleagues have published in journals such as Nature and the Proceedings of the National Academy of Sciences (USA). In 1996, Andy Pargellis created a Tierra-like system called Amoeba that evolved self-replication from a randomly seeded initial condition. More recently REvoSim - a software package based around binary digital organisms - has allowed evolutionary simulations of large populations that can be run for geological timescales.
Computer audition
Computer audition (CA) or machine listening is the general field of study of algorithms and systems for audio interpretation by machines. Since the notion of what it means for a machine to "hear" is very broad and somewhat vague, computer audition attempts to bring together several disciplines that originally dealt with specific problems or had a concrete application in mind. The engineer Paris Smaragdis, interviewed in Technology Review, talks about these systems — "software that uses sound to locate people moving through rooms, monitor machinery for impending breakdowns, or activate traffic cameras to record accidents." Inspired by models of human audition, CA deals with questions of representation, transduction, grouping, use of musical knowledge and general sound semantics for the purpose of performing intelligent operations on audio and music signals by the computer. Technically this requires a combination of methods from the fields of signal processing, auditory modelling, music perception and cognition, pattern recognition, and machine learning, as well as more traditional methods of artificial intelligence for musical knowledge representation. == Applications == Like computer vision versus image processing, computer audition versus audio engineering deals with understanding of audio rather than processing. It also differs from problems of speech understanding by machine since it deals with general audio signals, such as natural sounds and musical recordings. Applications of computer audition are widely varying, and include search for sounds, genre recognition, acoustic monitoring, music transcription, score following, audio texture, music improvisation, emotion in audio and so on. == Related disciplines == Computer Audition overlaps with the following disciplines: Music information retrieval: methods for search and analysis of similarity between music signals. Auditory scene analysis: understanding and description of audio sources and events. Computational musicology and mathematical music theory: use of algorithms that employ musical knowledge for analysis of music data. Computer music: use of computers in creative musical applications. Machine musicianship: audition driven interactive music systems. == Areas of study == Since audio signals are interpreted by the human ear–brain system, that complex perceptual mechanism should be simulated somehow in software for "machine listening". In other words, to perform on par with humans, the computer should hear and understand audio content much as humans do. Analyzing audio accurately involves several fields: electrical engineering (spectrum analysis, filtering, and audio transforms); artificial intelligence (machine learning and sound classification); psychoacoustics (sound perception); cognitive sciences (neuroscience and artificial intelligence); acoustics (physics of sound production); and music (harmony, rhythm, and timbre). Furthermore, audio transformations such as pitch shifting, time stretching, and sound object filtering, should be perceptually and musically meaningful. For best results, these transformations require perceptual understanding of spectral models, high-level feature extraction, and sound analysis/synthesis. Finally, structuring and coding the content of an audio file (sound and metadata) could benefit from efficient compression schemes, which discard inaudible information in the sound. Computational models of music and sound perception and cognition can lead to a more meaningful representation, a more intuitive digital manipulation and generation of sound and music in musical human-machine interfaces. The study of CA could be roughly divided into the following sub-problems: Representation: signal and symbolic. This aspect deals with time-frequency representations, both in terms of notes and spectral models, including pattern playback and audio texture. Feature extraction: sound descriptors, segmentation, onset, pitch and envelope detection, chroma, and auditory representations. Musical knowledge structures: analysis of tonality, rhythm, and harmonies. Sound similarity: methods for comparison between sounds, sound identification, novelty detection, segmentation, and clustering. Sequence modeling: matching and alignment between signals and note sequences. Source separation: methods of grouping of simultaneous sounds, such as multiple pitch detection and time-frequency clustering methods. Auditory cognition: modeling of emotions, anticipation and familiarity, auditory surprise, and analysis of musical structure. Multi-modal analysis: finding correspondences between textual, visual, and audio signals. === Representation issues === Computer audition deals with audio signals that can be represented in a variety of fashions, from direct encoding of digital audio in two or more channels to symbolically represented synthesis instructions. Audio signals are usually represented in terms of analogue or digital recordings. Digital recordings are samples of acoustic waveform or parameters of audio compression algorithms. One of the unique properties of musical signals is that they often combine different types of representations, such as graphical scores and sequences of performance actions that are encoded as MIDI files. Since audio signals usually comprise multiple sound sources, then unlike speech signals that can be efficiently described in terms of specific models (such as source-filter model), it is hard to devise a parametric representation for general audio. Parametric audio representations usually use filter banks or sinusoidal models to capture multiple sound parameters, sometimes increasing the representation size in order to capture internal structure in the signal. Additional types of data that are relevant for computer audition are textual descriptions of audio contents, such as annotations, reviews, and visual information in the case of audio-visual recordings. === Features === Description of contents of general audio signals usually requires extraction of features that capture specific aspects of the audio signal. Generally speaking, one could divide the features into signal or mathematical descriptors such as energy, description of spectral shape etc., statistical characterization such as change or novelty detection, special representations that are better adapted to the nature of musical signals or the auditory system, such as logarithmic growth of sensitivity (bandwidth) in frequency or octave invariance (chroma). Since parametric models in audio usually require very many parameters, the features are used to summarize properties of multiple parameters in a more compact or salient representation. === Musical knowledge === Finding specific musical structures is possible by using musical knowledge as well as supervised and unsupervised machine learning methods. Examples of this include detection of tonality according to distribution of frequencies that correspond to patterns of occurrence of notes in musical scales, distribution of note onset times for detection of beat structure, distribution of energies in different frequencies to detect musical chords and so on. === Sound similarity and sequence modeling === Comparison of sounds can be done by comparison of features with or without reference to time. In some cases an overall similarity can be assessed by close values of features between two sounds. In other cases when temporal structure is important, methods of dynamic time warping need to be applied to "correct" for different temporal scales of acoustic events. Finding repetitions and similar sub-sequences of sonic events is important for tasks such as texture synthesis and machine improvisation. === Source separation === Since one of the basic characteristics of general audio is that it comprises multiple simultaneously sounding sources, such as multiple musical instruments, people talking, machine noises or animal vocalization, the ability to identify and separate individual sources is very desirable. Unfortunately, there are no methods that can solve this problem in a robust fashion. Existing methods of source separation rely sometimes on correlation between different audio channels in multi-channel recordings. The ability to separate sources from stereo signals requires different techniques than those usually applied in communications where multiple sensors are available. Other source separation methods rely on training or clustering of features in mono recording, such as tracking harmonically related partials for multiple pitch detection. Some methods, before explicit recognition, rely on revealing structures in data without knowing the structures (like recognizing objects in abstract pictures without attributing them meaningful labels) by finding the least complex data representations, for instance describing audio scenes as generated by a few tone patterns and their trajectories (polyphonic voices) and acoustical contours drawn by a tone (c
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. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. == Automated proof checking == Automated proof checking is the process of using software for checking proofs for correctness. It is one of the most developed fields in automated reasoning. Automated proof checking differs from automated theorem proving in that automated proof checking simply mechanically checks the formal workings of an existing proof, instead of trying to develop new proofs or theorems itself. Because of this, the task of automated proof verification is much simpler than that of automated theorem proving, allowing automated proof checking software to be much simpler than automated theorem proving software. Because of this small size, some automated proof checking systems can have less than a thousand lines of core code, and are thus themselves amenable to both hand-checking and automated software verification. The Mizar system, HOL Light, and Metamath are examples of automated proof checking systems. Automated proof checking can be done either as a batch operation, or interactively, as part of an interactive theorem proving system. == History == Automath, which was developed by Nicolaas Govert de Bruijn starting in 1967, is often considered the first proof checker and the first system to utilize the Curry–Howard correspondence between programs and proofs. Automath was used by L.S. van Benthem Jutting in 1977 to formalize Landau's Foundations of Analysis, which was the first formalization of the real numbers. In 1973, Robert Boyer and J Moore published Proving Theorems about LISP Functions which aimed to verify programs, not mathematics. Their theorem prover is now known as ACL2. In the 1970s, Edinburgh LCF introduced the idea of using a functional programming language as the metalanguage for a theorem prover, and led to the HOL family of proof assistants. The 1990s saw the rise of Rocq, (then known as Coq), which has been used for many large-scale formalization projects. Since the late 2010s, Lean, a proof assistant strongly influenced by Rocq, has become another popular choice, especially for formalizing mathematics. == 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. 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. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include: HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license. HOL Light – A thriving "minimalist fork". OCaml based. ProofPower – Went proprietary, then returned to open source. Based on Standard ML. IMPS, An Interactive Mathematical Proof System. Isabelle is an interactive theorem prover where other systems can be encoded. Isabelle/HOL is its most popular instance, whose foundation is close to that of the HOL prover. Other instances include Isabelle/ZF and Isabelle/FOL. The main code-base is BSD-licensed, but the Isabelle distribution bundles many add-on tools with different licenses. Jape – Java based. Lean is both an interactive theorem prover and a functional, dependently-typed programming language. It is based on the calculus of inductive constructions with non-cumulative universes. Since version 4 (released in 2023), it is self-hosting. It can be used to formalise mathematics (and has a large, coherent library for formal mathematics), but also for software and hardware verification. LEGO Matita – A light system based on the calculus of inductive constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck set theory. PhoX – A proof assistant based on higher-order logic which is eXtensible. Prototype Verification System (PVS) – a proof language and system based on higher-order logic. Rocq (formerly named Coq) – A popular interactive theorem prover based on the calculus of inductive constructions. Theorem Proving System (TPS) and ETPS – Interactive theorem provers also based on simply typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation. == User interfaces == A commonly used front-end for proof assistants was the Emacs-based Proof General, developed at the University of Edinburgh. Nowadays, many provers include their own editor. Rocq includes RocqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/Scala infrastructure for document-oriented proof processing. More recently, Visual Studio Code extensions have been developed for Rocq, Isabelle by Makarius Wenzel, and for Lean 4 by the leanprover developers. == Formalization extent == Freek Wiedijk has been keeping a ranking of proof assistants by the amount of formalized theorems out of a list of 100 well-known theorems. As of September 2025, only six systems have formalized proofs of more than 70% of the theorems, namely Isabelle, HOL Light, Lean, Rocq, Metamath and Mizar. == Notable formalized proofs == The following is a list of notable proofs that have been formalized within proof assistants.