Suno is a generative artificial intelligence music creation platform. It is designed to generate music that can include vocals and instrumentation. The platform was initially developed by Suno, Inc., of Cambridge, Massachusetts. Suno has been widely available since December 20, 2023, after the launch of a web application and a partnership with Microsoft, which included Suno as a plugin in Microsoft Copilot. The program operates by producing songs based on text or audio prompts provided by its users. Suno does not disclose the dataset used to train its artificial intelligence. == History == Suno, Inc., was founded by four people: Michael Shulman, Georg Kucsko, Martin Camacho, and Keenan Freyberg. They all worked for Kensho, an AI startup, before starting their own company in Cambridge, Massachusetts. In April 2023, Suno released their open-source text-to-speech and audio model called "Bark" on GitHub. On March 21, 2024, Suno released its V3 version for all users. The new version allowed users to create a limited number of four-minute songs using a free account. Users can pay for more features. In April 2024, a sentimental ballad was generated with Suno based on the text of the MIT License. In June 2024, a lawsuit, led by the Recording Industry Association of America, was filed against Suno and Udio alleging widespread infringement of copyrighted sound recordings. The lawsuit sought to bar the companies from training on copyrighted music, as well as damages of up to $150,000 per work from infringements that have already taken place. On July 1, 2024, a mobile app for Suno was released. On November 19, 2024, Suno upgraded its AI song model program to v4. In January 2025, Michael Shulman remarked on a podcast, "I think the majority of people don't enjoy the majority of the time they spend making music." In March 2025, one day after thousands of musicians including Thom Yorke and ABBA's Björn Ulvaeus signed a letter calling for Suno to stop training its model on copyrighted music, Timbaland endorsed Suno in a video on the company's website. In July 2025, Suno user imoliver signed a record deal with Hallwood Media, which became the first instance of a traditional music label signing an AI-based creator. Hallwood later signed with AI-artist Xania Monet for US$3 million. Monet's songs were generated by Suno AI by poet Telisha Jones. In November 2025, Suno agreed to a $500 million dollar lawsuit settlement, in which Suno would be allowed to train its models on Warner Music Group's music catalog, and WMG would control aspects of AI likeness, music, audio, software, copyrights, AI tools and music created by users on Suno. As part of the settlement, Suno also acquired the concert discovery platform Songkick from WMG. == Controversy == Suno, Inc., has been sued by the Recording Industry Association of America for copyright infringement, and thousands of musicians have signed a letter demanding that the company cease using copyrighted music in their training data. Suno does not disclose the dataset used to train its artificial intelligence.
Information retrieval
Information retrieval (IR) in computing and information science is the task of identifying and retrieving information system resources that are relevant to an information need. The information need can be specified in the form of a search query. In the case of document retrieval, queries can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images, or sounds. Cross-modal retrieval implies retrieval across modalities. Automated information retrieval systems are used to reduce what has been called information overload. An IR system is a software system that provides access to books, journals, and other documents, as well as storing and managing those documents. Web search engines are the most visible IR applications. == Overview == An information retrieval process begins when a user enters a query into the system. Queries are formal statements of information needs, for example search strings in web search engines. In information retrieval, a query does not uniquely identify a single object in the collection. Instead, several objects may match the query, perhaps with different degrees of relevance. An object is an entity that is represented by information in a content collection or database. User queries are matched against the database information. However, as opposed to classical SQL queries of a database, in information retrieval the results returned may or may not match the query, so results are typically ranked. This ranking of results is a key difference of information retrieval searching compared to database searching. Depending on the application the data objects may be, for example, text documents, images, audio, mind maps or videos. Often the documents themselves are not kept or stored directly in the IR system, but are instead represented in the system by document surrogates or metadata. Most IR systems compute a numeric score on how well each object in the database matches the query, and rank the objects according to this value. The top ranking objects are then shown to the user. The process may then be iterated if the user wishes to refine the query. == History == there is ... a machine called the Univac ... whereby letters and figures are coded as a pattern of magnetic spots on a long steel tape. By this means the text of a document, preceded by its subject code symbol, can be recorded ... the machine ... automatically selects and types out those references which have been coded in any desired way at a rate of 120 words a minute The idea of using computers to search for relevant pieces of information was popularized in the article As We May Think by Vannevar Bush in 1945. It would appear that Bush was inspired by patents for a 'statistical machine' – filed by Emanuel Goldberg in the 1920s and 1930s – that searched for documents stored on film. The first description of a computer searching for information was described by Holmstrom in 1948, detailing an early mention of the Univac computer. Automated information retrieval systems were introduced in the 1950s: one even featured in the 1957 romantic comedy Desk Set. In the 1960s, the first large information retrieval research group was formed by Gerard Salton at Cornell. By the 1970s several different retrieval techniques had been shown to perform well on small text corpora such as the Cranfield collection (several thousand documents). Large-scale retrieval systems, such as the Lockheed Dialog system, came into use early in the 1970s. In 1992, the US Department of Defense along with the National Institute of Standards and Technology (NIST), cosponsored the Text Retrieval Conference (TREC) as part of the TIPSTER text program. The aim of this was to look into the information retrieval community by supplying the infrastructure that was needed for evaluation of text retrieval methodologies on a very large text collection. This catalyzed research on methods that scale to huge corpora. The introduction of web search engines has boosted the need for very large scale retrieval systems even further. By the late 1990s, the rise of the World Wide Web fundamentally transformed information retrieval. While early search engines such as AltaVista (1995) and Yahoo! (1994) offered keyword-based retrieval, they were limited in scale and ranking refinement. The breakthrough came in 1998 with the founding of Google, which introduced the PageRank algorithm, using the web's hyperlink structure to assess page importance and improve relevance ranking. During the 2000s, web search systems evolved rapidly with the integration of machine learning techniques. These systems began to incorporate user behavior data (e.g., click-through logs), query reformulation, and content-based signals to improve search accuracy and personalization. In 2009, Microsoft launched Bing, introducing features that would later incorporate semantic web technologies through the development of its Satori knowledge base. Academic analysis have highlighted Bing's semantic capabilities, including structured data use and entity recognition, as part of a broader industry shift toward improving search relevance and understanding user intent through natural language processing. A major leap occurred in 2018, when Google deployed BERT (Bidirectional Encoder Representations from Transformers) to better understand the contextual meaning of queries and documents. This marked one of the first times deep neural language models were used at scale in real-world retrieval systems. BERT's bidirectional training enabled a more refined comprehension of word relationships in context, improving the handling of natural language queries. Because of its success, transformer-based models gained traction in academic research and commercial search applications. Simultaneously, the research community began exploring neural ranking models that outperformed traditional lexical-based methods. Long-standing benchmarks such as the Text REtrieval Conference (TREC), initiated in 1992, and more recent evaluation frameworks Microsoft MARCO(MAchine Reading COmprehension) (2019) became central to training and evaluating retrieval systems across multiple tasks and domains. MS MARCO has also been adopted in the TREC Deep Learning Tracks, where it serves as a core dataset for evaluating advances in neural ranking models within a standardized benchmarking environment. As deep learning became integral to information retrieval systems, researchers began to categorize neural approaches into three broad classes: sparse, dense, and hybrid models. Sparse models, including traditional term-based methods and learned variants like SPLADE, rely on interpretable representations and inverted indexes to enable efficient exact term matching with added semantic signals. Dense models, such as dual-encoder architectures like ColBERT, use continuous vector embeddings to support semantic similarity beyond keyword overlap. Hybrid models aim to combine the advantages of both, balancing the lexical (token) precision of sparse methods with the semantic depth of dense models. This way of categorizing models balances scalability, relevance, and efficiency in retrieval systems. As IR systems increasingly rely on deep learning, concerns around bias, fairness, and explainability have also come to the picture. Research is now focused not just on relevance and efficiency, but on transparency, accountability, and user trust in retrieval algorithms. == Applications == Areas where information retrieval techniques are employed include (the entries are in alphabetical order within each category): === General applications === Digital libraries Information filtering Recommender systems Media search Blog search Image retrieval 3D retrieval Music retrieval News search Speech retrieval Video retrieval Search engines Site search Desktop search Enterprise search Federated search Mobile search Social search Web search === Domain-specific applications === Expert search finding Genomic information retrieval Geographic information retrieval Information retrieval for chemical structures Information retrieval in software engineering Legal information retrieval Vertical search === Other retrieval methods === Methods/Techniques in which information retrieval techniques are employed include: Cross-modal retrieval Adversarial information retrieval Automatic summarization Multi-document summarization Compound term processing Cross-lingual retrieval Document classification Spam filtering Question answering == Model types == In order to effectively retrieve relevant documents by IR strategies, the documents are typically transformed into a suitable representation. Each retrieval strategy incorporates a specific model for its document representation purposes. The picture on the right illustrates the relationship of som
Document
A document is a written, drawn, presented, or memorialized representation of thought, often the manifestation of non-fictional, as well as fictional, content. The etymology of the word "document" derives from the Latin documentum, which denotes a "teaching" or "lesson": the verb doceō denotes "to teach". Historically, the term "document" was usually used to indicate written proof useful as evidence of a truth or fact. In the Computer Age, the term "document" typically refers to a primarily textual computer file, encompassing its structural and format elements, such as fonts, colors, and images. In the contemporary era, the definition of "document" has expanded beyond its traditional medium, such as paper, to encompass electronic documents as well. History, events, examples, opinions, stories, and creativity can all be expressed in documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize or represent thought. Documents are usually considered to be two-dimensional representations. == Abstract definitions == The concept of "document" has been defined by Suzanne Briet as "any concrete or symbolic indication, preserved or recorded, for reconstructing or for proving a phenomenon, whether physical or mental." An often-cited article concludes that "the evolving notion of document" among Jonathan Priest, Paul Otlet, Briet, Walter Schürmeyer, and the other documentalists increasingly emphasized whatever functioned as a document rather than traditional physical forms of documents. The shift to digital technology would seem to make this distinction even more important. David M. Levy has said that an emphasis on the technology of digital documents has impeded our understanding of digital documents as documents. A conventional document, such as a mail message or a technical report, exists physically in digital technology as a string of bits, as does everything else in a digital environment. As an object of study, it has been made into a document. It has become physical evidence by those who study it. "Document" is defined in library and information science and documentation science as a fundamental, abstract idea: the word denotes everything that may be represented or memorialized to serve as evidence. The classic example provided by Briet is an antelope: "An antelope running wild on the plains of Africa should not be considered a document[;] she rules. But if it were to be captured, taken to a zoo and made an object of study, it has been made into a document. It has become physical evidence being used by those who study it. Indeed, scholarly articles written about the antelope are secondary documents, since the antelope itself is the primary document." This opinion has been interpreted as an early expression of actor–network theory. == Kinds == A document can be structured, like tabular documents, lists, forms, or scientific charts, semi-structured like a book or a newspaper article, or unstructured like a handwritten note. Documents are sometimes classified as secret, private, or public. They may also be described as drafts or proofs. When a document is copied, the source is denominated the "original". Documents are used in numerous fields, e.g.: Academia: manuscript, thesis, paper, journal, chart, and technical drawing Media: mock-up, script, image, photography, and newspaper article Administration, law, and politics: application, brief, certificate, commission, constitutional document, form, gazette, identity document, license, manifesto, summons, census, and white paper Business: invoice, request for proposal, proposal, contract, packing slip, manifest, report (detailed and summary), spreadsheet, material safety data sheet, waybill, bill of lading, financial statement, nondisclosure agreement (NDA), mutual nondisclosure agreement, and user guide Geography and planning: topographic map, cadastre, legend, and architectural plan Such standard documents can be drafted based on a template. == Drafting == The page layout of a document is how information is graphically arranged in the space of the document, e.g., on a page. If the appearance of the document is of concern, the page layout is generally the responsibility of a graphic designer. Typography concerns the design of letter and symbol forms and their physical arrangement in the document (see typesetting). Information design concerns the effective communication of information, especially in industrial documents and public signs. Simple textual documents may not require visual design and may be drafted only by an author, clerk, or transcriber. Forms may require a visual design for their initial fields, but not to complete the forms. == Media == Traditionally, the medium of a document was paper and the information was applied to it in ink, either by handwriting (to make a manuscript) or by a mechanical process (e.g., a printing press or laser printer). Today, some short documents also may consist of sheets of paper stapled together. Historically, documents were inscribed with ink on papyrus (starting in ancient Egypt) or parchment; scratched as runes or carved on stone using a sharp tool, e.g., the Tablets of Stone described in the Bible; stamped or incised in clay and then baked to make clay tablets, e.g., in the Sumerian and other Mesopotamian civilizations. The papyrus or parchment was often rolled into a scroll or cut into sheets and bound into a codex (book). Contemporary electronic means of memorializing and displaying documents include: Monitor of a desktop computer, laptop, tablet; optionally with a printer to produce a hard copy; Personal digital assistant; Dedicated e-book device; Electronic paper, typically, using the Portable Document Format (PDF); Information appliance; Digital audio player; and Radio and television service provider. Digital documents usually require a specific file format to be presentable in a specific medium. == In law == Documents in all forms frequently serve as material evidence in criminal and civil proceedings. The forensic analysis of such a document is within the scope of questioned document examination. To catalog and manage the large number of documents that may be produced during litigation, Bates numbering is often applied to all documents in the lawsuit so that each document has a unique, arbitrary, identification number.
Transaction data
Transaction data or transaction information is a category of data describing transactions. Transaction data/information gather variables generally referring to reference data or master data – e.g. dates, times, time zones, currencies. Typical transactions are: Financial transactions about orders, invoices, payments; Work transactions about plans, activity records; Logistic transactions about deliveries, storage records, travel records, etc.. == Management == Recording and storing transactions is called records management. The record of the transaction is stored in a place where the retention can be guaranteed and where data is archived or removed following a retention period. Formats of recorded transactions can be digital data in databases and spreadsheets, or handwritten texts in physical documents like former bankbooks. Transaction processing systems are application software that generate transactions and manage transaction data/information, e.g. SAP and Oracle Financials. == Data warehousing == Transaction data can be summarised in a data warehouse, which helps accessibility and analysis of the data.
EdgeRank
EdgeRank is the name commonly given to the algorithm that Facebook uses to determine what articles should be displayed in a user's News Feed. As of 2011, Facebook has stopped using the EdgeRank system and uses a machine learning algorithm that, as of 2013, takes more than 100,000 factors into account. EdgeRank was developed and implemented by Serkan Piantino. == Formula and factors == In 2010, a simplified version of the EdgeRank algorithm was presented as: ∑ e d g e s e u e w e d e {\displaystyle \sum _{\mathrm {edges\,} e}u_{e}w_{e}d_{e}} where: u e {\displaystyle u_{e}} is user affinity. w e {\displaystyle w_{e}} is how the content is weighted. d e {\displaystyle d_{e}} is a time-based decay parameter. User Affinity: The User Affinity part of the algorithm in Facebook's EdgeRank looks at the relationship and proximity of the user and the content (post/status update). Content Weight: What action was taken by the user on the content. Time-Based Decay Parameter: New or old. Newer posts tend to hold a higher place than older posts. Some of the methods that Facebook uses to adjust the parameters are proprietary and not available to the public. A study has shown that it is possible to hypothesize a disadvantage of the "like" reaction and advantages of other interactions (e.g., the "haha" reaction or "comments") in content algorithmic ranking on Facebook. The "like" button can decrease the organic reach as a "brake effect of viral reach". The "haha" reaction, "comments" and the "love" reaction could achieve the highest increase in total organic reach. == Impact == EdgeRank and its successors have a broad impact on what users actually see out of what they ostensibly follow: for instance, the selection can produce a filter bubble (if users are exposed to updates which confirm their opinions etc.) or alter people's mood (if users are shown a disproportionate amount of positive or negative updates). As a result, for Facebook pages, the typical engagement rate is less than 1% (or less than 0.1% for the bigger ones), and organic reach 10% or less for most non-profits. As a consequence, for pages, it may be nearly impossible to reach any significant audience without paying to promote their content.
Integreat
Integreat (former project name: Refguide+) is an open source mobile app that provides local information and services tailored to refugees and migrants coming to Germany. The content is maintained by local organizations, such as local governments or integration officers, and made available in locally relevant languages. It was developed by Tür an Tür - Digitalfabrik gGmbH (formerly Tür an Tür - Digital Factory gGmbH) in Augsburg together with a team of researchers and students from the Technical University of Munich. == History == In 1997, the Augsburg association "Tür an Tür", which has been working for refugees since 1992, published the brochure "First Steps", which answers local everyday questions. Since addresses and contact persons change quickly, some information is already outdated after a few weeks. Students of business informatics at the Technical University of Munich therefore developed the app Integreat within eight months together with the association and the social department of the city of Augsburg. The app was then also used by other cities and districts within months. As of February 3, 2022, information is available at 72 locations, including Munich, Dortmund, Nuremberg and Augsburg. == Mode of action == Refugees need information on areas such as registration, contact persons, health care, education, family, work and everyday life. Integreat seeks to provide refugees with this information by allowing them to select their geographic location and receive locally relevant information. This information is available offline once the app is opened so it can be used without an internet connection. In addition, the content is translated into the native languages of refugees and migrants to facilitate access. The content is licensed with a CC BY 4.0 license to facilitate collaboration and translation between content creators and dissemination of the content. Integreat is now being used for a broader migrant audience and says it can also support professionals, volunteers, and counseling centers. == Comparable mobile apps == Other mobile apps that are likewise intended to provide initial orientation for refugees include the app Ankommen, a joint project of the Federal Office for Migration and Refugees, the Goethe-Institut, the Federal Employment Agency and the Bavarian Broadcasting Corporation, which is intended as a companion for the first few weeks in Germany, and the Welcome App, a company-sponsored non-profit initiative for information about Germany and asylum procedures with a regional focus, and a book by the Konrad Adenauer Foundation (KAS) and Verlag Herder with a corresponding app Deutschland - Erste Informationen für Flüchtlinge (Germany - First Information for Refugees) as a companion for Arabic-speaking refugees in Germany.
Hindley–Milner type system
A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to infer the most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully applied on large code bases, although it has a high theoretical complexity. HM is preferably used for functional programming languages. It was first implemented as part of the type system of the programming language ML. Since then, HM has been extended in various ways, most notably with type class constraints like those in Haskell. == Introduction == As a type inference method, Hindley–Milner is able to deduce the types of variables, expressions and functions from programs written in an entirely untyped style. Being scope sensitive, it is not limited to deriving the types only from a small portion of source code, but rather from complete programs or modules. Being able to cope with parametric types, too, it is core to the type systems of many functional programming languages. It was first applied in this manner in the ML programming language. The origin is the type inference algorithm for the simply typed lambda calculus that was devised by Haskell Curry and Robert Feys in 1958. In 1969, J. Roger Hindley extended this work and proved that their algorithm always inferred the most general type. In 1978, Robin Milner, independently of Hindley's work, provided an equivalent algorithm, Algorithm W. In 1982, Luis Damas finally proved that Milner's algorithm is complete and extended it to support systems with polymorphic references. === Monomorphism vs. polymorphism === In the simply typed lambda calculus, types T are either atomic type constants or function types of form T → T {\displaystyle T\rightarrow T} . Such types are monomorphic. Typical examples are the types used in arithmetic values: 3 : N u m b e r a d d 3 4 : N u m b e r a d d : N u m b e r → N u m b e r → N u m b e r {\displaystyle {\begin{array}{ll}3&:{\mathtt {Number}}\\{\mathtt {add}}\ 3\ 4&:{\mathtt {Number}}\\{\mathtt {add}}&:{\mathtt {Number}}\rightarrow {\mathtt {Number}}\rightarrow {\mathtt {Number}}\end{array}}} Contrary to this, the untyped lambda calculus is neutral to typing at all, and many of its functions can be meaningfully applied to all type of arguments. The trivial example is the identity function i d ≡ λ x . x {\displaystyle {\mathtt {id}}\equiv \lambda x.x} which simply returns whatever value it is applied to. Less trivial examples include parametric types like lists. While polymorphism in general means that operations accept values of more than one type, the polymorphism used here is parametric. One finds the notation of type schemes in the literature, too, emphasizing the parametric nature of the polymorphism. Additionally, constants may be typed with (quantified) type variables. For example, the following type schemes quantify universally over α {\displaystyle \alpha } , meaning that they are true for all possible α {\displaystyle \alpha } : c o n s : ∀ α . α → L i s t α → L i s t α n i l : ∀ α . L i s t α i d : ∀ α . α → α {\displaystyle {\begin{array}{ll}{\mathtt {cons}}&:\forall \alpha .\alpha \rightarrow {\mathtt {List}}\ \alpha \rightarrow {\mathtt {List}}\ \alpha \\{\mathtt {nil}}&:\forall \alpha .{\mathtt {List}}\ \alpha \\{\mathtt {id}}&:\forall \alpha .\alpha \rightarrow \alpha \end{array}}} Polymorphic types can become monomorphic by consistent substitution of their variables. Examples of monomorphic instances are: i d ′ : S t r i n g → S t r i n g n i l ′ : L i s t N u m b e r {\displaystyle {\begin{array}{ll}{\mathtt {id}}'&:{\mathtt {String}}\rightarrow {\mathtt {String}}\\{\mathtt {nil}}'&:{\mathtt {List}}\ {\mathtt {Number}}\end{array}}} More generally, types are polymorphic when they contain type variables, while types without them are monomorphic. Contrary to the type systems used for example in Pascal (1970) or C (1972), which only support monomorphic types, HM is designed with emphasis on parametric polymorphism. The successors of the languages mentioned, like C++ (1985), focused on different types of polymorphism, namely subtyping in connection with object-oriented programming and overloading. While subtyping is incompatible with HM, a variant of systematic overloading is available in the HM-based type system of Haskell. === Let-polymorphism === When extending the type inference for the simply-typed lambda calculus towards polymorphism, one has to decide whether assigning a polymorphic type not only as type of an expression, but also as the type of a λ-bound variable is admissible. This would allow the generic identity type to be assigned to the variable 'id' in: (λ id . ... (id 3) ... (id "text") ... ) (λ x . x) Allowing this gives rise to the polymorphic lambda calculus; however, type inference in this system is not decidable. Instead, HM distinguishes variables that are immediately bound to an expression from more general λ-bound variables, calling the former let-bound variables, and allows polymorphic types to be assigned only to these. This leads to let-polymorphism where the above example takes the form let id = λ x . x in ... (id 3) ... (id "text") ... which can be typed with a polymorphic type for 'id'. As indicated, the expression syntax is extended to make the let-bound variables explicit, and by restricting the type system to allow only let-bound variable to have polymorphic types, while the parameters in lambda-abstractions must get a monomorphic type, type inference becomes decidable. == Overview == The remainder of this article proceeds as follows: The HM type system is defined. This is done by describing a deduction system that makes precise what expressions have what type, if any. From there, it works towards an implementation of the type inference method. After introducing a syntax-driven variant of the above deductive system, it sketches an efficient implementation (algorithm J), appealing mostly to the reader's metalogical intuition. Because it remains open whether algorithm J indeed realises the initial deduction system, a less efficient implementation (algorithm W), is introduced and its use in a proof is hinted. Finally, further topics related to the algorithm are discussed. The same description of the deduction system is used throughout, even for the two algorithms, to make the various forms in which the HM method is presented directly comparable. == The Hindley–Milner type system == The type system can be formally described by syntax rules that fix a language for the expressions, types, etc. The presentation here of such a syntax is not too formal, in that it is written down not to study the surface grammar, but rather the depth grammar, and leaves some syntactical details open. This form of presentation is usual. Building on this, typing rules are used to define how expressions and types are related. As before, the form used is a bit liberal. === Syntax === The expressions to be typed are exactly those of the lambda calculus extended with a let-expression as shown in the adjacent table. Parentheses can be used to disambiguate an expression. The application is left-binding and binds stronger than abstraction or the let-in construct. Types are syntactically split into two groups, monotypes and polytypes. ==== Monotypes ==== Monotypes always designate a particular type. Monotypes τ {\displaystyle \tau } are syntactically represented as terms. Examples of monotypes include type constants like i n t {\displaystyle {\mathtt {int}}} or s t r i n g {\displaystyle {\mathtt {string}}} , and parametric types like M a p ( S e t s t r i n g ) i n t {\displaystyle {\mathtt {Map\ (Set\ string)\ int}}} . The latter types are examples of applications of type functions, for example, from the set { M a p 2 , S e t 1 , s t r i n g 0 , i n t 0 , → 2 } {\displaystyle \{{\mathtt {Map^{2},\ Set^{1},\ string^{0},\ int^{0}}},\ \rightarrow ^{2}\}} , where the superscript indicates the number of type parameters. The complete set of type functions C {\displaystyle C} is arbitrary in HM, except that it must contain at least → 2 {\displaystyle \rightarrow ^{2}} , the type of functions. It is often written in infix notation for convenience. For example, a function mapping integers to strings has type i n t → s t r i n g {\displaystyle {\mathtt {int}}\rightarrow {\mathtt {string}}} . Again, parentheses can be used to disambiguate a type expression. The application binds stronger than the infix arrow, which is right-binding. Type variables are admitted as monotypes. Monotypes are not to be confused with monomorphic types, which exc