Yahoo! Groups was a free-to-use system of electronic mailing lists offered by Yahoo!. Prior to February 2020, Yahoo! Groups was one of the world's largest collections of online discussion boards. It allowed members to subscribe to various groups, read subscribed discussions online, view and share photos, files and bookmarks within a group, access a group calendar, create polls for group members, and receive email notifications of new discussion topics. Some groups were simply announcement boards, to which only the group moderators could post, while others were discussion forums. Depending on each group's settings, membership could be open to everyone or only to invited or approved people. On February 1, 2020, Yahoo! removed online access to discussions and all other features except simple membership management, essentially turning all groups into mailing lists, and on October 13, 2020, it announced that Yahoo Groups would shut down completely on December 15, 2020. == History == In 1998 Yahoo! Clubs was launched as an extension of services developed by Yahoo! Messenger. In August 2000 Yahoo acquired eGroups.com. Yahoo! Groups was launched in early 2001 as an integration of technology from eGroups.com and community groups from both eGroups.com and Yahoo! Clubs. In 2001 Yahoo! deleted adult groups from its search directory, making it very difficult to locate Yahoo! groups with adult content. The Groups Updates Email feature was introduced in 2010. It summarized, in a single email, all the updates that occurred every twenty-four hours in all groups. In September 2010, a major facelift was rolled out, making Yahoo! Groups look very similar to Facebook. In December, Yahoo! Groups Japan emailed its users and posted a notice on its homepage, to announce that its service, which commenced in February 2004, would be closing on May 28, 2014. In October 2019, Yahoo! announced that all content that had been posted to Yahoo! Groups will be deleted on December 14, 2019; that date was later amended to January 31, 2020. Yahoo! announced that adding new content would be blocked on October 28, 2019. Once the content was deleted, users of Yahoo! Groups were only able to browse the group directory, request invitations and, if members of a group, send messages to that group. On October 13, 2020, Yahoo! announced they would be shutting down Yahoo! Groups on December 15, 2020. The site was closed down a few days after the advertised date, displaying a message that the service was officially shut down. This message stopped appearing at the end of January 2021 and the Yahoo! Groups web address began redirecting to the main Yahoo! page. === Criticism and controversy === On August 31, 2010, Yahoo! Groups started rolling out a major software change, which was denounced by a large number of users. The re-model was completely abandoned on January 12, 2011. == Site statistics == In August 2008, Yahoo! Group staff reported that there were 113 million users, and nine million Groups using 22 languages. In July 2010, the web analytics website Quantcast reported around 915 thousand unique visitors daily to the Yahoo! Groups website (US). In January 2011, that number had increased to 933 thousand unique visitors daily. The number did not include Yahoo! Group members who accessed the Groups site via email. In September 2010, at its "Product Runway" event, Yahoo! told reporters that Yahoo! Groups had 115 million group members and that there were 10 million Yahoo! groups. == Archives ==
Deductive language
A deductive language is a computer programming language in which the program is a collection of predicates ('facts') and rules that connect them. Such a language is used to create knowledge based systems or expert systems which can deduce answers to problem sets by applying the rules to the facts they have been given. An example of a deductive language is Prolog, or its database-query cousin, Datalog. == History == As the name implies, deductive languages are rooted in the principles of deductive reasoning; making inferences based upon current knowledge. The first recommendation to use a clausal form of logic for representing computer programs was made by Cordell Green (1969) at Stanford Research Institute (now SRI International). This idea can also be linked back to the battle between procedural and declarative information representation in early artificial intelligence systems. Deductive languages and their use in logic programming can also be dated to the same year when Foster and Elcock introduced Absys, the first deductive/logical programming language. Shortly after, the first Prolog system was introduced in 1972 by Colmerauer through collaboration with Robert Kowalski. == Components == The components of a deductive language are a system of formal logic and a knowledge base upon which the logic is applied. === Formal Logic === Formal logic is the study of inference in regards to formal content. The distinguishing feature between formal and informal logic is that in the former case, the logical rule applied to the content is not specific to a situation. The laws hold regardless of a change in context. Although first-order logic is described in the example below to demonstrate the uses of a deductive language, no formal system is mandated and the use of a specific system is defined within the language rules or grammar. As input, a predicate takes any object(s) in the domain of interest and outputs either one of two Boolean values: true or false. For example, consider the sentences "Barack Obama is the 44th president" and "If it rains today, I will bring an umbrella". The first is a statement with an associated truth value. The second is a conditional statement relying on the value of some other statement. Either of these sentences can be broken down into predicates which can be compared and form the knowledge base of a deductive language. Moreover, variables such as 'Barack Obama' or 'president' can be quantified over. For example, take 'Barack Obama' as variable 'x'. In the sentence "There exists an 'x' such that if 'x' is the president, then 'x' is the commander in chief." This is an example of the existential quantifier in first order logic. Take 'president' to be the variable 'y'. In the sentence "For every 'y', 'y' is the leader of their nation." This is an example of the universal quantifier. === Knowledge Base === A collection of 'facts' or predicates and variables form the knowledge base of a deductive language. Depending on the language, the order of declaration of these predicates within the knowledge base may or may not influence the result of applying logical rules. Upon application of certain 'rules' or inferences, new predicates may be added to a knowledge base. As new facts are established or added, they form the basis for new inferences. As the core of early expert systems, artificial intelligence systems which can make decisions like an expert human, knowledge bases provided more information than databases. They contained structured data, with classes, subclasses, and instances. == Prolog == Prolog is an example of a deductive, declarative language that applies first- order logic to a knowledge base. To run a program in Prolog, a query is posed and based upon the inference engine and the specific facts in the knowledge base, a result is returned. The result can be anything appropriate from a new relation or predicate, to a literal such as a Boolean (true/false), depending on the engine and type system.
C4.5 algorithm
C4.5 is an algorithm used to generate a decision tree developed by Ross Quinlan. C4.5 is an extension of Quinlan's earlier ID3 algorithm. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a statistical classifier. In 2011, authors of the Weka machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date". It became quite popular after ranking #1 in the Top 10 Algorithms in Data Mining pre-eminent paper published by Springer LNCS in 2008. == Algorithm == C4.5 builds decision trees from a set of training data in the same way as ID3, using the concept of information entropy. The training data is a set S = s 1 , s 2 , . . . {\displaystyle S={s_{1},s_{2},...}} of already classified samples. Each sample s i {\displaystyle s_{i}} consists of a p-dimensional vector ( x 1 , i , x 2 , i , . . . , x p , i ) {\displaystyle (x_{1,i},x_{2,i},...,x_{p,i})} , where the x j {\displaystyle x_{j}} represent attribute values or features of the sample, as well as the class in which s i {\displaystyle s_{i}} falls. At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized information gain (difference in entropy). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then recurses on the partitioned sublists. This algorithm has a few base cases. All the samples in the list belong to the same class. When this happens, it simply creates a leaf node for the decision tree saying to choose that class. None of the features provide any information gain. In this case, C4.5 creates a decision node higher up the tree using the expected value of the class. Instance of previously unseen class encountered. Again, C4.5 creates a decision node higher up the tree using the expected value. === Pseudocode === In pseudocode, the general algorithm for building decision trees is: Check for the above base cases. For each attribute a, find the normalized information gain ratio from splitting on a. Let a_best be the attribute with the highest normalized information gain. Create a decision node that splits on a_best. Recurse on the sublists obtained by splitting on a_best, and add those nodes as children of node. == Improvements from ID3 algorithm == C4.5 made a number of improvements to ID3. Some of these are: Handling both continuous and discrete attributes: In order to handle continuous attributes, C4.5 creates a threshold and then splits the list into those whose attribute value is above the threshold and those that are less than or equal to it. Handling training data with missing attribute values: C4.5 allows attribute values to be marked as missing. Missing attribute values are simply not used in gain and entropy calculations. Handling attributes with differing costs. Pruning trees after creation: C4.5 goes back through the tree once it's been created and attempts to remove branches that do not help by replacing them with leaf nodes. == Improvements in C5.0/See5 algorithm == Quinlan went on to create C5.0 and See5 (C5.0 for Unix/Linux, See5 for Windows) which he markets commercially. C5.0 offers a number of improvements on C4.5. Some of these are: Speed - C5.0 is significantly faster than C4.5 (several orders of magnitude) Memory usage - C5.0 is more memory efficient than C4.5 Smaller decision trees - C5.0 gets similar results to C4.5 with considerably smaller decision trees. Support for boosting - Boosting improves the trees and gives them more accuracy. Weighting - C5.0 allows you to weight different cases and misclassification types. Winnowing - a C5.0 option automatically winnows the attributes to remove those that may be unhelpful. Source for a single-threaded Linux version of C5.0 is available under the GNU General Public License (GPL).
U-matrix
The U-matrix (unified distance matrix) is a representation of a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of neighboring neurons is depicted in a grayscale image. This image is used to visualize the data in a high-dimensional space using a 2D image. == Construction procedure == Once the SOM is trained using the input data, the final map is not expected to have any twists. If the map is twist-free, the distance between the codebook vectors of neighboring neurons gives an approximation of the distance between different parts of the underlying data. When such distances are depicted in a grayscale image, light colors depict closely spaced node codebook vectors and darker colors indicate more widely separated node codebook vectors. Thus, groups of light colors can be considered as clusters, and the dark parts as the boundaries between the clusters. This representation can help to visualize the clusters in the high-dimensional spaces, or to automatically recognize them using relatively simple image processing techniques.
Elastic map
Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the data space. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (for high bending and low stretching modules). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996–1998. == Energy of elastic map == Let S {\displaystyle {\mathcal {S}}} be a data set in a finite-dimensional Euclidean space. Elastic map is represented by a set of nodes w j {\displaystyle {\bf {w}}_{j}} in the same space. Each datapoint s ∈ S {\displaystyle s\in {\mathcal {S}}} has a host node, namely the closest node w j {\displaystyle {\bf {w}}_{j}} (if there are several closest nodes then one takes the node with the smallest number). The data set S {\displaystyle {\mathcal {S}}} is divided into classes K j = { s | w j is a host of s } {\displaystyle K_{j}=\{s\ |\ {\bf {w}}_{j}{\mbox{ is a host of }}s\}} . The approximation energy D is the distortion D = 1 2 ∑ j = 1 k ∑ s ∈ K j ‖ s − w j ‖ 2 {\displaystyle D={\frac {1}{2}}\sum _{j=1}^{k}\sum _{s\in K_{j}}\|s-{\bf {w}}_{j}\|^{2}} , which is the energy of the springs with unit elasticity which connect each data point with its host node. It is possible to apply weighting factors to the terms of this sum, for example to reflect the standard deviation of the probability density function of any subset of data points { s i } {\displaystyle \{s_{i}\}} . On the set of nodes an additional structure is defined. Some pairs of nodes, ( w i , w j ) {\displaystyle ({\bf {w}}_{i},{\bf {w}}_{j})} , are connected by elastic edges. Call this set of pairs E {\displaystyle E} . Some triplets of nodes, ( w i , w j , w k ) {\displaystyle ({\bf {w}}_{i},{\bf {w}}_{j},{\bf {w}}_{k})} , form bending ribs. Call this set of triplets G {\displaystyle G} . The stretching energy is U E = 1 2 λ ∑ ( w i , w j ) ∈ E ‖ w i − w j ‖ 2 {\displaystyle U_{E}={\frac {1}{2}}\lambda \sum _{({\bf {w}}_{i},{\bf {w}}_{j})\in E}\|{\bf {w}}_{i}-{\bf {w}}_{j}\|^{2}} , The bending energy is U G = 1 2 μ ∑ ( w i , w j , w k ) ∈ G ‖ w i − 2 w j + w k ‖ 2 {\displaystyle U_{G}={\frac {1}{2}}\mu \sum _{({\bf {w}}_{i},{\bf {w}}_{j},{\bf {w}}_{k})\in G}\|{\bf {w}}_{i}-2{\bf {w}}_{j}+{\bf {w}}_{k}\|^{2}} , where λ {\displaystyle \lambda } and μ {\displaystyle \mu } are the stretching and bending moduli respectively. The stretching energy is sometimes referred to as the membrane, while the bending energy is referred to as the thin plate term. For example, on the 2D rectangular grid the elastic edges are just vertical and horizontal edges (pairs of closest vertices) and the bending ribs are the vertical or horizontal triplets of consecutive (closest) vertices. The total energy of the elastic map is thus U = D + U E + U G . {\displaystyle U=D+U_{E}+U_{G}.} The position of the nodes { w j } {\displaystyle \{{\bf {w}}_{j}\}} is determined by the mechanical equilibrium of the elastic map, i.e. its location is such that it minimizes the total energy U {\displaystyle U} . == Expectation-maximization algorithm == For a given splitting of dataset S {\displaystyle {\mathcal {S}}} in classes K j {\displaystyle K_{j}} , minimization of the quadratic functional U {\displaystyle U} is a linear problem with the sparse matrix of coefficients. Therefore, similar to principal component analysis or k-means, a splitting method is used: For given { w j } {\displaystyle \{{\bf {w}}_{j}\}} find { K j } {\displaystyle \{K_{j}\}} ; For given { K j } {\displaystyle \{K_{j}\}} minimize U {\displaystyle U} and find { w j } {\displaystyle \{{\bf {w}}_{j}\}} ; If no change, terminate. This expectation-maximization algorithm guarantees a local minimum of U {\displaystyle U} . For improving the approximation various additional methods are proposed. For example, the softening strategy is used. This strategy starts with a rigid grids (small length, small bending and large elasticity modules λ {\displaystyle \lambda } and μ {\displaystyle \mu } coefficients) and finishes with soft grids (small λ {\displaystyle \lambda } and μ {\displaystyle \mu } ). The training goes in several epochs, each epoch with its own grid rigidness. Another adaptive strategy is growing net: one starts from a small number of nodes and gradually adds new nodes. Each epoch goes with its own number of nodes. == Applications == Most important applications of the method and free software are in bioinformatics for exploratory data analysis and visualisation of multidimensional data, for data visualisation in economics, social and political sciences, as an auxiliary tool for data mapping in geographic informational systems and for visualisation of data of various nature. The method is applied in quantitative biology for reconstructing the curved surface of a tree leaf from a stack of light microscopy images. This reconstruction is used for quantifying the geodesic distances between trichomes and their patterning, which is a marker of the capability of a plant to resist to pathogenes. Recently, the method is adapted as a support tool in the decision process underlying the selection, optimization, and management of financial portfolios. The method of elastic maps has been systematically tested and compared with several machine learning methods on the applied problem of identification of the flow regime of a gas-liquid flow in a pipe. There are various regimes: Single phase water or air flow, Bubbly flow, Bubbly-slug flow, Slug flow, Slug-churn flow, Churn flow, Churn-annular flow, and Annular flow. The simplest and most common method used to identify the flow regime is visual observation. This approach is, however, subjective and unsuitable for relatively high gas and liquid flow rates. Therefore, the machine learning methods are proposed by many authors. The methods are applied to differential pressure data collected during a calibration process. The method of elastic maps provided a 2D map, where the area of each regime is represented. The comparison with some other machine learning methods is presented in Table 1 for various pipe diameters and pressure. Here, ANN stands for the backpropagation artificial neural networks, SVM stands for the support vector machine, SOM for the self-organizing maps. The hybrid technology was developed for engineering applications. In this technology, elastic maps are used in combination with Principal Component Analysis (PCA), Independent Component Analysis (ICA) and backpropagation ANN. The textbook provides a systematic comparison of elastic maps and self-organizing maps (SOMs) in applications to economic and financial decision-making.
Database
In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application associated with the database. Before digital storage and retrieval of data became widespread, index cards were used for data storage in a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flash cards or other visual aids; and in academic research to hold data such as bibliographical citations or notes in a card file. Professional book indexers used index cards in the creation of book indexes until they were replaced by indexing software in the 1980s and 1990s. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spans formal techniques and practical considerations, including data modeling, efficient data representation and storage, query languages, security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance. Computer scientists may classify database management systems according to the database models that they support. Relational databases became dominant in the 1980s. These model data as rows and columns in a series of tables, and the vast majority use SQL for writing and querying data. In the 2000s, non-relational databases became popular, collectively referred to as NoSQL, because they use different query languages. == Terminology and overview == Formally, a "database" refers to a set of related data accessed through the use of a "database management system" (DBMS), which is an integrated set of computer software that allows users to interact with one or more databases and provides access to all of the data contained in the database (although restrictions may exist that limit access to particular data). The DBMS provides various functions that allow entry, storage and retrieval of large quantities of information and provides ways to manage how that information is organized. Because of the close relationship between them, the term "database" is often used casually to refer to both a database and the DBMS used to manipulate it. Outside the world of professional information technology, the term database is often used to refer to any collection of related data (such as a spreadsheet or a card index) as size and usage requirements typically necessitate use of a database management system. Existing DBMSs provide various functions that allow management of a database and its data which can be classified into four main functional groups: Data definition – Creation, modification and removal of definitions that detail how the data is to be organized. Update – Insertion, modification, and deletion of the data itself. Retrieval – Selecting data according to specified criteria (e.g., a query, a position in a hierarchy, or a position in relation to other data) and providing that data either directly to the user, or making it available for further processing by the database itself or by other applications. The retrieved data may be made available in a more or less direct form without modification, as it is stored in the database, or in a new form obtained by altering it or combining it with existing data from the database. Administration – Registering and monitoring users, enforcing data security, monitoring performance, maintaining data integrity, dealing with concurrency control, and recovering information that has been corrupted by some event such as an unexpected system failure. Both a database and its DBMS conform to the principles of a particular database model. "Database system" refers collectively to the database model, database management system, and database. Physically, database servers are dedicated computers that hold the actual databases and run only the DBMS and related software. Database servers are usually multiprocessor computers, with generous memory and RAID disk arrays used for stable storage. Hardware database accelerators, connected to one or more servers via a high-speed channel, are also used in large-volume transaction processing environments. DBMSs are found at the heart of most database applications. DBMSs may be built around a custom multitasking kernel with built-in networking support, but modern DBMSs typically rely on a standard operating system to provide these functions. Since DBMSs comprise a significant market, computer and storage vendors often take into account DBMS requirements in their own development plans. Databases and DBMSs can be categorized according to the database model(s) that they support (such as relational or XML), the type(s) of computer they run on (from a server cluster to a mobile phone), the query language(s) used to access the database (such as SQL or XQuery), and their internal engineering, which affects performance, scalability, resilience, and security. == History == The sizes, capabilities, and performance of databases and their respective DBMSs have grown in orders of magnitude. These performance increases were enabled by the technology progress in the areas of processors, computer memory, computer storage, and computer networks. The concept of a database was made possible by the emergence of direct access storage media such as magnetic disks, which became widely available in the mid-1960s; earlier systems relied on sequential storage of data on magnetic tape. The subsequent development of database technology can be divided into three eras based on data model or structure: navigational, SQL/relational, and post-relational. The two main early navigational data models were the hierarchical model and the CODASYL model (network model). These were characterized by the use of pointers (often physical disk addresses) to follow relationships from one record to another. The relational model, first proposed in 1970 by Edgar F. Codd, departed from this tradition by insisting that applications should search for data by content, rather than by following links. The relational model employs sets of ledger-style tables, each used for a different type of entity. Only in the mid-1980s did computing hardware become powerful enough to allow the wide deployment of relational systems (DBMSs plus applications). By the early 1990s, however, relational systems dominated in all large-scale data processing applications, and as of 2018 they remain dominant: IBM Db2, Oracle, MySQL, and Microsoft SQL Server are the most searched DBMS. The dominant database language, standardized SQL for the relational model, has influenced database languages for other data models. Object databases were developed in the 1980s to overcome the inconvenience of object–relational impedance mismatch, which led to the coining of the term "post-relational" and also the development of hybrid object–relational databases. The next generation of post-relational databases in the late 2000s became known as NoSQL databases, introducing fast key–value stores and document-oriented databases. A competing "next generation" known as NewSQL databases attempted new implementations that retained the relational/SQL model while aiming to match the high performance of NoSQL compared to commercially available relational DBMSs. === 1960s, navigational DBMS === The introduction of the term database coincided with the availability of direct-access storage (disks and drums) from the mid-1960s onwards. The term represented a contrast with the tape-based systems of the past, allowing shared interactive use rather than daily batch processing. The Oxford English Dictionary cites a 1962 report by the System Development Corporation of California as the first to use the term "data-base" in a specific technical sense. As computers grew in speed and capability, a number of general-purpose database systems emerged; by the mid-1960s a number of such systems had come into commercial use. Interest in a standard began to grow, and Charles Bachman, author of one such product, the Integrated Data Store (IDS), founded the Database Task Group within CODASYL, the group responsible for the creation and standardization of COBOL. In 1971, the Database Task Group delivered their standard, which generally became known as the CODASYL approach, and soon a number of commercial products based on this approach entered the market. The CODASYL approach of
Multi expression programming
Multi Expression Programming (MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is a Genetic Programming variant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have been tested). In the simplest variant, MEP chromosomes are linear strings of instructions. This representation was inspired by Three-address code. MEP strength consists in the ability to encode multiple solutions, of a problem, in the same chromosome. In this way, one can explore larger zones of the search space. For most of the problems this advantage comes with no running-time penalty compared with genetic programming variants encoding a single solution in a chromosome. == Representation == MEP chromosomes are arrays of instructions represented in Three-address code format. Each instruction contains a variable, a constant, or a function. If the instruction is a function, then the arguments (given as instruction's addresses) are also present. === Example of MEP program === Here is a simple MEP chromosome (labels on the left side are not a part of the chromosome): 1: a 2: b 3: + 1, 2 4: c 5: d 6: + 4, 5 7: 3, 5 == Fitness computation == When the chromosome is evaluated it is unclear which instruction will provide the output of the program. In many cases, a set of programs is obtained, some of them being completely unrelated (they do not have common instructions). For the above chromosome, here is the list of possible programs obtained during decoding: E1 = a, E2 = b, E4 = c, E5 = d, E3 = a + b. E6 = c + d. E7 = (a + b) d. Each instruction is evaluated as a possible output of the program. The fitness (or error) is computed in a standard manner. For instance, in the case of symbolic regression, the fitness is the sum of differences (in absolute value) between the expected output (called target) and the actual output. == Fitness assignment process == Which expression will represent the chromosome? Which one will give the fitness of the chromosome? In MEP, the best of them (which has the lowest error) will represent the chromosome. This is different from other GP techniques: In Linear genetic programming the last instruction will give the output. In Cartesian Genetic Programming the gene providing the output is evolved like all other genes. Note that, for many problems, this evaluation has the same complexity as in the case of encoding a single solution in each chromosome. Thus, there is no penalty in running time compared to other techniques. == Software == === MEPX === MEPX is a cross-platform (Windows, macOS, and Linux Ubuntu) free software for the automatic generation of computer programs. It can be used for data analysis, particularly for solving symbolic regression, statistical classification and time-series problems. === libmep === Libmep is a free and open source library implementing Multi Expression Programming technique. It is written in C++. === hmep === hmep is a new open source library implementing Multi Expression Programming technique in Haskell programming language.