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113-470: Computing systems may be modeled in VDM-SL at a higher level of abstraction than is achievable using programming languages, allowing the analysis of designs and identification of key features, including defects, at an early stage of system development. Models that have been validated can be transformed into detailed system designs through a refinement process. The language has a formal semantics, enabling proof of

226-418: A contract that to be satisfied by any program claiming to implement the function. The precondition records the assumptions under which the function guarantees to return a result satisfying the postcondition. If a function is called on inputs that do not satisfy its precondition, the outcome is undefined (indeed, termination is not even guaranteed). VDM-SL also supports the definition of executable functions in

339-566: A holding company of manufacturers of record-keeping and measuring systems. It was renamed "International Business Machines" in 1924 and soon became the leading manufacturer of punch-card tabulating systems . During the 1960s and 1970s, the IBM mainframe , exemplified by the System/360 , was the world's dominant computing platform , with the company producing 80 percent of computers in the U.S. and 70 percent of computers worldwide. IBM debuted in

452-575: A neuromorphic CMOS integrated circuit and announced a $ 3 billion investment over the following five years to design a neural chip that mimics the human brain, with 10 billion neurons and 100 trillion synapses, but that uses just 1 kilowatt of power. In 2016, the company launched all-flash arrays designed for small and midsized companies, which includes software for data compression, provisioning, and snapshots across various systems. In January 2019, IBM introduced its first commercial quantum computer: IBM Q System One . In March 2020, it

565-649: A Hollerith department called Hollerith Abteilung, which had IBM machines, including calculating and sorting machines. IBM as a military contractor produced 6% of the M1 Carbine rifles used in World War II, about 346,500 of them, between August 1943 and May. IBM built the Automatic Sequence Controlled Calculator , an electromechanical computer, during World War II. It offered its first commercial stored-program computer,

678-530: A back-end Map. Enums were added in PHP version 8.1. Enumerators may be backed by string or integer values to aid serialization: The Enum's interface exposes a method that gives a collection of its enumerators and their names. String/integer-backed Enums also expose the backing value and methods to (attempt) deserialization. Users may add further methods. Though Rust uses the enum keyword like C, it uses it to describe tagged unions , which enums can be considered

791-581: A consequence, IBM quickly began losing its market dominance to emerging competitors in the PC market. In 1985, IBM collaborated with Microsoft to develop a new operating system , which was released as OS/2 . Following a dispute, Microsoft severed the collaboration and IBM continued development of OS/2 on its own but it failed in the marketplace against Microsoft's Windows during the mid-1990s. In 1991 IBM began spinning off its many divisions into autonomous subsidiaries (so-called "Baby Blues") in an attempt to make

904-555: A conversion from arithmetic types to enumerations, however. Extended Pascal offers this functionality via an extended succ function. Some other Pascal dialects allow it via type-casts. Some modern descendants of Pascal, such as Modula-3 , provide a special conversion syntax using a method called VAL ; Modula-3 also treats BOOLEAN and CHAR as special pre-defined enumerated types and uses ORD and VAL for standard ASCII decoding and encoding. Pascal style languages also allow enumeration to be used as array index: In Ada ,

1017-546: A date d , the expression d.month is a natural number representing the month. Restrictions on days per month and leap years could be incorporated into the invariant if desired. Combining these: Collection types model groups of values. Sets are finite unordered collections in which duplication between values is suppressed. Sequences are finite ordered collections (lists) in which duplication may occur and mappings represent finite correspondences between two sets of values. The set type constructor (written set of T where T

1130-432: A degenerate form of. Rust's enums are therefore much more flexible and can contain struct and tuple variants. Like C, Rust also supports specifying the values of each variant, In C, enumerations assign related names to a set of integer values. In Swift , enumerations are much more flexible and need not provide a value for each case of the enumeration. If a value (termed a raw value) is provided for each enumeration case,

1243-677: A fifth company, the Computing-Tabulating-Recording Company (CTR) based in Endicott, New York. The five companies had 1,300 employees and offices and plants in Endicott and Binghamton , New York; Dayton, Ohio ; Detroit, Michigan ; Washington, D.C. ; and Toronto , Canada. Collectively, the companies manufactured a wide array of machinery for sale and lease, ranging from commercial scales and industrial time recorders, meat and cheese slicers, to tabulators and punched cards. Thomas J. Watson, Sr. , fired from

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1356-580: A first-class type. They adopt many features traditionally supported only by classes, such as computed properties to provide additional information about the enumeration's current value, and instance methods to provide functionality related to the values the enumeration represents. Enumerations can also define initializers to provide an initial case value and can be extended to expand their functionality beyond their original implementation; and can conform to protocols to provide standard functionality. Unlike C and Objective-C , Swift enumeration cases are not assigned

1469-447: A focus on customer service, an insistence on well-groomed, dark-suited salesmen and had an evangelical fervor for instilling company pride and loyalty in every worker". His favorite slogan, " THINK ", became a mantra for each company's employees. During Watson's first four years, revenues reached $ 9 million ($ 158 million today) and the company's operations expanded to Europe, South America, Asia and Australia. Watson never liked

1582-421: A function that returned the negative root of 4 but the positive root of all other valid inputs. Note that functions in VDM-SL are required to be deterministic so that a function satisfying the example specification above must always return the same result for the same input. A more constrained function specification is arrived at by strengthening the postcondition. For example, the following definition constrains

1695-398: A maximum or minimum representable number or a precision for real numbers. Such constraints are defined where they are required in each model by means of data type invariants—Boolean expressions denoting conditions that must be respected by all elements of the defined type. For example, a requirement that user identifiers must be no greater than 9999 would be expressed as follows (where <=

1808-415: A programmer wanted a variable, for example myColor , to have a value of red, the variable red would be declared and assigned some arbitrary value, usually an integer constant. The variable red would then be assigned to myColor . Other techniques assigned arbitrary values to strings containing the names of the enumerators. These arbitrary values were sometimes referred to as magic numbers since there often

1921-626: A separate lawsuit. In 2015, IBM bought the digital part of The Weather Company , Truven Health Analytics for $ 2.6 billion in 2016, and in October 2018, IBM announced its intention to acquire Red Hat for $ 34 billion, which was completed on July 9, 2019. In February 2020, IBM's John Kelly III joined Brad Smith of Microsoft to sign a pledge with the Vatican to ensure the ethical use and practice of Artificial Intelligence (AI) . IBM announced in October 2020 that it would divest

2034-480: A sharp drop in profit margins during the second quarter of fiscal year 1992; market analysts attributed the drop to a fierce price war in the personal computer market over the summer of 1992. The corporate restructuring was one of the largest and most expensive in history up to that point. By the summer of 1993, the IBM PC Co. had divided into multiple business units itself, including Ambra Computer Corporation and

2147-402: A traffic signal controller, it may be convenient to define values to represent the colours of the traffic signal as quote types: The basic types alone are of limited value. New, more structured data types are built using type constructors. The most basic type constructor forms the union of two predefined types. The type (A|B) contains all elements of the type A and all of the type B . In

2260-527: A value into this variable might be specified as: The externals clause ( ext ) specifies which parts of the state can be accessed by the operation; rd indicating read-only access and wr being read/write access. IBM International Business Machines Corporation (using the trademark IBM ), nicknamed Big Blue , is an American multinational technology company headquartered in Armonk, New York and present in over 175 countries. It

2373-483: A value. In other words, an enumerated type has values that are different from each other, and that can be compared and assigned, but are not specified by the programmer as having any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily. For example, the four suits in a deck of playing cards may be four enumerators named Club , Diamond , Heart , and Spade , belonging to an enumerated type named suit . If

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2486-408: A variable V is declared having suit as its data type, one can assign any of those four values to it. Although the enumerators are usually distinct, some languages may allow the same enumerator to be listed twice in the type's declaration. The names of enumerators need not be semantically complete or compatible in any sense. For example, an enumerated type called color may be defined to consist of

2599-405: Is a data type consisting of a set of named values called elements , members , enumeral , or enumerators of the type. The enumerator names are usually identifiers that behave as constants in the language. An enumerated type can be seen as a degenerate tagged union of unit type . A variable that has been declared as having an enumerated type can be assigned any of the enumerators as

2712-507: Is a publicly traded company and one of the 30 companies in the Dow Jones Industrial Average . IBM is the largest industrial research organization in the world, with 19 research facilities across a dozen countries, having held the record for most annual U.S. patents generated by a business for 29 consecutive years from 1993 to 2021. IBM was founded in 1911 as the Computing-Tabulating-Recording Company (CTR),

2825-502: Is a Cartesian product with labels for the fields. The type is the Cartesian product with fields labelled f1,…,fn . An element of type T can be composed from its constituent parts by a constructor, written mk_T . Conversely, given an element of type T , the field names can be used to select the named component. For example, the type models a simple date type. The value mk_Date(1,4,2001) corresponds to 1 April 2001. Given

2938-457: Is a predefined type) constructs the type composed of all finite lists of values drawn from the type T . For example, the type definition Defines a type String composed of all finite strings of characters. Various operators are defined on sequences for constructing concatenation, selection of elements and subsequences etc. Many of these operators are partial in the sense that they are not defined for certain applications. For example, selecting

3051-432: Is a predefined type) constructs the type composed of all finite sets of values drawn from the type T . For example, the type definition defines a type UGroup composed of all finite sets of UserId values. Various operators are defined on sets for constructing their union, intersections, determining proper and non-strict subset relationships etc. The finite sequence type constructor (written seq of T where T

3164-485: Is an implementation-defined integral type that is large enough to hold all enumerated values; it does not have to be the smallest possible type. The underlying type can be specified directly, which allows "forward declarations" of enumerations: Go uses the iota keyword to create enumerated constants. Enumerated types are an important feature of the language; they can have type parameters and be recursive. They provide basic support for algebraic data types , allowing

3277-562: Is dealt with. In VDM-SL there is a conventional modular extension whereas VDM++ has a traditional object-oriented structuring mechanism with classes and inheritance. In the ISO standard for VDM-SL there is an informative annex that contains different structuring principles. These all follow traditional information hiding principles with modules and they can be explained as: In VDM++ structuring are done using classes and multiple inheritance. The key concepts are: In VDM-SL, functions are defined over

3390-416: Is even possible for an enum variable to hold an integer that does not represent any of the enumeration values. In fact, according to the language definition, the above code will define Clubs , Diamonds , Hearts , and Spades as constants of type int , which will only be converted (silently) to enum cardsuit if they are stored in a variable of that type. C also allows the programmer to choose

3503-521: Is not relevant to the model's purpose and would only add complexity. In such cases, the members of the type may be represented as structureless tokens. Values of token types can only be compared for equality – no other operators are defined on them. Where specific named values are required, these are introduced as quote types. Each quote type consists of one named value of the same name as the type itself. Values of quote types (known as quote literals) may only be compared for equality. For example, in modelling

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3616-451: Is possible to assign to an enum variable other integer values that are not in the scope of the enum definition. C++ has enumeration types that are directly inherited from C's and work mostly like these, except that an enumeration is a real type in C++, giving added compile-time checking. Also (as with structs), the C++ enum keyword is combined with a typedef , so that instead of naming

3729-568: Is similar to that of C : The Java type system, however, treats enumerations as a type separate from integers, and intermixing of enum and integer values is not allowed. In fact, an enum type in Java is actually a special compiler-generated class rather than an arithmetic type, and enum values behave as global pre-generated instances of that class. Enum types can have instance methods and a constructor (the arguments of which can be specified separately for each enum value). All enum types implicitly extend

3842-430: Is that enumerated types can allow compilers to enforce semantic correctness. For instance: myColor = TRIANGLE can be forbidden, whilst myColor = RED is accepted, even if TRIANGLE and RED are both internally represented as 1 . Conceptually, an enumerated type is similar to a list of nominals (numeric codes), since each possible value of the type is assigned a distinctive natural number. A given enumerated type

3955-481: Is that the enumerators do not leak, so usage requires prefixing with the name of the enumeration (e.g., Color::Red for the first enumerator in the example below), unless a using enum declaration (introduced in C++20 ) has been used to bring the enumerators into the current scope. A scoped enumeration is specified by the phrase enum class (or enum struct ). For example: The underlying type of an enumeration

4068-400: Is the "less than or equal to" Boolean operator on natural numbers): Since invariants can be arbitrarily complex logical expressions, and membership of a defined type is limited to only those values satisfying the invariant, type correctness in VDM-SL is not automatically decidable in all situations. The other basic types include char for characters. In some cases, the representation of a type

4181-440: Is the largest shareholder of IBM and as of March 31, 2023, held 15.7% of total shares outstanding. In 2011, IBM became the first technology company Warren Buffett 's holding company Berkshire Hathaway invested in. Initially he bought 64 million shares costing $ 10.5 billion. Over the years, Buffett increased his IBM holdings, but by the end of 2017 had reduced them by 94.5% to 2.05 million shares; by May 2018, he

4294-546: Is thus a concrete implementation of this notion. When order is meaningful and/or used for comparison, then an enumerated type becomes an ordinal type. Programming languages tend to have their own, oftentimes multiple, programming styles and naming conventions . The variable assigned to an enumeration is usually a noun in singular form, and frequently follows either a PascalCase or uppercase convention, while lowercase and others are seen less frequently. In Pascal , an enumerated type can be implicitly declared by listing

4407-447: The Enum abstract class. An enum type cannot be instantiated directly. Internally, each enum value contains an integer, corresponding to the order in which they are declared in the source code, starting from 0. The programmer cannot set a custom integer for an enum value directly, but one can define overloaded constructors that can then assign arbitrary values to self-defined members of

4520-574: The FORTRAN scientific programming language was developed. In 1961, IBM developed the SABRE reservation system for American Airlines and introduced the highly successful Selectric typewriter. In 1963, IBM employees and computers helped NASA track the orbital flights of the Mercury astronauts. A year later, it moved its corporate headquarters from New York City to Armonk, New York. The latter half of

4633-851: The IBM Rome Software Lab (Rome, Italy), Hursley House (Winchester, UK), 330 North Wabash (Chicago, Illinois, United States), the Cambridge Scientific Center (Cambridge, Massachusetts, United States), the IBM Toronto Software Lab (Toronto, Canada), the IBM Building, Johannesburg (Johannesburg, South Africa), the IBM Building (Seattle) (Seattle, Washington, United States), the IBM Hakozaki Facility (Tokyo, Japan),

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4746-888: The IBM Yamato Facility (Yamato, Japan), the IBM Canada Head Office Building (Ontario, Canada) and the Watson IoT Headquarters (Munich, Germany). Defunct IBM campuses include the IBM Somers Office Complex (Somers, New York), Spango Valley (Greenock, Scotland), and Tour Descartes (Paris, France). The company's contributions to industrial architecture and design include works by Marcel Breuer , Eero Saarinen , Ludwig Mies van der Rohe , I.M. Pei and Ricardo Legorreta . Van der Rohe's building in Chicago

4859-544: The National Cash Register Company by John Henry Patterson , called on Flint and, in 1914, was offered a position at CTR. Watson joined CTR as general manager and then, 11 months later, was made President when antitrust cases relating to his time at NCR were resolved. Having learned Patterson's pioneering business practices, Watson proceeded to put the stamp of NCR onto CTR's companies. He implemented sales conventions, "generous sales incentives,

4972-448: The UPC barcode . The company has made inroads in advanced computer chips , quantum computing , artificial intelligence , and data infrastructure . IBM employees and alumni have won various recognitions for their scientific research and inventions, including six Nobel Prizes and six Turing Awards . IBM originated with several technological innovations developed and commercialized in

5085-681: The Universal Product Code . IBM and the World Bank first introduced financial swaps to the public in 1981, when they entered into a swap agreement. IBM entered the microcomputer market in the 1980s with the IBM Personal Computer (IBM 5150), which soon became known as the PC , one of IBM's best selling products. Due to a lack of foresight by IBM, the PC was not well protected by intellectual property laws. As

5198-410: The magnetic stripe card that would become ubiquitous for credit/debit/ATM cards, driver's licenses, rapid transit cards and a multitude of other identity and access control applications. IBM pioneered the manufacture of these cards, and for most of the 1970s, the data processing systems and software for such applications ran exclusively on IBM computers. In 1974, IBM engineer George J. Laurer developed

5311-606: The microcomputer market in 1981 with the IBM Personal Computer , — its DOS software provided by Microsoft , — which became the basis for the majority of personal computers to the present day. The company later also found success in the portable space with the ThinkPad . Since the 1990s, IBM has concentrated on computer services , software , supercomputers , and scientific research ; it sold its microcomputer division to Lenovo in 2005. IBM continues to develop mainframes, and its supercomputers have consistently ranked among

5424-561: The "Vienna Development Method"... The meta-language actually adopted ("Meta-IV") is used to define major portions of PL/1 (as given in ECMA 74 – interestingly a "formal standards document written as an abstract interpreter") in BEKIČ 74.» There is no connection between Meta-IV , and Schorre's META II language, or its successor Tree Meta ; these were compiler-compiler systems rather than being suitable for formal problem descriptions. So Meta-IV

5537-577: The 1960s saw IBM continue its support of space exploration, participating in the 1965 Gemini flights, 1966 Saturn flights, and 1969 lunar mission. IBM also developed and manufactured the Saturn V's Instrument Unit and Apollo spacecraft guidance computers. On April 7, 1964, IBM launched the first computer system family, the IBM System/360 . It spanned the complete range of commercial and scientific applications from large to small, allowing companies for

5650-521: The 5th element of a sequence that contains only three elements is undefined. The order and repetition of items in a sequence is significant, so [a, b] is not equal to [b, a] , and [a] is not equal to [a, a] . A finite mapping is a correspondence between two sets, the domain and range, with the domain indexing elements of the range. It is therefore similar to a finite function. The mapping type constructor in VDM-SL (written map T1 to T2 where T1 and T2 are predefined types) constructs

5763-521: The C-like feature of being able to define specific integer values for enumerations. By doing this it is possible to perform binary operations on enumerations, thus treating enumeration values as sets of flags. These flags can be tested using binary operations or with the Enum type's builtin 'HasFlag' method. The enumeration definition defines names for the selected integer values and is syntactic sugar , as it

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5876-465: The Danish, English and Irish Schools. The "English School" derived from work by Cliff Jones on the aspects of VDM not specifically related to language definition and compiler design (Jones 1980, 1990). It stresses modelling persistent state through the use of data types constructed from a rich collection of base types. Functionality is typically described through operations which may have side-effects on

5989-490: The IBM PC Co. was dissolved and merged into IBM Personal Systems Group. In 2002 IBM acquired PwC Consulting, the consulting arm of PwC which was merged into its IBM Global Services . On September 14, 2004, LG and IBM announced that their business alliance in the South Korean market would end at the end of that year. Both companies stated that it was unrelated to the charges of bribery earlier that year. Xnote

6102-506: The IBM Power Personal Systems Group, the former an attempt to design and market " clone " computers of IBM's own architecture and the latter responsible for IBM's PowerPC -based workstations . IBM PC Co. introduced the ThinkPad clone computers, which IBM would heavily market and would eventually become one of the best-selling series of notebook computers . In 1993, IBM posted an $ 8 billion loss – at

6215-789: The IBM website. On June 7, Krishna announced that IBM would carry out an "orderly wind-down" of its operations in Russia. In late 2022, IBM started a collaboration with new Japanese manufacturer Rapidus , which led GlobalFoundries to file a lawsuit against IBM the following year. In 2023, IBM acquired Manta Software Inc. to complement its data and A.I. governance capabilities for an undisclosed amount. On November 16, 2023, IBM suspended ads on Twitter after ads were found next to pro-Nazi content. In December 2023, IBM announced it would acquire Software AG 's StreamSets and webMethods platforms for €2.13 billion ($ 2.33 billion). IBM's market capitalization

6328-551: The Managed Infrastructure Services unit of its Global Technology Services division into a new public company. The new company, Kyndryl , will have 90,000 employees, 4,600 clients in 115 countries, with a backlog of $ 60 billion. IBM's spin off was greater than any of its previous divestitures, and welcomed by investors. IBM appointed Martin Schroeter, who had been IBM's CFO from 2014 through

6441-701: The VDMTools language manuals and in the available texts. The ISO Standard contains a formal definition of the language's semantics. In the remainder of this article, the ISO-defined interchange (ASCII) syntax is used. Some texts prefer a more concise mathematical syntax . A VDM-SL model is a system description given in terms of the functionality performed on data. It consists of a series of definitions of data types and functions or operations performed upon them. VDM-SL includes basic types modelling numbers and characters as follows: Data types are defined to represent

6554-516: The Weather Channel mobile app. Also that year, IBM employees created the film A Boy and His Atom , which was the first molecule movie to tell a story. In 2016, IBM acquired video conferencing service Ustream and formed a new cloud video unit. In April 2016, it posted a 14-year low in quarterly sales. The following month, Groupon sued IBM accusing it of patent infringement, two months after IBM accused Groupon of patent infringement in

6667-469: The antitrust laws in IBM's actions directed against leasing companies and plug-compatible peripheral manufacturers. Shortly after, IBM unbundled its software and services in what many observers believed was a direct result of the lawsuit, creating a competitive market for software. In 1982, the Department of Justice dropped the case as "without merit". Also in 1969, IBM engineer Forrest Parry invented

6780-601: The city's seventh tallest building and overlooking Beijing National Stadium ("Bird's Nest") , home to the 2008 Summer Olympics . IBM India Private Limited is the Indian subsidiary of IBM, which is headquartered at Bangalore , Karnataka. It has facilities in Coimbatore , Chennai , Kochi , Ahmedabad , Delhi , Kolkata , Mumbai , Pune , Gurugram , Noida , Bhubaneshwar , Surat , Visakhapatnam , Hyderabad , Bangalore and Jamshedpur . Other notable buildings include

6893-560: The clumsy hyphenated name "Computing-Tabulating-Recording Company" and chose to replace it with the more expansive title "International Business Machines" which had previously been used as the name of CTR's Canadian Division; the name was changed on February 14, 1924. By 1933, most of the subsidiaries had been merged into one company, IBM. The Nazis made extensive use of Hollerith punch card and alphabetical accounting equipment and IBM's majority-owned German subsidiary, Deutsche Hollerith Maschinen GmbH ( Dehomag ), supplied this equipment from

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7006-461: The company designed a video surveillance system for Davao City . In 2014 IBM announced it would sell its x86 server division to Lenovo for $ 2.1 billion. while continuing to offer Power ISA -based servers. Also that year, IBM began announcing several major partnerships with other companies, including Apple Inc. , Twitter, Facebook, Tencent , Cisco , UnderArmour , Box , Microsoft , VMware , CSC , Macy's , Sesame Workshop ,

7119-421: The company more manageable and to streamline IBM by having other investors finance those companies. These included AdStar , dedicated to disk drives and other data storage products; IBM Application Business Systems, dedicated to mid-range computers; IBM Enterprise Systems, dedicated to mainframes; Pennant Systems, dedicated to mid-range and large printers; Lexmark , dedicated to small printers; and more. Lexmark

7232-413: The data types defined in a model. Support for abstraction requires that it should be possible to characterize the result that a function should compute without having to say how it should be computed. The main mechanism for doing this is the implicit function definition in which, instead of a formula computing a result, a logical predicate over the input and result variables, termed a postcondition , gives

7345-475: The early 1930s. This equipment was critical to Nazi efforts to categorize citizens of both Germany and other nations that fell under Nazi control through ongoing censuses. These census data were used to facilitate the round-up of Jews and other targeted groups, and to catalog their movements through the machinery of the Holocaust , including internment in the concentration camps. Nazi concentration camps operated

7458-553: The end of 2017, as CEO of Kyndryl. In 2021, IBM announced the acquisition of the enterprise software company Turbonomic for $ 1.5 billion. In January 2022, IBM announced it would sell Watson Health to private equity firm Francisco Partners . On March 7, 2022, a few days after the start of the Russian invasion of Ukraine , IBM CEO Arvind Krishna published a Ukrainian flag and announced that "we have suspended all business in Russia". All Russian articles were also removed from

7571-445: The enterprise-oriented Personal Systems Group of the IBM PC Co. into IBM's own Global Services personal computer consulting and customer service division. The resulting merged business units then became known simply as IBM Personal Systems Group. A year later, IBM stopped selling their computers at retail outlets after their market share in this sector had fallen considerably behind competitors Compaq and Dell . Immediately afterwards,

7684-412: The enum class. Defining getters allows then access to those self-defined members. The internal integer can be obtained from an enum value using the ordinal() method, and the list of enum values of an enumeration type can be obtained in order using the values() method. It is generally discouraged for programmers to convert enums to integers and vice versa. Enumerated types are Comparable , using

7797-421: The enum definition. For example, given the expressions CardSuit.Diamonds + 1 and CardSuit.Hearts - CardSuit.Clubs are allowed directly (because it may make sense to step through the sequence of values or ask how many steps there are between two values), but CardSuit.Hearts * CardSuit.Spades is deemed to make less sense and is only allowed if the values are first converted to integers. C# also provides

7910-481: The enumerators Red , Green , Zebra , Missing , and Bacon . In some languages, the declaration of an enumerated type also intentionally defines an ordering of its members ( High , Medium and Low priorities); in others, the enumerators are unordered ( English , French , German and Spanish supported languages); in others still, an implicit ordering arises from the compiler concretely representing enumerators as integers. Some enumerator types may be built into

8023-492: The first time to upgrade to models with greater computing capability without having to rewrite their applications. It was followed by the IBM System/370 in 1970. Together the 360 and 370 made the IBM mainframe the dominant mainframe computer and the dominant computing platform in the industry throughout this period and into the early 1980s. They and the operating systems that ran on them such as OS/VS1 and MVS , and

8136-433: The function to return the positive root. All function specifications may be restricted by preconditions which are logical predicates over the input variables only and which describe constraints that are assumed to be satisfied when the function is executed. For example, a square root calculating function that works only on positive real numbers might be specified as follows: The precondition and postcondition together form

8249-512: The inclusion of product types , in a fashion similar to Haskell and ML . A switch expression can apply pattern matching to an enum value, allowing for elegant solutions to complex programming problems: Examples of parametric enum types are the Haxe standard library types Option and Either: The J2SE version 5.0 of the Java programming language added enumerated types whose declaration syntax

8362-552: The integer value of the enum value serving as the index. Dynamically typed languages in the syntactic tradition of C (e.g., Perl or JavaScript ) do not, in general, provide enumerations. But in Perl programming the same result can be obtained with the shorthand strings list and hashes (possibly slices ): Raku (formerly known as Perl 6) supports enumerations. There are multiple ways to declare enumerations in Raku, all creating

8475-423: The internal integer; as a result, they can be sorted. The Java standard library provides utility classes to use with enumerations. The EnumSet class implements a Set of enum values; it is implemented as a bit array , which makes it very compact and as efficient as explicit bit manipulation, but safer. The EnumMap class implements a Map of enum values to object. It is implemented as an array, with

8588-448: The language. The Boolean type , for example is often a pre-defined enumeration of the values False and True . A unit type consisting of a single value may also be defined to represent null . Many languages allow users to define new enumerated types. Values and variables of an enumerated type are usually implemented with some integer type as the underlying representation. Some languages, especially system programming languages , allow

8701-749: The larger ones. In New York City, IBM has several offices besides CHQ, including the IBM Watson headquarters at Astor Place in Manhattan. Outside of New York, major campuses in the United States include Austin, Texas ; Research Triangle Park (Raleigh-Durham), North Carolina ; Rochester, Minnesota ; and Silicon Valley, California . IBM's real estate holdings are varied and globally diverse. Towers occupied by IBM include 1250 René-Lévesque (Montreal, Canada) and One Atlantic Center (Atlanta, Georgia, US). In Beijing, China, IBM occupies Pangu Plaza ,

8814-570: The late 19th century. Julius E. Pitrap patented the computing scale in 1885; Alexander Dey invented the dial recorder (1888); Herman Hollerith patented the Electric Tabulating Machine (1889); and Willard Bundy invented a time clock to record workers' arrival and departure times on a paper tape (1889). On June 16, 1911, their four companies were amalgamated in New York State by Charles Ranlett Flint forming

8927-451: The latest being the IBM z series. The most recent model, the IBM z16 , was released in 2022. In 1990, IBM released the Power microprocessors , which were designed into many console gaming systems, including Xbox 360 , PlayStation 3 , and Nintendo 's Wii U . IBM Secure Blue is encryption hardware that can be built into microprocessors, and in 2014, the company revealed TrueNorth ,

9040-425: The longer term. The key trends of IBM are (as at the financial year ending December 31): The company's 15-member board of directors are responsible for overall corporate management and includes the current or former CEOs of Anthem , Dow Chemical , Johnson and Johnson , Royal Dutch Shell , UPS , and Vanguard as well as the president of Cornell University and a retired U.S. Navy admiral . Vanguard Group

9153-522: The main data of the modelled system. Each type definition introduces a new type name and gives a representation in terms of the basic types or in terms of types already introduced. For example, a type modelling user identifiers for a log-in management system might be defined as follows: For manipulating values belonging to data types, operators are defined on the values. Thus, natural number addition, subtraction etc. are provided, as are Boolean operators such as equality and inequality. The language does not fix

9266-410: The manner of a functional programming language. In an explicit function definition, the result is defined by means of an expression over the inputs. For example, a function that produces a list of the squares of a list of numbers might be defined as follows: This recursive definition consists of a function signature giving the types of the input and result and a function body. An implicit definition of

9379-585: The mid-1950s. There are two other IBM buildings within walking distance of CHQ: the North Castle office, which previously served as IBM's headquarters; and the Louis V. Gerstner, Jr., Center for Learning (formerly known as IBM Learning Center (ILC)), a resort hotel and training center, which has 182 guest rooms, 31 meeting rooms, and various amenities. IBM operates in 174 countries as of 2016 , with mobility centers in smaller market areas and major campuses in

9492-613: The middleware built on top of those such as the CICS transaction processing monitor, had a near-monopoly-level market share and became the thing IBM was most known for during this period. In 1969, the United States of America alleged that IBM violated the Sherman Antitrust Act by monopolizing or attempting to monopolize the general-purpose electronic digital computer system market, specifically computers designed primarily for business, and subsequently alleged that IBM violated

9605-450: The most powerful in the world in the 21st century. As one of the world's oldest and largest technology companies, IBM has been responsible for several technological innovations , including the automated teller machine (ATM), dynamic random-access memory (DRAM), the floppy disk , the hard disk drive , the magnetic stripe card , the relational database , the SQL programming language , and

9718-400: The parent company of Sesame Street , and Salesforce.com . In 2015, its chip division transitioned to a fabless model with semiconductors design, offloading manufacturing to GlobalFoundries . In 2015, IBM announced three major acquisitions: Merge Healthcare for $ 1 billion, data storage vendor Cleversafe , and all digital assets from The Weather Company , including Weather.com and

9831-464: The programmer. These values may not even be visible to the programmer (see information hiding ). Enumerated types can also prevent a programmer from writing illogical code such as performing mathematical operations on the values of the enumerators. If the value of a variable that was assigned an enumerator were to be printed, some programming languages could also print the name of the enumerator rather than its underlying numerical value. A further advantage

9944-465: The programming language C had no enumerated types. In C, enumerations are created by explicit definitions (the enum keyword by itself does not cause allocation of storage) which use the enum keyword and are reminiscent of struct and union definitions: C exposes the integer representation of enumeration values directly to the programmer. Integers and enum values can be mixed freely, and all arithmetic operations on enum values are permitted. It

10057-515: The properties of models to a high level of assurance. It also has an executable subset, so that models may be analyzed by testing and can be executed through graphical user interfaces, so that models can be evaluated by experts who are not necessarily familiar with the modeling language itself. The origins of VDM-SL lie in the IBM Laboratory in Vienna where the first version of the language

10170-477: The result's properties. For example, a function SQRT for calculating a square root of a natural number might be defined as follows: Here the postcondition does not define a method for calculating the result r but states what properties can be assumed to hold of it. Note that this defines a function that returns a valid square root; there is no requirement that it should be the positive or negative root. The specification above would be satisfied, for example, by

10283-465: The same function might take the following form: The explicit definition is in a simple sense an implementation of the implicitly specified function. The correctness of an explicit function definition with respect to an implicit specification may be defined as follows. Given an implicit specification: and an explicit function: we say it satisfies the specification iff : So, " f is a correct implementation" should be interpreted as " f satisfies

10396-514: The specification". In VDM-SL, functions do not have side-effects such as changing the state of a persistent global variable. This is a useful ability in many programming languages, so a similar concept exists; instead of functions, operations are used to change state variables (also known as globals ). For example, if we have a state consisting of a single variable someStateRegister : nat , we could define this in VDM-SL as: In VDM++ this would instead be defined as: An operation to load

10509-468: The state and which are mostly specified implicitly using a precondition and postcondition. The "Danish School" ( Bjørner et al. 1982) has tended to stress a constructive approach with explicit operational specification used to a greater extent. Work in the Danish school led to the first European validated Ada compiler. An ISO Standard for the language was released in 1996 (ISO, 1996). The VDM-SL and VDM++ syntax and semantics are described at length in

10622-543: The time the biggest in American corporate history. Lou Gerstner was hired as CEO from RJR Nabisco to turn the company around. In 1995, IBM purchased Lotus Software , best known for its Lotus 1-2-3 spreadsheet software. During the decade, IBM was working on a new operating system, named the Workplace OS project. Despite a large amount of money spent on the project, it was cancelled in 1996. In 1998, IBM merged

10735-454: The traffic signal controller example, the type modelling the colour of a traffic signal could be defined as follows: Enumerated types in VDM-SL are defined as shown above as unions on quote types. Cartesian product types may also be defined in VDM-SL. The type (A1*…*An) is the type composed of all tuples of values, the first element of which is from the type A1 and the second from the type A2 and so on. The composite or record type

10848-441: The type enum name , simply name it name . This can be simulated in C using a typedef: typedef enum { Value1 , Value2 } name ; C++11 also provides a second kind of enumeration, called a scoped enumeration . These are type-safe: the enumerators are not implicitly converted to an integer type. Among other things, this allows I/O streaming to be defined for the enumeration type. Another feature of scoped enumerations

10961-420: The type composed of all finite mappings from sets of T1 values to sets of T2 values. For example, the type definition Defines a type Birthdays which maps character strings to Date . Again, operators are defined on mappings for indexing into the mapping, merging mappings, overwriting extracting sub-mappings. The main difference between the VDM-SL and VDM++ notations are the way in which structuring

11074-813: The use of "=" was replaced with "is" leaving the definition quite similar: In addition to Pred , Succ , Val and Pos Ada also supports simple string conversions via Image and Value . Similar to C-style languages Ada allows the internal representation of the enumeration to be specified: Unlike C-style languages Ada also allows the number of bits of the enumeration to be specified: Additionally, one can use enumerations as indexes for arrays, like in Pascal, but there are attributes defined for enumerations Like Modula-3 Ada treats Boolean and Character as special pre-defined (in package " Standard ") enumerated types. Unlike Modula-3 one can also define own character types: The original K&R dialect of

11187-510: The user to specify the bit combination to be used for each enumerator, which can be useful to efficiently represent sets of enumerators as fixed-length bit strings. In type theory , enumerated types are often regarded as tagged unions of unit types . Since such types are of the form 1 + 1 + ⋯ + 1 {\displaystyle 1+1+\cdots +1} , they may also be written as natural numbers. Some early programming languages did not originally have enumerated types. If

11300-608: The vacuum tube based IBM 701 , in 1952. The IBM 305 RAMAC introduced the hard disk drive in 1956. The company switched to transistorized designs with the 7000 and 1400 series, beginning in 1958. In which, IBM considered the 1400 series the ''model T'' of computing, due to it being the first computer with over ten thousand sales by IBM. In 1956, the company demonstrated the first practical example of artificial intelligence when Arthur L. Samuel of IBM's Poughkeepsie , New York, laboratory programmed an IBM 704 not merely to play checkers but "learn" from its own experience. In 1957,

11413-454: The value can be a string, a character, or a value of any integer or floating-point type. Alternatively, enumeration cases can specify associated values of any type to be stored along with each different case value, much as unions or variants do in other languages. One can define a common set of related cases as part of one enumeration, each of which has a different set of values of appropriate types associated with it. In Swift, enumerations are

11526-454: The values in a parenthesised list: The declaration will often appear in a type synonym declaration, such that it can be used for multiple variables: The order in which the enumeration values are given matters. An enumerated type is an ordinal type, and the pred and succ functions will give the prior or next value of the enumeration, and ord can convert enumeration values to their integer representation. Standard Pascal does not offer

11639-668: The values of the enumeration constants explicitly, even without type. For example, could be used to define a type that allows mathematical sets of suits to be represented as an enum cardsuit by bitwise logic operations. Since C23 , the underlying type of an enumeration can be specified by the programmer: Enumerated types in the C# programming language preserve most of the "small integer" semantics of C's enums. Some arithmetic operations are not defined for enums, but an enum value can be explicitly converted to an integer and back again, and an enum variable can have values that were not declared by

11752-653: Was "used to define major portions of" the PL/I programming language. Other programming languages retrospectively described, or partially described, using Meta-IV and VDM-SL include the BASIC programming language , FORTRAN , the APL programming language , ALGOL 60, the Ada programming language and the Pascal programming language . Meta-IV evolved into several variants, generally described as

11865-488: Was acquired by Clayton & Dubilier in a leveraged buyout shortly after its formation. In September 1992, IBM completed the spin-off of their various non-mainframe and non-midrange, personal computer manufacturing divisions, combining them into an autonomous wholly owned subsidiary known as the IBM Personal Computer Company (IBM PC Co.). This corporate restructuring came after IBM reported

11978-543: Was announced that IBM will build Europe's first quantum computer in Ehningen, Germany . The center, to be operated by the Fraunhofer Society , was still in construction as of 2023, with cloud access planned in 2024. Enumerated type In computer programming , an enumerated type (also called enumeration , enum , or factor in the R programming language , and a categorical variable in statistics)

12091-507: Was called the V ienna D efinition L anguage (VDL). The VDL was essentially used for giving operational semantics descriptions in contrast to the VDM – Meta-IV which provided denotational semantics «Towards the end of 1972 the Vienna group again turned their attention to the problem of systematically developing a compiler from a language definition. The overall approach adopted has been termed

12204-400: Was completely out of IBM. IBM is headquartered in Armonk, New York , a community 37 miles (60 km) north of Midtown Manhattan. A nickname for the company is the " Colossus of Armonk ". Its principal building, referred to as CHQ, is a 283,000-square-foot (26,300 m ) glass and stone edifice on a 25-acre (10 ha) parcel amid a 432-acre former apple orchard the company purchased in

12317-400: Was exhibited on Jeopardy! where it won against game-show champions Ken Jennings and Brad Rutter. The company also celebrated its 100th anniversary in the same year on June 16. In 2012, IBM announced it had agreed to buy Kenexa and Texas Memory Systems, and a year later it also acquired SoftLayer Technologies, a web hosting service , in a deal worth around $ 2 billion. Also that year,

12430-412: Was no explanation as to how the numbers were obtained or whether their actual values were significant. These magic numbers could make the source code harder for others to understand and maintain. Enumerated types, on the other hand, make the code more self-documenting. Depending on the language, the compiler could automatically assign default values to the enumerators thereby hiding unnecessary detail from

12543-640: Was originally part of the joint venture and was sold by LG in 2012. Continuing a trend started in the 1990s of downsizing its operations and divesting from commodity production , IBM sold all of its personal computer business to Chinese technology company Lenovo and, in 2009, it acquired software company SPSS Inc. Later in 2009, IBM's Blue Gene supercomputing program was awarded the National Medal of Technology and Innovation by U.S. President Barack Obama . In 2011, IBM gained worldwide attention for its artificial intelligence program Watson , which

12656-507: Was recognized with the 1990 Honor Award from the National Building Museum . IBM has a large and diverse portfolio of products and services. As of 2016 , these offerings fall into the categories of cloud computing , artificial intelligence, commerce , data and analytics , Internet of things (IoT), IT infrastructure , mobile , digital workplace and cybersecurity . Since 1954, IBM sells mainframe computers ,

12769-480: Was valued at over $ 153 billion as of May 2024. Despite its relative decline within the technology sector, IBM remains the seventh largest technology company by revenue, and 67th largest overall company by revenue in the United States . IBM ranked No. 38 on the 2020 Fortune 500 rankings of the largest United States corporations by total revenue. In 2014, IBM was accused of using "financial engineering" to hit its quarterly earnings targets rather than investing for

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