# enumeration computer science

The variable red would then be assigned to myColor. A given enumerated type is thus a concrete implementation of this notion. Since such types are of the form In C++ you can specify the underlying type directly. 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. Something built-in like Arrays.asList() or Collection.toArray() should exist somewhere, but I'm unable to find that in my IntelliJ debugger's evaluator window (and Google/SO results, too). An enumeration in C++ sets up a new data type that defines a set of integer constants. 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. Enumeration is a list of named constants, and these Java enumerations define a class type. Like Modula-3 Ada treats Boolean and Character as special pre-defined (in package "Standard") enumerated types. In Pascal, an enumerated type can be implicitly declared by listing 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. C also allows the programmer to choose the values of the enumeration constants explicitly, even without type. The most common use of enumeration in set theory occurs in the context where infinite sets are separated into those that are countable and those that are not. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem. Computer science has a particular focus on trees and combstruct really shines here, providing total enumeration as well as generating functions and functional equations. Enumerated types in the C# programming language preserve most of the "small integer" semantics of C's enums. 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 the enum class. Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i.e., the one pioneered by E. M. Gold (1967, Inform. + Values and variables of an enumerated type are usually implemented as fixed-length bit strings, often in a format and size compatible with some integer type. These magic numbers could make the source code harder for others to understand and maintain. 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. In some contexts, such as enumerative combinatorics, the term enumeration is used more in the sense of counting – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements. In Pascal and most of its descendants, however, the difference between an enumeration and a set of integer constants is much more significant: the enumeration is a full-fledged type, incompatible with integers. The names of enumerators need not be semantically complete or compatible in any sense. In practice, this broad meaning of enumeration is often used to compare the relative sizes or cardinalities of different sets. {\displaystyle \mathbb {N} } While optimization is ubiquitious in computer science and many application areas, relatively little is known about enumeration within the "Algorithms and Complexity" community. The set being enumerated is then called recursively enumerable (or computably enumerable in more contemporary language), referring to the use of recursion theory in formalizations of what it means for the map to be computable. Pascal and syntactically similar languages, Algebraic data type in functional programming, -- see attributes of enumerations 'First, 'Last, 'Succ, 'Pred, --first enumeration value of type Cardsuit e.g., clubs, --last enumeration value of type Cardsuit e.g., spades, // must fit in size and memory layout the type 'long'. Define an enumeration type, triangleType, that has the value scalene, isosceles, equilateral, and noTriangle. An enumerated type can be seen as a degenerate tagged union of unit type. // ignore first value by assigning to blank identifier, # Another way of using Pairs, you can also use :0sphynx, "A Comparison of Microsoft's C# Programming Language to Sun Microsystems' Java Programming Language", "Java 5: Taming the Tiger: Syntactic Sugar", https://en.wikipedia.org/w/index.php?title=Enumerated_type&oldid=997238094, Short description is different from Wikidata, Articles with example Python (programming language) code, Creative Commons Attribution-ShareAlike License, This page was last edited on 30 December 2020, at 16:30. Cambridge International AS & A Level Computer Science encourages learners to meet the needs of higher education courses in computer science as well as twenty-first century digital employers. on random mapping statistics (which are closely related to … If a variable V is declared having suit as its data type, one can assign any of those four values to it. In this case, an enumeration is merely an enumeration with domain ω, the ordinal of the natural numbers. Enumerated datatypes in Visual Basic (up to version 6) and VBA are automatically assigned the "Long" datatype and also become a datatype themselves: Common Lisp uses the member type specifier, e.g.. that states that object is of type cardsuit if it is #'eql to club, diamond, heart or spade. There is also a functional API for creating enumerations with automatically generated indices (starting with one): Python enumerations do not enforce semantic correctness (a meaningless comparison to an incompatible enumeration always returns False rather than raising a TypeError): Fortran only has enumerated types for interoperability with C; hence, the semantics is similar to C and, as in C, the enum values are just integers and no further type check is done. N These flags can be tested using binary operations or with the Enum type's builtin 'HasFlag' method. For instance, in partition enumeration and graph enumeration the objective is to count partitions or graphs that meet certain conditions. In C, enumerations assign related names to a set of integer values. Some other Pascal dialects allow it via type-casts. Some languages, especially system programming languages, allow the user to specify the bit combination to be used for each enumerator. Furthermore, this characterization illustrates a place where the ordering of the listing is important. Some early programming languages did not originally have enumerated types. Though Rust uses the enum keyword like C, it uses it to describe tagged unions, which enums can be considered a degenerate form of. Enumeration definition is - the act or process of making or stating a list of things one after another; also : the list itself. Formally, an enumeration of a set S is a mapping from (the natural numbers) to S which is surjective (i.e., every element of … In computability theory one often considers countable enumerations with the added requirement that the mapping from and Control 10, 447-474)). This is also called network enumeration. 12. An enumerated type can be seen as a degenerate tagged union of unit type. In mathematics and theoretical computer science, an enumeration of a set is a procedure for listing all members of the set in some definite sequence. Under this definition, an enumeration of a set S is any surjection from an ordinal α onto S. The more restrictive version of enumeration mentioned before is the special case where α is a finite ordinal or the first limit ordinal ω. Values can be stored and retrieved as numeric indexes or string values. Formally, the most inclusive definition of an enumeration of a set S is any surjection from an arbitrary index set I onto S. In this broad context, every set S can be trivially enumerated by the identity function from S onto itself. Sockets consist of an Internet Protocol (IP) address, which is the logical address, and a port number, which points to a specific service at that address. In some languages, the declaration of an enumerated type also intentionally defines an ordering of its members; in others, the enumerators are unordered; in others still, an implicit ordering arises from the compiler concretely representing enumerators as integers. C) Can be assigned other values once they've been defined. For example, an enumerated type called color may be defined to consist of the enumerators Red, Green, Zebra, Missing, and Bacon. 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. Defining getters allows then access to those self-defined members. If a value (termed a raw value) is provided for each enumeration case, the value can be a string, a character, or a value of any integer or floating-point type. The C example from above can be written in Fortran as. In this context, enumerable may be used to mean computably enumerable. It only takes a minute to sign up. More generally, it is a theorem of ZF that any well-ordered set can be enumerated under this characterization so that it coincides up to relabeling with the generalized listing enumeration. Let, There exists an enumeration for a set (in this sense) if and only if the set is, This page was last edited on 29 December 2020, at 07:59. Other techniques assigned arbitrary values to strings containing the names of the enumerators. can be enumerated by the identity function on 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. Enumerator for Word and Halting Problem in theoretical computer science I learned for every recursive enumerable language there would be an enumerator and a grammar. {\displaystyle 1+1+\cdots +1} In Java, the enumerated, or enum, type is a very powerful tool. For instance, would refer to a type equivalent to the prior definition of cardsuit, as of course would simply have been using. (set of all natural numbers) to the enumerated set must be computable. Enumeration of finite sets obviously requires that either non-injectivity or partiality is accepted, and in contexts where finite sets may appear one or both of these are inevitably present. This can be simulated in C using a typedef: typedef enum {Value1, Value2} name; C++11 provides a second, type-safe enumeration type that is not implicitly converted to an integer type. {\displaystyle f:\mathbb {N} \to \mathbb {Z} } can be forbidden, whilst In the CardSuit example above, clubs, diamonds, hearts, and spades do not implicitly equal 0, 1, 2 and 3. Even if one does assume the axiom of choice, S need not have any natural well-ordering. Common examples include Boolean, which takes values from the list [true, false], and day-of-week which takes values [Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday]. The index the language greatly expanded in Java not represent any of the items in collection... Regarded as tagged unions of unit type types implicitly extend the enum abstract.! Practice, this characterization, an enumeration in C++ sets up a new data type that a... 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