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72-525: A DTD defines the valid building blocks of an XML document. It defines the document structure with a list of validated elements and attributes. A DTD can be declared inline inside an XML document, or as an external reference. A namespace-aware version of DTDs is being developed as Part 9 of ISO DSDL . DTDs persist in applications that need special publishing characters, such as the XML and HTML Character Entity References , which derive from larger sets defined as part of

144-570: A system identifier . Programs for reading documents may not be required to read the external subset. Any valid SGML or XML document that references an external subset in its DTD, or whose body contains references to parsed external entities declared in its DTD (including those declared within its internal subset ), may only be partially parsed but cannot be fully validated by validating SGML or XML parsers in their standalone mode (this means that these validating parsers do not attempt to retrieve these external entities, and their replacement text

216-400: A XML Catalog ) the schema used in the parsed XML document and that is validated in another language. A common misconception holds that a non-validating XML parser does not have to read document type declarations, when in fact, the document type declarations must still be scanned for correct syntax as well as validity of declarations, and the parser must still parse all entity declarations in

288-515: A macro . The entity declaration assigns it a value that is retained throughout the document. A common use is to have a name more recognizable than a numeric character reference for an unfamiliar character. Entities help to improve legibility of an XML text. In general, there are two types: internal and external. An example of internal entity declarations (here in an internal DTD subset of an SGML document) is: Internal entities may be defined in any order, as long as they are not referenced and parsed in

360-402: A structured programming model would tend to not include code, and are called plain old data structures . Data types may be categorized according to several factors: The terminology varies - in the literature, primitive, built-in, basic, atomic, and fundamental may be used interchangeably. All data in computers based on digital electronics is represented as bits (alternatives 0 and 1) on

432-421: A to forall r. (forall a. f a -> r) -> r or a similar type. A refinement type is a type endowed with a predicate which is assumed to hold for any element of the refined type. For instance, the type of natural numbers greater than 5 may be written as { n ∈ N | n > 5 } {\displaystyle \{n\in \mathbb {N} \,|\,n>5\}} A dependent type

504-422: A MIME type, interpreted as a relative URI, but it could be an absolute URI to a specific renderer, or a URN indicating an OS-specific object identifier such as a UUID). The declared notation name must be unique within all the document type declaration, i.e. in the external subset as well as the internal subset, at least for conformance with XML. Notations can be associated to unparsed external entities included in

576-597: A corresponding native type does not exist on the target platform, the compiler will break them down into code using types that do exist. For instance, if a 32-bit integer is requested on a 16 bit platform, the compiler will tacitly treat it as an array of two 16 bit integers. Floating point data types represent certain fractional values ( rational numbers , mathematically). Although they have predefined limits on both their maximum values and their precision, they are sometimes misleadingly called reals (evocative of mathematical real numbers ). They are typically stored internally in

648-561: A family of function types differentiated by argument and return types, such as the type Int -> Bool denoting functions taking an integer and returning a Boolean. In C, a function is not a first-class data type but function pointers can be manipulated by the program. Java and C++ originally did not have function values but have added them in C++11 and Java 8. A type constructor builds new types from old ones, and can be thought of as an operator taking zero or more types as arguments and producing

720-408: A fixed value ( #FIXED ), or which value should be used as a default value ("…") in case the given attribute is left out in an XML tag. Attribute list declarations are ignored by non-validating SGML and XML parsers (in which cases any attribute is accepted within all elements of the parsed document), but these declarations are still checked for well-formedness and validity. An entity is similar to

792-475: A language-defined machine representation. The C programming language , for instance, supplies types such as Booleans, integers, floating-point numbers, etc., but the precise bit representations of these types are implementation-defined. The only C type with a precise machine representation is the char type that represents a byte. The Boolean type represents the values true and false . Although only two values are possible, they are more often represented as

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864-408: A notation name "type-image-svg". However, notation names usually follow a naming convention that is specific to the application generating or using the notation: notations are interpreted as additional meta-data whose effective content is an external entity and either a PUBLIC FPI, registered in the catalogs used by XML or SGML parsers, or a SYSTEM URI, whose interpretation is application dependent (here

936-446: A notation named "type-image-svg" that references the standard public FPI and the system identifier (the standard URI) of an SVG 1.1 document, instead of specifying just a system identifier as in the first example (which was a relative URI interpreted locally as a MIME type). This annotation is referenced directly within the unparsed "type" attribute of the "img" element, but its content is not retrieved. It also declares another notation for

1008-419: A numeric string, such as "1234" . These numeric strings are usually considered distinct from numeric values such as 1234 , although some languages automatically convert between them. A union type definition will specify which of a number of permitted subtypes may be stored in its instances, e.g. "float or long integer". In contrast with a record , which could be defined to contain a float and an integer,

1080-617: A pointer whose value was never a valid memory address would cause a program to crash. To ameliorate this potential problem, a pointer type is typically considered distinct from the corresponding integer type, even if the underlying representation is the same. Functional programming languages treat functions as a distinct datatype and allow values of this type to be stored in variables and passed to functions. Some multi-paradigm languages such as JavaScript also have mechanisms for treating functions as data. Most contemporary type systems go beyond JavaScript's simple type "function object" and have

1152-484: A precision limited only by the available memory and computational resources on the system. Bignum implementations of arithmetic operations on machine-sized values are significantly slower than the corresponding machine operations. The enumerated type has distinct values, which can be compared and assigned, but which do not necessarily have any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily. For example,

1224-464: A resolvable location. SGML allows mapping public identifiers to system identifiers in catalogs that are optionally available to the URI resolvers used by document parsing software. This DOCTYPE can only appear after the optional XML declaration , and before the document body, if the document syntax conforms to XML. This includes XHTML documents: An additional internal subset can also be provided after

1296-409: A sequence of characters used to store words or plain text , most often textual markup languages representing formatted text . Characters may be a letter of some alphabet , a digit, a blank space, a punctuation mark, etc. Characters are drawn from a character set such as ASCII . Character and string types can have different subtypes according to the character encoding. The original 7-bit wide ASCII

1368-434: A single technology. It is specified as a multi-part ISO / IEC Standard, ISO/IEC 19757. It was developed by ISO/IEC JTC 1/SC 34 (ISO/IEC Joint Technical Committee 1, Subcommittee 34 - Document description and processing languages). DSDL defines a modular set of specifications for describing the document structures, data types, and data relationships in structured information resources. This markup language article

1440-406: A type system, a data type represents a constraint placed upon the interpretation of data, describing representation, interpretation and structure of values or objects stored in computer memory. The type system uses data type information to check correctness of computer programs that access or manipulate the data. A compiler may use the static type of a value to optimize the storage it needs and

1512-421: A type. Product types, function types, power types and list types can be made into type constructors. Universally-quantified and existentially-quantified types are based on predicate logic . Universal quantification is written as ∀ x . f ( x ) {\displaystyle \forall x.f(x)} or forall x. f x and is the intersection over all types x of the body f x , i.e.

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1584-413: A union may only contain one subtype at a time. A tagged union (also called a variant , variant record, discriminated union, or disjoint union) contains an additional field indicating its current type for enhanced type safety. An algebraic data type (ADT) is a possibly recursive sum type of product types . A value of an ADT consists of a constructor tag together with zero or more field values, with

1656-452: A vendor-specific application, to annotate the "sgml" root element in the document. In both cases, the declared notation named is used directly in a declared "type" attribute, whose content is specified in the DTD with the "NOTATION" attribute type (this "type" attribute is declared for the "sgml" element, as well as for the "img" element). However, the "title" attribute of the "img" element specifies

1728-433: A way that it becomes possible to parse XML documents with non-validating XML parsers (if the only purpose of the external DTD subset was to define the schema). In addition, documents for these XML schema languages must be parsed separately, so validating the schema of XML documents in pure standalone mode is not really possible with these languages: the document type declaration remains necessary for at least identifying (with

1800-415: A word rather as a single bit as it requires more machine instructions to store and retrieve an individual bit. Many programming languages do not have an explicit Boolean type, instead using an integer type and interpreting (for instance) 0 as false and other values as true. Boolean data refers to the logical structure of how the language is interpreted to the machine language. In this case a Boolean 0 refers to

1872-404: Is a stub . You can help Misplaced Pages by expanding it . Data type In computer science and computer programming , a data type (or simply type ) is a collection or grouping of data values , usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains

1944-544: Is a data type that does not specify the concrete representation of the data. Instead, a formal specification based on the data type's operations is used to describe it. Any implementation of a specification must fulfill the rules given. For example, a stack has push/pop operations that follow a Last-In-First-Out rule, and can be concretely implemented using either a list or an array. Abstract data types are used in formal semantics and program verification and, less strictly, in design . The main non-composite, derived type

2016-488: Is a type whose definition depends on a value. Two common examples of dependent types are dependent functions and dependent pairs. The return type of a dependent function may depend on the value (not just type) of one of its arguments. A dependent pair may have a second value of which the type depends on the first value. An intersection type is a type containing those values that are members of two specified types. For example, in Java

2088-446: Is also declared with its own notation). Notations are also completely opaque for XML and SGML parsers, so they are not differentiated by the type of the external entity that they may reference (for these parsers they just have a unique name associated to a public identifier (an FPI) and/or a system identifier (a URI)). Some applications (but not XML or SGML parsers themselves) also allow referencing notations indirectly by naming them in

2160-837: Is also possible to define a dependent intersection type, denoted ( x : σ ) ∩ τ {\displaystyle (x:\sigma )\cap \tau } , where the type τ {\displaystyle \tau } may depend on the term variable x {\displaystyle x} . Some programming languages represent the type information as data, enabling type introspection and reflection . In contrast, higher order type systems , while allowing types to be constructed from other types and passed to functions as values, typically avoid basing computational decisions on them. For convenience, high-level languages and databases may supply ready-made "real world" data types, for instance times, dates, and monetary values (currency). These may be built-in to

2232-538: Is located by its defined SYSTEM identifier "example1.svg" (also interpreted as a relative URI). The effective content for the "img" element be the content of this second external resource. The difference with the GIF image, is that the SVG image is parsed within the SGML document, according to the declarations in the DTD, where the GIF image is just referenced as an opaque external object (which

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2304-410: Is not accessible). However, such documents are still fully parsable in the non -standalone mode of validating parsers, which signals an error if it can not locate these external entities with their specified public identifier (FPI) or system identifier (a URI), or are inaccessible. (Notations declared in the DTD are also referencing external entities, but these unparsed entities are not needed for

2376-488: Is not parsable with SGML) via its "data" attribute (whose value type is an opaque ENTITY). Only one notation name may be specified in the value of ENTITY attributes (there is no support in SGML, XML 1.0 or XML 1.1 for multiple notation names in the same declared external ENTITY, so separate attributes are needed). However multiple external entities may be referenced (in a space-separated list of names) in attributes declared with type ENTITIES, and where each named external entity

2448-424: Is parsed as if it was: Reference to the "author" internal entity is not substituted in the replacement text of the "signature" internal entity. Instead, it is replaced only when the "signature" entity reference is parsed within the content of the "sgml" element, but only by validating parsers (non-validating parsers do not substitute entity references occurring within contents of element or within attribute values, in

2520-403: Is specified between "&" and ";") are not replaced like usual named entities (defined with a CDATA value), but are left as distinct unparsed tokens that may be used either as the value of an element attribute (like above) or within the element contents, provided that either the DTD allows such external entities in the declared content type of elements or in the declared type of attributes (here

2592-411: Is the pointer , a data type whose value refers directly to (or "points to") another value stored elsewhere in the computer memory using its address . It is a primitive kind of reference . (In everyday terms, a page number in a book could be considered a piece of data that refers to another one). Pointers are often stored in a format similar to an integer; however, attempting to dereference or "look up"

2664-434: The "URN:''name''" value of a standard CDATA attribute, everywhere a URI can be specified. However this behaviour is application-specific, and requires that the application maintains a catalog of known URNs to resolve them into the notations that have been parsed in a standard SGML or XML parser. This use allows notations to be defined only in a DTD stored as an external entity and referenced only as

2736-484: The ENTITY type for the data attribute), or the SGML parser is not validating the content. Notations may also be associated directly to elements as additional meta-data, without associating them to another external entity, by giving their names as possible values of some additional attributes (also declared in the DTD within the <!ATTLIST ...> declaration of the element). For example: The example above shows

2808-464: The ISO SGML standard effort. XML uses a subset of SGML DTD. As of 2009, newer XML namespace -aware schema languages (such as W3C XML Schema and ISO RELAX NG ) have largely superseded DTDs as a better way to validate XML structure. A DTD is associated with an XML or SGML document by means of a document type declaration (DOCTYPE). The DOCTYPE appears in the syntactic fragment doctypedecl near

2880-411: The internal subset , and substitute the replacement texts of internal entities occurring anywhere in the document type declaration or in the document body. DSDL Document Schema Definition Languages (DSDL) is a framework within which multiple validation tasks of different types can be applied to an XML document in order to achieve more complete validation results than just the application of

2952-654: The type of each attribute value, if not an explicit set of valid values. DTD markup declarations declare which element types , attribute lists , entities , and notations are allowed in the structure of the corresponding class of XML documents. An element type declaration defines an element and its possible content. A valid XML document contains only elements that are defined in the DTD. Various keywords and characters specify an element's content: For example: Element type declarations are ignored by non-validating SGML and XML parsers (in which cases, any elements are accepted in any order, and in any number of occurrences in

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3024-582: The ADT corresponds to a product type similar to a tuple or record. A constructor with no fields corresponds to the empty product (unit type). If all constructors have no fields then the ADT corresponds to an enumerated type . One common ADT is the option type , defined in Haskell as data Maybe a = Nothing | Just a . Some types are very useful for storing and retrieving data and are called data structures . Common data structures include: An abstract data type

3096-400: The DTD loses its special role outside the DTD and it becomes a literal character. However, the references to predefined character entities are substituted wherever they occur, without needing a validating parser (they are only introduced by the "&" character). Notations are used in SGML or XML. They provide a complete reference to unparsed external entities whose interpretation is left to

3168-444: The DTD or in the body of the document, in their order of parsing: it is valid to include a reference to a still undefined entity within the content of a parsed entity, but it is invalid to include anywhere else any named entity reference before this entity has been fully defined, including all other internal entities referenced in its defined content (this also prevents circular or recursive definitions of internal entities). This document

3240-734: The DTD or in the document body but not declared: The XML DTD syntax is one of several XML schema languages. However, many of the schema languages do not fully replace the XML DTD. Notably, the XML DTD allows defining entities and notations that have no direct equivalents in DTD-less XML (because internal entities and parsable external entities are not part of XML schema languages, and because other unparsed external entities and notations have no simple equivalent mappings in most XML schema languages). Most XML schema languages are only replacements for element declarations and attribute list declarations, in such

3312-467: The application (which interprets them directly or retrieves the external entity themselves), by assigning them a simple name, which is usable in the body of the document. For example, notations may be used to reference non-XML data in an XML 1.1 document. For example, to annotate SVG images to associate them with a specific renderer: This declares the TEXT of external images with this type, and associates it with

3384-420: The attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of data type, though the possible data types are often restricted by considerations of simplicity, computability, or regularity. An explicit data type declaration typically allows the compiler to choose an efficient machine representation, but

3456-530: The body of the SGML or XML document. The PUBLIC or SYSTEM parameter of these external entities specifies the FPI and/or the URI where the unparsed data of the external entity is located, and the additional NDATA parameter of these defined entities specifies the additional notation (i.e., effectively the MIME type here). For example: Within the body of the SGML document, these referenced external entities (whose name

3528-504: The body of the document. This is possible because the replacement text specified in the internal entity definitions permits a distinction between parameter entity references (that are introduced by the "%" character and whose replacement applies to the parsed DTD contents) and general entity references (that are introduced by the "&" character and whose replacement is delayed until they are effectively parsed and validated). The "%" character for introducing parameter entity references in

3600-519: The choice of algorithms for operations on the value. In many C compilers the float data type, for example, is represented in 32 bits , in accord with the IEEE specification for single-precision floating point numbers . They will thus use floating-point-specific microprocessor operations on those values (floating-point addition, multiplication, etc.). Most data types in statistics have comparable types in computer programming, and vice versa, as shown in

3672-615: The class Boolean implements both the Serializable and the Comparable interfaces. Therefore, an object of type Boolean is a member of the type Serializable & Comparable . Considering types as sets of values, the intersection type σ ∩ τ {\displaystyle \sigma \cap \tau } is the set-theoretic intersection of σ {\displaystyle \sigma } and τ {\displaystyle \tau } . It

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3744-462: The conceptual organization offered by data types should not be discounted. Different languages may use different data types or similar types with different semantics. For example, in the Python programming language , int represents an arbitrary-precision integer which has the traditional numeric operations such as addition, subtraction, and multiplication. However, in the Java programming language ,

3816-461: The content model of these documents. The following example of a DOCTYPE contains both public and system identifiers: All HTML 4.01 documents conform to one of three SGML DTDs. The public identifiers of these DTDs are constant and are as follows: The system identifiers of these DTDs, if present in the DOCTYPE, are URI references . A system identifier usually points to a specific set of declarations in

3888-458: The external subset of documents, and allows these documents to remain compatible with validating XML or SGML parsers that have no direct support for notations. Notations are not used in HTML, or in basic profiles for XHTML and SVG, because: Even in validating SGML or XML 1.0 or XML 1.1 parsers, the external entities referenced by an FPI and/or URI in declared notations are not retrieved automatically by

3960-406: The external subset: Alternatively, only the internal subset may be provided: Finally, the document type definition may include no subset at all; in that case, it just specifies that the document has a single top-level element (this is an implicit requirement for all valid XML and HTML documents, but not for document fragments or for all SGML documents, whose top-level elements may be different from

4032-474: The following table: Parnas, Shore & Weiss (1976) identified five definitions of a "type" that were used—sometimes implicitly—in the literature: The definition in terms of a representation was often done in imperative languages such as ALGOL and Pascal , while the definition in terms of a value space and behaviour was used in higher-level languages such as Simula and CLU . Types including behavior align more closely with object-oriented models, whereas

4104-410: The form a × 2 (where a and b are integers), but displayed in familiar decimal form. Fixed point data types are convenient for representing monetary values. They are often implemented internally as integers, leading to predefined limits. For independence from architecture details, a Bignum or arbitrary precision numeric type might be supplied. This represents an integer or rational to

4176-422: The four suits in a deck of playing cards may be four enumerators named CLUB , DIAMOND , HEART , SPADE , belonging to an enumerated type named suit . If a variable V is declared having suit as its data type, one can assign any of those four values to it. Some implementations allow programmers to assign integer values to the enumeration values, or even treat them as type-equivalent to integers. Strings are

4248-467: The implied root element), and it indicates the type name of the root element: DTDs describe the structure of a class of documents via element and attribute-list declarations. Element declarations name the allowable set of elements within the document, and specify whether and how declared elements and runs of character data may be contained within each element. Attribute-list declarations name the allowable set of attributes for each declared element, including

4320-401: The internal entity "example1SVGTitle" whose declaration that does not define an annotation, so it is parsed by validating parsers and the entity replacement text is "Title of example1.svg". The content of the "img" element references another external entity "example1SVG" whose declaration also does not define an notation, so it is also parsed by validating parsers and the entity replacement text

4392-472: The logic False. True is always a non zero, especially a one which is known as Boolean 1. Almost all programming languages supply one or more integer data types. They may either supply a small number of predefined subtypes restricted to certain ranges (such as short and long and their corresponding unsigned variants in C/C++); or allow users to freely define subranges such as 1..12 (e.g. Pascal / Ada ). If

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4464-592: The lowest level. The smallest addressable unit of data is usually a group of bits called a byte (usually an octet , which is 8 bits). The unit processed by machine code instructions is called a word (as of 2011 , typically 32 or 64 bits). Machine data types expose or make available fine-grained control over hardware, but this can also expose implementation details that make code less portable. Hence machine types are mainly used in systems programming or low-level programming languages . In higher-level languages most data types are abstracted in that they do not have

4536-400: The number and type of the field values fixed by the constructor. The set of all possible values of an ADT is the set-theoretic disjoint union (sum), of the sets of all possible values of its variants (product of fields). Values of algebraic types are analyzed with pattern matching, which identifies a value's constructor and extracts the fields it contains. If there is only one constructor, then

4608-441: The parsed document), but these declarations are still checked for form and validity. An attribute list specifies for a given element type the list of all possible attribute associated with that type. For each possible attribute, it contains: For example: Here are some attribute types supported by both SGML and XML: A default value can define whether an attribute must occur ( #REQUIRED ) or not ( #IMPLIED ), or whether it has

4680-418: The parsers themselves. Instead, these parsers just provide to the application the parsed FPI and/or URI associated to the notations found in the parsed SGML or XML document, and with a facility for a dictionary containing all notation names declared in the DTD; these validating parsers also check the uniqueness of notation name declarations, and report a validation error if some notation names are used anywhere in

4752-465: The possible values that an expression , such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers ), characters and Booleans . A data type may be specified for many reasons: similarity, convenience, or to focus

4824-417: The start of an XML document. The declaration establishes that the document is an instance of the type defined by the referenced DTD. DOCTYPEs make two sorts of declarations: The declarations in the internal subset form part of the DOCTYPE in the document itself. The declarations in the external subset are located in a separate text file. The external subset may be referenced via a public identifier and/or

4896-413: The type int represents the set of 32-bit integers ranging in value from −2,147,483,648 to 2,147,483,647, with arithmetic operations that wrap on overflow . In Rust this 32-bit integer type is denoted i32 and panics on overflow in debug mode. Most programming languages also allow the programmer to define additional data types, usually by combining multiple elements of other types and defining

4968-429: The valid operations of the new data type. For example, a programmer might create a new data type named " complex number " that would include real and imaginary parts, or a color data type represented by three bytes denoting the amounts each of red, green, and blue, and a string representing the color's name. Data types are used within type systems , which offer various ways of defining, implementing, and using them. In

5040-409: The validation of documents in the standalone mode of these parsers: the validation of all external entities referenced by notations is left to the application using the SGML or XML parser). Non-validating parsers may eventually attempt to locate these external entities in the non -standalone mode (by partially interpreting the DTD only to resolve their declared parsable entities), but do not validate

5112-436: The value is of type f x for every x . Existential quantification written as ∃ x . f ( x ) {\displaystyle \exists x.f(x)} or exists x. f x and is the union over all types x of the body f x , i.e. the value is of type f x for some x . In Haskell, universal quantification is commonly used, but existential types must be encoded by transforming exists a. f

5184-400: Was found to be limited, and superseded by 8, 16 and 32-bit sets, which can encode a wide variety of non-Latin alphabets (such as Hebrew and Chinese ) and other symbols. Strings may be of either variable length or fixed length, and some programming languages have both types. They may also be subtyped by their maximum size. Since most character sets include the digits , it is possible to have

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