H Glossary (Non-Normative)

Overview: Mathematical Markup Language (MathML) Version 2.0 (Second Edition)
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H Glossary (Non-Normative)

Several of the following definitions of terms have been borrowed or modified from similar definitions in documents originating from W3C or standards organizations. See the individual definitions for more information.


A child of a presentation layout schema. That is, "A is an argument of B" means "A is a child of B and B is a presentation layout schema". Thus, token elements have no arguments, even if they have children (which can only be malignmark).


A parameter used to specify some property of an SGML or XML element type. It is defined in terms of an attribute name, attribute type, and a default value. A value may be specified for it on a start-tag for that element type.


The axis is an imaginary alignment line upon which a fraction line is centered. Often, operators as well as characters that can stretch, such as parentheses, brackets, braces, summation signs etc., are centered on the axis, and are symmetric with respect to it.


The baseline is an imaginary alignment line upon which a glyph without a descender rests. The baseline is an intrinsic property of the glyph (namely a horizontal line). Often baselines are aligned (joined) during typesetting.

Black box

The bounding box of the actual size taken up by the viewable portion (ink) of a glyph or expression.

Bounding box

The rectangular box of smallest size, taking into account the constraints on boxes allowed in a particular context, which contains some specific part of a rendered display.


A rectangular plane area considered to contain a character or further sub-boxes, used in discussions of rendering for display. It is usually considered to have a baseline, height, depth and width.

Cascading Style Sheets (CSS)

A language that allows authors and readers to attach style (e.g. fonts, colors and spacing) to HTML and XML documents.


A member of a set of identifiers used for the organization, control or representation of text. ISO/IEC Standard 10646-1:1993 uses the word "data" here instead of "text".

Character data (CDATA)

A data type in SGML and XML for raw data that does not include markup or entity references. Attributes of type CDATA may contain entity references. These are expanded by an XML processor before the attribute value is processed as CDATA.

Character or expression depth

Distance between the baseline and bottom edge of the character glyph or expression. Also known as the descent.

Character or expression height

Distance between the baseline and top edge of the character glyph or expression. Also known as the ascent.

Character or expression width

Horizontal distance taken by the character glyph as indicated in the font metrics, or the total width of an expression.


A MathML content element used to place a mathematical condition on one or more variables.

Contained (element A is contained in element B)

A is part of B's content.

Container (Constructor)

A non-empty MathML Content element that is used to construct a mathematical object such as a number, set, or list.

Content elements

MathML elements that explicitly specify the mathematical meaning of a portion of a MathML expression (defined in Chapter 4 Content Markup).

Content token element

Content element having only PCDATA, sep and presentation expressions as content. Represents either an identifier (ci) or a number (cn).

Context (of a given MathML expression)

Information provided during the rendering of some MathML data to the rendering process for the given MathML expression; especially information about the MathML markup surrounding the expression.


An instance of the declare element.


(of a box) The distance from the baseline of the box to the bottom edge of the box.

Direct sub-expression (of a MathML expression "E")

A sub-expression directly contained in E.

Directly contained (element A in element B)

A is a child of B (as defined in XML), in other words A is contained in B, but not in any element that is itself contained in B.

Document Object Model

A model in which the document or Web page is treated as an object repository. This model is developed by the DOM Working Group (DOM) of the W3C.

Document Style Semantics and Specification Language (DSSSL)

A method of specifying the formatting and transformation of SGML documents. ISO International Standard 10179:1996.

Document Type Definition (DTD)

In SGML or XML, a DTD is a formal definition of the elements and the relationship among the data elements (the structure) for a particular type of document.


A font-relative measure encoded by the font. Before electronic typesetting, an "em" was the width of an "M" in the font. In modern usage, an "em" is either specified by the designer of the font or is taken to be the height (point size) of the font. Em's are typically used for font-relative horizontal sizes.


A font-relative measure that is the height of an "x" in the font. "ex"s are typically used for font-relative vertical sizes.


(of a box) The distance from the baseline of the box to the top edge of the box.

Inferred mrow

An mrow element that is "inferred" around the contents of certain layout schemata when they have other than exactly one argument. Defined precisely in Section 3.1.6 Summary of Presentation Elements

Embedded object

Embedded objects such as Java applets, Microsoft Component Object Model (COM) objects (e.g. ActiveX Controls and ActiveX Document embeddings), and plug-ins that reside in an HTML document.

Embellished operator

An operator, including any "embellishment" it may have, such as superscripts or style information. The "embellishment" is represented by a layout schema that contains the operator itself. Defined precisely in Section 3.2.5 Operator, Fence, Separator or Accent (mo).

Entity reference

A sequence of ASCII characters of the form &name; representing some other data, typically a non-ASCII character, a sequence of characters, or an external source of data, e.g. a file containing a set of standard entity definitions such as ISO Latin 1.

Extensible Markup Language (XML)

A simple dialect of SGML intended to enable generic SGML to be served, received, and processed on the Web.


In typesetting, bracketing tokens like parentheses, braces, and brackets, which usually appear in matched pairs.


A particular collection of glyphs of a typeface of a given size, weight and style, for example "Times Roman Bold 12 point".


The actual shape (bit pattern, outline) of a character. ISO/IEC Standard 9541-1:1991 defines a glyph as a recognizable abstract graphic symbol that is independent of any specific design.

Indirectly contained

A is contained in B, but not directly contained in B.

Instance of MathML

A single instance of the top level element of MathML, and/or a single instance of embedded MathML in some other data format.

Inverse function

A mathematical function that, when composed with the original function acts like an identity function.

Lambda expression

A mathematical expression used to define a function in terms of variables and an expression in those variables.

Layout schema (plural: schemata)

A presentation element defined in chapter 3, other than the token elements and empty elements defined there (i.e. not the elements defined in Section 3.2 Token Elements and Section 3.5.5 Alignment Markers, or the empty elements none and mprescripts defined in Section 3.4.7 Prescripts and Tensor Indices (mmultiscripts)). The layout schemata are never empty elements (though their content may contain nothing in some cases), are always expressions, and all allow any MathML expressions as arguments (except for requirements on argument count, and the requirement for a certain empty element in mmultiscripts).

Mathematical Markup Language (MathML)

The markup language specified in this document for describing the structure of mathematical expressions, together with a mathematical context.

MathML element

An XML element that forms part of the logical structure of a MathML document.

MathML expression (within some valid MathML data)

A single instance of a presentation element, except for the empty elements none or mprescripts, or an instance of malignmark within a token element (defined below); or a single instance of certain of the content elements (see Chapter 4 Content Markup for a precise definition of which ones).

Multi-purpose Internet Mail Extensions (MIME)

A set of specifications that offers a way to interchange text in languages with different character sets, and multimedia content among many different computer systems that use Internet mail standards.

Operator, content element

A mathematical object that is applied to arguments using the apply element.

Operator, an mo element

Used to represent ordinary operators, fences, separators in MathML presentation. (The token element mo is defined in Section 3.2.5 Operator, Fence, Separator or Accent (mo)).


A general representation language for communicating mathematical objects between application programs.

Parsed character data (PCDATA)

An SGML/XML data type for raw data occurring in a context where text is parsed and markup (for instance entity references and element start/end tags) is recognized.


Point is often abbreviated "pt". The value of 1 pt is approximately 1/72 inch. Points are typically used to specify absolute sizes for font-related objects.

Pre-defined function

One of the empty elements defined in Section 4.2.3 Functions, Operators and Qualifiers and used with the apply construct to build function applications.

Presentation elements

MathML tags and entities intended to express the syntactic structure of mathematical notation (defined in Chapter 3 Presentation Markup).

Presentation layout schema

A presentation element that can have other MathML elements as content.

Presentation token element

A presentation element that can contain only parsed character data or the malignmark element.


A MathML content element that is used to specify the value of a specific named parameter in the application of selected pre-defined functions.


A MathML content element used to construct expressions such as a < b.


Faithfully translate into application-specific form allowing native application operations to be performed.


Schema (plural: schemata or schemas). See "presentation layout schema".

Scope of a declaration

The portion of a MathML document in which a particular definition is active.

Selected sub-expression (of an maction element)

The argument of an maction element (a layout schema defined in Section 3.6 Enlivening Expressions) that is (at any given time) "selected" within the viewing state of a MathML renderer, or by the selection attribute when the element exists only in MathML data. Defined precisely in the abovementioned section.

Space-like (MathML expression)

A MathML expression that is ignored by the suggested rendering rules for MathML presentation elements when they determine operator forms and effective operator rendering attributes based on operator positions in mrow elements. Defined precisely in Section 3.2.7 Space (mspace).

Standard Generalized Markup Language (SGML)

An ISO standard (ISO 8879:1986) that provides a formal mechanism for the definition of document structure via DTDs (Document Type Definitions), and a notation for the markup of document instances conforming to a DTD.

Sub-expression (of a MathML expression "E")

A MathML expression contained (directly or indirectly) in the content of E.

Suggested rendering rules for MathML presentation elements

Defined throughout Chapter 3 Presentation Markup; the ones that use other terms defined here occur mainly in Section 3.2.5 Operator, Fence, Separator or Accent (mo) and in Section 3.6 Enlivening Expressions.


A software system developed by Professor Donald Knuth for typesetting documents.

Token element

Presentation token element or a Content token element. (See above.)

Top-level element (of MathML)

math (defined in Chapter 7 The MathML Interface).


A typeface is a specific design of a set of letters, numbers and symbols, such as "Times Roman" or "Chicago".

Valid MathML data

MathML data that (1) conforms to the MathML DTD, (2) obeys the additional rules defined in the MathML standard for the legal contents and attribute values of each MathML element, and (3) satisfies the EBNF grammar for content elements.

Width (of a box)

The distance from the left edge of the box to the right edge of the box.

Extensible Style Language (XSL)

A style language for XML developed by W3C. See XSL FO and XSLT.

XSL Formatting Objects (XSL FO)

An XML vocabulary to express formatting, which is a part of XSL.

XSL Transformation (XSLT)

A language to express the transformation of XML documents into other XML documents.

Overview: Mathematical Markup Language (MathML) Version 2.0 (Second Edition)
Previous: G Sample CSS Style Sheet for MathML
Next: I Working Group Membership and Acknowledgments