Accessibility/MathML

Summary

This page describes a draft of changes to be made to add MathML accessibility to Gecko (WIP).

Background

Scope

For now, this will cover the translation of Presentation MathML to an accessible tree. Content MathML support can be added at a later time (display is currently unsupported by Gecko). An interface will be provided to allow ATs to traverse the MathML tree.

Element types

The following includes descriptions and examples for the various types of MathML elements for the purpose of this document. Some examples are pulled from MDN.

Tokens

These are the smallest units in MathML carrying semantic meaning. They are often represented by a single symbol or number. These include the following:

• mi - identifier
• mn - number
• mo - operator
• mtext - text
• mspace - spacing
• ms - string literal

Valid token values include single characters, numbers, and many MathML-specific constants and symbols, e.g. α for the Greek lower alpha symbol. mtext is used for arbitrary text with no particular semantic meaning to the equation itself. ms is used for arbitrary string literals meant to be interpreted by a programming language or other system. A special case is mglyph (image), which is used inside other token elements when a Unicode character is unavailable. Another special case is the malignmark element, which will be described below in the table and matrix section. Example markup is listed below.

<math> 
  <mi>y</mi>
  <mo>+</mo>
  <mn>10</mn>
  <mspace width="1em"/>
  <mtext>Arbitrary text</mtext>
  <mspace width="1em"/>
  <ms>InterpretedStringLiteral</ms>
  <mspace width="1em"/>
  <mi>
    <mglyph src="x.png" alt="x"/>
  </mi>
</math>

The above describes y + 10, arbitrary text, an interpreted string literal, and a glyph (an image of x). Rendered using MathJax due to lack of glyph support in Gecko.

Layout

These have been split into three groups: layout elements that describe semantic meaning, layout elements only for formatting and styling, and layout elements for describing elementary math.

Semantic meaning

These carry semantic meaning in the presentation. Nested inside them are either more layout elements or tokens. These include the following:

• mrow - row, containing any number of elements
• mfrac - fraction, containing a numerator and denominator
• msqrt - square root, containing a base
• mroot - root, containing a base and index
• mfenced - fenced block, containing any number of elements
• menclose - enclosed block, containing any number of elements

mrow is used for grouping a logical sub-expression in an equation. mfenced is used for enclosing an expression in parentheses with separators. Custom values can be used (defaults to '(', ')', and ','). menclose is used to enclose an expression in a specified notation. Example markup is listed below.

<math>
  <mrow>
    <mfenced>
      <mrow>
        <mi>x</mi>
        <mo>+</mo>
        <mi>y</mi>
      </mrow>
    </mfenced>
    <mo>+</mo>
    <mrow>
      <mn>2</mn>
    </mrow>
  </mrow>
  <mspace width="1em"/>
  <mfrac>
    <mi>x</mi>
    <mn>2</mn>
  </mfrac>
  <mspace width="1em"/>
  <msqrt>
    <mn>2</mn>
  </msqrt>
  <mspace width="1em"/>
  <mroot>
    <mi>x</mi>
    <mn>5</mn>
  </mroot>
  <mspace width="1em"/>
  <mfenced>
    <mi>x</mi>
    <mi>y</mi>
    <mi>z</mi>
  </mfenced>
  <mspace width="1em"/>
  <menclose notation="circle">
    <mi>a</mi>
    <mo>+</mo>
    <mi>b</mi>
  </menclose>
</math>

The above describes (x+y) + 2, x/2 as a fraction, the square root of 2, the 5th root of x, a 3D vector (x, y, z), and (a + b) circled. Rendered using Gecko.

Formatting

These add formatting information when displaying content. These include the following:

• mstyle - changes styling for child elements, containing any number of elements
• mpadded - adds padding for child elements, containing any number of elements
• mphantom - renders child elements invisibly, containing any number of elements

Example markup is listed below.

<math>
  <mstyle dir="rtl" mathcolor="blue">
    <mpadded height="100px" width="200px">
      <mi>x</mi>
      <mphantom>
        <mo>+</mo>
        <mi>y</mi>
      </mphantom>
    </mpadded>
  </mstyle>
</math>

The above describes the expression "x + y" rendered in blue from right to left, with extra padding, and with the "+ y" not displayed. Rendered using Gecko.

Elementary math

These describe elements for formatting elementary math problems. These include the following:

• mstack - rows of numbers aligned on digits, containing any number of elements
• mlongdiv - a long division container, containing a divisor, the result, then any number of elements
• msgroup - groups rows together for horizontal alignment, containing any number of elements
• msrow - a row in the stack, containing any number of elements
• mscarries - carries, borrows, and crossouts for the following row, containing any number of elements
• mscarry - a single carry, borrow, or crossout for a column, containing any number of elements
• msline - a drawn line in a stack

After the first two elements inside mlongdiv, it behaves like an mstack. The <none/> element is used to insert spacing, e.g. in msrow to offset an operator, or mscarries to denote no carrying needs to be done. mscarries contains mscarry elements or <none/>. Example markup is listed below.

<math>
  <mstack>
    <mscarries>
      <none/>
      <mscarry crossout="updiagonalstrike">
        <mn>1</mn>
      </mscarry>
      <mscarry location="w">
        <mn>1</mn>
      </mscarry>
    </mscarries>
    <mn>523</mn>
    <msrow>
      <mo>-</mo>
      <none/>
      <mn>15</mn>
    </msrow>
    <msline/>
    <mn>508</mn>
  </mstack>
  <mspace width="1em"/>
  <mlongdiv>
    <mn>5</mn>
    <mn>1</mn>
    <mn>5</mn>
  </mlongdiv>
</math>

The above describes the subtraction of 15 from 523, with a borrow from the ten's column to the one's column, as well as the division of 5 by 5 resulting in 1. Rendered using the MathML-mml3ff addon with Gecko as elementary math support is not natively available in Gecko.

Scripts and limits

These elements describe various scripts and limits. These include the following:

• msub - subscript, containing a base and a subscript
• msup - superscript, containing a base and a superscript
• msubsup - subscript and superscript, containing a base, a subscript, and a superscript
• munder - underscript, containing a base and an underscript
• mover - overscript, containing a base and an overscript
• munderover - underscript and overscript, containing a base, an underscript, and an overscript
• mmultiscripts - multiple scripts, with children described below

mmultiscripts uses a special syntax. The first child is the base, then any number of pairs of post-subscripts and post-superscripts. If prescripts are desired, a <mprescripts/> tag is included, then any number of pairs of pre-subscripts and pre-superscripts. <none/> can be substituted for scripts if no script is desired in a particular pair. Example markup is listed below.

<math display="block">
  <msubsup>
    <mi>b</mi>
    <mn>1</mn>
    <mn>2</mn>
  </msubsup>
  <mspace width="1em"/>
  <munderover>
    <mo>∑</mo>
    <mrow>
      <mi>n</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mi>5</mi>
  </munderover>
  <mi>n</mi>
  <mo>=</mo>
  <mn>15</mn>
  <mspace width="1em"/>
  <mmultiscripts>
    <mi>x</mi>
    <none/>
    <mi>a</mi>
    <mprescripts/>
    <mi>b</mi>
    <none/>
  </mmultiscripts>
</math>

The above describes the base b with subscript 1 and superscript 2, the summation of n from 1 to 5 being 15, and x with post-superscript a and pre-subscript b. Rendered using Gecko.

Tables/matrices

These elements describe a table or matrix. This is also used for layout. These include the following:

• mtable - the container for a table, contains any number of mtr or mlabeledtr elements
• mtr - a row, containing any number of mtd elements
• mlabeledtr - a labelled row, having a caption on the side, containing any number of mtd elements
• mtd - a table cell, containing any number of elements

For mlabeledtr, the first mtd contained inside becomes the caption.

In addition, there are two elements used for table formatting:

• maligngroup - denotes a column in a table, used for alignment
• malignmark - denotes an alignment point inside an alignment group

malignmark is used inside a token element to set the alignment point. Example markup is listed below.

<math>
  <mrow>
    <mo>[</mo>
    <mtable>
      <mtr>
        <mtd>
          <mn>1</mn>
        </mtd>
        <mtd>
          <mn>0</mn>
        </mtd>
      </mtr>
      <mtr>
        <mtd>
          <mn>0</mn>
        </mtd>
        <mtd>
          <mn>1</mn>
        </mtd>
      </mtr>
    </mtable>
    <mo>]</mo>
  </mrow>
  <mspace width="1em"/>
  <mtable>
    <mlabeledtr>
      <mtd>
        <mtext>Volume of a sphere</mtext>
      </mtd>
      <mtd>
        <mi>V</mi>
        <mo>=</mo>
        <mfrac>
          <mn>4</mn>
          <mn>3</mn>
        </mfrac>
        <mo>⁢</mo>
        <mi>π</mi>
        <mo>⁢</mo>
        <msup>
          <mi>r</mi>
          <mn>3</mn>
        </msup>
      </mtd>
    </mlabeledtr>
  </mtable>
  <mspace width="1em"/>
  <mtable>
    <mtr>
      <mrow>
        <mn>3</mn>
        <mo>⁢</mo>
        <maligngroup/>
        <mi>x</mi>
        <maligngroup/>
        <mo>+</mo>
        <maligngroup/>
        <mi>y</mi>
        <maligngroup/>
        <mo>=</mo>
        <maligngroup/>
        <mn>7</mn>
      </mrow>
    </mtr>
    <mtr>
      <mrow>
        <mphantom>
          <mn>0</mn>
          <mo>⁢</mo>
          <maligngroup/>
          <mi>x</mi>
          <maligngroup/>
          <mo>+</mo>
        </mphantom>
        <maligngroup/>
        <mi>y</mi>
        <maligngroup/>
        <mo>=</mo>
        <maligngroup/>
        <mn>1</mn>
      </mrow>
    </mtr>
  </mtable>
</math>

The above describes the two-by-two identity matrix, the equation to determine the volume of a sphere, and two aligned equations. Rendered using MathJax due to lack of support of maligngroup and malignmark in Gecko.

Semantics annotation

These elements provide explicit annotation for MathML. These include the following:

• semantics - starts a semantic annotation block, containing MathML and annotations
• annotation - annotation information in non-XML format
• annotation-xml - annotation information in XML format

The first child of semantics is the content being annotated, with the following annotation elements annotating the content.

Example markup is listed below.

<math>
  <semantics>
    <!-- Presentation MathML -->
    <mrow>
      <msup>
        <mi>x</mi>
        <mn>2</mn>
      </msup>
      <mo>+</mo>
      <mi>y</mi>
    </mrow>
    <!-- Content MathML -->
    <annotation-xml encoding="MathML-Content">
      <apply>
        <plus/>
        <apply>
          <power/>
          <ci>x</ci>
          <cn type="integer">2</cn>
        </apply>
        <ci>y</ci>
      </apply>
    </annotation-xml>
    <!-- annotate TeX -->
    <annotation encoding="application/x-tex">
      x^{2} + y 
    </annotation> 
  </semantics>
</math>

The above is the square of x added to y, with the content also annotated (invisibly) as Content MathML and TeX markup. Rendered using Gecko.

Other

Other elements not fitting into the above categories.

• maction - binds actions to expressions
• merror - displays content as an error message

maction elements allow for interactivity with MathML content. Example markup is listed below.

<math>
  <merror>
    <mrow>
      <mtext>Division by zero: </mtext>
      <mfrac>
        <mn>1</mn>
        <mn>0</mn>
      </mfrac>
    </mrow>
  </merror>
</math>

The above is a divide by zero error. Rendered using Gecko.

<math>
  <maction actiontype="toggle">
    <mfrac>
      <mn>6</mn>
      <mn>8</mn>
    </mfrac>
    <mfrac>
      <mrow>
        <mn>3</mn>
        <mo>⋅</mo>
        <mn>2</mn>
      </mrow>
      <mrow>
        <mn>4</mn>
        <mo>⋅</mo>
        <mn>2</mn>
      </mrow>    
    </mfrac>
    <mfrac>
      <mn>3</mn>
      <mn>4</mn>
    </mfrac>
  </maction>
</math>

The above is a togglable expression displaying 6/8, (3*2)/(4*2), and 3/4 upon each mouse press. Rendered using Gecko.

Interface

nsIAccessibleMathML

Inherit from nsISupports.

readonly attribute AString tokenValue;
// Get token value for token MathML elements (mi, mo, mn, mtext, mspace, ms,
// mglyph).  Returns empty string if not a token element.

readonly attribute boolean isToken;
// Check if this element is a token MathML element.

readonly attribute nsIPersistentProperties attributes;
// Get attributes specific to the MathML element.

There's several different options for describing relations between MathML elements:

Option 1: Relations linking accessibles based on role, so we won't have attributes/functions in the interface. An example would be for a fraction structure, as follows.

<math>
  <mfrac>
    <mi>a</mi>
    <mn>2</mn>
  </mfrac>
</math>

mfrac would have RELATION_NUMERATOR_IS -> mi and RELATION_DENOMINATOR_IS -> mn or similar. mi would have RELATION_NUMERATOR_FOR -> mfrac and mn would have RELATION_DENOMINATOR_FOR -> mfrac.

A list of potential relations is as follows:

• MATHML_NUMERATOR_FOR
• MATHML_NUMERATOR_IS
• MATHML_DENOMINATOR_FOR
• MATHML_DENOMINATOR_IS
• MATHML_RADICAND_FOR
• MATHML_RADICAND_IS
• MATHML_ROOT_INDEX_FOR
• MATHML_ROOT_INDEX_IS
• MATHML_UNDER_FOR
• MATHML_UNDER_IS
• MATHML_OVER_FOR
• MATHML_OVER_IS
• MATHML_BASE_FOR
• MATHML_BASE_IS
• MATHML_SUBSCRIPT_FOR
• MATHML_SUBSCRIPT_IS
• MATHML_SUPERSCRIPT_FOR
• MATHML_SUPERSCRIPT_IS
• MATHML_PRE_SUBSCRIPT_FOR
• MATHML_PRE_SUBSCRIPT_IS
• MATHML_PRE_SUPERSCRIPT_FOR
• MATHML_PRE_SUPERSCRIPT_IS
• MATHML_POST_SUBSCRIPT_FOR
• MATHML_POST_SUBSCRIPT_IS
• MATHML_POST_SUPERSCRIPT_FOR
• MATHML_POST_SUPERSCRIPT_IS
• MATHML_ROW_FOR
• MATHML_IN_ROW

Option 2: Explicit readonly attributes (accessors) for going from parent elements to children and vice versa. e.g.

readonly attribute nsIAccessibleMathML radicand;
readonly attribute nsIAccessibleMathML rootIndex;
readonly attribute nsIAccessibleMathML under;
...
readonly attribute nsIAccessibleMathML parent;

Returns nullptr if the related accessible doesn't exist.

In addition, something similar to nsIAccessibleTable should be provided for table access and manipulation.

MathMLAccessible

Inherit from AccessibleWrap, and implements nsIAccessibleMathML.

• NativeAttributes - Override Accessible, and append MathML specific attributes if the element accepts them.
• RelationByType - Override Accessible, process MathML specific relations if we go that route.
• GetTokenValue - Sets token value string if applicable.
• GetIsToken - Returns true if element is a token element.

Roles

One role for each of the following constructs (41 of them):

Tokens

• mi
• mn
• mo
• mtext
• mspace
• ms
• mglyph

Layout (semantic meaning)

• mrow
• mfrac
• msqrt
• mroot
• mfenced
• menclose

Layout (formatting)

• mstyle
• mpadded
• mphantom

Layout (elementary math)

• mstack
• mlongdiv
• msgroup
• msrow
• mscarries
• mscarry
• msline

Script/limits

• msub
• msup
• msubsup
• munder
• mover
• munderover
• mmultiscripts

Tables/matrices

• mtable
• mlabeledtr
• mtr
• mtd

Table formatting

• maligngroup
• malignmark

Semantics annotation

• semantics
• annotation
• annotation-xml

Other

• maction
• merror

Sample Gecko roles

• MATHML_IDENTIFIER
• MATHML_NUMBER
• MATHML_OPERATOR
• MATHML_TEXT
• MATHML_SPACE
• MATHML_STRING_LITERAL
• MATHML_GLYPH
• MATHML_ROW
• MATHML_FRACTION
• MATHML_SQUARE_ROOT
• MATHML_ROOT
• MATHML_FENCED
• MATHML_ENCLOSED
• MATHML_STYLE
• MATHML_PADDED
• MATHML_PHANTOM
• MATHML_SUB
• MATHML_SUP
• MATHML_SUB_SUP
• MATHML_UNDER
• MATHML_OVER
• MATHML_UNDER_OVER
• MATHML_MULTISCRIPTS
• MATHML_TABLE
• MATHML_LABELED_ROW
• MATHML_TABLE_ROW
• MATHML_CELL
• MATHML_ALIGNMENT_GROUP
• MATHML_ALIGNMENT_MARK
• MATHML_ACTION
• MATHML_ERROR
• MATHML_SEMANTICS
• MATHML_ANNOTATION
• MATHML_XML_ANNOTATION
• MATHML_STACK
• MATHML_LONG_DIVISION
• MATHML_STACK_GROUP
• MATHML_STACK_ROW
• MATHML_STACK_CARRIES
• MATHML_STACK_CARRY
• MATHML_STACK_LINE