Easily Editing and Browsing Complex OpenMath Markup with SWiM

OpenMath CDs SWiM Knowledge Representation Editing Related Work Outlook/Conclusion

Easily Editing and Browsing Complex OpenMath
Markup with SWiM
Mathematical User Interfaces 2008

Christoph Lange, Alberto González Palomo

Jacobs University, Bremen, Germany
Universität des Saarlandes, Saarbrücken, Germany
KWARC – Knowledge Adaptation and Reasoning for Content

June 27, 2008

Lange/González Palomo (Jacobs/Saarland Univ.) Editing and Browsing OpenMath with SWiM June 27, 2008 1


OpenMath Content Dictionaries

OpenMath: semantic markup language for math. formulæ and content
dictionaries (CDs)
CDs semi-formally deﬁne new mathematical symbols:
informal description
formal description in terms of other symbols
optional: type declaration, human-readable notation
Formula editors exist, . . .
. . . and ways to make CDs readable for humans
(www.openmath.org/cd/) . . .
but no proper editors for CDs



Why create or edit CDs?

standard CDs exist; pick your favourite ones from
www.openmath.org/cd/
your favourite ﬁeld of mathematics may not be covered (cf. geometry)
or you want to have it more rigorously
cf. James Davenport’s landau_in operator for f = O(n)



Collaboration on CDs: The Good, the Bad, and the Ugly

writing, structuring; also browsing, collaborating
CDs reuse symbols from other CDs (link symbol occurrences to their
deﬁnitions)
use case: revising a notation of a symbol in a CD; one author revises,
the other one tests
The bad way: Notepad, send ﬁle to collaborator by e-mail
Manual transformation to XHTML+MathML, open
browser
The ugly way: Emacs with nxml-mode, commit into shared
Subversion repository
Update, run make, open browser (Michael Kohlhase’s
favorite )
The wiki way: interactive editing right in the browser ⇒ instant
feedback for both collaborators


Debugging Notation Definitions

Consider the symbol times in arith1.ocd:

<OMA>
<OMS name="times" cd="arith1"/> Possible renderings:
<OMI>2</OMI> 2 · x , 2 × x , or 2x
<OMV name="x"/> (defined in arith1.ntn)
</OMA>

Typical workflow:
Change/fix/improve/enhance the notation definition (ND) for a
symbol
Check the appearance of a sample formula in a sample document



SWiM, a Semantic Wiki for Mathematics

SWiM: semantic wiki + OMDoc. Added OpenMath and MathML 3
notation deﬁnitions
mmlproc/JOMDoc renderer (→ MKM talk “notations for living
documents”)
editing, import, export (exchange with external repositories, legacy
editors)
Try it at http://swim.kwarc.info, see more in the demo session!



SWiM, a Semantic Wiki for Mathematics



Knowledge Representation in OpenMath

CDs have metadata (e. g. review date) and contain symbol
definitions
Symbols have
name
informal, natural-language description (authoritative)
metadata
mathematical properties: informal (CMP), formal
(FMP), examples
FMPs and Examples contain mathematical formulæ
Separate dictionary files with
type signatures
notation definitions (in a few minutes)
for symbols.


Knowledge Representation on the Semantic Web

Ontologies: smarter, extensible, web-scalable metadata vocabularies
RDF: graph with nodes and edges have types from ontologies, e. g.
<christoph> foaf:knows <paul>.
We have developed an ontology that models the structures of CDs
semantics given by OpenMath spec
more expressive than Relax NG XML schema
e. g. for dependent CDs (URIref vs. CD):
<CDUses>arith1 transc1</CDUses>
reused existing vocabularies where appropriate (→ OpenMath 3)
e. g. Dublin Core: om:Name→dc:identiﬁer



Knowledge Representation in SWiM

small pages are more suitable for wiki collaboration
page granularity: CD, symbol, CMP, FMP, example
split imported CDs into these parts, preserve
containment information by XInclude links, reassemble
on export
OpenMath 3: review units below CD granularity)
extract RDF graph from OpenMath for a more
networked, searchable, web-scalable representation
exploit links for navigation, soon for editing, too
represent formulæ shallowly (FMP/Example uses
symbol)



Editing

SWiM uses the HTML WYSIWYG editor TinyMCE
Great potential for more user-friendliness, but ﬁrst need to get the
basics running
Make any (OpenMath) XML element editable as a table, e. g.
<element xml:id="id" attr="value">...</element>:
element id attr=value
...
Not user-friendly for deeply nested structures
Dedicated editing support for special aspects of the markup
form-based metadata editor (e. g. CDName, CDDate)
diﬀerently arranged tables in some cases:
notation
prototype rendering
visual formula editor (next slides)



The Formula Editor

visual OpenMath formula editor from Sentido environment integrated
it into TinyMCE
encode formulæ as HTML <span/> elements, editable in a “linear”
ASCII/Unicode syntax
supporting own syntax, but also popular CAS syntaxes
pop-up window with linear input (undoable), OpenMath CD symbol
tool palette, 2D MathML preview
when done with editing, linear formula is parsed to OpenMath XML
Sorry, we cannot easily display MathML inside TinyMCE



The Formula Editor



Defining Notations for Symbols

Notation definitions map patterns of semantic markup to fragments
of presentation markup, apply rules recursively (MathML 3 extension
→ MKM talk)
√
e. g. @(arith1#root, arg, n) n arg (actually written in XML)
link notation definition → symbol definition in RDF:
<url/of/NotDef> omo:rendersSymbol <url/of/arith1/root>
What if an author changes this?
1 identify the change: XML diff
2 identify documents affected by the change: query RDF graph for all
resources using the symbol in a formula – and for all resources that
xi:include the former



Determining the Eﬀect of Changing a Notation Deﬁnition

1 SELECT DISTINCT ?page WHERE {
2 <changed-ntn-def> omo:rendersSymbol ?sym .
3 { ?page omo:usesSymbol ?sym } UNION
4 { ?exOrFMP omo:usesSymbol ?sym .
5 { ?page omo:contains ?exOrFMP } UNION
6 { ?page omo:contains ?symDef .
7 ?symDef omo:contains ?exOrFMP } } }

fmp
fmp
fmp
renders- usesSymbol (3,4) contains (5,7)
Symbol (2) contains (6)
notDef sym symDef
symDef
symDef cd
cd
cd
usesSymbol (3,4)
contains (5,7)
ex
ex
ex



Related Work
ProofWiki: wiki with Coq proof assistant integrated. Content either
A
completely formal or LTEX, SWiM aims at the full formality
scale between that (→ OMDoc)
OMPE: OpenMath Presentation Editor from ActiveMath, visual
editor for notation deﬁnitions (add this to our roadmap!).
No integrated authoring/browsing environment ⇒ no
immediate debugging
PlatΩ: TEXmacs with semantic markup. Parsing notations from
natural language (not a focus of SWiM), eﬃciently reacting
to notation changes.
Visual editors: two examples of extending HTMLArea (former TinyMCE
competitor) with Presentation MathML
ASciencePad: Tiddly“Wiki” plus a translation from linear
math syntax to Presentation MathML
WIRIS: 2D visual editor (Java applet)
OpenMath editor exists, but not integrated


Future Work (OpenMath)

Cover full OpenMath object spec in linear syntax; particularly
CDBase!
Deploy SWiM as an editor for the OpenMath CDs on
www.openmath.org
Integrate upcoming OpenMath 3 extensions (in ontology and GUI)



Future Work (Use Cases)

So far one notation per symbol. The mmlproc/JOMDoc renderer can
do more (e. g. user’s preferred notation)
Browsing CDs and SPARQL queries are nice, but formula search? –
Integrate MathWebSearch! (→ MKM demo)
Splitting CDs on import works, but users also want refactoring within
SWiM.



Conclusion

SWiM facilitates editing OpenMath CDs
. . . by integrating a visual formula editor
. . . by immediately re-rendering documents aﬀected by notational
changes
How would you like to edit your CDs?


Easily Editing and Browsing Complex OpenMath Markup with SWiM

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Easily Editing and Browsing Complex OpenMath Markup with SWiM