Attribute Grammars and XML

Workshop on Attribute Grammars, XML, and RDF

Institute for Media and Communications Management

University of St. Gallen

20/21 Sept. 2000

Harold Boley, DFKI Kaiserslautern

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“What Are” and “How Relate”Attribute Grammars and XML?

• Both are extensions of context-free grammars:– Attribute grammars via semantic (evaluation) rules

over attributes– XML via (document-markup) tags, attribute DTDs,

stylesheets, etc.

• Will be compared on two exemplary levels:– Decorated parse trees as attributed element trees– XML markups for semantic rules

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Attribute Grammar Example:Cartesian Move Sequences

• In the Cartesian plane move stepwise in the directions north, east, south, west

• Starting from the coordinates X = 0, Y = 0 compute the end position after a finite sequence of moves

• Sample computations:– Sequence e,e,n shall compute X = 2, Y = 1– Sequence s,w,s,e shall compute X = 0, Y = -2

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Grammar with Attributes on Nonterminals

Grammar: path path step pathstep nstep estep sstep w

Attributes: path.Ex x-coordinate of end positionpath.Ey y-coordinate of end positionstep .Dx incremental change of x-coordinatestep .Dy incremental change of y-coordinate

We will only consider synthesized attributes,often prefixed by a “”, not inherited attributes

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Attribute Grammar with Semantic Rules

Grammar:

path

path step path

step nstep estep sstep w

Semantic Rules:

path.Ex := 0 path.Ey := 0

path1.Ex := step .Dx + path2.Ex path1.Ey := step .Dy + path2.Ey

step .Dx := 0 step .Dy := 1step .Dx := 1 step .Dy := 0step .Dx := 0 step .Dy := -1step .Dx := -1 step .Dy := 0

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Decorated Parse Treefor Sequence e,e,n

path

pathstep

pathstep

pathstep

e

n

e

Ex = 0 Ey = 0

Ex = 0 Ey = 1

Ex = 1 Ey = 1

Ex = 2 Ey = 1

Dx = 0 Dy = 1

Dx = 1 Dy = 0

Dx = 1 Dy = 0

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“e,e,n”-Parse Tree as XML Element

<path Ex="2" Ey="1"> <step Dx ="1" Dy="0"> e </step> <path Ex="1" Ey="1"> <step Dx ="1" Dy="0"> e </step> <path Ex="0" Ey="1"> <step Dx ="0" Dy="1"> n </step> <path Ex="0" Ey="0"> </path> </path> </path></path>

path

pathstep

pathstep

pathstep

e

n

eEx = 0 Ey = 0

Ex = 0 Ey = 1

Ex = 1 Ey = 1

Ex = 2 Ey = 1

Dx = 0 Dy = 1

Dx = 1 Dy = 0

Dx = 1 Dy = 0

Attributed XML element tree = Decorated parse tree

Attribute grammarparse results andintermediate statescan thus be representedas XML elements

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DTD Approximation forAttribute Grammar (AG)

<!ELEMENT path (EMPTY | (step, path)) ><!ELEMENT step (n | e | s | w) ><!ELEMENT n EMPTY ><!ELEMENT e EMPTY ><!ELEMENT s EMPTY ><!ELEMENT w EMPTY >

<!ATTLIST path Ex CDATA #REQUIRED ><!ATTLIST path Ey CDATA #REQUIRED ><!ATTLIST step Dx CDATA #REQUIRED ><!ATTLIST step Dy CDATA #REQUIRED >

‘Canonical empty elements’instead of terminals

CDATAinstead ofintegers

Semantic Rules of full AGs can be added(via XML stylesheets, Java, Prolog, ...)

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“e,e,n”-XML ElementAccording to DTD

<path Ex="2" Ey="1"> <step Dx ="1" Dy="0"> e </step> <path Ex="1" Ey="1"> <step Dx ="1" Dy="0"> e </step> <path Ex="0" Ey="1"> <step Dx ="0" Dy="1"> n </step> <path Ex="0" Ey="0"> </path> </path> </path></path>

Terminal e becomes empty element <e/>Terminal n becomes empty element <n/>

<path Ex="2" Ey="1"> <step Dx ="1" Dy="0"> <e/> </step> <path Ex="1" Ey="1"> <step Dx ="1" Dy="0"> <e/> </step> <path Ex="0" Ey="1"> <step Dx ="0" Dy="1"> <n/> </step> <path Ex="0" Ey="0"> </path> </path> </path></path>

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path[0,0]([]).path[Nx,Ny]([Head|Tail]) :- step[Dx,Dy](Head), path[Ex,Ey](Tail), Nx .= +(Dx,Ex), Ny .= +(Dy,Ey).

step[0,1](n).step[1,0](e).step[0,-1](s).step[-1,0](w).

Prolog-like Form of AGwith Semantic Rules

Attribute values represented as “[...]”-parameters.Call path[X,Y]([e,e,n]) computes X = 2, Y = 1,

e.g. using Relfun interpreter

path.Ex := 0 path.Ey := 0

path1.Ex := step .Dx + path2.Ex path1.Ey := step .Dy + path2.Ey

path

path step path

step nstep estep sstep w

step .Dx := 0 step .Dy := 1step .Dx := 1 step .Dy := 0step .Dx := 0 step .Dy := -1step .Dx := -1 step .Dy := 0

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Parameter-XML Form of AG via RFML-like Generic Markup

<hn> <pattop> <struc> <con>path</con> <con>0</con> <con>0</con> </struc> <tup/> </pattop></hn>

path[0,0]([]).

<hn> <pattop> <struc> <con>path</con> <var>nx</var> <var>ny</var> </struc> <tup> <var>head</var> <rest/> <var>tail</var> </tup> </pattop>

path[Nx,Ny] ([Head|Tail])

:-

<callop> <struc> <con>step</con> <var>dx</var> <var>dy</var> </struc> <var>head</var> </callop> <callop> <struc> <con>path</con> <var>ex</var> <var>ey</var> </struc> <var>tail</var> </callop> <is> <var>nx</var> <callop> <con>+</con> <var>dx</var> <var>ex</var> </callop> </is> <is> <var>ny</var> <callop> <con>+</con> <var>dy</var> <var>ey</var> </callop> </is></hn>

step[Dx,D

y](Head),path[E

x,Ey](T

ail), Nx .=

+(D

x,Ex), N

y .= +

(Dy,E

y).

<hn> <pattop> <struc> <con>step</con> <con>0</con> <con>1</con> </struc> <con>n</con> </pattop></hn>

<hn> <pattop> <struc> <con>step</con> <con>1</con> <con>0</con> </struc> <con>e</con> </pattop></hn>

<hn> <pattop> <struc> <con>step</con> <con>0</con> <con>-1</con> </struc> <con>s</con> </pattop></hn>

<hn> <pattop> <struc> <con>step</con> <con>-1</con> <con>0</con> </struc> <con>w</con> </pattop></hn>

step[0,1](n).

step[1,0](e).

step[0,-1](s).

step[-1,0](w).

Generic: User-definednonterminals (e.g. path)don’t appear as tags,only between tags

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Attribute-XML Form of AG via RFML/MathML-likeNon-Generic Markup

<hn> <pattop> <path ex="0" ey="0"/> <tup/> </pattop></hn>

path [Ex=0, Ey=0] ([]).

<callop> <step dx="?" dy="?"/> <var>head</var></callop>

Step [Dx=?, Dy=?] (Head),

<callop> <path ex="?" ey="?"/> <var>tail</var></callop>

Path [Ex=?, Ey=?] (Tail),

<is> <var>nx</var> <callop> <+/> <var>dx</var> <var>ex</var> </callop> </is>

Nx .= +(Dx,Ex),

<is> <var>ny</var> <callop> <+/> <var>dy</var> <var>ey</var> </callop> </is></hn>

Ny .= +(Dy,Ey).

<hn> <pattop> <path nx="?" ny="?"/> <tup> <var>head</var> <rest/> <var>tail</var> </tup> </pattop>

path [Nx=?, Ny=?] ([Head|Tail])

:-

Output attributes made explicit via “?”-values

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Conclusions

• Attribute Grammars and XML use the same parse and element trees

• There are various possible XML markups for AG’s semantic rules (cf. RFML/MathML)

• In future work an AG-markup language could be developed and applied for grammar sharing

• Further levels of the XML/AG relationships should be studied, e.g. attribute dependencies, rule-evaluation methods, and DOM-level rules