Attribute Grammars and XML Workshop on Attribute Grammars, XML, and RDF Institute for Media and Communications Management University of St. Gallen 20/21 Sept Harold Boley, DFKI Kaiserslautern

1 “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

2 Attribute Grammar Example: Cartesian Move Sequences 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

3 Grammar with Attributes on Nonterminals Grammar: path   path  step path step  n step  e step  s step  w Attributes: path.  Exx-coordinate of end position path.  Eyy-coordinate of end position step.  Dxincremental change of x-coordinate step.  Dyincremental change of y-coordinate We will only consider synthesized attributes, often prefixed by a “  ”, not inherited attributes

4 Attribute Grammar with Semantic Rules Grammar: path   path  step path step  n step  e step  s step  w Semantic Rules: path.  Ex := 0  path.  Ey := 0 path 1.  Ex := step.  Dx + path 2.  Ex  path 1.  Ey := step.  Dy + path 2.  Ey step.  Dx := 0  step.  Dy := 1 step.  Dx := 1  step.  Dy := 0 step.  Dx := 0  step.  Dy := -1 step.  Dx := -1  step.  Dy := 0

5 Decorated Parse Tree for Sequence e,e,n path step path step path step  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

6 “e,e,n”-Parse Tree as XML Element e e n path step path step path step  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 Attributed XML element tree = Decorated parse tree Attribute grammar parse results and intermediate states can thus be represented as XML elements

7 DTD Approximation for Attribute Grammar (AG) ‘Canonical empty elements’ instead of terminals CDATA instead of integers Semantic Rules of full AGs can be added (via XML stylesheets, Java, Prolog,...)

8 “e,e,n”-XML Element According to DTD e e n Terminal e becomes empty element Terminal n becomes empty element

9 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 AG with Semantic Rules Attribute values represented as “[...]”-parameters. Call path[X,Y]([e,e,n]) computes X = 2, Y = 1, e.g. using Relfun interpreterRelfun interpreter path.  Ex := 0  path.  Ey := 0 path 1.  Ex := step.  Dx + path 2.  Ex  path 1.  Ey := step.  Dy + path 2.  Ey path   path  step path step  n step  e step  s step  w step.  Dx := 0  step.  Dy := 1 step.  Dx := 1  step.  Dy := 0 step.  Dx := 0  step.  Dy := -1 step.  Dx := -1  step.  Dy := 0

10 Parameter-XML Form of AG via RFML-like Generic Markup path 0 path[0,0]([]). path nx ny head tail path[Nx,Ny] ([Head|Tail]) :- step dx dy head path ex ey tail nx + dx ex ny + dy ey step[Dx,Dy](Head), path[Ex,Ey](Tail), Nx.= +(Dx,Ex), Ny.= +(Dy,Ey). step 0 1 n step 1 0 e step 0 s step 0 w step[0,1](n). step[1,0](e). step[0,-1](s). step[-1,0](w). Generic: User-defined nonterminals (e.g. path ) don’t appear as tags, only between tags

11 Attribute-XML Form of AG via RFML/MathML-like Non-Generic Markup <path ex="0" ey="0"/> path [Ex=0, Ey=0] ([]). <step dx="?" dy="?"/> head Step [Dx=?, Dy=?] (Head), <path ex="?" ey="?"/> tail Path [Ex=?, Ey=?] (Tail), nx dx ex Nx.= +(Dx,Ex), ny dy ey Ny.= +(Dy,Ey). <path nx="?" ny="?"/> head tail path [Nx=?, Ny=?] ([Head|Tail]) :- Output attributes made explicit via “?”-values

12 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