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3.2. A MODEL FOR PATH EXPRESSIONS 47
has the following representation in the model:
n 0 = (0, element, ”item” , λ, λ, {n 1 , n 3 })
n 1 = (1, element, ”name” , λ, n 0 , {n 2 })
n 2 = (2, text, λ, ”SinusMP 3P layer” , n 1 , ∅)
n 3 = (3, element, ”location” , λ, n 0 , {n 4 })
n 4 = (4, text, λ, ”Luebeck, Germany” , n 3 , ∅)
The node n o is the root node of the tree model; it is the only node with λ as parent
node.
Definition 3 (Function t.nodes)
The function t.node : T → P(N) is called on an XML data t ∈ T and returns all
nodes of t. The function is defined as follows:
t.nodes ::= {n ∈ N|n is a node of t}
Definition 4 (Function t.root)
For an XML data t ∈ T the function t.root : T → N returns the root node of the
tree model of t. The function is defined as follows:
t.root ::= n with n ∈ t.nodes is the root node
Based on this simple model for XML data we define a model for path expressions
as follows:
3.2 A Model for Path Expressions
XPath is an essential fundamental of this thesis that is used at various places, especially
for defining indexes and database operations. In order to analyze theoretical
properties of XPath and to implement the index system we need an abstract
and formal model of XPath that is more precise than the semantic description
given in [126].
Because not all features of XPath are required in this thesis, a restricted subset of
XPath is defined formally. This is done to keep the model and the implementation
simple and manageable without loosing most of XPath’s expressiveness.
The restrictions of the XPath fragment are as follows
• The attribute-axis is omitted because attributes are not supported by the
underlying XML model. This is also done because attributes do not significantly
increase the expressiveness of XML (see 2.1.2).