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3.2. A MODEL FOR PATH EXPRESSIONS 53
The set of all regular expressions that can be built with the symbol alphabet
Σ and α is denoted by REG Σ,α
Example 8 The linear path expression p = /a//b/c/∗/d with Σ(p) = {a, b, c, d} leads
to the following regular path expression:
a (a|b|c|d|α) ∗ k
b c (a|b|c|d|α) d
Definition 15 Any regular expression r ∈ REG Σ,α defines a language L r consisting
of all words that match the pattern of the path expression.
We use regular path expressions when building finite automata in section 7.2.2.
The reverse transformation from regular expressions to linear path expressions
is not always possible: for instance, for the regular expressions a(b|c)d there is
no corresponding linear path expression because the choice (b|c) cannot be expressed.
With the wildcard (*) a path expression would accept all symbols and
not only b and c. With a normal node test the choice is not expressible.
Even in full XPath 1.0 a(b|c)d cannot be expressed in a simple way. A workaround
may use a node function called name and looks like /a/∗[name(.) = ′ b ′ or name(.) = ′
c ′ ]/d.
XPath 2.0 supports a choice in node tests. The corresponding path expression is
/a/(b|c)/d.
3.2.2 Tailing Predicates and Normalization
The grammar for general path expressions allows only one predicate that is always
the last part of a path expression. This raises the question whether these
tailing predicates are expressive enough for realistic queries. With a small example
we show how a more general path expression with multiple predicates can be
normalized to an equivalent path expression with one tailing predicate:
e 1 = //a/b[//c = ′ x ′ ]/d[/e = ′ y ′ ]/f
The XPath expression e 1 returns all elements with the label f that are child of an
element d having another child e that has the value y. In addition, the element
d must be the child of an element b that is ancestor of a c with value x. Finally,
b is child of an element a that appears somewhere in the XML data. The same
semantic can be expressed with path expression e 2 .
e 2 = //a/b/d/f[../e = ′ y ′ and ../..//c = ′ x ′ ]
The normalization process combines all predicates by using AND statements. The
resulting predicate (with multiple value comparisons) is moved to the end while