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Derivation byextension (1)
Schema
<complexType name="Address">
<element name="street" type="string"/>
<element name="city"
type="string"/>
</complexType>
<complexType name="USAddress">
<complexContent>
<extension base="Address">
<element name="state" type="USState"/>
<element name="zip"
type="positiveInteger"/>
</extension>
</complexContent>
</complexType>
<complexType name="UKAddress">
<complexContent>
<extension base="Address">
<element name="postcode" type="UKPostcode"/>
<attribute name="exportCode" type="positiveInteger" fixed="1"/>
</extension>
</complexContent>
</complexType>
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Derivation by extension (2)
XQuery type
DEFINE TYPE Address {
ELEMENT street { xsd:string },
ELEMENT city { xsd:string }
( () {!-- possibly empty, except if Address is abstract --}
{!-- extensions from USAddress --}
| (ELEMENT state { USState },
ELEMENT zip { xsd:positiveInteger })
!-- extensions from UKAddress --
| (ELEMENT postcode { UKPostcode },
ATTRIBUTE exportCode { xsd:positiveInteger })
)
}
Group contains base type and all types derived from it.
Thereby USAddress and UKAddress are substitutable for Ad-
dress.
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Substitution groups (1)
Schema
<element name="shipTo" address="ipo:Address">
<element name="shipToUS" type="ipo:USAddress"
substitutionGroup="ipo:shipTo"/>
<element name="order">
<complexType>
<sequence>
<element name="item" type="integer"/>
<element ref="shipTo"/>
</sequence>
</complexType>
<element>
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Substitution groups (2)
XQuery types
DEFINE ELEMENT shipTo { Address }
DEFINE ELEMENT shipToUS { USAddress }
DEFINE TYPE shipTo_group {
shipTo | shipToUS
}
DEFINE ELEMENT order {
ELEMENT item { integer },
shipTo_group
}
Union semantics: group p contains s ’representative’ element t &all
elements in its substitution group
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XML Schema vs. XQuery Types - summary
XQuery types are aware of
• Global and local elements
• Sequence, choice, and simple repetition
• Derivation hierarchies and substitution groups
• Mixed content
• Built-in simple types
XQuery types are not aware of
• complex type names
open issue
• value constraints
check with VALIDATE
Part V
Type Inference and Subsumption
What is a type system?
• Validation: Valuehas type
v∈ t
• Static semantics: Expression has type
e: t
• Dynamic semantics: Expression has value
e⇒ v
• Soundness theorem: Values,expressions, andtypes match
if e:t and
e⇒ v
then
v∈ t
What is a type system? (with variables)
• Validation: Valuehas type
v∈ t
• Static semantics: Expression has type
¯x :
¯
t e : t
• Dynamic semantics: Expression has value
¯x ⇒ ¯v  e ⇒ v
• Soundness theorem: Values,expressions, andtypes match
if ¯v∈
¯
and
¯x :
¯
t e : t and
¯x ⇒ ¯v  e ⇒ v
then
v∈ t
Documents
string
::=
"" , "a", "b", ..., "aa", ...
integer
::=
..., -1, 0, 1, ...
document d ::=
s
string
|
i
integer
|
attribute a { d }
attribute
|
element a { d }
element
|
()
empty sequence
|
d, d
sequence
Type of a document
• OverallApproach:
Walk down the document tree
Prove the type of d by proving the types of its con-
stituent nodes.
• Example:
d t
element a { d } element a { t }
(element)
Read: the type of element a { d } is element a { t } if the
type of d is t.
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