Jonathan Borden The Open Healthcare Group May 4, 2001
This paper forms the foundation for a schema independent type framework. The relationship between URIs, Resources and Entities are formally defined. XML Namespaces are defined using tuples.
We define a schema generically through a validity predicate. This predicate tests an instance with respect to a schema. This predicate serves to define the set of Instances of a particular schema.
The predicate valid(a,A) is true for all documents awhich are valid with respect to a schema A. Validity with respect to a particular schema is defined by the particular schema specification.
The set of all documents valid with respect to a schema A.
The schemata A and B are equal if the set of documents valid with respect to A is equal to the set of documents valid with respect to B. Note, the schemata may have different specifications (e.g. DTD vs. XML Schema). This predicate provides a way to test for equality of schema having different specifications (e.g. an XML Schema equal to a TREX schema)
Two schemata are equivalent if there exists a pair of transforms capable of transforming instances of A into instances of B and vis versa.
We move on to define a generic type hierarchy built on membership in schema instance sets.
Extension is the inverse of restriction.
A class may be a subType of another class. There are two types of subType class relationships: extension and restruction. In the restriction subType relationship: derivation by restriction, a subClass is a proper subSet of the parent class.
In this section we define a simple set of relationships between URIs, Resources and Entities. A Resource is defined in RFC 2396 as the conceptual mapping of a URI. A URI may be resolved into an entity which represents the resource at a particular point in time. A URI is thus mapped to a set of entities which may vary over time and/or the conditions on which the entity has been retrieved given the URI (e.g. content negotiation).
Two URIs are equivalent when they map to the same set of entities.
Two resources a and b are equivalent if the set of entities given the URIa and URIb are equal where URIa identifies a and URIb identifies b.
An issue arises given the mapping of a URI to a set of entities and a URI reference to a particular node within an entity. Some usages of the term resource do not distinguish between the entity retrieved from resolution of a URI, from the node obtained from resolution of the URI and a fragment identifier (together a URI reference).
A namespace qualified name (QName) is a pair consisting of a namespace URI reference and a localname. The URI reference corresponding to a QName is formed by composing the URI part of the namespace URI reference with the localname as a fragment identifier.
Note: Is this correct syntax to express "the set of resource descriptions identified by the set of ids in the entity obtained from the namespace URI"?
According to the RDDL specification a namespace is formally defined as a set of tuples each which defines a resource description. A resource description has an id, a title, a nature, a purpose, a language and refers to a URI which identifies the resource being described.
A hierachical URI has a set of child URIs each of which starts with a URI prefix equivalent to the parent URI
The next section describes the relationships between URIs, fragment identifiers, and what they identify. URIs identify a resources. URIs are rendered at various points in time and under various situations such as content negotiation into a set of entities. A rendered entity typically is associated with a MIME media type which defines the document format. Formats are typically specified using grammars such as EBNF. Generally a grammar defines a parse tree or directed labelled graph in which an entity defines a set of related nodes. In the absense of a well defined logical structure, an entity transferred over a network as a stream of characters can be represented as a root node and a series of ordered child nodes, one for each character. Generically a document is represented as a set of nodes.
Every identifier id in the set of identifiers of an entity (Ids(e)) identifies a node
A URI reference is defined to identify an abstract node. The node is termed abstract because a URI identifies a single abstract resource yet references a set of entities. For each entity in this set, the fragment identifier identifies a single node hence the abstract node is instanciated as this set of concrete nodes. In a similar fashion to which a URI indicates a single resource and a set of entities, a URI reference indicates a single abstract node and set of nodes. The relationships between URI, URI reference, Resource, Entity, Abstract Node and Node are represented by the following table:
A node may be subclassed with respect to a schema.