RIF Datatypes and Built-Ins 1.0

W3C Editor's Draft 22 September 2008

This version:: http://www.w3.org/2005/rules/wg/draft/ED-rif-dtb-20080922/
Latest editor's draft:: http://www.w3.org/2005/rules/wg/draft/rif-dtb/
Previous version:: http://www.w3.org/2005/rules/wg/draft/ED-rif-dtb-20080730/ (color-coded diff)

Editors:: Axel Polleres, DERI; Harold Boley, National Research Council Canada; Michael Kifer, State University of New York at Stony Brook

This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.

This document is being published as one of a set of 8 documents:

Please Comment By 2008-09-25

The Rule Interchange Format (RIF) Working Group seeks public feedback on these Working Drafts. Please send your comments to public-rif-comments@w3.org (public archive). If possible, please offer specific changes to the text that would address your concern. You may also wish to check the Wiki Version of this document for internal-review comments and changes being drafted which may address your concerns.

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This document, developed by the Rule Interchange Format (RIF) Working Group, specifies a list of primitive datatypes, built-in functions and built-in predicates expected to be supported by RIF dialects such as the RIF Basic Logic Dialect. Each dialect supporting a superset or subset of the primitive datatypes, built-in functions and built-in predicates defined here shall specify these additions or restrictions. Some of the datatypes are adopted from [XML-SCHEMA2]. A large part of the definitions of the listed functions and operators are adapted from [XPath-Functions].

1 Constants, Symbol Spaces, and Datatypes
2 Syntax and Semantics of Built-ins
- 2.1 Syntax of Built-ins
- 2.2 Semantics of Built-ins
3 List of RIF Built-in Predicates and Functions
4 References
5 Appendix: Schemas for Externally Defined Terms

1 Constants, Symbol Spaces, and Datatypes

1.1 Constants and Symbol Spaces

Each constant (that is, each non-keyword symbol) in RIF belongs to a particular symbol space. A constant in a particular RIF symbol space has the following presentation syntax:

"literal"^^<symbolSpaceIri>

where literal is called the lexical part of the symbol, and symbolSpaceIri is an (absolute or relative) IRI identifying the symbol space. Here literal is a Unicode string that must be an element in the lexical space of the symbol space identified by the IRI symbolSpaceIri.

1.2 The Base and Prefix Directives

Since IRI typically require long strings of characters, many Web languages have special provisions for abbreviating these strings. One popular technique is called compact URI [CURIE], and RIF uses a similar technique by allowing RIF documents to have the directives Base and Prefix.

A base directive has the form Base(iri), where iri is a unicode string in the form of an IRI [RFC-3987].
The Base directive defines a syntactic shortcut for expanding relative IRIs into full IRIs.
A prefix directive has the form Prefix(p v), where p is called a prefix and v is its expansion. A prefix is an alphanumeric string an expansion is a string that forms an IRI. (An alphanumeric string is a sequence of ASCII characters, where each character is a letter, a digit, or an underscore "_", and the first character is a letter.)
The basic idea is that in certain contexts prefixes can be used instead of their much longer expansions, and this provides for a much more concise and simple notation. The precise way this mechanism works is explained in Section Shortcuts for Constants in RIF's Presentation Syntax.

The precise way in which these directives work is explained in Section Shortcuts for Constants in RIF's Presentation Syntax.

To avoid writing down long IRIs, this document will assume that the following Prefix directives have been specified in all the RIF documents under consideration:

Prefix(xs http://www.w3.org/2001/XMLSchema#). This prefix stands for the XML Schema namespace URI.
Prefix(rdf http://www.w3.org/1999/02/22-rdf-syntax-ns#). This prefix stands for the RDF URI.
Prefix(rif http://www.w3.org/2007/rif#). The rif prefix stands for the RIF URI.
Prefix(func http://www.w3.org/2007/rif-builtin-function#). This prefix expands into a URI used for RIF builtin functions.
Prefix(pred http://www.w3.org/2007/rif-builtin-predicate#). This is the prefix used for RIF builtin predicates.

Using these prefixes and the shorthand mechanism defined in Section Shortcuts for Constants in RIF's Presentation Syntax, we can, for example, abbreviate a constant such as "http://www.example.org"^^<http://www.w3.org/2007/rif#iri> into "http://www.example.org"^^rif:iri.

1.2.1 Symbol Spaces

Formally, we define symbol spaces as follows.

Definition (Symbol space). A symbol space is a named subset of the set of all constants, Const in RIF. Each symbol in Const belongs to exactly one symbol space.

Each symbol space has an associated lexical space and a unique IRI identifying it. More precisely,

The lexical space of a symbol space is a non-empty set of Unicode character strings.
The identifier of a symbol space is a sequence of Unicode characters that form an absolute IRI.
Different symbol spaces supported by a dialect cannot share the same identifier.

The identifiers of symbol spaces are not themselves constant symbols in RIF.

For convenience we will often use symbol space identifiers to refer to the actual symbol spaces (for instance, we may use "symbol space xs:string" instead of "symbol space identified by xs:string").

RIF dialects are expected to include the following symbol spaces. However, rule sets that are exchanged through RIF can use additional symbol spaces.

xs:string (http://www.w3.org/2001/XMLSchema#string)

xs:time (http://www.w3.org/2001/XMLSchema#time)

xs:date (http://www.w3.org/2001/XMLSchema#date)

xs:dateTime (http://www.w3.org/2001/XMLSchema#dateTime)

xs:double (http://www.w3.org/2001/XMLSchema#double)

xs:integer (http://www.w3.org/2001/XMLSchema#integer)

xs:decimal (http://www.w3.org/2001/XMLSchema#decimal)
The lexical spaces of the above symbol spaces are defined in the document [XML-SCHEMA2].
xs:dayTimeDuration (http://www.w3.org/2001/XMLSchema#dayTimeDuration)
xs:yearMonthDuration (http://www.w3.org/2001/XMLSchema#yearMonthDuration)
These two symbol spaces represent two subtypes of the XML Schema datatype xs:duration with well-defined value spaces, since xs:duration does not have a well-defined value space (this may be corrected in later revisions of XML Schema datatypes, in which case the revised datatype would be suitable for RIF DTB). The lexical spaces of the above symbol spaces are defined in the document [XDM].
rdf:XMLLiteral (http://www.w3.org/1999/02/22-rdf-syntax-ns#XMLLiteral).
This symbol space represents XML content. The lexical space of rdf:XMLLiteral is defined in the document [RDF-CONCEPTS].
rif:text (http://www.w3.org/2007/rif#text, for text strings with language tags attached).
This symbol space represents text strings with a language tag attached. The lexical space of rif:text is the set of all Unicode strings of the form ...@LANG, i.e., strings that end with @LANG where LANG is a language identifier as defined in [BCP-47].

Editor's Note: rif:text (in particular, its identifying IRI) is an AT RISK feature. We expect a joint effort with the OWL WG to discuss rif:text and the equivalent OWL datatype, striving for a uniform symbol space for such text strings with a language tag.
rif:iri (http://www.w3.org/2007/rif#iri, for internationalized resource identifiers or IRIs).
Constants in this symbol space are intended to be used in a way similar to RDF resources [RDF-SCHEMA]. The lexical space consists of all absolute IRIs as specified in [RFC-3987]; it is unrelated to the XML primitive type anyURI. A rif:iri constant must be interpreted as a reference to one and the same object regardless of the context in which that constant occurs.
rif:local (http://www.w3.org/2007/rif#local, for constant symbols that are not visible outside of the RIF document in which they occur).
Constants in this symbol space are local to the RIF documents in which they occur. This means that occurrences of the same rif:local constant in different documents are viewed as unrelated distinct constants, but occurrences of the same rif:local constant in the same document must refer to the same object. The lexical space of rif:local is the same as the lexical space of xs:string.

Note that, by the associated lexical space, not all unicode strings are syntactically valid lexical parts for all symbol spaces. That is, for instance "1.2"^^xs:decimal and "1"^^xs:integer are syntactically valid constant because 1.2 and 1 are members of the lexical space of symbol spaces xs:decimal and xs:integer, respectively. On the other hand, "a+2"^^xs:decimal is not a syntactically valid constant, since a+2 is not part of the lexical space of xs:decimal.

We will often refer to constant symbols that come from a particular symbol space, X, as X-constants. For instance the constants in the symbol space rif:iri will be referred to as IRI constants or rif:iri constants and the constants found in the symbol space rif:local as local constants or rif:local constants.

1.2.2 Shortcuts for Constants in RIF's Presentation Syntax

Besides the basic notion

"literal"^^<identifier>

RIF's presentation syntax introduces several shortcuts for particular symbol spaces, in order to make the presentation syntax more readable. RIF's presentation syntax for constants is defined by the following EBNF.

  ANGLEBRACKIRI::= IRI_REF
  SYMSPACE     ::= ANGLEBRACKIRI | CURIE
  CURIE        ::= PNAME_LN | PNAME_NS
  Const        ::= '"' UNICODESTRING '"^^' SYMSPACE | CONSTSHORT
  CONSTSHORT   ::= ANGLEBRACKIRI              // shortcut for "..."^^rif:iri
                  | CURIE                      // shortcut for "..."^^rif:iri
                  | '"' UNICODESTRING '"'      // shortcut for "..."^^xs:string
                  | NumericLiteral             // shortcut for "..."^^xs:integer,xs:decimal,xs:double
                  | '_' LocalName              // shortcut for "..."^^rif:local

The EBNF grammar relies on reuse of nonterminals defined in the following grammar productions from other documents:

PNAME_LN, cf. http://www.w3.org/TR/rdf-sparql-query/#rPNAME_LN
PNAME_NS, cf. http://www.w3.org/TR/rdf-sparql-query/#rPNAME_NS
NumericLiteral, cf. http://www.w3.org/TR/rdf-sparql-query/#rNumericLiteral
IRI_REF, cf. http://www.w3.org/TR/rdf-sparql-query/#rIRI_REF
LocalName, cf. http://www.w3.org/TR/2006/REC-xml-names11-20060816/#NT-LocalPart
UNICODESTRING, any Unicode string where quotes are escaped and additionally all the other escape sequences defined in http://www.w3.org/TR/rdf-sparql-query/#grammarEscapes and http://www.w3.org/TR/rdf-sparql-query/#codepointEscape.

In this grammar, CURIE stands for compact IRIs [CURIE], which are used to abbreviate symbol space IRIs. For instance, one can write "http://www.example.org"^^rif:iri instead of "http://www.example.org"^^<http://www.w3.org/2007/rif#iri>, where rif is a prefix defined in Section Base and Prefix Directives. <p>Apart from compact IRIs, there exist convenient shortcut notations for constants in specific symbol spaces, namely for constants in the symbol spaces rif:iri, xs:string, xs:integer, xs:decimal, xs:double, and rif:local:

Constants in the the symbol space rif:iri can be abbreviated in two ways, either by simply using an absolute or relative IRI enclosed in angle brackets, or by writing a compact IRI. The symbol space identifier is dropped in both of these alternatives. For instance <http://www.example.org/xyz> is a valid abbreviation for "http://www.example.org/xyz"^^rif:iri and , ex:xyz is a valid abbreviation for this constant, if the directive

Prefix(ex http://www.example.org/)

is present in the RIF document in question.
Constants in the symbol space xs:string can be abbreviated by simply using quoted strings, i.e. "My String!" is a valid abbreviation for the constant "My String!"^^xs:string (which in turn is itself an abbreviation for "My String!"^^<http://www.w3.org/2001/XMLSchema#string>).
Numeric constants can be abbreviated using the grammar rules for NumericLiterals from the [SPARQL] grammar: Integers can be written directly (without quotation marks and explicit symbol space identifier) and are interpreted as constants in the symbol space xs:integer; decimal numbers for which there is '.' in the number but no exponent are interpreted as constants in the symbol space xs:decimal; and numbers with exponents are interpreted as xs:double. For instance, one could use 1.2 and 1 as shortcuts for "1.2"^^xs:decimal and "1"^^xs:integer, respectively. However, there is no shortcut for "1"^^xs:decimal.
The shortcut notation for rif:local applies to only a subset of the lexical space of syntactically valid lexical parts of constants in this symbol space: We allow "_"-prefixed unicode strings which are also valid XML NCNames as defined in [XML-NS]. For other constants in the rif:local symbol space one has to use the long notation. That is, for instance _myLocalConstant is a valid abbreviation for the constant "myLocalConstant"^^rif:local, whereas "http://www.example.org"^^rif:local cannot be abbreviated.

Editor's Note: We might introduce additional shortcuts, e.g. for rif:text in future versions of this draft.

1.2.3 Relative IRIs

Relative IRIs in RIF documents are resolved with respect to the base IRI. Relative IRIs are combined with base IRIs as per Uniform Resource Identifier (URI): Generic Syntax [RFC-3986] using only the basic algorithm in Section 5.2. Neither Syntax-Based Normalization nor Scheme-Based Normalization (described in sections 6.2.2 and 6.2.3 of RFC-3986) are performed. Characters additionally allowed in IRI references are treated in the same way that unreserved characters are treated in URI references, per section 6.5 of Internationalized Resource Identifiers (IRIs) [RFC-3987].

Base IRIs are specified using the Base directive described in Section Base and Prefix Directives. At most one base directive per document is allowed. In the XML syntax, base IRIs are specified using the attribute xml:base.

For instance, the constant <./xyz> or "./xyz"^^rif:iri are both valid abbreviations in RIF for the constant http://www.example.org/xyz"^^rif:iri, if the following directive is present in the document:

Base(http://www.example.org)

1.3 Primitive Datatypes

Datatypes in RIF are symbol spaces which have special semantics. That is, each datatype is characterized by a fixed lexical space, value space and lexical-to-value-mapping.

Definition (Primitive datatype). A primitive datatype (or just a datatype, for short) is a symbol space that has

an associated set, called the value space, and
a mapping from the lexical space of the symbol space to the value space, called lexical-to-value-space mapping. ☐

Semantic structures are always defined with respect to a particular set of datatypes, denoted by DTS. In a concrete dialect, DTS always includes the datatypes supported by that dialect. RIF dialects are expected to support the following primitive datatypes. However, RIF dialects may include additional datatypes.

xs:string
xs:time
xs:date
xs:dateTime
xs:double
xs:integer
xs:decimal
xs:dayTimeDuration
xs:yearMonthDuration
rdf:XMLLiteral
rif:text

Editor's Note: rif:text (in particular, its identifying IRI) is an AT RISK feature. We expect a joint effort with the OWL WG to discuss rif:text and the equivalent OWL datatype, striving for a uniform symbol space for such text strings with a language tag.

Their value spaces and the lexical-to-value-space mappings are defined as follows:

For the XML Schema datatypes of RIF, namely xs:double, xs:integer, xs:decimal, xs:string, xs:time, and xs:dateTime, the value spaces and the lexical-to-value-space mappings are defined in the XML Schema specification [XML-SCHEMA2].
The value spaces and the lexical-to-value-space mappings for the primitive datatypes xs:dayTimeDuration and xs:yearMonthDuration are defined in the XQuery 1.0 and XPath 2.0 Data Model [XDM].
The value space and lexical-to-value-space mapping for the primitive datatype rdf:XMLLiteral is defined in RDF [RDF-CONCEPTS].
The value space rif:text is the set of all pairs of the form (string,lang), where string is a Unicode character sequence and lang is a lowercase Unicode character sequence which is a language identifier as defined by [BCP-47]. The lexical-to-value-space mapping of rif:text, denoted L_rif:text, maps each symbol string@lang in the lexical space of rif:text to (string,lower-case(lang)), where lower-case(lang) is lang written in all-lowercase letters.

The value space and the lexical-to-value-space mapping for rif:text defined here are compatible with RDF's semantics for strings with named tags [RDF-SEMANTICS].

2 Syntax and Semantics of Built-ins

2.1 Syntax of Built-ins

A RIF built-in function or predicate is a special case of externally defined terms, which are defined in RIF Framework for Logic Dialects and also reproduced in the direct definition of RIF Basic Logic Dialect (RIF-BLD).

In RIF's presentation syntax built-in predicates and functions are syntactically represented as external terms of the form:

'External' '(' Expr ')'

where Expr is a positional term as defined in RIF Framework for Logic Dialects (see also in RIF Basic Logic Dialect). For RIF's normative syntax, see the XML Serialization Framework in RIF-FLD, or, specifically for RIF-BLD, see XML Serialization Syntax for RIF-BLD.

RIF-FLD introduces the notion of an external schema to describe both both the syntax and semantics of exernally defined terms. In the special case of a RIF built-in, external schemas have an especially simple form. A built-in named f that takes n arguments has the schema

(?X₁ ...?X_n; f(?X₁ ...?X_n) )

Here f(?X₁ ...?X_n) is the actual term that is used to refer to the built-in (in expressions of the form External(f(?X₁ ...?X_n))) and ?X₁ ...?X_n is the list of all variables in that term.

For convenience, a complete definition of external schemas is reproduced in Appendix: Schemas for Externally Defined Terms.

2.2 Semantics of Built-ins

The semantics of external terms in RIF-FLD and RIF-BLD is defined using two mappings: I_external and I_truth I_external.

I_external. This mapping takes an external schema, , and returns a mapping, I_external(). If represents a built-in function, I_external() must be that function. For each built-in function with external schema , the present document specifies the mapping I_external().

I_truth. This mapping takes an element of the domain of interpretation and returns a truth value. In RIF logical semantics, this mapping is used to assign truth values to formulas. In the special case of RIF built-ins, it is used to assign truth values to RIF built-in predicates. The built-in predicates can have the truth values t or f only. For a built-in predicate with schema , RIF-FLD and RIF-BLD require that the truth-valued mapping I_truth I_external() must agree with the specification of the corresponding built-in predicate. For each RIF built-in predicate with schema , the present document specifies I_truth I_external().

3 List of RIF Built-in Predicates and Functions This section provides a catalogue defining the syntax and semantics of a list of built-in predicates and functions in RIF. For each built-in, the following is defined: The name of the built-in. The external schema of the built-in. For a built-in function, how it maps its arguments into a result. As explained in Section Semantics of Built-ins, this corresponds to the mapping I_external() in the formal semantics of RIF-FLD and RIF-BLD, where is the external schema of the built-in. For a built-in predicate, its truth value when the arguments are substituted with values in the domain. As explained in Section Semantics of Built-ins, this corresponds to the mapping I_truth I_external() in the formal semantics of RIF-FLD and RIF-BLD, where is the external schema of the built-in. The intended domains for the arguments of the built-in. Typically, built-in functions and predicates are defined over the value spaces of appropriate datatypes. These are the intended domains of the arguments. When an argument falls outside of its intended domain, it is understood as an error. Since this document defines a model-theoretic semantics for RIF built-ins, which does not support the notion of an error, the definitions leave the values of the built-in predicates and functions unspecified in such cases. This means that if one or more of the arguments is not in its intended domain, the value of I_external()(a₁ ... a_n) can vary from one semantic structure to another. Similarly, I_truth I_external()(a₁ ... a_n) can be t in some interpretations and f in others when an argument is not in the intended domain. This indeterminacy in case of an error implies that applications must not make any assumptions about the values of built-ins in such situations. Implementations are even allowed to abort in such cases and the only safe way to communicate rule sets that contain built-ins among RIF-compliant systems is to use datatype guards. Many built-in functions and predicates described below are adapted from [XPath-Functions] and, when appropriate, we will refer to the definitions in that specification in order to avoid copying them. 3.1 Guard Predicates for Datatypes RIF defines guard predicates for all datatypes in Section Primitive Datatypes. Schema: The schemas for these predicates have the general form (?arg₁; pred:isDATATYPE (?arg₁ ) ) Here, DATATYPE is the short name for a datatype. As a naming convention we use the capitalized non-prefix XML local name part of the IRI denoting the datatype, for instance we use pred:isString for the guard predicate for xs:string, or pred:isText for the guard predicate for rif:text. Parties defining their own datatypes to be used in RIF exchanged rules may define their own guard predicates for these datatypes. Labels used for such additional guard predicates for datatypes not mentioned in the present document MAY follow the same naming convention where applicable without creating ambiguities with predicate names defined in the present document. Editor's Note: The naming convention for guard predicates, particularly whether third parties defining their own datatypes should be encouraged/discouraged to reuse the standard pred: and func: namespaces to define their own built-in predicates and functions, are still under discussion in the working group. Intended domain: Guard predicates do not depend on a specific intended domain. Mapping: I_truth I_external(?arg₁; pred:isDATATYPE (?arg₁ ) )(s₁) = t if and only if s₁ is in the value space of DATATYPE and f otherwise. Accordingly, the following schemas are defined. 3.1.1 pred:isInteger Schema: (?arg₁; pred:isInteger(?arg₁ ) ) 3.1.2 pred:isDecimal Schema: (?arg₁; pred:isDecimal (?arg₁ ) ) 3.1.3 pred:isDouble Schema: (?arg₁; pred:isDouble (?arg₁ ) ) 3.1.4 pred:isString Schema: (?arg₁; pred:isString (?arg₁ ) ) 3.1.5 pred:isTime Schema: (?arg₁; pred:isTime (?arg₁ ) ) 3.1.6 pred:isDate Schema: (?arg₁; pred:isDate (?arg₁ ) ) 3.1.7 pred:isDateTime Schema: (?arg₁; pred:isDateTime (?arg₁ ) ) 3.1.8 pred:isDayTimeDuration Schema: (?arg₁; pred:isDayTimeDuration (?arg₁ ) ) 3.1.9 pred:isYearMonthDuration Schema: (?arg₁; pred:isYearMonthDuration (?arg₁ ) ) 3.1.10 pred:isXMLLiteral Schema: (?arg₁; pred:isXMLLiteral (?arg₁ ) ) 3.1.11 pred:isText Schema: (?arg₁; pred:isText (?arg₁ ) ) Editor's Note: It was noted in discussions of the working group, that except guard predicates, also an analogous built-in function or predicate to SPARQL's datatype function is needed. This however has some technical implications, see http://lists.w3.org/Archives/Public/public-rif-wg/2008Jul/0096.html 3.2 Negative Guard Predicates for Datatypes Likewise, RIF defines negative guard predicates for all datatypes in Section Primitive Datatypes. Schema: The schemas for negative guards have the general form (?arg₁; pred:isNotDATATYPE (?arg₁ ) ) Here, DATATYPE is the short name for one of the datatypes mentioned in this document. As a naming convention we use the capitalized non-prefix XML local name part of the IRI denoting the datatype, for instance we use pred:isNotString for the negative guard predicate for xs:string, or pred:isNotText for the negative guard predicate for rif:text. Parties defining their own datatypes to be used in RIF exchanged rules may define their own negative guard predicates for these datatypes. Labels used for such additional negative guard predicates for datatypes not mentioned in the present document MAY follow the same naming convention where applicable without creating ambiguities with predicate names defined in the present document. Editor's Note: The naming convention for negative guard predicates, particularly whether third parties defining their own datatypes should be encouraged/discouraged to reuse the standard pred: and func: namespaces to define their own built-in predicates and functions, are still under discussion in the working group. Intended domain: Negative guard predicates do not depend on a specific intended domain. Mapping: I_truth I_external(?arg₁; pred:isNotDATATYPE (?arg₁ ) )(s₁) = f if and only if s₁ is in the value space of DATATYPE and t otherwise. Accordingly, the following schemas are defined. 3.2.1 pred:isNotInteger Schema: (?arg₁; pred:isNotInteger (?arg₁ ) ) 3.2.2 pred:isNotDecimal Schema: (?arg₁; pred:isNotDecimal (?arg₁ ) ) 3.2.3 pred:isNotDouble Schema: (?arg₁; pred:isNotDouble (?arg₁ ) ) 3.2.4 pred:isNotString Schema: (?arg₁; pred:isNotString (?arg₁ ) ) 3.2.5 pred:isNotTime Schema: (?arg₁; pred:isNotTime (?arg₁ ) ) 3.2.6 pred:isNotDate Schema: (?arg₁; pred:isNotDate (?arg₁ ) ) 3.2.7 pred:isNotDateTime Schema: (?arg₁; pred:isNotDateTime (?arg₁ ) ) 3.2.8 pred:isNotDayTimeDuration Schema: (?arg₁; pred:isNotDayTimeDuration (?arg₁ ) ) 3.2.9 pred:isNotYearMonthDuration Schema: (?arg₁; pred:isNotYearMonthDuration (?arg₁ ) ) 3.2.10 pred:isNotXMLLiteral Schema: (?arg₁; pred:isNotXMLLiteral (?arg₁ ) ) 3.2.11 pred:isNotText Schema: (?arg₁; pred:isNotText (?arg₁ ) ) Future dialects may extend this list of guards to other datatypes, but RIF does not require guards for all datatypes. 3.3 Cast Functions and Conversion Predicates for Datatypes and rif:iri RIF defines cast functions for all datatypes mentioned in this document, i.e. for each datatype with IRI DATATYPEIRI there is an external function with the following schema: Schema: (?arg₁; <DATATYPEIRI> (?arg₁ ) ) We now discuss the intended domains and mappings for these cast functions. Editor's Note: In the following, we adapt several cast functions from [XPath-Functions]. Due to the subtle differences in e.g. error handling between RIF and [XPath-Functions], these definitions might still need refinement in future versions of this draft. 3.3.1 xs:double, xs:integer, xs:decimal, xs:time, xs:date, xs:date,xs:dateTime, xs:dayTimeDuration, xs:yearMonthDuration Schemata: (?arg₁; xs:double (?arg₁ ) ) (?arg₁; xs:integer (?arg₁ ) ) and accordingly for all subtypes of xs:integer (?arg₁; xs:decimal (?arg₁ ) ) (?arg₁; xs:time (?arg₁ ) ) (?arg₁; xs:date (?arg₁ ) ) (?arg₁; xs:dateTime (?arg₁ ) ) (?arg₁; xs:dayTimeDuration (?arg₁ ) ) (?arg₁; xs:yearMonthDuration (?arg₁ ) ) Intended domains: The value spaces of datatypes castable to xs:DATATYPE according to Section 17.1 of [XPath-Functions]. Mappings: I_external(?arg₁; xs:DATATYPE (?arg₁ ) )(s₁) = s₁' such that s₁' is the conversion of s₁ to the value space of xs:DATATYPE according to Section 17.1 of [XPath-Functions]. Note that these conversions are only partial and note further that the subtypes of xs:integer do appear in the conversion table. Conversions from and to subtypes of xs:integer follow the same considerations as xs:integer in that table, by the XPath, XQuery type hierarchy in Section 1.6 of [XPath-Functions]. If the argument value is outside of the intended domain or outside the partial conversions defined in [XPath-Functions], the value of the function is left unspecified and can vary from one semantic structure to another. Editor's Note: We might split this subsection into separate subsections per casting function in future versions of this document, following the convention of having one separate subsection per funtcion/predicate in the rest of the document. However, it seemed convenient here to group the cast functions which purely rely on XML Schema datatype casting into one common subsection. 3.3.2 xs:string Schema: (?arg₁; xs:string (?arg₁ ) ) Intended domain: The union of the value space of rif:text with the value spaces of datatypes castable to xs:string according to the table in Section 17.1 of [XPath-Functions]. Mapping: I_external(?arg₁; xs:DATATYPE (?arg₁ ) )(s₁) = s₁' such that s₁' is the conversion of s₁ to the value space of xs:string according to the table in Section 17.1 of [XPath-Functions], in case s₁ is in the value space of a datatype mentioned in that table. by preserving the lexical value of its string part, if s₁ is in the value space of rif:text. If the argument is outside the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. Editor's Note: The cast from rif:text to xs:string is still under discussion, i.e. whether the lang tag should be included when casting to xs:string or not. 3.3.3 rdf:XMLLiteral Schema: (?arg₁; rdf:XMLLiteral (?arg₁ ) ) Intended domain: The intersection of the value space of xs:string with the lexical space of rdf:XMLLiteral, i.e. an xs:string can be cast to rdf:XMLLiteral if and only if its value is in the lexical space of rdf:XMLLiteral as defined in Resource Description Framework (RDF): Concepts and Abstract Syntax Mapping: I_external(?arg₁; xs:DATATYPE (?arg₁ ) )(s₁) = s₁' such that s₁' is the XMLLiteral corresponding to the given string s₁. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.3.4 rif:text Schema: (?arg₁; rif:text (?arg₁?arg₂ ) ) Intended domains: The value space of xs:string for ?arg₁ and the intersection of the value space of xs:string with all Unicode character sequences which are language identifiers as defined by [BCP-47] for ?arg₂. Mapping: I_external(?arg₁; rif:text (?arg₁?arg₂ ) )(s₁ s₂) = s' where s₁ is a Unicode string and s₂ is a Unicode character sequence which is language as defined by [BCP-47]. Then s' is defined exactly as the pair (s₁, lowercase(s₂)). If the argument values are outside of the intended domains, the value of the function is left unspecified and can vary from one semantic structure to another. 3.3.5 pred:iri-to-string Editor's Note: Conversion from rif:iri to xs:string and vice versa is still under discussion in the working group since rif:iri is not a datatype. For details, we refer to Issue-61. The following is a strawman proposal which might still change in future versions of this working draft. Conversions from rif:iri to xs:string and vice versa cannot be defined by the casting functions as above since rif:iri is not a datatype with a well-defined value space. To this end, since conversions from IRIs (resources) to strings are a needed feature for instance for conversions between RDF formats (see example below), we add a built-in predicate which supports such conversions. Schema: (?arg₁; pred:iri-to-string (?arg₁,?arg₂ ) ) Intended domains: The first argument is not restricted by a specific domain, the second argument is the value space of xs:string. Mapping: I_external(?arg₁?arg₂; pred:iri-to-string (?arg₁?arg₂ ) )(iri₁ str₁) = t if and only if str₁ is an element in the lexical space of rif:iri and iri₁ is an element of the domain such that I( "str₁"^^rif:iri ) = iri₁ holds in the current interpretation. Note that this definition restricts allowed RIF interpretations in such a way that the interpretation of pred:iri-to-string always needs to comply with respect to the symbols in the rif:iri symbol space for the first argument and elements of the xs:string value space for the second argument. The truth value of the predicate is left unspecified for other elements of the domain and can vary from one semantic structure to another. This predicate could be usable for instance to map telephone numbers between an RDF Format for vCard (http://www.w3.org/TR/vcard-rdf) and FOAF (http://xmlns.com/foaf/0.1/). vCard stores telephone numbers as string literals, whereas FOAF uses resources, i.e., URIs with the tel: URI-scheme. So, a mapping from FOAF to vCard would need to convert the tel: URI to a string and then cut off the first four characters ("tel:"). Such a mapping expressed in RIF could involve e.g. a rule as follows: ... Prefix( VCard http://www.w3.org/TR/vcard-rdf#) Prefix( foaf http://xmlns.com/foaf/0.1/) ... Forall?X?foafTelIri?foafTelString ( ?X[ VCard:tel -> External( func:substring(?foafTelString 4 ) ]:- And (?X[ foaf:phone ->?foafTelIri ] External( pred:iri-to-string(?foafTelIri?foafTelString ) ) ) 3.4 Numeric Functions and Predicates The following functions and predicates are adapted from the respective numeric functions and operators in [XPath-Functions]. 3.4.1 Numeric Functions 3.4.1.1 func:numeric-add (adapted from op:numeric-add) Schema: (?arg₁?arg₂; func:numeric-add(?arg₁?arg₂)) Intended domains: The value spaces of xs:integer, xs:double, or xs:decimal for both arguments. Mapping: When both s₁ and s₂ belong to their intended domains, External(func:numeric-add(s₁ s₂)) evaluates to the result of op:numeric-add(s₁, s₂) as defined in [XPath-Functions]. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. The following numeric built-in functions func:numeric-subtract, func:numeric-multiply, func:numeric-divide, func:numeric-integer-divide, and func:numeric-mod are defined accordingly with respect to their corresponding operators in [XPath-Functions] and we will only add further explanations where needed. 3.4.1.2 func:numeric-subtract (adapted from op:numeric-subtract) Schema: (?arg₁?arg₂; func:numeric-subtract(?arg₁?arg₂) ) 3.4.1.3 func:numeric-multiply (adapted from op:numeric-multiply) Schema: (?arg₁?arg₂; func:numeric-multiply(?arg₁?arg₂) ) 3.4.1.4 func:numeric-divide (adapted from op:numeric-divide) Schema: (?arg₁?arg₂; func:numeric-divide(?arg₁?arg₂) ) Intended domains: The value spaces of xs:integer, xs:double, or xs:decimal for the first argument and xs:integer, xs:double, or xs:decimal without zero for the second argument. Mapping: This function backs up the "div" operator and returns the arithmetic quotient of its operands If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another, which here particularly means that RIF does not prescribe the behavior on division by zero. 3.4.1.5 func:numeric-integer-divide (adapted from op:numeric-integer-divide) Schema: (?arg₁?arg₂; func:numeric-integer-divide(?arg₁?arg₂) ) Intended domains: The value spaces of xs:integer, xs:double, or xs:decimal for the first argument and xs:integer, xs:double, or xs:decimal without zero for the second argument. Mapping: This function backs up the "idiv" operator and performs an integer division: that is, it divides the first argument by the second, and returns the integer obtained by truncating the fractional part of the result. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another, which here particularly means that RIF does not prescribe the behavior on division by zero. 3.4.1.6 func:numeric-mod (adapted from op:numeric-mod) Schema: (?arg₁?arg₂; func:numeric-mod(?arg₁?arg₂) ) Intended domains: The value spaces of xs:integer, xs:double, or xs:decimal for the first argument and xs:integer, xs:double, or xs:decimal without zero for the second argument. Mapping: Backs up the "mod" operator. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another, which here particularly means that RIF does not prescribe the behavior if the second argument is zero. 3.4.2 Numeric Predicates 3.4.2.1 pred:numeric-equal (adapted from op:numeric-equal) Schema: (?arg₁?arg₂; pred:numeric-equal(?arg₁?arg₂)) Intended domains: The value spaces of xs:integer, xs:double, or xs:decimal for both arguments. Mapping: When both s₁ and s₂ belong to their intended domains, External(pred:numeric-equal(s₁ s₂)) is t if and only if op:numeric-equal(s₁, s₂) returns true, as defined in [XPath-Functions]. If an argument value is outside of the intended domain, the truth value of the function is left unspecified and can vary from one semantic structure to another. The following numeric built-in predicates pred:numeric-less-than and pred:numeric-greater-than are defined acordingly with respect to their corresponding operators in [XPath-Functions]. The predicate pred:numeric-not-equal has the same intended domain as pred:numeric-equal and is true whenever pred:numeric-equal is false. The predicates pred:numeric-less-than-or-equal (and pred:numeric-greater-than-or-equal, respectively) are true whenever pred:numeric-equal is true or pred:numeric-less-than (pred:numeric-greater-than-or-equal, respectively) is true. 3.4.2.2 pred:numeric-less-than (adapted from op:numeric-less-than) Schema: (?arg₁?arg₂; pred:numeric-less-than(?arg₁?arg₂) ) 3.4.2.3 pred:numeric-greater-than (adapted from op:numeric-greater-than) Schema: (?arg₁?arg₂; pred:numeric-greater-than(?arg₁?arg₂) ) 3.4.2.4 pred:numeric-not-equal Schema: (?arg₁?arg₂; pred:numeric-not-equal(?arg₁?arg₂) ) 3.4.2.5 pred:numeric-less-than-or-equal Schema: (?arg₁?arg₂; pred:numeric-less-than-or-equal(?arg₁?arg₂) ) 3.4.2.6 pred:numeric-greater-than-or-equal Schema: (?arg₁?arg₂; pred:numeric-greater-than-or-equal(?arg₁?arg₂) ) 3.5 Functions and Predicates on Strings The following functions and predicates are adapted from the respective functions and operators on strings in [XPath-Functions]. Editor's Note: The following treatment of built-ins which may have multiple arities is a strawman proposal currently under discussion in the working group. In the following, we encounter several versions of some built-ins with varying arity, since XPath and XQuery allow overloading, i.e. the same function or operator name occurring with different arities. We treat this likewise in RIF, by numbering the different versions of the respective built-ins and treating the unnumbered version as syntactic sugar, i.e. for instance instead of External( func:concat2( str₁, str₂) ) and External( func:concat3( str₁ str₂ str₃ ) ) we allow the equivalent forms External( func:concat( str₁, str₂) ) and External( func:concat( str₁ str₂ str₃ ) ). Note that this is really purely syntactic sugar, and does not mean that for external predicates and functions we lift the restriction made in BLD that each function and predicate has a unique assigned arity. Those schemata for which we allow this syntactic sugar, appear in the same box. 3.5.1 Functions on Strings 3.5.1.1 func:compare (adapted from fn:compare) Schema: (?comparand₁?comparand₂; func:compare1(?comparand₁?comparand₂) ) (?comparand₁ $comparand₂ $collation; func:compare2(?comparand₁?comparand₂?collation) ) Intended domains: The value space of xs:string for all arguments. Mapping: I_external( (?comparand₁?comparand₂; func:compare1(?comparand₁?comparand₂) )(s₁ s₂) = res such that res = -1, 0, or 0 (from the value space of xs:integer), depending on whether the value of the s₁ is respectively less than, equal to, or greater than the value of s₂, according to the rules of the collation that is used. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. Editor's Note: The working group is currently discussing, whether in addition to adopting the fn:compare function from [XPath-Functions], own predicates pred:string-equal, pred:string-less-than, pred:string-greater-than, pred:string-not-equal, pred:string-less-than-or-equal, pred:string-greater-than-or-equal not defined in [XPath-Functions] shall be introduced, following the convention of having such predicates for other datatypes. The following schemata are defined analogously with respect to their corresponding operators as defined in [XPath-Functions] and we only give informal descriptions of the respective mappings I_external. 3.5.1.2 func:concat (adapted from fn:concat) Schema: (?arg₁; func:concat1(?arg₁ ) ) (?arg₁?arg₂; func:concat2(?arg₁?arg₂ ) ) ... (?arg₁ ?arg₂ ...?arg_n; func:concatn(?arg₁?arg₂ ...?arg_n ) ) Intended domains: Following the definition of fn:concat this function accepts xs:anyAtomicType arguments and casts them to xs:string. Thus, the intended domain for all arguments is the union of all value spaces castable to String xs:string as defined in Section Cast Functions and Conversion Predicates for Datatypes and rif:iri above. Mapping: Returns the xs:string that is the concatenation of the values of its arguments after conversion. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.3 func:string-join (adapted from fn:string-join) Schema: (?arg₁?arg₂; func:string-join2(?arg₁?arg₂ ) ) (?arg₁?arg₂?arg₃; func:string-join3(?arg₁?arg₂?arg₃ ) ) ... (?arg₁ ?arg₂ ...?arg_n; func:string-joinn(?arg₁?arg₂ ...?arg_n ) ) Intended domains: The value space of xs:string for all arguments. Mapping: Returns a xs:string created by concatenating the arguments 1 to (n-1) using the n^th argument as a separator. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.4 func:substring (adapted from fn:substring) Schema: (?sourceString?startingLoc; func:substring1(?sourceString?startingLoc) ) (?sourceString?startingLoc?length; func:substring2(?sourceString?startingLoc?length) ) Intended domains: The value space of xs:string for ?sourceString and the union of the value spaces of xs:integer, xs:long, or xs:decimal for the remaining two arguments. Mapping: Returns the portion of the value of?sourceString beginning at the position indicated by the value of?startingLoc and continuing for the number of characters indicated by the value of?length. The characters returned do not extend beyond?sourceString. If?startingLoc is zero or negative, only those characters in positions greater than zero are returned. If an argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.5 func:string-length (adapted from fn:string-length) Schema: ( func:string-length1() ) (?arg; func:string-length2(?arg ) ) Intended domains: The value space of xs:string for ?arg. Mapping: Returns an xs:integer equal to the length in characters of the argument if it is a xs:string. If the argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.6 func:upper-case (adapted from fn:upper-case) Schema: (?arg; func:upper-case(?arg ) ) Intended domain: The value space of xs:string for ?arg. Mapping: Returns the value of?arg after translating every character to its upper-case correspondent as defined in the appropriate case mappings section in the Unicode standard. If the argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.7 func:lower-case (adapted from fn:lower-case) Schema: (?arg; func:lower-case(?arg ) ) Intended domain: The value space of xs:string for ?arg. Mapping: Returns the value of?arg after translating every character to its lower-case correspondent as defined in the appropriate case mappings section in the Unicode standard. If the argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.8 func:encode-for-uri (adapted from fn:encode-for-uri) Schema: (?arg; func:encode-for-uri(?arg ) ) Intended domains: The value space of xs:string for ?arg. Mapping: This function encodes reserved characters in an xs:string that is intended to be used in the path segment of a URI. It is invertible but not idempotent. If the argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.9 func:iri-to-uri (adapted from fn:iri-to-uri) Schema: (?iri; func:iri-to-uri (?iri ) ) Intended domains: The value space of xs:string for ?iri. Mapping: This function converts an xs:string containing an IRI into a URI according to the rules spelled out in Section 3.1 of RFC 3987. It is idempotent but not invertible. If the argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.10 func:escape-html-uri (adapted from fn:escape-html-uri) Schema: (?uri;func:escape-html-uri(?uri ) ) Intended domains: The value space of xs:string for ?uri. Mapping: This function escapes all characters except printable characters of the US-ASCII coded character set, specifically the octets ranging from 32 to 126 (decimal). The effect of the function is to escape a URI in the manner html user agents handle attribute values that expect URIs. Each character in $uri to be escaped is replaced by an escape sequence, which is formed by encoding the character as a sequence of octets in UTF-8, and then representing each of these octets in the form%HH, where HH is the hexadecimal representation of the octet. This function must always generate hexadecimal values using the upper-case letters A-F. If the argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.11 func:substring-before (adapted from fn:substring-before) Schema: (?arg₁?arg₂; func:substring-before1(?arg₁?arg₂ ) ) (?arg₁?arg₂?collation; func:substring-before2(?arg₁?arg₂?collation ) ) Intended domains: The value space of xs:string for all arguments. Mapping: Returns the substring of the value of?arg1 that precedes in the value of?arg1 the first occurrence of a sequence of collation units that provides a minimal match to the collation units of?arg2 according to the collation that is used. If any argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.12 func:substring-after (adapted from fn:substring-after) Schema: (?arg₁?arg₂; func:substring-after1(?arg₁?arg₂ ) ) (?arg₁?arg₂?collation; func:substring-after2(?arg₁?arg₂?collation ) ) Intended domains: The value space of xs:string for all arguments. Mapping: Returns the substring of the value of?arg1 that follows in the value of?arg1 the first occurrence of a sequence of collation units that provides a minimal match to the collation units of?arg2 according to the collation that is used. If any argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.1.13 func:replace (adapted from fn:replace) Schema: (?input?pattern?replacement; func:replace1(?input?pattern?replacement ) ) (?input?pattern?replacement?flags; func:replace2(?input?pattern?replacement?flags ) ) Intended domains: The value space of xs:string for all arguments. Mapping: The function returns the xs:string that is obtained by replacing each non-overlapping substring of?input that matches the given?pattern with an occurrence of the?replacement string. If any argument value is outside of its intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.2 Predicates on Strings 3.5.2.1 pred:contains (adapted from fn:contains) Schema: (?arg₁?arg₂; pred:contains1(?arg₁?arg₂ ) ) (?arg₁?arg₂?collation; pred:contains2(?arg₁?arg₂?collation ) ) Intended domains: The value space of xs:string for all arguments. Mapping: Returns true or false indicating whether or not the value of?arg1 contains (at the beginning, at the end, or anywhere within) at least one sequence of collation units that provides a minimal match to the collation units in the value of?arg2, according to the collation that is used. "Minimal match" is defined in Unicode Collation Algorithm. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.2.2 pred:starts-with (adapted from fn:starts-with) Schema: (?arg₁?arg₂; pred:starts-with1(?arg₁?arg₂ ) (?arg₁?arg₂?collation; pred:starts-with2(?arg₁?arg₂?collation) Intended domains: The value space of xs:string for all arguments. Mapping: Returns true or false indicating whether or not the value of?arg1 starts with a sequence of collation units that provides a minimal match to the collation units of?arg2 according to the collation that is used. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.2.3 pred:ends-with (adapted from fn:ends-with) Schema: (?arg₁?arg₂; fn:ends-with1(?arg₁?arg₂ ) ) (?arg₁?arg₂?collation; fn:ends-with2(?arg₁?arg₂?collation) ) Intended domains: The value space of xs:string for all arguments. Mapping: Returns true or false indicating whether or not the value of?arg1 ends with a sequence of collation units that provides a minimal match to the collation units of?arg2 according to the collation that is used. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.5.2.4 pred:matches (adapted from fn:matches) Schema: (?input?pattern; pred:matches1(?input?pattern) ) (?input?pattern?flags; pred:matches2(?input?pattern?flags ) ) Intended domains: The value space of xs:string for all arguments. Mapping: Returns true if the input matches the regular expression supplied as pattern as influenced by the flags, if present; otherwise, it returns false. The effect of calling the first version of this function (omitting the flags) is the same as the effect of calling the second version with the flags argument set to a zero-length string. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6 Functions and Predicates on Dates, Times, and Durations If not stated otherwise, in the following we define schemas for functions and operators defined on the date and time datatypes in [XPath-Functions]. As defined in Section 3.3.2 Dates and Times, xs:dateTime, xs:date, xs:time, xs:gYearMonth, xs:gYear, xs:gMonthDay, xs:gMonth, xs:gDay values, referred to collectively as date/time values, are represented as seven components or properties: year, month, day, hour, minute, second and timezone. The value of the first five components are xs:integers. The value of the second component is an xs:decimal and the value of the timezone component is an xs:dayTimeDuration. For all the date/time datatypes, the timezone property is optional and may or may not be present. Depending on the datatype, some of the remaining six properties must be present and some must be absent. Absent, or missing, properties are represented by the empty sequence. This value is referred to as the local value in that the value is in the given timezone. Before comparing or subtracting xs:dateTime values, this local value must be translated or normalized to UTC. 3.6.1 Functions on Dates, Times, and Durations 3.6.1.1 func:year-from-dateTime (adapted from fn:year-from-dateTime) Schema: (?arg; func:year-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime for?arg. Mapping: I_external(?arg; func:year-from-dateTime(?arg ) )(s) = res such that res is the result of fn:year-from-dateTime(s) as defined in [XPath-Functions]. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. Note that we we slightly deviate here from the original definition of fn:year-from-dateTime which says: "If?arg is the empty sequence, returns the empty sequence." We have no terminology of "sequence". The following schemata are defined analogously with respect to their corresponding operators as defined in [XPath-Functions] and we only give informal descriptions of the respective mappings I_external. 3.6.1.2 func:month-from-dateTime (adapted from fn:month-from-dateTime) Schema: (?arg; func:month-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime for?arg. Mapping: Returns an xs:integer between 1 and 12, both inclusive, representing the month component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.3 func:day-from-dateTime (adapted from fn:day-from-dateTime) Schema: (?arg; func:day-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime for?arg. Mapping: Returns an xs:integer between 1 and 31, both inclusive, representing the day component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.4 func:hours-from-dateTime (adapted from fn:hours-from-dateTime) Schema: (?arg; func:hours-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime for?arg. Mapping: Returns an xs:integer between 0 and 23, both inclusive, representing the hours component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.5 func:minutes-from-dateTime (adapted from fn:minutes-from-dateTime) Schema: (?arg; func:minutes-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime for?arg. Mapping: Returns an xs:integer between 0 and 59, both inclusive, representing the minutes component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.6 func:seconds-from-dateTime (adapted from fn:seconds-from-dateTime) Schema: (?arg; func:seconds-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime for?arg. Mapping: Returns an xs:decimal value greater than or equal to zero and less than 60, representing the seconds and fractional seconds in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.7 func:year-from-date (adapted from fn:year-from-date) Schema: (?arg; func:year-from-date(?arg ) ) Intended domains: The value space of xs:date for?arg. Mapping: Returns an xs:integer representing the year in the localized value of?arg. The value may be negative. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.8 func:month-from-date (adapted from fn:month-from-date) Schema: (?arg; func:month-from-date(?arg ) ) Intended domains: The value space of xs:date for?arg. Mapping: Returns an xs:integer between 1 and 12, both inclusive, representing the month component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.9 func:day-from-date (adapted from fn:day-from-date) Schema: (?arg; func:day-from-date(?arg ) ) Intended domains: The value space of xs:date for?arg. Mapping: Returns an xs:integer between 1 and 31, both inclusive, representing the day component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.10 func:hours-from-time (adapted from fn:hours-from-time) Schema: (?arg; func:hours-from-time(?arg ) ) Intended domains: The value space of xs:time for?arg. Mapping: Returns an xs:integer between 0 and 23, both inclusive, representing the hours component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.11 func:minutes-from-time (adapted from fn:minutes-from-time) Schema: (?arg; func:minutes-from-time(?arg ) ) Intended domains: The value space of xs:time for?arg. Mapping: Returns an xs:integer between 0 and 59, both inclusive, representing the minutes component in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.12 func:seconds-from-time (adapted from fn:seconds-from-time) Schema: (?arg; func:seconds-from-time(?arg ) ) Intended domains: The value space of xs:time for?arg. Mapping: Returns an xs:decimal value greater than or equal to zero and less than 60, representing the seconds and fractional seconds in the localized value of?arg. If an argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.13 func:years-from-duration (adapted from fn:years-from-duration) Schema: (?arg; func:years-from-duration(?arg ) ) Intended domains: The union of the value spaces of datatypes castable to xs:yearMonthDuration according to the table in Section 17.1 of [XPath-Functions]. Mapping: Returns an xs:integer representing the years component in the value of?arg. The result is obtained by casting?arg to an xs:yearMonthDuration and then computing the years component. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.14 func:months-from-duration (adapted from fn:months-from-duration) Schema: (?arg; func:months-from-duration(?arg ) ) Intended domains: The union of the value spaces of datatypes castable to xs:yearMonthDuration according to the table in Section 17.1 of [XPath-Functions]. Mapping: Returns an xs:integer representing the months component in the value of?arg. The result is obtained by casting?arg to an xs:yearMonthDuration and then computing the months component. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.15 func:days-from-duration (adapted from fn:days-from-duration) Schema: (?arg; func:days-from-duration(?arg ) ) Intended domains: The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions]. Mapping: Returns an xs:integer representing the days component in the value of?arg. The result is obtained by casting?arg to an xs:dayTimeDuration and then computing the days component. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.16 func:hours-from-duration (adapted from fn:hours-from-duration) Schema: (?arg; func:hours-from-duration(?arg ) ) Intended domains: The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions]. Mapping: Returns an xs:integer representing the hours component in the value of?arg. The result is obtained by casting?arg to an xs:dayTimeDuration and then computing the hours component. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.17 func:minutes-from-duration (adapted from fn:minutes-from-duration) Schema: (?arg; func:minutes-from-duration(?arg ) ) Intended domains: The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions]. Mapping: Returns an xs:integer representing the minutes component in the value of?arg. The result is obtained by casting?arg to an xs:dayTimeDuration and then computing the minutes component. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.18 func:seconds-from-duration (adapted from fn:seconds-from-duration) Schema: (?arg; func:seconds-from-duration(?arg ) ) Intended domains: The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions]. Mapping: Returns an xs:decimal representing the seconds component in the value of?arg. The result is obtained by casting?arg to an xs:dayTimeDuration and then computing the seconds component. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. 3.6.1.19 func:timezone-from-dateTime (adapted from fn:timezone-from-dateTime) Schema: (?arg; func:timezone-from-dateTime(?arg ) ) Intended domains: The value space of xs:dateTime. Mapping: Returns the timezone component of?arg if any. If $arg has a timezone component, then the result is an xs:dayTimeDuration that indicates deviation from UTC; its value may range from +14:00 to -14:00 hours, both inclusive. If the argument value is outside of the intended domain, the value of the function is left unspecified and can vary from one semantic structure to another. The following two functions are defined analogously for intended domains xs:date and xs:time 3.6.1.20 func:timezone-from-date (adapted from fn:timezone-from-date) Schema: (?arg; func:timezone-from-date(?arg ) ) 3.6.1.21 func:timezone-from-time (adapted from fn:timezone-from-time) Schema: (?arg; func:timezone-from-time(?arg ) ) 3.6.1.22 func:subtract-dateTimes (adapted from op:subtract-dateTimes) Schema: (?arg₁?arg₂; func:subtract-dateTimes(?arg₁?arg₂ ) ) Subtracts two xs:dateTimes. Returns an xs:xs:dayTimeDuration. 3.6.1.23 func:subtract-dates (adapted from op:subtract-dates) Schema: (?arg₁?arg₂; func:subtract-dates(?arg₁?arg₂ ) ) Subtracts two xs:dates. Returns an xs:xs:dayTimeDuration. 3.6.1.24 func:subtract-times (adapted from op:subtract-times) Schema: (?arg₁?arg₂; func:subtract-times(?arg₁?arg₂ ) ) Subtracts two xs:times. Returns an xs:xs:dayTimeDuration. 3.6.1.25 func:add-yearMonthDurations (adapted from op:add-yearMonthDurations) Schema: (?arg₁?arg₂; func:add-yearMonthDurations(?arg₁?arg₂ ) ) Adds two xs:yearMonthDurations. Returns an xs:yearMonthDuration. 3.6.1.26 func:subtract-yearMonthDurations (adapted from op:subtract-yearMonthDurations) Schema: (?arg₁?arg₂; func:subtract-yearMonthDurations(?arg₁?arg₂ ) ) Subtracts one xs:yearMonthDuration from another. Returns an xs:yearMonthDuration. 3.6.1.27 func:multiply-yearMonthDuration (adapted from op:multiply-yearMonthDuration) Schema: (?arg₁?arg₂; func:multiply-yearMonthDuration(?arg₁?arg₂ ) ) Multiplies an xs:yearMonthDuration by an xs:double. Returns an xs:yearMonthDuration. 3.6.1.28 func:divide-yearMonthDuration (adapted from op:divide-yearMonthDuration) Schema: (?arg₁?arg₂; func:divide-yearMonthDuration(?arg₁?arg₂ ) ) Divides an xs:yearMonthDuration by an xs:double. Returns an xs:yearMonthDuration. 3.6.1.29 func:divide-by-yearMonthDuration (adapted from op:divide-yearMonthDuration-by-yearMonthDuration) Schema: (?arg₁?arg₂; func:divide-yearMonthDuration-by-yearMonthDuration(?arg₁?arg₂ ) ) Divides an xs:yearMonthDuration by an xs:yearMonthDuration. Returns an xs:decimal. 3.6.1.30 func:add-dayTimeDurations (adapted from op:add-dayTimeDurations) Schema: (?arg₁?arg₂; func:add-dayTimeDurations(?arg₁?arg₂ ) ) Adds two xs:dayTimeDurations. Returns an xs:dayTimeDuration. 3.6.1.31 func:subtract-dayTimeDurations (adapted from op:subtract-dayTimeDurations) Schema: (?arg₁?arg₂; func:subtract-dayTimeDurations(?arg₁?arg₂ ) ) Subtracts one xs:dayTimeDuration from another. Returns an xs:dayTimeDuration. 3.6.1.32 func:multiply-dayTimeDuration (adapted from op:multiply-dayTimeDuration) Schema: (?arg₁?arg₂; func:multiply-dayTimeDuration(?arg₁?arg₂ ) ) Multiplies an xs:dayTimeDuration by a xs:double. Returns an xs:dayTimeDuration. 3.6.1.33 func:divide-dayTimeDuration (adapted from op:divide-dayTimeDuration) Schema: (?arg₁?arg₂; func:divide-dayTimeDuration(?arg₁?arg₂ ) ) Divides an xs:dayTimeDuration by an xs:double. Returns an xs:dayTimeDuration. 3.6.1.34 func:divide-dayTimeDuration-by-dayTimeDuration (adapted from op:divide-dayTimeDuration-by-dayTimeDuration) Schema: (?arg₁?arg₂; func:divide-dayTimeDuration-by-dayTimeDuration(?arg₁?arg₂ ) ) Divides an xs:dayTimeDuration by an xs:dayTimeDuration. Returns an xs:decimal. 3.6.1.35 func:add-yearMonthDuration-to-dateTime (adapted from op:add-yearMonthDuration-to-dateTime) Schema: (?arg₁?arg₂; func:add-yearMonthDuration-to-dateTime(?arg₁?arg₂ ) ) Adds a xs:yearMonthDuration (?arg₂) to a xs:dateTime (?arg₁). Returns an xs:dateTime. 3.6.1.36 func:add-yearMonthDuration-to-date (adapted from op:add-yearMonthDuration-to-date) Schema: (?arg₁?arg₂; func:add-yearMonthDuration-to-date(?arg₁?arg₂ ) ) Adds a xs:yearMonthDuration (?arg₂) to a xs:date (?arg₁). Returns an xs:date. 3.6.1.37 func:add-dayTimeDuration-to-dateTime (adapted from op:add-dayTimeDuration-to-dateTime) Schema: (?arg₁?arg₂; func:add-dayTimeDuration-to-dateTime(?arg₁?arg₂ ) ) Adds a xs:dayTimeDuration (?arg₂) to a xs:dateTime (?arg₁). Returns an xs:dateTime. 3.6.1.38 func:add-dayTimeDuration-to-date (adapted from op:add-dayTimeDuration-to-date) Schema: (?arg₁?arg₂; func:add-dayTimeDuration-to-date(?arg₁?arg₂ ) ) Adds a xs:dayTimeDuration (?arg₂) to a xs:date (?arg₁). Returns an xs:date. 3.6.1.39 func:add-dayTimeDuration-to-time (adapted from op:add-dayTimeDuration-to-time) Schema: (?arg₁?arg₂; func:add-dayTimeDuration-to-time(?arg₁?arg₂ ) ) Adds a xs:dayTimeDuration (?arg₂) to a xs:time (?arg₁). Returns an xs:time. 3.6.1.40 func:subtract-yearMonthDuration-from-dateTime (adapted from op:subtract-yearMonthDuration-from-dateTime) Schema: (?arg₁?arg₂; func:subtract-yearMonthDuration-from-dateTime(?arg₁?arg₂ ) ) Subtracts a xs:yearMonthDuration (?arg₂) from a xs:dateTime (?arg₁). Returns an xs:dateTime. 3.6.1.41 func:subtract-yearMonthDuration-from-date (adapted from op:subtract-yearMonthDuration-from-date) Schema: (?arg₁?arg₂; func:subtract-yearMonthDuration-from-date(?arg₁?arg₂ ) ) Subtracts a xs:yearMonthDuration (?arg₂) from a xs:date (?arg₁). Returns an xs:date. 3.6.1.42 func:subtract-dayTimeDuration-from-dateTime (adapted from op:subtract-dayTimeDuration-from-dateTime) Schema: (?arg₁?arg₂; func:subtract-dayTimeDuration-from-dateTime(?arg₁?arg₂ ) ) Subtracts a xs:dayTimeDuration (?arg₂) from a xs:dateTime (?arg₁). Returns an xs:dateTime. 3.6.1.43 func:subtract-dayTimeDuration-from-date (adapted from op:subtract-dayTimeDuration-from-date) Schema: (?arg₁?arg₂; func:subtract-dayTimeDuration-from-date(?arg₁?arg₂ ) ) Subtracts a xs:dayTimeDuration (?arg₂) from a xs:date (?arg₁). Returns an xs:date. 3.6.1.44 func:subtract-dayTimeDuration-from-time (adapted from op:subtract-dayTimeDuration-from-time) Schema: (?arg₁?arg₂; func:subtract-dayTimeDuration-from-time(?arg₁?arg₂ ) ) Subtracts a xs:dayTimeDuration (?arg₂) from a xs:time (?arg₁). Returns an xs:time. 3.6.2 Predicates on Dates, Times, and Durations 3.6.2.1 pred:dateTime-equal (adapted from op:dateTime-equal) Schema: (?arg₁?arg₂; pred:dateTime-equal(?arg₁?arg₂) ) Intended domains: The value space of xs:dateTime for both arguments. Mapping: where I_truth I_external(?arg₁?arg₂; pred:dateTime-equal(?arg₁?arg₂ ) )(s₁ s₂) = t if and only if op:dateTime-equal(s₁, s₂) returns true, as defined in [XPath-Functions], f in case false is returned. If an argument value is outside of the intended domain, the truth value of the function is left unspecified and can vary from one semantic structure to another. The following schemata for comparison operators are defined analogously with respect to their corresponding operators as defined in [XPath-Functions], where the intended domain for both arguments is implicit by the operator name and we only give additional details on intended domains and mapping as needed. 3.6.2.2 pred:dateTime-less-than (adapted from op:dateTime-less-than) Schema: (?arg₁?arg₂; pred:dateTime-less-than(?arg₁?arg₂ ) ) 3.6.2.3 pred:dateTime-greater-thanl (adapted from op:dateTime-greater-than) Schema: (?arg₁?arg₂; pred:dateTime-greater-than(?arg₁?arg₂ ) ) 3.6.2.4 pred:date-equal (adapted from op:date-equal) Schema: (?arg₁?arg₂; pred:date-equal(?arg₁?arg₂) ) 3.6.2.5 pred:date-less-than (adapted from op:date-less-than) Schema: (?arg₁?arg₂; pred:date-less-than(?arg₁?arg₂ ) ) 3.6.2.6 pred:date-greater-than (adapted from op:date-greater-than) Schema: (?arg₁?arg₂; pred:date-greater-than(?arg₁?arg₂ ) ) 3.6.2.7 pred:time-equal (adapted from op:time-equal) Schema: (?arg₁?arg₂; pred:time-equal(?arg₁?arg₂) ) 3.6.2.8 pred:time-less-than (adapted from op:time-less-than) Schema: (?arg₁?arg₂; pred:time-less-than(?arg₁?arg₂ ) ) 3.6.2.9 pred:time-greater-than (adapted from op:time-greater-than) Schema: (?arg₁?arg₂; pred:time-greater-than(?arg₁?arg₂ ) ) 3.6.2.10 pred:duration-equal (adapted from op:duration-equal) Schema: (?arg₁?arg₂; pred:duration-equal(?arg₁?arg₂) ) Intended domains: The union of the value spaces of xs:dayTimeDuration and xs:yearMonthDuration for both arguments. 3.6.2.11 pred:dateTimeDuration-less-than (adapted from op:dayTimeDuration-less-than) Schema: (?arg₁?arg₂; pred:dayTimeDuration-less-than(?arg₁?arg₂ ) ) 3.6.2.12 pred:dayTimeDuration-greater-than (adapted from op:dayTimeDuration-greater-than) Schema: (?arg₁?arg₂; pred:dayTimeDuration-greater-than(?arg₁?arg₂ ) ) 3.6.2.13 pred:yearMonthDuration-less-than (adapted from op:yearMonthDuration-less-than) Schema: (?arg₁?arg₂; pred:yearMonthDuration-less-than(?arg₁?arg₂ ) ) 3.6.2.14 pred:yearMonthDuration-greater-than (adapted from op:yearMonthDuration-greater-than) Schema: (?arg₁?arg₂; pred:yearMonthDuration-greater-than(?arg₁?arg₂ ) ) 3.6.2.15 pred:dateTime-not-equal Schema: (?arg₁?arg₂; pred:dateTime-not-equal(?arg₁?arg₂) ) 3.6.2.16 pred:dateTime-less-than-or-equal Schema: (?arg₁?arg₂; pred:dateTime-less-than-or-equal(?arg₁?arg₂) ) 3.6.2.17 pred:dateTime-greater-than-or-equal Schema: (?arg₁?arg₂; pred:dateTime-greater-than-or-equal(?arg₁?arg₂) ) 3.6.2.18 pred:date-not-equal Schema: (?arg₁?arg₂; pred:date-not-equal(?arg₁?arg₂) ) 3.6.2.19 pred:date-less-than-or-equal Schema: (?arg₁?arg₂; pred:date-less-than-or-equal(?arg₁?arg₂) ) 3.6.2.20 pred:date-greater-than-or-equal Schema: (?arg₁?arg₂; pred:date-greater-than-or-equal(?arg₁?arg₂) ) 3.6.2.21 pred:time-not-equal Schema: (?arg₁?arg₂; pred:time-not-equal(?arg₁?arg₂) ) 3.6.2.22 pred:time-less-than-or-equal Schema: (?arg₁?arg₂; pred:time-less-than-or-equal(?arg₁?arg₂) ) 3.6.2.23 pred:time-greater-than-or-equal Schema: (?arg₁?arg₂; pred:time-greater-than-or-equal(?arg₁?arg₂) ) 3.6.2.24 pred:duration-not-equal Schema: (?arg₁?arg₂; pred:duration-not-equal(?arg₁?arg₂) ) Editor's Note: No less-than-or-equal or greater-than-or-equal predicates are defined in this draft for durations, since there are no separate op:dayTimeDuration-equal nor op:yearMonthDuration-equalpredicates in [XPath-Functions], but only a common predicate op:duration-equal. Future versions of this working draft may resolve this by introducing new equality predicates pred:dayTimeDuration-equal and pred:yearMonthDuration-equal with restricted intended domains. 3.7 Functions and Predicates on rdf:XMLLiterals Editor's Note: Predicates for rdf:XMLLiteral such as at least comparison predicates (equals, not-equals) are still under discussion in the working group. 3.8 Functions and Predicates on rif:text The following function serves to extract the language tag from values in the rif:text value space. 3.8.1 func:lang (adapted from SPARQL's lang function) Schema: (?arg; func:lang(?arg ) ) Intended domains: The value space of rif:text for?arg. Mapping: I_external(?arg; func:lang(?arg ) )(s) = res such that res is the language tag string of s, if s is in the value space of rif:text and ""^^xs:string otherwise. Editor's Note: The current name of this function is still under disscussion in the working group. Alternative proposals include e.g. func:lang-from-text, which follows the XPath/XQuery naming convention for extraction functions from datatypes than the SPARQL naming convention. Editor's Note: We have not yet included comparison predicates (equal, less-than, greater-than, or compare ...) for rif:text. Future versions of this document might introduce these. 4 References [BCP-47] BCP 47 - Tags for the Identification of Languages, A. Phillips, M. Davis, IETF, Sep 2006, ftp://ftp.rfc-editor.org/in-notes/bcp/bcp47.txt. [BLD] RIF Basic Logic Dialect Harold Boley, Michael Kifer, eds. W3C Editor's Draft, 22 September 2008, http://www.w3.org/2005/rules/wg/draft/ED-rif-bld-20080922/. Latest version available at http://www.w3.org/2005/rules/wg/draft/rif-bld/. [CURIE] CURIE Syntax 1.0: A syntax for expressing Compact URIs, Mark Birbeck, Shane McCarron. W3C Working Draft 2 April 2008. Available at http://www.w3.org/TR/curie/. [RDF-CONCEPTS] Resource Description Framework (RDF): Concepts and Abstract Syntax, Klyne G., Carroll J. (Editors), W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/. Latest version available at http://www.w3.org/TR/rdf-concepts/. [RDF-SEMANTICS] RDF Semantics, Patrick Hayes, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-mt-20040210/. Latest version available at http://www.w3.org/TR/rdf-mt/. [RDF-SCHEMA] RDF Vocabulary Description Language 1.0: RDF Schema, Brian McBride, Editor, W3C Recommendation 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-schema-20040210/. Latest version available at http://www.w3.org/TR/rdf-schema/. [RFC-3986] RFC 3986 - Uniform Resource Identifier (URI): Generic Syntax, T. Berners-Lee, R. Fielding, L. Masinter, IETF, January 2005, http://www.ietf.org/rfc/rfc3986.txt. [RFC-3987] RFC 3987 - Internationalized Resource Identifiers (IRIs), M. Duerst and M. Suignard, IETF, January 2005, http://www.ietf.org/rfc/rfc3987.txt. [SPARQL] SPARQL Query Language for RDF, W3C Recommendation, World Wide Web Consortium, 12 January 2008, http://www.w3.org/TR/2008/REC-rdf-sparql-query-20080115/. Latest version available at http://www.w3.org/TR/rdf-sparql-query/. [XDM] XQuery 1.0 and XPath 2.0 Data Model (XDM), W3C Recommendation, World Wide Web Consortium, 23 January 2007. This version is http://www.w3.org/TR/2007/REC-xpath-datamodel-20070123/. Latest version available at http://www.w3.org/TR/xpath-datamodel/. [XML-NS] Namespaces in XML 1.1 (Second Edition), W3C Recommendation, World Wide Web Consortium, 16 August 2006, http://www.w3.org/TR/2006/REC-xml-names11-20060816/. Latest version available at http://www.w3.org/TR/xml-names11/. [XML-SCHEMA2] XML Schema Part 2: Datatypes Second Edition, W3C Recommendation, World Wide Web Consortium, 28 October 2004, http://www.w3.org/TR/2004/REC-xmlschema-2-20041028/. Latest version available at http://www.w3.org/TR/xmlschema-2/. [XPath-Functions] XQuery 1.0 and XPath 2.0 Functions and Operators, W3C Recommendation, World Wide Web Consortium, 23 January 2007, http://www.w3.org/TR/2007/REC-xpath-functions-20070123/. Latest version available at http://www.w3.org/TR/xpath-functions/. 5 Appendix: Schemas for Externally Defined Terms This section is an edited copy of a section from RIF Framework for Logic Dialects. It is reproduced here for convenience of readers familiar with the RIF-BLD document who might not have studied RIF-FLD. This section defines external schemas, which serve as templates for externally defined terms. These schemas determine which externally defined terms are acceptable in a RIF dialect. Externally defined terms include RIF built-ins, but are more general. They are designed to also accommodate the ideas of procedural attachments and querying of external data sources. Because of the need to accommodate many difference possibilities, the RIF logical framework supports a very general notion of an externally defined term. Such a term is not necessarily a function or a predicate -- it can be a frame, a classification term, and so on. Definition (Schema for external term). An external schema is a statement of the form (?X₁ ...?X_n;) where is a constant, a positional, named-argument, or a frame term. ?X₁ ...?X_n is a list of all distinct variables that occur in The names of the variables in an external schema are immaterial, but their order is important. For instance, (?X?Y;?X[foo->?Y]) and (?V?W;?V[foo->?W]) are considered to be indistinguishable, but (?X?Y;?X[foo->?Y]) and (?Y?X;?X[foo->?Y]) are viewed as different schemas. A term t is an instance of an external schema (?X₁ ...?X_n;) iff t can be obtained from by a simultaneous substitution ?X₁/s₁ ...?X_n/s_n of the variables ?X₁ ...?X_n with terms s₁ ... s_n, respectively. Some of the terms s_i can be variables themselves. For example, ?Z[foo->f(a?P)] is an instance of (?X?Y;?X[foo->?Y]) by the substitution ?X/?Z?Y/f(a?P). ☐ Observe that a variable cannot be an instance of an external schema, since in the above definition cannot be a variable. It will be seen later that this implies that a term of the form External(?X) is not well-formed in RIF. The intuition behind the notion of an external schema, such as (?X?Y;?X["foo"^^xs:string->?Y]) or (?V; "pred:isTime"^^rif:iri(?V)), is that ?X["foo"^^xs:string->?Y] or "pred:isTime"^^rif:iri(?V) are invocation patterns for querying external sources, and instances of those schemas correspond to concrete invocations. Thus, External("http://foo.bar.com"^^rif:iri["foo"^^xs:string->"123"^^xs:integer]) and External("pred:isTime"^^rif:iri("22:33:44"^^xs:time) are examples of invocations of external terms -- one querying an external source and another invoking a built-in. Definition (Coherent set of external schemas). A set of external schemas is coherent if there is no term, t, that is an instance of two distinct schemas in the set. ☐ The intuition behind this notion is to ensure that any use of an external term is associated with at most one external schema. This assumption is relied upon in the definition of the semantics of externally defined terms. Note that the coherence condition is easy to verify syntactically and that it implies that schemas like (?X?Y;?X[foo->?Y]) and (?Y?X;?X[foo->?Y]), which differ only in the order of their variables, cannot be in the same coherent set. It is important to keep in mind that external schemas are not part of the language in RIF, since they do not appear anywhere in RIF statements. Instead, they are best thought of as part of the grammar of the language.

RIF Datatypes and Built-Ins 1.0

W3C Editor's Draft 22 September 2008

Abstract

Status of this Document

May Be Superseded

Set of Documents

Please Comment By 2008-09-25

No Endorsement

Patents

Contents

1 Constants, Symbol Spaces, and Datatypes

1.1 Constants and Symbol Spaces

1.2 The Base and Prefix Directives

1.2.1 Symbol Spaces

1.2.2 Shortcuts for Constants in RIF's Presentation Syntax

1.2.3 Relative IRIs

1.3 Primitive Datatypes

2 Syntax and Semantics of Built-ins

2.1 Syntax of Built-ins

2.2 Semantics of Built-ins

3 List of RIF Built-in Predicates and Functions

3.1 Guard Predicates for Datatypes

3.1.1 pred:isInteger

3.1.2 pred:isDecimal

3.1.3 pred:isDouble

3.1.4 pred:isString

3.1.5 pred:isTime

3.1.6 pred:isDate

3.1.7 pred:isDateTime

3.1.8 pred:isDayTimeDuration

3.1.9 pred:isYearMonthDuration

3.1.10 pred:isXMLLiteral

3.1.11 pred:isText

3.2 Negative Guard Predicates for Datatypes

3.2.1 pred:isNotInteger

3.2.2 pred:isNotDecimal

3.2.3 pred:isNotDouble

3.2.4 pred:isNotString

3.2.5 pred:isNotTime

3.2.6 pred:isNotDate

3.2.7 pred:isNotDateTime

3.2.8 pred:isNotDayTimeDuration

3.2.9 pred:isNotYearMonthDuration

3.2.10 pred:isNotXMLLiteral

3.2.11 pred:isNotText

3.3 Cast Functions and Conversion Predicates for Datatypes and rif:iri

3.3.1 xs:double, xs:integer, xs:decimal, xs:time, xs:date, xs:date,xs:dateTime, xs:dayTimeDuration, xs:yearMonthDuration

3.3.2 xs:string

3.3.3 rdf:XMLLiteral

3.3.4 rif:text

3.3.5 pred:iri-to-string

3.4 Numeric Functions and Predicates

3.4.1 Numeric Functions

3.4.1.1 func:numeric-add (adapted from op:numeric-add)

3.4.1.2 func:numeric-subtract (adapted from op:numeric-subtract)

3.4.1.3 func:numeric-multiply (adapted from op:numeric-multiply)

3.4.1.4 func:numeric-divide (adapted from op:numeric-divide)

3.4.1.5 func:numeric-integer-divide (adapted from op:numeric-integer-divide)

3.4.1.6 func:numeric-mod (adapted from op:numeric-mod)

3.4.2 Numeric Predicates

3.4.2.1 pred:numeric-equal (adapted from op:numeric-equal)

3.4.2.2 pred:numeric-less-than (adapted from op:numeric-less-than)

3.4.2.3 pred:numeric-greater-than (adapted from op:numeric-greater-than)

3.4.2.4 pred:numeric-not-equal

3.4.2.5 pred:numeric-less-than-or-equal

3.4.2.6 pred:numeric-greater-than-or-equal

3.5 Functions and Predicates on Strings

3.5.1 Functions on Strings

3.5.1.1 func:compare (adapted from fn:compare)

3.5.1.2 func:concat (adapted from fn:concat)

3.5.1.3 func:string-join (adapted from fn:string-join)

3.5.1.4 func:substring (adapted from fn:substring)

3.5.1.5 func:string-length (adapted from fn:string-length)

3.5.1.6 func:upper-case (adapted from fn:upper-case)

3.5.1.7 func:lower-case (adapted from fn:lower-case)

3.5.1.8 func:encode-for-uri (adapted from fn:encode-for-uri)

3.5.1.9 func:iri-to-uri (adapted from fn:iri-to-uri)

3.5.1.10 func:escape-html-uri (adapted from fn:escape-html-uri)

3.5.1.11 func:substring-before (adapted from fn:substring-before)

3.5.1.12 func:substring-after (adapted from fn:substring-after)

3.1.1 `pred:isInteger`

3.1.2 `pred:isDecimal`

3.1.3 `pred:isDouble`

3.1.4 `pred:isString`

3.1.5 `pred:isTime`

3.1.6 `pred:isDate`

3.1.7 `pred:isDateTime`

3.1.8 `pred:isDayTimeDuration`

3.1.9 `pred:isYearMonthDuration`

3.1.10 `pred:isXMLLiteral`

3.1.11 `pred:isText`

3.2.1 `pred:isNotInteger`

3.2.2 `pred:isNotDecimal`

3.2.3 `pred:isNotDouble`

3.2.4 `pred:isNotString`

3.2.5 `pred:isNotTime`

3.2.6 `pred:isNotDate`

3.2.7 `pred:isNotDateTime`

3.2.8 `pred:isNotDayTimeDuration`

3.2.9 `pred:isNotYearMonthDuration`

3.2.10 `pred:isNotXMLLiteral`

3.2.11 `pred:isNotText`

3.3 Cast Functions and Conversion Predicates for Datatypes and `rif:iri`

3.3.1 `xs:double`, `xs:integer`, `xs:decimal`, `xs:time`, `xs:date`, `xs:date`,`xs:dateTime`, `xs:dayTimeDuration`, `xs:yearMonthDuration`

3.3.2 `xs:string`

3.3.3 `rdf:XMLLiteral`

3.3.4 `rif:text`

3.3.5 `pred:iri-to-string`

3.4.1.1 `func:numeric-add` (adapted from `op:numeric-add`)

3.4.1.2 `func:numeric-subtract` (adapted from `op:numeric-subtract`)

3.4.1.3 `func:numeric-multiply` (adapted from `op:numeric-multiply`)

3.4.1.4 `func:numeric-divide` (adapted from `op:numeric-divide`)

3.4.1.5 `func:numeric-integer-divide` (adapted from `op:numeric-integer-divide`)

3.4.1.6 `func:numeric-mod` (adapted from `op:numeric-mod`)

3.4.2.1 `pred:numeric-equal` (adapted from `op:numeric-equal`)

3.4.2.2 `pred:numeric-less-than` (adapted from `op:numeric-less-than`)

3.4.2.3 `pred:numeric-greater-than` (adapted from `op:numeric-greater-than`)

3.4.2.4 `pred:numeric-not-equal`

3.4.2.5 `pred:numeric-less-than-or-equal`

3.4.2.6 `pred:numeric-greater-than-or-equal`

3.5.1.1 `func:compare` (adapted from `fn:compare`)

3.5.1.2 `func:concat` (adapted from `fn:concat`)

3.5.1.3 `func:string-join` (adapted from `fn:string-join`)

3.5.1.4 `func:substring` (adapted from `fn:substring`)

3.5.1.5 `func:string-length` (adapted from `fn:string-length`)

3.5.1.6 `func:upper-case` (adapted from `fn:upper-case`)

3.5.1.7 `func:lower-case` (adapted from `fn:lower-case`)

3.5.1.8 `func:encode-for-uri` (adapted from `fn:encode-for-uri`)

3.5.1.9 `func:iri-to-uri` (adapted from `fn:iri-to-uri`)

3.5.1.10 `func:escape-html-uri` (adapted from `fn:escape-html-uri`)

3.5.1.11 `func:substring-before` (adapted from `fn:substring-before`)

3.5.1.12 `func:substring-after` (adapted from `fn:substring-after`)

3.5.1.13 `func:replace` (adapted from `fn:replace`)

3.5.2.1 `pred:contains` (adapted from `fn:contains`)

3.5.2.2 `pred:starts-with` (adapted from `fn:starts-with`)

3.5.2.3 `pred:ends-with` (adapted from `fn:ends-with`)

3.5.2.4 `pred:matches` (adapted from `fn:matches`)

3.6.1.1 `func:year-from-dateTime` (adapted from `fn:year-from-dateTime`)

3.6.1.2 `func:month-from-dateTime` (adapted from `fn:month-from-dateTime`)

3.6.1.3 `func:day-from-dateTime` (adapted from `fn:day-from-dateTime`)

3.6.1.4 `func:hours-from-dateTime` (adapted from `fn:hours-from-dateTime`)

3.6.1.5 `func:minutes-from-dateTime` (adapted from `fn:minutes-from-dateTime`)

3.6.1.6 `func:seconds-from-dateTime` (adapted from `fn:seconds-from-dateTime`)

3.6.1.7 `func:year-from-date` (adapted from `fn:year-from-date`)

3.6.1.8 `func:month-from-date` (adapted from `fn:month-from-date`)

3.6.1.9 `func:day-from-date` (adapted from `fn:day-from-date`)

3.6.1.10 `func:hours-from-time` (adapted from `fn:hours-from-time`)

3.6.1.11 `func:minutes-from-time` (adapted from `fn:minutes-from-time`)

3.6.1.12 `func:seconds-from-time` (adapted from `fn:seconds-from-time`)

3.6.1.13 `func:years-from-duration` (adapted from `fn:years-from-duration`)

3.6.1.14 `func:months-from-duration` (adapted from `fn:months-from-duration`)

3.6.1.15 `func:days-from-duration` (adapted from `fn:days-from-duration`)

3.6.1.16 `func:hours-from-duration` (adapted from `fn:hours-from-duration`)

3.6.1.17 `func:minutes-from-duration` (adapted from `fn:minutes-from-duration`)

3.6.1.18 `func:seconds-from-duration` (adapted from `fn:seconds-from-duration`)

3.6.1.19 `func:timezone-from-dateTime` (adapted from `fn:timezone-from-dateTime`)

3.6.1.20 `func:timezone-from-date` (adapted from `fn:timezone-from-date`)

3.6.1.21 `func:timezone-from-time` (adapted from `fn:timezone-from-time`)

3.6.1.22 `func:subtract-dateTimes` (adapted from `op:subtract-dateTimes`)

3.6.1.23 `func:subtract-dates` (adapted from `op:subtract-dates`)