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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 adopted from [XPath-Functions]. The rdf:text datatype as well as functions and operators associated with that datatype are adopted from [RDF-TEXT].
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.
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.
The Base directive defines a syntactic shortcut for expanding relative IRIs into full IRIs.
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:
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.
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 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.
The lexical spaces of the above symbol spaces are defined in the document [XML-SCHEMA2].
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].
This symbol space represents text strings with a language tag attached. The lexical space of rdf:text is defined in the document [RDF-TEXT].
This symbol space represents XML content. The lexical space of rdf:XMLLiteral is defined in the document [RDF-CONCEPTS].
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.
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.
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 | '"' UNICODESTRING '"' '@' languageTag // shortcut for "...@..."^^rdf:text
The EBNF grammar relies on reuse of nonterminals defined in the following grammar productions from other documents:
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.
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)
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
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.
Their value spaces and the lexical-to-value-space mappings are defined as follows:
Note that the value space and the lexical-to-value-space mapping for rdf:text defined here are compatible with RDF's semantics for string literals with named tags [RDF-SEMANTICS]. Moreover, the value space and the lexical-to-value-space mapping for xs:string are compatible with RDF's semantics for plain literals. RIF implementations MAY choose to interpret xs:string and its subtypes as subtypes of rdf:text following Section 3.1 of [RDF-TEXT], i.e., interpreting strings as texts with an empty language tag.
Editor's Note: Whether or not we allow the treatment of xs:string as a subtype of rdf:text in RIF implementations is still under discussion, cf. the mail thread starting at http://lists.w3.org/Archives/Public/public-rif-wg/2008Nov/0067.html.
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
( ?X_{1} ... ?X_{n}; f(?X_{1} ... ?X_{n}) )
Here f(?X_{1} ... ?X_{n}) is the actual term that is used to refer to the built-in (in expressions of the form External(f(?X_{1} ... ?X_{n}))) and ?X_{1} ... ?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.
The semantics of external terms in RIF-FLD and RIF-BLD is defined using two mappings: I_{external} and I_{truth} ο I_{external}.
If σ represents a built-in function, I_{external}(σ) must be that function.
For each built-in function with external schema σ, the present document specifies the mapping I_{external}(σ).
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 σ, RIF-FLD and RIF-BLD require that the truth-valued mapping I_{truth} ο I_{external}(σ) must agree with the specification of the corresponding built-in predicate.
For each RIF built-in predicate with schema σ, the present document specifies I_{truth} ο I_{external}(σ).
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:
As explained in Section Semantics of Built-ins, this corresponds to the mapping I_{external}(σ) in the formal semantics of RIF-FLD and RIF-BLD, where σ is the external schema of the built-in.
As explained in Section Semantics of Built-ins, this corresponds to the mapping I_{truth} ο I_{external}(σ) in the formal semantics of RIF-FLD and RIF-BLD, where σ is the external schema 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}(σ)(a_{1} ... a_{n}) can vary from one semantic structure to another. Similarly, I_{truth} ο I_{external}(σ)(a_{1} ... 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.
RIF defines guard predicates for all datatypes in Section Primitive Datatypes.
( ?arg_{1}; pred:isDATATYPE ( ?arg_{1} ) )
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 a similar naming convention where applicable without creating ambiguities with predicate names defined in the present document. Particularly, upcoming W3C specifications MAY - but 3rd party dialects MUST NOT - reuse the pred: namespace for such guard predicates.
Editor's Note: The formulation of the clause on namespace-reuse is under discussion, for instance, whether we shall allow guards and negative guards for all of the XML Schema primitive datatypes under the pred: namespace.
Guard predicates do not depend on a specific intended domain.
I_{truth} ο I_{external}( ?arg_{1}; pred:isDATATYPE ( ?arg_{1} ) )(s_{1}) = t if and only if s_{1} is in the value space of DATATYPE and f otherwise.
Accordingly, the following schemas are defined.
( ?arg_{1}; pred:isInteger( ?arg_{1} ) )
( ?arg_{1}; pred:isDecimal ( ?arg_{1} ) )
( ?arg_{1}; pred:isDouble ( ?arg_{1} ) )
( ?arg_{1}; pred:isString ( ?arg_{1} ) )
( ?arg_{1}; pred:isTime ( ?arg_{1} ) )
( ?arg_{1}; pred:isDate ( ?arg_{1} ) )
( ?arg_{1}; pred:isDateTime ( ?arg_{1} ) )
( ?arg_{1}; pred:isDayTimeDuration ( ?arg_{1} ) )
( ?arg_{1}; pred:isYearMonthDuration ( ?arg_{1} ) )
( ?arg_{1}; pred:isXMLLiteral ( ?arg_{1} ) )
( ?arg_{1}; pred:isText ( ?arg_{1} ) )
Future dialects may extend this list of guards to other datatypes, but RIF does not require guards for all datatypes.
Likewise, RIF defines negative guard predicates for all datatypes in Section Primitive Datatypes.
( ?arg_{1}; pred:isNotDATATYPE ( ?arg_{1} ) )
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 a similar naming convention where applicable without creating ambiguities with predicate names defined in the present document. Particularly, upcoming W3C specifications MAY, but 3rd party dialects MUST NOT reuse, the pred: namespace for such negative guard predicates.
Editor's Note: The formulation of the clause on namespace-reuse is under discussion, for instance, whether we shall allow guards and negative guards for all of the XML Schema primitive datatypes under the pred: namespace.
Negative guard predicates do not depend on a specific intended domain.
I_{truth} ο I_{external}( ?arg_{1}; pred:isNotDATATYPE ( ?arg_{1} ) )(s_{1}) = f if and only if s_{1} is in the value space of DATATYPE and t otherwise.
Accordingly, the following schemas are defined.
( ?arg_{1}; pred:isNotInteger ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotDecimal ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotDouble ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotString ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotTime ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotDate ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotDateTime ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotDayTimeDuration ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotYearMonthDuration ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotXMLLiteral ( ?arg_{1} ) )
( ?arg_{1}; pred:isNotText ( ?arg_{1} ) )
Future dialects may extend this list of guards to other datatypes, but RIF does not require negative guards for all datatypes.
In the following, we adapt several cast functions according to the conversions defined in Section 17.1 of [XPath-Functions]. Note that some of these conversions are only partially defined, which affects the intended domains of these cast functions.
Editor's Note: Due to the subtle differences in casting, e.g., concerning error handling, between RIF and [XPath-Functions], the definitions of cast functions might still need refinement in terms of defining the intended domains in future versions of this draft. Also, the definition of the mappings need refinement.
Likewise we define a conversion predicate useful for converting between rif:iri constants and strings, as well as a predicate to check the datatype of a constant.
( ?arg_{1}; xs:double ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:double according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:double ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:double according to Section 17.1 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.
( ?arg_{1}; xs:integer ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:integer according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:integer ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:integer according to Section 17.1 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.
( ?arg_{1}; xs:decimal ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:decimal according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:decimal ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:decimal according to Section 17.1 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.
( ?arg_{1}; xs:time ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:time according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:time ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:time according to Section 17.1 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.
( ?arg_{1}; xs:date ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:date according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:date ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:date according to Section 17.1 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.
( ?arg_{1}; xs:dateTime ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:dateTime according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:dateTime ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:dateTime according to Section 17.1 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.
( ?arg_{1}; xs:dayTimeDuration ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:dayTimeDuration according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:dayTimeDuration ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:dayTimeDuration according to Section 17.1 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.
( ?arg_{1}; xs:yearMonthDuration ( ?arg_{1} ) )
The union of the (subsets of the) value spaces of datatypes castable to xs:yearMonthDuration according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:yearMonthDuration ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:yearMonthDuration according to Section 17.1 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.
( ?arg_{1}; xs:string ( ?arg_{1} ) )
The union of the value spaces of datatypes castable to xs:string according to Section 17.1 of [XPath-Functions].
I_{external}( ?arg_{1}; xs:string> ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the conversion of s_{1} to the value space of xs:string according to the table in Section 17.1 of [XPath-Functions], in case s_{1} is in the value space of a datatype mentioned in that table.
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.
Note: Since RIF implementations MAY choose to interpret xs:string and its subtypes as subtypes of rdf:text following Section 3.1 of [RDF-TEXT], in such implementations this cast function also serves for conversions to rdf:text.
( ?arg_{1}; rdf:XMLLiteral ( ?arg_{1} ) )
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
I_{external}( ?arg_{1}; xs:XMLLiteral ( ?arg_{1} ) )(s_{1}) = s_{1}' such that s_{1}' is the XMLLiteral corresponding to the given string s_{1}.
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.
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 introduce a built-in predicate which supports such conversions.
( ?arg_{1} ?arg_{2}; pred:iri-string ( ?arg_{1}, ?arg_{2} ) )
The first argument is not restricted by a specific domain, the second argument is the value space of xs:string.
I_{external}( ?arg_{1} ?arg_{2}; pred:iri-string ( ?arg_{1} ?arg_{2} ) )(iri_{1} str_{1}) = t if and only if str_{1} is a string in the lexical space of rif:iri and iri_{1} is an element of the domain such that I( "str_{1}"^^rif:iri ) = iri_{1} holds in the current interpretation.
Note that this definition restricts allowed RIF interpretations in such a way that the interpretation of pred:iri-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-string( ?foafTelIri ?foafTelString ) ) )
Extractions of the Datatype from a constant cannot be defined by a function (like for instance in SPARQL's datatype function) since the value spaces of datatypes may overlap.
To this end, we introduce a built-in predicate which supports extraction of the datatypes for a constant at hand.
( ?arg_{1} ?arg_{2}; pred:hasDatatype ( ?arg_{1}, ?arg_{2} ) )
None of the arguments is restricted to a specific domain.
I_{external}( ?arg_{1} ?arg_{2}; pred:hasDatatype ( ?arg_{1} ?arg_{2} ) )(const_{1} iri_{1}) = t if and only if in the current interpretation iri_{1} = I( "DatatypeIRI"^^rif:iri ) where DatatypeIRI is the IRI identifier of a datatype d and const_{1} is in the value space of d.
Editor's Note: It is still under discussion in the WG whether this predicate should restrict the domain of the second argument rather to strings that represent valid IRIs than just being true for any constants that have the same interpretation as the particular rif:iri representing the datatype.
This predicate can be usable for extracting the datatype from a constant but due to the overlap of the calue spaces of datatypes, such extraction is not necessarily unique; for example, the following is entailed in any RIF ruleset:
And ( External( pred:hasDatatype( "1.0"^^xs:decimal xs:decimal ) ) External( pred:hasDatatype( "1.0"^^xs:decimal xs:integer ) ) External( pred:hasDatatype( "1.0"^^xs:decimal xs:double ) ) )
Editor's Note: Note that this example shows that pred:hasDatatype is not adequate for emulating SPARQL's datatype function http://www.w3.org/TR/rdf-sparql-query/#func-datatype, cf. the mail thread starting at http://lists.w3.org/Archives/Public/public-rif-wg/2008Nov/0067.html
The following example shows that also whether or not a RIF implementation that treats xs:string as a subtype of rdf:text may affect the entailments for pred:hasDatatype:
Forall ?X ( ?P [ ex:nameType -> ?D ] :- And ( ?P[ foaf:name -> ?N ] External( pred:hasDatatype( ?N ?D ) ) ) ex:alice [foaf:name -> "Alice"]
In a RIF implementation that treats xs:string as a subtype of rdf:text, following Section 3.1 of [RDF-TEXT], this ruleset would entail both ex:alice [ex:nameType -> rdf:text] and ex:alice [ex:nameType -> xs:string].
Editor's Note: Whether or not we allow the treatment of xs:string as a subtype of rdf:text in RIF implementations is still under discussion, cf. the mail thread starting at http://lists.w3.org/Archives/Public/public-rif-wg/2008Nov/0067.html.
The following functions and predicates are adapted from the respective numeric functions and operators in [XPath-Functions].
(?arg_{1} ?arg_{2}; func:numeric-add(?arg_{1} ?arg_{2}))
The value spaces of xs:integer, xs:double, or xs:decimal for both arguments.
When both s_{1} and s_{2} belong to their intended domains, External(func:numeric-add(s_{1} s_{2})) evaluates to the result of op:numeric-add(s_{1}, s_{2}) 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.
(?arg_{1} ?arg_{2}; func:numeric-subtract( ?arg_{1} ?arg_{2}) )
(?arg_{1} ?arg_{2}; func:numeric-multiply( ?arg_{1} ?arg_{2}) )
(?arg_{1} ?arg_{2}; func:numeric-divide( ?arg_{1} ?arg_{2}) )
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.
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.
(?arg_{1} ?arg_{2}; func:numeric-integer-divide( ?arg_{1} ?arg_{2}) )
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.
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.
(?arg_{1} ?arg_{2}; func:numeric-mod( ?arg_{1} ?arg_{2}) )
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.
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.
(?arg_{1} ?arg_{2}; pred:numeric-equal(?arg_{1} ?arg_{2}))
The value spaces of xs:integer, xs:double, or xs:decimal for both arguments.
When both s_{1} and s_{2} belong to their intended domains, External(pred:numeric-equal(s_{1} s_{2})) is t if and only if op:numeric-equal(s_{1}, s_{2}) 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 accordingly with respect to their corresponding operators in [XPath-Functions].
(?arg_{1} ?arg_{2}; pred:numeric-less-than( ?arg_{1} ?arg_{2}) )
(?arg_{1} ?arg_{2}; pred:numeric-greater-than( ?arg_{1} ?arg_{2}) )
(?arg_{1} ?arg_{2}; pred:numeric-not-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:numeric-not-equal has the same intended domains as pred:numeric-equal and is true whenever pred:numeric-equal is false.
(?arg_{1} ?arg_{2}; pred:numeric-less-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:numeric-less-than-or-equal has the same intended domains as pred:numeric-equal and is true whenever pred:numeric-equal is true or pred:numeric-less-than is true.
(?arg_{1} ?arg_{2}; pred:numeric-greater-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:numeric-greater-than-or-equal has the same intended domains as pred:numeric-equal and is true whenever pred:numeric-equal is true or pred:numeric-greater-than is true.
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( str_{1}, str_{2}) ) and External( func:concat3( str_{1} str_{2} str_{3} ) ) we allow the equivalent forms External( func:concat( str_{1}, str_{2}) ) and External( func:concat( str_{1} str_{2} str_{3} ) ). 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.
( ?comparand_{1} ?comparand_{2}; func:compare1(?comparand_{1} ?comparand_{2}) )
( ?comparand_{1} ?comparand_{2} ?collation; func:compare2(?comparand_{1} ?comparand_{2} ?collation) )
The value space of xs:string for all arguments.
I_{external}( ( ?comparand_{1} ?comparand_{2}; func:compare1(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = res such that res = -1, 0, or 1 (from the value space of xs:integer), depending on whether the value of the s_{1} is respectively less than, equal to, or greater than the value of s_{2}, 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.
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}.
( ?arg_{1}; func:concat1( ?arg_{1} ) )
( ?arg_{1} ?arg_{2}; func:concat2(?arg_{1} ?arg_{2} ) )
...
( ?arg_{1} ?arg_{2} ... ?arg_{n}; func:concatn(?arg_{1} ?arg_{2} ... ?arg_{n} ) )
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.
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.
( ?arg_{1} ?arg_{2}; func:string-join2(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2} ?arg_{3}; func:string-join3(?arg_{1} ?arg_{2} ?arg_{3} ) )
...
( ?arg_{1} ?arg_{2} ... ?arg_{n}; func:string-joinn(?arg_{1} ?arg_{2} ... ?arg_{n} ) )
The value space of xs:string for all arguments.
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.
( ?sourceString ?startingLoc; func:substring1( ?sourceString ?startingLoc) )
( ?sourceString ?startingLoc ?length ; func:substring2( ?sourceString ?startingLoc ?length) )
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.
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.
( func:string-length1() )
( ?arg ; func:string-length2( ?arg ) )
The value space of xs:string for ?arg.
Returns an xs:integer equal to the length in characters of the argument if it is a xs:string, returns 0 when called without an argument.
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.
( ?arg ; func:upper-case( ?arg ) )
The value space of xs:string for ?arg.
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.
( ?arg ; func:lower-case( ?arg ) )
The value space of xs:string for ?arg.
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.
( ?arg ; func:encode-for-uri( ?arg ) )
The value space of xs:string for ?arg.
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.
( ?iri ; func:iri-to-uri ( ?iri ) )
The value space of xs:string for ?iri.
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.
( ?uri ;func:escape-html-uri( ?uri ) )
The value space of xs:string for ?uri.
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.
( ?arg_{1} ?arg_{2}; func:substring-before1( ?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2} ?collation; func:substring-before2( ?arg_{1} ?arg_{2} ?collation ) )
The value space of xs:string for all arguments.
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.
( ?arg_{1} ?arg_{2}; func:substring-after1( ?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2} ?collation; func:substring-after2( ?arg_{1} ?arg_{2} ?collation ) )
The value space of xs:string for all arguments.
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.
( ?input ?pattern ?replacement; func:replace1( ?input ?pattern ?replacement ) )
( ?input ?pattern ?replacement ?flags; func:replace2( ?input ?pattern ?replacement ?flags ) )
The value space of xs:string for all arguments.
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.
( ?arg_{1} ?arg_{2}; pred:contains1( ?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2} ?collation ; pred:contains2( ?arg_{1} ?arg_{2} ?collation ) )
The value space of xs:string for all arguments.
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.
( ?arg_{1} ?arg_{2}; pred:starts-with1( ?arg_{1} ?arg_{2} )
( ?arg_{1} ?arg_{2} ?collation; pred:starts-with2( ?arg_{1} ?arg_{2} ?collation)
The value space of xs:string for all arguments.
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.
(?arg_{1} ?arg_{2}; fn:ends-with1( ?arg_{1} ?arg_{2} ) )
(?arg_{1} ?arg_{2} ?collation; fn:ends-with2( ?arg_{1} ?arg_{2} ?collation) )
The value space of xs:string for all arguments.
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.
( ?input ?pattern; pred:matches1( ?input ?pattern) )
( ?input ?pattern ?flags; pred:matches2( ?input ?pattern ?flags ) )
The value space of xs:string for all arguments.
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.
Following the convention of having separate equality, inequality, less-than, greater-than, less-than-or-equal, greater-than-or-equal predicates for other datatypes, RIF defines such predicates as syntactic sugar over func:compare also for xs:string in the following.
Editor's Note: The need of separate less-than, greater-than, less-than-or-equal, greater-than-or-equal predicates for strings is still under discussion, cf. ISSUE-67.
( ?comparand_{1} ?comparand_{2}; pred:string-equal(?comparand_{1} ?comparand_{2}) )
The value space of xs:string for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:string-equal(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = t if and only if I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:compare(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = 0.
If an argument value is outside of the intended domain, the value of the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
( ?comparand_{1} ?comparand_{2}; pred:string-less-than(?comparand_{1} ?comparand_{2}) )
The value space of xs:string for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:string-less-than(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = t if and only if I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:compare(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = -1.
If an argument value is outside of the intended domain, the value of the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
( ?comparand_{1} ?comparand_{2}; pred:string-greater-than(?comparand_{1} ?comparand_{2}) )
The value space of xs:string for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:string-greater-than(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = t if and only if I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:compare(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = 1.
If an argument value is outside of the intended domain, the value of the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
The following built-in predicates pred:string-not-equal, pred:string-less-than-or-equal and pred:string-greater-than-or-equal are defined accordingly.
( ?comparand_{1} ?comparand_{2}; pred:string-not-equal(?comparand_{1} ?comparand_{2}) )
The predicate pred:string-not-equal has the same intended domains as pred:string-equal and is true whenever pred:string-equal is false.
( ?comparand_{1} ?comparand_{2}; pred:string-less-than-or-equal(?comparand_{1} ?comparand_{2}) )
The predicate pred:string-less-than-or-equal has the same intended domains as pred:string-equal and is true whenever pred:string-equal is true or pred:string-less-than is true.
( ?comparand_{1} ?comparand_{2}; pred:string-greater-than-or-equal(?comparand_{1} ?comparand_{2}) )
The predicate pred:string-greater-than-or-equal has the same intended domains as pred:string-equal and is true whenever pred:string-equal is true or pred:string-greater-than is true.
If not stated otherwise, in the following we define schemas for functions and operators defined on the date, time and duration 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.
( ?arg ; func:year-from-dateTime( ?arg ) )
The value space of xs:dateTime for ?arg.
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}.
( ?arg ; func:month-from-dateTime( ?arg ) )
The value space of xs:dateTime for ?arg.
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.
( ?arg ; func:day-from-dateTime( ?arg ) )
The value space of xs:dateTime for ?arg.
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.
( ?arg ; func:hours-from-dateTime( ?arg ) )
The value space of xs:dateTime for ?arg.
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.
( ?arg ; func:minutes-from-dateTime( ?arg ) )
The value space of xs:dateTime for ?arg.
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.
( ?arg ; func:seconds-from-dateTime( ?arg ) )
The value space of xs:dateTime for ?arg.
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.
( ?arg ; func:year-from-date( ?arg ) )
The value space of xs:date for ?arg.
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.
( ?arg ; func:month-from-date( ?arg ) )
The value space of xs:date for ?arg.
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.
( ?arg ; func:day-from-date( ?arg ) )
The value space of xs:date for ?arg.
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.
( ?arg ; func:hours-from-time( ?arg ) )
The value space of xs:time for ?arg.
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.
( ?arg ; func:minutes-from-time( ?arg ) )
The value space of xs:time for ?arg.
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.
( ?arg ; func:seconds-from-time( ?arg ) )
The value space of xs:time for ?arg.
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.
( ?arg ; func:years-from-duration( ?arg ) )
The union of the value spaces of datatypes castable to xs:yearMonthDuration according to the table in Section 17.1 of [XPath-Functions].
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.
( ?arg ; func:months-from-duration( ?arg ) )
The union of the value spaces of datatypes castable to xs:yearMonthDuration according to the table in Section 17.1 of [XPath-Functions].
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.
( ?arg ; func:days-from-duration( ?arg ) )
The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions].
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.
( ?arg ; func:hours-from-duration( ?arg ) )
The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions].
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.
( ?arg ; func:minutes-from-duration( ?arg ) )
The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions].
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.
( ?arg ; func:seconds-from-duration( ?arg ) )
The union of the value spaces of datatypes castable to xs:dayTimeDuration according to the table in Section 17.1 of [XPath-Functions].
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.
( ?arg ; func:timezone-from-dateTime( ?arg ) )
The value space of xs:dateTime.
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
( ?arg ; func:timezone-from-date( ?arg ) )
( ?arg ; func:timezone-from-time( ?arg ) )
( ?arg_{1} ?arg_{2}; func:subtract-dateTimes( ?arg_{1} ?arg_{2} ) )
Subtracts two xs:dateTimes. Returns an xs:xs:dayTimeDuration.
( ?arg_{1} ?arg_{2}; func:subtract-dates( ?arg_{1} ?arg_{2} ) )
Subtracts two xs:dates. Returns an xs:xs:dayTimeDuration.
( ?arg_{1} ?arg_{2}; func:subtract-times( ?arg_{1} ?arg_{2} ) )
Subtracts two xs:times. Returns an xs:xs:dayTimeDuration.
( ?arg_{1} ?arg_{2}; func:add-yearMonthDurations( ?arg_{1} ?arg_{2} ) )
Adds two xs:yearMonthDurations. Returns an xs:yearMonthDuration.
( ?arg_{1} ?arg_{2}; func:subtract-yearMonthDurations( ?arg_{1} ?arg_{2} ) )
Subtracts one xs:yearMonthDuration from another. Returns an xs:yearMonthDuration.
( ?arg_{1} ?arg_{2}; func:multiply-yearMonthDuration( ?arg_{1} ?arg_{2} ) )
Multiplies an xs:yearMonthDuration by an xs:double. Returns an xs:yearMonthDuration.
( ?arg_{1} ?arg_{2} ; func:divide-yearMonthDuration( ?arg_{1} ?arg_{2} ) )
Divides an xs:yearMonthDuration by an xs:double. Returns an xs:yearMonthDuration.
( ?arg_{1} ?arg_{2}; func:divide-yearMonthDuration-by-yearMonthDuration( ?arg_{1} ?arg_{2} ) )
Divides an xs:yearMonthDuration by an xs:yearMonthDuration. Returns an xs:decimal.
( ?arg_{1} ?arg_{2}; func:add-dayTimeDurations( ?arg_{1} ?arg_{2} ) )
Adds two xs:dayTimeDurations. Returns an xs:dayTimeDuration.
( ?arg_{1} ?arg_{2}; func:subtract-dayTimeDurations( ?arg_{1} ?arg_{2} ) )
Subtracts one xs:dayTimeDuration from another. Returns an xs:dayTimeDuration.
( ?arg_{1} ?arg_{2} ; func:multiply-dayTimeDuration( ?arg_{1} ?arg_{2} ) )
Multiplies an xs:dayTimeDuration by a xs:double. Returns an xs:dayTimeDuration.
( ?arg_{1} ?arg_{2} ; func:divide-dayTimeDuration( ?arg_{1} ?arg_{2} ) )
Divides an xs:dayTimeDuration by an xs:double. Returns an xs:dayTimeDuration.
( ?arg_{1} ?arg_{2} ; func:divide-dayTimeDuration-by-dayTimeDuration( ?arg_{1} ?arg_{2} ) )
Divides an xs:dayTimeDuration by an xs:dayTimeDuration. Returns an xs:decimal.
( ?arg_{1} ?arg_{2} ; func:add-yearMonthDuration-to-dateTime( ?arg_{1} ?arg_{2} ) )
Adds a xs:yearMonthDuration (?arg_{2}) to a xs:dateTime (?arg_{1}). Returns an xs:dateTime.
( ?arg_{1} ?arg_{2} ; func:add-yearMonthDuration-to-date( ?arg_{1} ?arg_{2} ) )
Adds a xs:yearMonthDuration (?arg_{2}) to a xs:date (?arg_{1}). Returns an xs:date.
( ?arg_{1} ?arg_{2} ; func:add-dayTimeDuration-to-dateTime( ?arg_{1} ?arg_{2} ) )
Adds a xs:dayTimeDuration (?arg_{2}) to a xs:dateTime (?arg_{1}). Returns an xs:dateTime.
( ?arg_{1} ?arg_{2} ; func:add-dayTimeDuration-to-date( ?arg_{1} ?arg_{2} ) )
Adds a xs:dayTimeDuration (?arg_{2}) to a xs:date (?arg_{1}). Returns an xs:date.
( ?arg_{1} ?arg_{2} ; func:add-dayTimeDuration-to-time( ?arg_{1} ?arg_{2} ) )
Adds a xs:dayTimeDuration (?arg_{2}) to a xs:time (?arg_{1}). Returns an xs:time.
( ?arg_{1} ?arg_{2} ; func:subtract-yearMonthDuration-from-dateTime( ?arg_{1} ?arg_{2} ) )
Subtracts a xs:yearMonthDuration (?arg_{2}) from a xs:dateTime (?arg_{1}). Returns an xs:dateTime.
( ?arg_{1} ?arg_{2} ; func:subtract-yearMonthDuration-from-date( ?arg_{1} ?arg_{2} ) )
Subtracts a xs:yearMonthDuration (?arg_{2}) from a xs:date (?arg_{1}). Returns an xs:date.
( ?arg_{1} ?arg_{2} ; func:subtract-dayTimeDuration-from-dateTime( ?arg_{1} ?arg_{2} ) )
Subtracts a xs:dayTimeDuration (?arg_{2}) from a xs:dateTime (?arg_{1}). Returns an xs:dateTime.
( ?arg_{1} ?arg_{2} ; func:subtract-dayTimeDuration-from-date( ?arg_{1} ?arg_{2} ) )
Subtracts a xs:dayTimeDuration (?arg_{2}) from a xs:date (?arg_{1}). Returns an xs:date.
( ?arg_{1} ?arg_{2} ; func:subtract-dayTimeDuration-from-time( ?arg_{1} ?arg_{2} ) )
Subtracts a xs:dayTimeDuration (?arg_{2}) from a xs:time (?arg_{1}). Returns an xs:time.
( ?arg_{1} ?arg_{2}; pred:dateTime-equal( ?arg_{1} ?arg_{2}) )
The value space of xs:dateTime for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ?arg_{1} ?arg_{2}; pred:dateTime-equal( ?arg_{1} ?arg_{2} ) )(s_{1} s_{2}) = t
if and only if op:dateTime-equal(s_{1}, s_{2}) 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.
( ?arg_{1} ?arg_{2}; pred:dateTime-less-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:dateTime-greater-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:date-equal( ?arg_{1} ?arg_{2}) )
( ?arg_{1} ?arg_{2}; pred:date-less-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:date-greater-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:time-equal( ?arg_{1} ?arg_{2}) )
( ?arg_{1} ?arg_{2}; pred:time-less-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:time-greater-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:duration-equal( ?arg_{1} ?arg_{2}) )
The union of the value spaces of xs:dayTimeDuration and xs:yearMonthDuration for both arguments.
( ?arg_{1} ?arg_{2}; pred:dayTimeDuration-less-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:dayTimeDuration-greater-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:yearMonthDuration-less-than(?arg_{1} ?arg_{2} ) )
( ?arg_{1} ?arg_{2}; pred:yearMonthDuration-greater-than(?arg_{1} ?arg_{2} ) )
(?arg_{1} ?arg_{2}; pred:dateTime-not-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:dateTime-not-equal has the same intended domains as pred:dateTime-equal and is true whenever pred:dateTime-equal is false.
(?arg_{1} ?arg_{2}; pred:dateTime-less-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:dateTime-less-than-or-equal has the same intended domains as pred:dateTime-equal and is true whenever pred:dateTime-equal is true or pred:dateTime-less-than is true.
(?arg_{1} ?arg_{2}; pred:dateTime-greater-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:dateTime-greater-than-or-equal has the same intended domains as pred:dateTime-equal and is true whenever pred:dateTime-equal is true or pred:dateTime-greater-than is true.
(?arg_{1} ?arg_{2}; pred:date-not-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:date-not-equal has the same intended domains as pred:date-equal and is true whenever pred:date-equal is false.
(?arg_{1} ?arg_{2}; pred:date-less-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:date-less-than-or-equal has the same intended domains as pred:date-equal and is true whenever pred:date-equal is true or pred:date-less-than is true.
(?arg_{1} ?arg_{2}; pred:date-greater-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:date-greater-than-or-equal has the same intended domains as pred:date-equal and is true whenever pred:date-equal is true or pred:date-greater-than is true.
(?arg_{1} ?arg_{2}; pred:time-not-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:time-not-equal has the same intended domains as pred:time-equal and is true whenever pred:time-equal is false.
(?arg_{1} ?arg_{2}; pred:time-less-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:time-less-than-or-equal has the same intended domains as pred:time-equal and is true whenever pred:time-equal is true or pred:time-less-than is true.
(?arg_{1} ?arg_{2}; pred:time-greater-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:time-greater-than-or-equal has the same intended domains as pred:time-equal and is true whenever pred:time-equal is true or pred:time-greater-than is true.
(?arg_{1} ?arg_{2}; pred:duration-not-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:duration-equal has the same intended domains as pred:duration-equal and is true whenever pred:duration-equal is false.
Editor's Note: The introduction of less-than-or-eaual and greater-than-or-equal predicates for dayTimeDuration and yearMonthDuration still needs a WG resolution.
(?arg_{1} ?arg_{2}; pred:dayTimeDuration-less-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:dayTimeDuration-less-than-or-equal has the same intended domains as pred:dayTimeDuration-less-than and is true whenever pred:duration-equal is true or pred:dayTimeDuration-less-than is true.
(?arg_{1} ?arg_{2}; pred:dayTimeDuration-greater-than( ?arg_{1} ?arg_{2}) )
The predicate pred:dayTimeDuration-greater-than-or-equal has the same intended domains as pred:dayTimeDuration-greater-than and is true whenever pred:duration-equal is true or pred:dayTimeDuration-greater-than is true.
(?arg_{1} ?arg_{2}; pred:yearMonthDuration-less-than-or-equal( ?arg_{1} ?arg_{2}) )
The predicate pred:yearMonthDuration-less-than-or-equal has the same intended domains as pred:yearMonthDuration-less-than and is true whenever pred:duration-equal is true or pred:yearMonthDuration-less-than is true.
(?arg_{1} ?arg_{2}; pred:yearMonthDuration--greater-than( ?arg_{1} ?arg_{2}) )
The predicate pred:yearMonthDuration-greater-than-or-equal has the same intended domains as pred:yearMonthDuration-greater-than and is true whenever pred:duration-equal is true or pred:yearMonthDuration-greater-than is true.
Editor's Note: Predicates for rdf:XMLLiteral such as at least comparison predicates (equals, not-equals) are still under discussion in the working group.
The following functions and predicates are adapted from the respective functions and operators in [RDF-TEXT].
Editor's Note: Issues which are still open in the rdf:text specification might imply future changes on the functions and predicates defined here. For instance reuse of the fn: namespace is still under discussion, cf. http://lists.w3.org/Archives/Public/public-rdf-text/2008OctDec/0020.html. Moreover, references and links to the [RDF-TEXT] document will be updated in future versions of this document.
(?arg_{1} ?arg_{2} ; func:text-from-string-lang( ?arg_{1} ?arg_{2} ) )
The value space of xs:string for ?arg_{1} and the intersection of the elements of the value space of xs:string which represent valid language tags according to [BCP-47] for ?arg_{2}.
I_{external}((?arg_{1} ?arg_{2} ; func:text-from-string-lang( ?arg_{1} ?arg_{2} ) )(s l) = res such that res is the pair ( s, l ) in the value space of rdf:text.
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.
(?arg ; func:text-from-string( ?arg ) )
The value space of xs:string for ?arg.
I_{external}( (?arg ; func:text-from-string( ?arg ) )(s) = res such that res is the pair ( s, "" ) in the value space of rdf:text.
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.
Note: Since RIF implementations MAY choose to interpret xs:string and its subtypes as subtypes of rdf:text following Section 3.1 of [RDF-TEXT], in such implementations this function may just be implemented as the identity function.
(?arg ; func:string-from-text( ?arg ) )
The value space of rdf:text for ?arg.
I_{external}(?arg ; func:string-from-text( ?arg ) )(t) = res such that res is the string part s of t if t=( s, l ) is in the intended domain.
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.
(?arg ; func:lang-from-text( ?arg ) )
The value space of rdf:text for ?arg.
I_{external}(?arg ; func:lang-from-text( ?arg ) )(t) = l such that l is the language tag string of t if t= ( s, l ) is in the intended domain and ""^^xs:string otherwise.
( ?comparand_{1} ?comparand_{2}; func:text-compare1(?comparand_{1} ?comparand_{2}) )
( ?comparand_{1} ?comparand_{2} ?collation; func:text-compare2(?comparand_{1} ?comparand_{2} ?collation) )
The value space of rdf:text for ?comparand_{1} and $comparand_{2}, and the value space of xs:string for ?collation.
I_{external}( ( ?comparand_{1} ?comparand_{2}; func:text-compare1(?comparand_{1} ?comparand_{2}) )(t_{1} t_{2}) = res such that, whenever t_{1}=( s_{1}, l ) and t_{2}=( s_{2}, l ) are two pairs with the same language tag l in the value space ofrdf:text, res = -1, 0, or 1 (from the value space of xs:integer), depending on whether the value of s_{1} is respectively less than, equal to, or greater than the value of s_{2} according to the rules of the collation that is used.
In case an argument value is outside of the intended domain, or if the language tags of the values for ?comparand_{1} and $comparand_{2} differ, the function value is left unspecified and can vary from one semantic structure to another.
( func:text-length1() )
( ?arg ; func:text-length2( ?arg ) )
The value space of rdf:text for ?arg.
Returns an xs:integer equal to the length in characters of the string part s of the argument if it is a pair ( s,l ) in the value space of rdf:text, returns 0 when called without an argument.
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.
( ?input ?range; pred:matches-language-range( ?input ?range) )
The value space of rdf:text for ?input and the value space of xs:string for all ?range.
Whenever both arguments are in their intended domains, returns true if and only if the language tag of ?input is a valid language tag according to BCP-47 [BCP-47], and if it matches the language-range expression supplied as ?range as specified by the algorithm for "Matching of Language Tags" which is part of BCP-47 [BCP-47]; otherwise, it returns false.
If an argument value is outside of the intended domain, the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
Following the convention of having separate equality, inequality, less-than, greater-than, less-than-or-equal, greater-than-or-equal predicates for other datatypes, RIF defines such predicates as syntactic sugar over func:text-compare also for rdf:text in the following.
( ?comparand_{1} ?comparand_{2}; pred:text-equal(?comparand_{1} ?comparand_{2}) )
The value space of rdf:text for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:text-equal(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = t if and only if I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:text-compare(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = 0.
If an argument value is outside of the intended domain, the value of the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
( ?comparand_{1} ?comparand_{2}; pred:text-less-than(?comparand_{1} ?comparand_{2}) )
The value space of rdf:text for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:text-less-than(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = t if and only if I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:compare(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = -1.
If an argument value is outside of the intended domain, the value of the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
( ?comparand_{1} ?comparand_{2}; pred:text-greater-than(?comparand_{1} ?comparand_{2}) )
The value space of rdf:text for both arguments.
When both s_{1} and s_{2} belong to their intended domains, I_{truth} ο I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:text-greater-than(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = t if and only if I_{external}( ( ?comparand_{1} ?comparand_{2}; pred:compare(?comparand_{1} ?comparand_{2}) )(s_{1} s_{2}) = 1.
If an argument value is outside of the intended domain, the value of the truth value of the predicate is left unspecified and can vary from one semantic structure to another.
The following built-in predicates pred:text-not-equal, pred:text-less-than-or-equal and text:text-greater-than-or-equal are defined accordingly.
( ?comparand_{1} ?comparand_{2}; pred:text-not-equal(?comparand_{1} ?comparand_{2}) )
The predicate pred:text-not-equal has the same intended domains as pred:text-equal and is true whenever pred:text-equal is false.
( ?comparand_{1} ?comparand_{2}; pred:text-less-than-or-equal(?comparand_{1} ?comparand_{2}) )
The predicate pred:text-less-than-or-equal has the same intended domains as pred:text-equal and is true whenever pred:text-equal is true or pred:text-less-than is true.
( ?comparand_{1} ?comparand_{2}; pred:text-greater-than-or-equal(?comparand_{1} ?comparand_{2}) )
The predicate pred:text-greater-than-or-equal has the same intended domains as pred:text-equal and is true whenever pred:text-equal is true or pred:text-greater-than is true.
(Reference will be adapted at publication time.)
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 (?X_{1} ... ?X_{n}; τ) where
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 (?X_{1} ... ?X_{n}; τ) iff t can be obtained from τ by a simultaneous substitution ?X_{1}/s_{1} ... ?X_{n}/s_{n} of the variables ?X_{1} ... ?X_{n} with terms s_{1} ... 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 τ 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.