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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<meta name="viewport" content="width=device-width"/>
<title>Shape Expressions Language 2.0</title>
<!-- link rel="stylesheet" href="css/wgio.min.css"/ ask Iovka -->
<link rel="stylesheet" href="local.css"/>
<script src='https://www.w3.org/Tools/respec/respec-w3c-common'
defer class='remove'></script>
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<body>
<section id="abstract">
<p>
The Shape Expressions (ShEx) language describes <a>RDF nodes</a> and <a>graph</a> structures.
A <span class="math">node constraint</span> describes an RDF node (<a>IRI</a>, <a>blank node</a> or <a>literal</a>) and a <span class="math">shape</span> describes the <a>triples</a> involving nodes in an <a>RDF graph</a>.
These descriptions identify <a data-lt="predicate">predicates</a> and their associated cardinalities and datatypes.
ShEx shapes can be used to communicate data structures associated with some process or interface, generate or validate data, or drive user interfaces.
</p>
<p>
This document defines the ShEx language.
See the <a href="../primer/index.html">Shape Expressions Primer</a> for a non-normative description of ShEx.
</p>
</section>
<section id="sotd">
<p>This document has been developed by the
<a href="https://www.w3.org/community/shex/">Shape Expressions Community Group</a>.
The specification has undergone
significant development since the 1.0 version.</p>
<p>This version of the document represents a Candidate Release, with stable features. Comments and implementations are solicited prior to an eventual Final 2.0 Release.</p>
<p>The Shape Expressions language is expected to remain stable with the exception of:</p>
<ul>
<li>addition of a UNIQUE function</li>
</ul>
</section>
<section id="introduction">
<h2>Introduction</h2>
<p>
The Shape Expressions (<dfn>ShEx</dfn>) language provides a structural schema for RDF data.
This can be used to document APIs or datasets, aid in development of API-conformant messages, minimize defensive programming, guide user interfaces, or anything else that involves a machine-readable description of data organization and typing requirements.
</p>
<p>
ShEx describes <a>RDF graph</a> [[RDF11-CONCEPTS]] structures as sets of potentially connected <a data-lt="shape">Shapes</a>.
These constrain the <a>triples</a> involving nodes in an <a>RDF graph</a>.
<code>Node Constraints</code> constrain RDF nodes by constraining their node kind (<a>IRI</a>, <a>blank node</a> or <a>Literal</a>), enumerating permissible values in value sets, specifying their datatype, and constraining value ranges of Literals.
Additionally, they constrain lexical forms of <a>Literals</a>, <a>IRIs</a> and <a>labeled blank nodes</a>.
Shape Expressions schemas share blank nodes with the constrained <a>RDF graphs</a> in the same way that graphs in <a data-cite="rdf11-concepts#dfn-rdf-dataset">RDF datasets</a> [[!rdf11-concepts]] share blank nodes.
</p>
<p>
ShEx can be represented in JSON structures (<a>ShExJ</a>) or a compact syntax (<a>ShExC</a>).
The compact syntax is intended for human consumption; the JSON structure for machine processing.
This document defines ShEx in terms of <a>ShExJ</a> and includes a <a href="#shexc">section on the ShEx Compact Syntax (ShEx)</a>.
</p>
</section>
<section id="notation">
<h2>Notation</h2>
<p>
The JSON [[!rfc4627]] Syntax serves as a serializable proxy for an abstract syntax.
This specification uses a simple grammar to describe the set of JSON documents that can be interpreted as a ShEx schema.
</p>
<ul>
<li>Typed data structures are represented as JSON objects:
<span class="shexj">typeName { <a data-cite="rfc4627#section-2.2">member*</a> }</span><br/>
<a data-cite="rfc4627#section-2.2">RFC4627 Section 2.2</a> provides syntactic constraints for JSON — this grammar constrains those to valid <a>ShExJ</a> constructs.
</li>
<li><code>typeName</code> is the name of the typed data structure.
Types are referenced in the definitions of object members and in the definitions of the semantics for those data structures.</li>
<li><code>member*</code> is a list of zero or more terminals or references to other typeExpressions.</li>
<li><code>Terminals</code> are JSON strings and are indicated by all-caps, e.g. <a>IRI</a>.
For brevity, RDF nodes are represented as JSON strings composed as:
<ul>
<li><dfn data-cite="rdf11-concepts#dfn-iri" data-lt="iris">IRI</dfn>: the lexical form of the IRI, e.g. <code class="json">"http://example.org/resource"</code></li>
<li><dfn data-cite="rdf11-concepts#blank-node" data-lt="bnodes">BNODE</dfn>: the concatenation of "<code>_:</code>" and a <dfn data-cite="rdf11-concepts#dfn-blank-node-identifier" data-lt="blank node identifiers|labeled blank nodes">blank node identifier</dfn>, e.g. <code class="json">"_:blank3"</code></li>
<li><dfn data-cite="rdf11-concepts#dfn-literal" data-lt="literal|literals|RDF Literal|RDF Literals">OBJECTLITERAL</dfn>: the concatenation of a U+0022 ('<code>"</code>'), the lexical form of the literal, U+0022, and the first matching of:
<ul>
<li>literal with type <code>http://www.w3.org/2001/XMLSchema#string</code>: empty string, e.g. <code class="json">"abc"</code>.</li>
<li><a>language-tagged string</a>: U+0040 ('<code>@</code>') and the <a>language tag</a>, e.g. <code class="json">"\"hello world\"@en-US"</code></li>
<li>datatyped literal: U+005E U+005E ('<code>^^</code>') and the lexical form of the datatype URI, e.g. <code class="json">"\"123\"^^http://www.w3.org/2001/XMLSchema#integer"</code></li>
</ul></li>
</ul>
</li>
<li>A <code>typeExpression</code> is one of:
<ul>
<li><code>typeName</code> — an object of corresponding type</li>
<li><code>array</code>: <span class="shexj">[ typeExpression+ ]</span>— an array of one or more JSON values matching the typeExpression.</li>
<li><code>choice</code>: <span class="shexj">typeExpression1 | typeExpression2 | …</span>— a choice between two or more typeExressions.</li>
</ul>
</li>
<li>Cardinalities are represented as by the strings <code>?</code>, <code>+</code>, <code>*</code> following the <a data-cite="XML#sec-notation">notation in the XML specification</a>[[!XML]] or <code>{m,}</code> to indicate a that at least <code>m</code> elements are required.</li>
</ul>
<p>
In javascript-enabled browsers, schemas with a <button class="show-repchoice">json</button> button can be converted between the JSON representation and the compact syntax by clicking the button.
The button text indicates the currently shown representation.
Selecting the example and pressing "j" or "c" converts the example to the JSON (ShExJ) or compact form (ShExC).
Pressing "shift J" or "shift C" converts all such examples to ShExJ or ShExC.
</p>
<p>
The following examples are excerpts from the definitions below.
In the JSON notation,
</p>
<div class="shexj simupre"><a class="obj">Schema</a> { <a class="param">startActs</a>:[<a class="objref">SemAct</a>]? <a class="param">start</a>:<a class="nobref">shapeExpr</a>? <a class="param">imports</a>:[<a>IRI</a>]? <a class="param">shapes</a>:[<a class="nobref">shapeExpr</a>+]? }</div>
<p>
signifies that a <code>Schema</code> has three optional components called <a class="param">startActs</a>, <a class="param">start</a> and <a class="param">shapes</a>:
</p>
<ul>
<li><span class="param">startActs</span> is a list of <a class="objref">SemAct</a>.</li>
<li><span class="param">start</span> is a <a class="objref">shapeExpr</a>.</li>
<li><span class="param">imports</span> is a list of <a class="objref">IRI</a>.</li>
<li><span class="param">shapes</span> is an array of <a class="nobref">shapeExpr</a>.</li>
</ul>
<div class="shexj simupre"><a class="nob">shapeExpr</a> = <a class="objref">ShapeOr</a> | <a class="objref">ShapeAnd</a> | <a class="objref">ShapeNot</a>
| <a class="objref">NodeConstraint</a> | <a class="objref">Shape</a> | <a class="objref">ShapeExternal</a> ;</div>
<p>
signifies that a <a>shapeExpr</a> is one of seven object types: <a class="objref .shexj">ShapeOr</a> | <a class="objref">ShapeAnd</a> | ….
</p>
<div class="shexj simupre"><a class="obj">NodeConstraint</a> { <span class="param">nodeKind</span>:(<span class="literal">"iri"</span> | <span class="literal">"bnode"</span> | <span class="literal">"nonliteral"</span> | <span class="literal">"literal"</span>)? <a class="nobref">xsFacet</a>* }
<a class="nob">xsFacet</a> = <a class="nobref">stringFacet</a> | <a class="nobref">numericFacet</a> ;</div>
<p>
signifies that a <code>NodeConstraint</code> has a <code class="param">nodeKind</code> of one of the four literals followed by any number of <a class="objref .shexj">xsFacet</a> and an <a class="objref .shexj">xsFacet</a> is either a <a class="objref .shexj">stringFacet</a> or a <a class="objref .shexj">numericFacet</a>.
</p>
<section id="shex-references">
<h3>References</h3>
<p>
<a>ShExJ</a> is a dialect of JSON-LD [[!JSON-LD]] and the member <code>id</code> is used as a <a data-cite="JSON-LD#node-identifiers">node identifier</a>.
An object may be represented inline or referenced by its <code>id</code> which may be either a <a>blank node</a> or an <a>IRI</a>.
</p>
<div class="shexj simupre"><a class="obj">ShapeOr</a> { <a class="param">id</a>:<a class="nobjref">shapeExprLabel</a>? <dfn class="param">shapeExprs</dfn>:[<a class="nobjref">shapeExpr</a>] }
<a class="nob">shapeExprLabel</a> = <a class="objref">IRI</a> | <a class="objref">BNODE</a> ;
<a class="obj">EachOf</a> { <a class="param">id</a>:<a class="nobjref">tripleExprLabel</a>? <dfn class="param">expressions</dfn>:[<a class="nobjref">tripleExpr</a>] ... }
<a class="nob">tripleExprLabel</a> = <a>IRI</a> | <a>BNODE</a> ;</div>
<p>
The JSON structure may include references to <a data-lt="shape">shape expressions</a> and <a>triple expressions</a>:
</p>
<div class="shexj simupre"><a class="obj">shapeExpr</a> = <a class="objref">ShapeOr</a> | ... | <a class="nobjref">shapeExprRef</a> ;
<a class="nob">shapeExprRef</a> = <a class="nobjref">shapeExprLabel</a> ;
<a class="nobjref">tripleExpr</a> = <a class="objref">EachOf</a> | ... | <a class="nobjref">tripleExprRef</a> ;
<a class="nob">tripleExprRef</a> = <a class="objref">tripleExprLabel</a> ;</div>
<p>
An object with a circular reference must be referenced by id.
This example uses a nested shape reference on a value expression (<a data-lt="TripleConstraint">defined below</a>).
</p>
<div class="json">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "<span class="lookit">http://schema.example/IssueShape</span>",
"type": "Shape", "expression": {
"type": "TripleConstraint", "predicate": "http://schema.example/related",
"valueExpr": "<span class="lookit">http://schema.example/IssueShape</span>", min: 0 } } ] }</pre>
</div>
<p>
Not captured in this JSON syntax definition is the rule that every <a class="nobjref">shapeExpr</a> referenced by a schema's <a class="param">shapes</a> must have an <dfn class="param">id</dfn> and no other <a class="nobjref">shapeExpr</a> may have an <a>id</a>.
The JSON syntax definitition simplifies this by adding <span style="border: thin solid #888888; background-color: #F8F8F0;"><a class="param">id</a>:<a class="nobjref">shapeExprLabel</a>?</span> to every <a class="nobjref">shapeExpr</a>.
</p>
</section>
<section id="style">
<h3>Document style</h3>
<p>
JSON examples are rendered in a <span class="json">.json</span> CSS style.
Partial examples include ranges in a <span class="comment">.comment</span> CSS style to indicate text which would be substituted in a complete example.
For example <span class="json">{ "type": "ShapeAnd", "shapeExprs": [ <span class="comment">SE<sub>1</sub></span>, <span class="comment">…</span> ] }</span> indicates that both <span class="comment">SE<sub>1</sub></span> and <span class="comment">…</span> would be substituted in a complete example.
</p>
<!--div class="issue">
<p id="json-triples">
When stable, consider switching to the rdfjs task force's <a href="https://github.com/rdfjs/representation-task-force/blob/master/interface-spec.md#term">JSON representation</a> i.e.
</p>
<ul>
<li>IRI: <code class="json">{ "termType": "NamedNode", "value": "http://example.org/resource" }</code></li>
<li>blank node: <code class="json">{ "termType": "BlankNode", "value": "blank3" }</code></li>
<li>literal:
<ul>
<li>literal with type <code>http://www.w3.org/2001/XMLSchema#</code>: <code class="json">{ "termType": "Literal", "value": "abc" }</code></li>
<li><a>language-tagged string</a>: <code class="json">{ "termType": "Literal", "value": "hello world", "language": "en-us", "datatype": "http://www.w3.org/1999/02/22-rdf-syntax-ns#langString" }</code></li>
<li>datatyped literal: <code class="json">{ "termType": "Literal", "value": "123", "language": "", "datatype": "http://www.w3.org/1999/02/22-rdf-syntax-ns#integer" }</code></li>
</ul></li>
</ul>
</div-->
</section>
<section id="graphAccess">
<h3>Graph access</h3>
<p>
The validation process defined in this document relies on matching <a>triple patterns</a> in the form <code>(subject, predicate, object)</code> where each position may be supplied by a constant, a previously defined term, or the underscore "<code>_</code>", which represents a previously undefined element or wildcard.
This corresponds to a <dfn data-cite="sparql11-query#defn_TriplePattern" data-lt="triple pattern|triple patterns">SPARQL Triple Pattern</dfn> where each "_" is replaced by a unique <a>blank node</a>.
Matching such a <a>triple pattern</a> against a <a>graph</a> is defined by <a data-cite="sparql11-query#BGPsparql">SPARQL Basic Graph Pattern Matching</a> (BGP) with a BGP containing only that <a>triple pattern</a>.
</p>
</section>
<!-- button id="toggleRDF">Toggle RDF ("r")</button> <button id="toggleExamples">Toggle Examples ("e")</button> <button id="toggleSquished">Render only abstract syntax ("a")</button -->
<section id="process">
<h3>Validation process</h3>
<div>
<p>
ShEx validation is defined in this document by the <a class="function" href="#isValid">isValid</a> function.
This process takes as input a <a>shapes schema</a>, an <a>RDF graph</a>, and a <dfn data-cite="shape-map#dfn-fixed-shapemap" data-lt="shapemap">fixed ShapeMap</dfn> (abbreviated as "ShapeMap" in this document).
ShEx validation results may be reported as a <dfn data-cite="shape-map#dfn-result-shapemap">result ShapeMap</dfn> [[!shape-map]].
For illustration purposes in this specification, both the fixed ShapeMap input and the result ShapeMap output are represented in a table with four columns: <span class="data fake-example">node</span>: a ShapeMap nodeSelector, <span class="schema fake-example">shape</span>: a ShapeMap shapeLabel, <span class="fake-example">result</span>: "<span class="pass">pass</span>" (conformant) or "<span class="fail">fail</span>" (nonconformant), and an optional <span class="fake-example">reason</span>: an informal, human-readable explanation.
</p>
<table class="example">
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><node1></td><td><Shape1></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><node2></td><td><Shape1></td><td>fail</td><td class="fail">no <code>ex:state</code> supplied.</td></tr>
</table>
</div>
</section>
<!-- <p> -->
<!-- The following HTML tags and CSS classes are used to highlight the roles of text in this document: -->
<!-- </p> -->
<!-- <ul> -->
<!-- <li><dfn><dfn data-lt="dfn-shacl-defined-term">defined term</dfn><dfn></li> -->
<!-- <li><a class="internalDFN"><a title="SHACL defined term" class="internalDFN">defined term</a></a></li> -->
<!-- <li><sup class="eval">eval</sup> — link to evaluation semantics</li> -->
<!-- </ul> -->
</section>
<section id="terminology">
<h2>Terminology</h2>
<p>Shape expressions are defined using terms from RDF semantics [[!rdf11-mt]]:</p>
<ul>
<li><dfn data-cite="rdf11-concepts#dfn-node" data-lt="nodes|rdf node|rdf nodes">Node</dfn>: one of <a>IRI</a>, <dfn data-cite="rdf11-concepts#dfn-blank-node">blank node</dfn>, <a>Literal</a></li>
<li><dfn data-cite="rdf11-concepts#dfn-rdf-graph" data-lt="RDF Graph|RDF Graphs">Graph</dfn>: a set of <dfn data-cite="rdf11-concepts#dfn-rdf-triple" data-lt="triple|rdf triple|rdf triples">Triples</dfn> of (<dfn data-cite="rdf11-concepts#dfn-subject">subject</dfn>, <dfn data-cite="rdf11-concepts#dfn-predicate">predicate</dfn>, <dfn data-cite="rdf11-concepts#dfn-object">object</dfn>)</li>
</ul>
<p>This specification makes use of the following namespaces:</p>
<dl>
<dt><code>foaf</code>:</dt>
<dd><code>http://xmlns.com/foaf/0.1/</code></dd>
<dt><code>rdf</code>:</dt>
<dd><code>http://www.w3.org/1999/02/22-rdf-syntax-ns#</code></dd>
<dt><code>rdfs</code>:</dt>
<dd><code>http://www.w3.org/2000/01/rdf-schema#</code></dd>
<dt><code>shex</code>:</dt>
<dd><code>http://www.w3.org/ns/shex#</code></dd>
<dt><code>xsd</code>:</dt>
<dd><code>http://www.w3.org/2001/XMLSchema#</code></dd>
</dl>
<p>
The following functions access the elements of an <a>RDF graph</a> <span class="math">G</span> containing a node <span class="math">n</span>:</p>
<ul>
<li>
<span class="math"><dfn>arcsOut</dfn>(G, n)</span> is the set of <a>triples</a> in a <a>graph</a> <span class="math">G</span> with <a>subject</a> <span class="math">n</span>.
</li>
<li>
<span class="math"><dfn>predicatesOut</dfn>(G, n)</span> is the set of <a data-lt="predicate">predicates</a> in <span class="math"><a>arcsOut</a>(G, n)</span>.
</li>
<li>
<span class="math"><dfn>arcsIn</dfn>(G, n)</span> is the set of <a>triples</a> in a <a>graph</a> <span class="math">G</span> with <a>object</a> <span class="math">n</span>.
</li>
<li>
<span class="math"><dfn>predicatesIn</dfn>(G, n)</span> is the set of <a data-lt="predicate">predicates</a> in <span class="math"><a>arcsIn</a>(G, n)</span>.
</li>
<li>
<span class="math"><dfn>neigh</dfn>(G, n)</span> is the neighbourhood of the <a>node</a> <span class="math">n</span> in the <a>graph</a> <span class="math">G</span>.<br/><span class="math"><a>neigh</a>(G, n) = <a>arcsOut</a>(G, n) ∪ <a>arcsIn</a>(G, n)</span>
</li>
<li>
<span class="math"><dfn>predicates</dfn>(G, n)</span> is the set of <a data-lt="predicate">predicates</a> in <span class="math"><a>neigh</a>(G, n)</span>.<br/><span class="math"><a>predicates</a>(G, n) = <a>predicatesOut</a>(G, n) ∪ <a>predicatesIn</a>(G, n)</span>
</li>
</ul>
<div class="example">
<p>
Consider the <a>RDF graph</a> <span class="math">G</span> represented in Turtle:
</p>
<pre class="graph">
PREFIX ex: http://schema.example/
PREFIX inst: http://inst.example/#
PREFIX foaf: http://xmlns.com/foaf/
PREFIX xsd: http://www.w3.org/2001/XMLSchema#
inst:Issue1
ex:state ex:unassigned ;
ex:reportedBy _:User2 .
_:User2
foaf:name "Bob Smith" ;
foaf:mbox <mailto:bob@example.org> .
</pre>
<p>
There are two arcs out of <span class="pre">_:User2</span>; <span class="math"><a>arcsOut</a>(G, <span class="pre">_:User2</span>)</span>:
</p>
<pre>
_:User2 foaf:name "Bob Smith" .
_:User2 foaf:mbox <mailto:bob@example.org> .
</pre>
<p>
There is one arc into <span class="pre">_:User2</span>; <span class="math"><a>arcsIn</a>(G, <span class="pre">_:User2</span>)</span>:
</p>
<pre>
inst:Issue1 ex:reportedBy _:User2 .
</pre>
<p>
There are three arcs in the neighbourhood of <span class="pre">_:User2</span> set, <span class="math"><a>neigh</a>(G, <span class="pre">_:User2</span>)</span>:
</p>
<pre>
_:User2 foaf:name "Bob Smith" .
_:User2 foaf:mbox <mailto:bob@example.org> .
inst:Issue1 ex:reportedBy _:User2 .
</pre>
</div>
</section>
<section id="conformance">
<p>Conformance criteria are relevant to authors and authoring tool implementers. As well
as sections marked as non-normative, all authoring guidelines, diagrams, examples,
and notes in this specification are non-normative. Everything else in this
specification is normative.</p>
<ul>
<li>A <a>ShExC</a> document complies with this specification if it
conforms to the grammar described in <a href="#shexc" class="sectionRef"></a> resulting
in a valid <a>ShExJ</a> document.</li>
<li>A <a>ShExJ</a> document complies with this specification if it is a valid
JSON-LD document [[!JSON-LD]], and conforms to the <a>ShExJ</a> syntax, as described in <a href="#shexj" class="sectionRef"></a>.</li>
<li>JSON documents can be interpreted as <a>ShExJ</a> by following the normative statements in
<a data-cite="JSON-LD#interpreting-json-as-json-ld">Section 4.8 Interpreting JSON as JSON-LD</a> in [[!JSON-LD]].</li>
<li>Other RDF documents comply with this specification, if they are <a href="https://www.w3.org/TR/rdf11-concepts/#dfn-graph-isomorphism">graph isomorphic</a>[[!rdf11-concepts]] to the RDF interpretation of some <a>ShExJ</a> document.</li>
</ul>
</section>
<section id="shapes-language">
<h2>The Shape Expressions Language</h2>
<p>
A Shape Expressions (ShEx) schema is a collection of labeled <a data-lt="shape">Shapes</a> and <a href="#node-constraints">Node Constraints</a>.
These can be used to describe or test nodes in <a>RDF graphs</a>.
ShEx does not prescribe a language for associating <a>nodes</a> with <a data-lt="shape">shapes</a> but several approaches are <a href="../primer/index.html#associating-nodes-with-shapes">described in the ShEx Primer</a>.
</p>
<section id="shapes-schema">
<h3>Shapes Schema</h3>
<p>
A shapes schema is captured in a <span class="jobjref"><dfn data-lt="shapes schema">Schema</dfn></span> object:
</p>
<div class="shexjTable">
<table class="shexj">
<tr class="obj"><th class="obj"><a>Schema</a></th><td>{</td><td><dfn class="param">startActs</dfn>:[<a class="objref">SemAct</a>]? <dfn class="param">start</dfn>:<a class="nobref">shapeExpr</a>? <dfn class="param">imports</dfn>:[<a class="nobref">IRI</a>]? <dfn class="param">shapes</dfn>:[<a class="nobref">shapeExpr</a>+]? }</td></tr>
</table>
</div>
<p>
where <a class="param">shapes</a> is a mapping from shape label to <a>shape expression</a>.
</p>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape", <span class="comment">…</span> },
{ "id": "_:UserShape", <span class="comment">…</span> },
{ "id": "http://schema.example/EmployeeShape", <span class="comment">…</span> } ] }</pre>
<pre class="shexc">
ex:IssueShape { … }
_:UserShape { … }
ex:EmployeeShape { … }
</pre>
</div>
</section>
<section id="validation">
<h3>Validation Definition</h3>
<p>
<span class="label" id="isValid">isValid</span>: The expression <code class="function">isValid(<span class="math">G</span>, <span class="math">m</span>)</code> indicates that for every nodeSelector/shapeLabel pair <span class="math">(n, s)</span> in <span class="math">m</span>, <span class="math">s</span> has a corresponding <a>shape expression</a> <span class="math">se</span> and <code class="function">satisfies(<span class="math">n</span>, <span class="math">se</span>, <span class="math">G</span>, <span class="math">m</span>)</code>.
<code class="function">satisfies</code> is defined below for each form of <a>shape expression</a>.
</p>
<div class="note">
<p>
Validation of a <a>graph</a> <span class="math">G</span> does not necessarily require the construction of a <a>ShapeMap</a> with every node in <span class="math">G</span>.
The validation semantics defined below imply a set of dependencies for validating some node as a shape.
A validation process that tests every <a>node</a> in a <a>graph</a> against every <a>shape</a> in a <a>schema</a> can be considered to have an input <a>ShapeMap</a> associating each node with the set of all shapes in the schema.
</p>
<p>
The semantics of ShEx are independent from the construction of an input <a>ShapeMap</a>.
<a href="https://www.w3.org/2001/sw/wiki/ShEx/ShapeMap">https://www.w3.org/2001/sw/wiki/ShEx/ShapeMap</a> has list of popular methods for constructing ShapeMaps.
</p>
</div>
<p>
Validation of a node against a shape in a schema requires that there is a consistent mapping from node to <!-- @@set of --> shape for every node and shape visited during a validation process.
The remainder of this document uses <span class="math">m</span> to indicate such a mapping.
</p>
</section>
<section id="shape-expressions">
<h3>Shape Expressions</h3>
<p>
A <dfn data-lt="shape expressions">shape expression</dfn> is composed of four kinds of objects combined with the algebraic operators And, Or and Not:
</p>
<ul>
<li>
a node constraint (<span class="jobjref"><a>NodeConstraint</a></span>) that defines the set of allowed values of a node.
These include specification of RDF node kind, literal datatype, XML String and numeric facets and enumeration of value sets.
</li>
<li>
a shape constraint (<span class="jobjref"><a>Shape</a></span>) that defines a constraint on the allowed neighbourhood of a node, that is, the allowed triples that contain this node as subject or object.
</li>
<li>
an external shape (<span class="jobjref"><a>ShapeExternal</a></span>) which is an extension mechanism to externally define e.g. functional shapes or prohibitively large value sets.
</li>
<li>
a shape reference (<span class="jobjref"><a>shapeExprLabel</a></span>) identifies another shape in the schema or an <a href="#import">imported schema</a>.
</li>
</ul>
<section id="shape-expressions-shexj">
<h4>JSON Syntax</h4>
<div class="shexjTable">
<table class="shexj">
<tr class="nob"><th class="nob"><dfn>shapeExpr</dfn></th> <td>=</td> <td><a class="objref">ShapeOr</a> | <a class="objref">ShapeAnd</a> | <a class="objref">ShapeNot</a> | <a class="objref">NodeConstraint</a> | <a class="objref">Shape</a> | <a class="objref">ShapeExternal</a> | <a class="objref">shapeExprRef</a> ;</td></tr>
<tr class="obj"><th class="obj"><dfn>ShapeOr</dfn></th> <td>{</td> <td><span class="param">id</span>:<a class="nobref">shapeExprLabel</a>? <span class="param">shapeExprs</span>:[<a class="nobref">shapeExpr</a>] }</td></tr>
<tr class="obj"><th class="obj"><dfn>ShapeAnd</dfn></th> <td>{</td> <td><span class="param">id</span>:<a class="nobref">shapeExprLabel</a>? <span class="param">shapeExprs</span>:[<a class="nobref">shapeExpr</a>] }</td></tr>
<tr class="obj"><th class="obj"><dfn>ShapeNot</dfn></th> <td>{</td> <td><span class="param">id</span>:<a class="nobref">shapeExprLabel</a>? <span class="param">shapeExpr</span>:<a class="nobref">shapeExpr</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>ShapeExternal</dfn></th> <td>{</td> <td><span class="param">id</span>:<a class="nobref">shapeExprLabel</a>? }</td></tr>
<tr class="nob"><th class="nob"><dfn data-lt="shapeExprRefs">shapeExprRef</dfn></th> <td>=</td> <td><a class="objref">shapeExprLabel</a> ;</td></tr>
<tr class="nob"><th class="nob"><dfn>shapeExprLabel</dfn></th> <td>=</td> <td><a>IRI</a> | <a>BNODE</a> ;</td></tr>
</table>
</div>
<div class="example">
<p>
Examples of shape expressions:
</p>
<div class="repchoice">
<pre class="json">{ "type": "Shape", <span class="comment">…</span> } </pre>
<pre class="shexc">{ <span class="comment">…</span> } </pre>
</div>
<div style="clear:both;"> </div>
<div class="repchoice">
<pre class="json">{ "type": "ShapeAnd", "shapeExprs": [
{ "type": "NodeConstraint", "nodeKind": "iri" },
{ "type": "ShapeOr", "shapeExprs": [
"http://schema.example/IssueShape",
{ "type": "ShapeNot", "shapeExpr": { "type": "Shape", <span class="comment">…</span> } }
] } ] }</pre>
<pre class="shexc">
<span class="keyword">IRI</span> AND
(
@<http://schema.example/IssueShape>
OR NOT { <span class="comment">…</span> }
)</pre>
</div>
<p>
In this ShapeOr's <span class="param">shapeExprs</span>,"http://schema.example/IssueShape" is a reference to the <a>shape expression</a> with the id "http://schema.example/IssueShape".
</p>
</div>
</section>
<section id="shape-expression-semantics">
<h4>Semantics</h4>
<p>
<span class="label" id="satisfies">satisfies</span>: The expression <code class="function">satisfies(<span class="math">n</span>, <span class="math">se</span>, <span class="math">G</span>, <span class="math">m</span>)</code> indicates that a node <span class="math">n</span> and <a>graph</a> <span class="math">G</span> satisfy a <a>shape expression</a> <span class="math">se</span> with <a>shapeMap</a> <span class="math">m</span>.<br/>
<span class="label" id="notSatisfies">notSatisfies</span>: Conversely, <code class="function">notSatisfies(<span class="math">n</span>, <span class="math">se</span>, <span class="math">G</span>, <span class="math">m</span>)</code> indicates that <span class="math">n</span> and <span class="math">G</span> do not satisfy <span class="math">se</span> with the given <a>shapeMap</a> <span class="math">m</span>.
<code class="function">notSatisfies(<span class="math">n</span>, <span class="math">se</span>, <span class="math">G</span>, <span class="math">_</span>)</code> indicates that no <a>shapeMap</a> would allow <span class="math">n</span> and <span class="math">G</span> to satisfy <span class="math">se</span>.
</p>
<p>
<code class="function">satisfies(<span class="math">n</span>, <span class="math">se</span>, <span class="math">G</span>, <span class="math">m</span>)</code> is true if and only if:
</p>
<ul>
<li id="satisfies-NodeConstraint"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">NodeConstraint</a></span> and <code class="function"><a href="#satisfies2-NodeConstraint">satisfies2</a>(<span class="math">n</span>, <span class="math">se</span>)</code> as described below in <a href="#node-constraints">Node Constraints</a>.
Note that testing if a node satisfies a node constraint does not require a <a>graph</a> or <a>shapeMap</a>.</li>
<li id="satisfies-Shape-proxy"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">Shape</a></span> and <code class="function">satisfies(<span class="math">n</span>, <span class="math">se</span>)</code> as <a href="#satisfies-Shape">defined below</a> in Shapes and Triple Expressions.</li>
<li id="satisfies-ShapeOr"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">ShapeOr</a></span> and there is some <a>shape expression</a> <span class="math">se2</span> in <span class="param">shapeExprs</span> such that <code class="function">satisfies(<span class="math">n</span>, <span class="math">se2</span>, <span class="math">G</span>, <span class="math">m</span>)</code>.</li>
<li id="satisfies-ShapeAnd"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">ShapeAnd</a></span> and for every <a>shape expression</a> <span class="math">se2</span> in <span class="param">shapeExprs</span>, <code class="function">satisfies(<span class="math">n</span>, <span class="math">se2</span>, <span class="math">G</span>, <span class="math">m</span>)</code>.</li>
<li id="satisfies-ShapeNot"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">ShapeNot</a></span> and for the <a>shape expression</a> <span class="math">se2</span> at <span class="param">shapeExpr</span>, <code class="function">notSatisfies(<span class="math">n</span>, <span class="math">se2</span>, <span class="math">G</span>, <span class="math">m</span>)</code>.</li>
<li id="satisfies-ShapeExternal"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">ShapeExternal</a></span> and implementation-specific mechansims not defined in this specification indicate success.</li>
<li id="satisfies-shapeExprRef"><span class="math">Se</span> is a <span class="jobjref"><a class="obj">shapeExprRef</a></span> and there exists in the schema a <a>shape expression</a> <span class="math">se2</span> with that <span class="param">id</span> and <code class="function">satisfies(<span class="math">n</span>, <span class="math">se2</span>, <span class="math">G</span>, <span class="math">m</span>)</code>.</li>
</ul>
<div class="example">
<p>
Given the three shape expressions <span class="math">SE<sub>1</sub></span>, <span class="math">SE<sub>2</sub></span>, <span class="math">SE<sub>3</sub></span> in a <span class="jobjref"><a class="obj">Schema</a></span> <span class="math">Sch</span>, such that:
</p>
<ul>
<li><code class="function">satisfies(<span class="math">n</span>, <span class="math">SE<sub>1</sub></span>, <span class="math">G</span>, <span class="math">m</span>)</code></li>
<li><code class="function">satisfies(<span class="math">n</span>, <span class="math">SE<sub>2</sub></span>, <span class="math">G</span>, <span class="math">m</span>)</code></li>
<li><code class="function">notSatisfies(<span class="math">n</span>, <span class="math">SE<sub>3</sub></span>, <span class="math">G</span>, <span class="math">m</span>)</code></li>
</ul>
<p>
the following hold:
</p>
<ul class="codelist">
<li><div><div style="float:left;" class="code function">satisfies(</div><div style="float:left;" class="code"><span class="math">n</span>,<br/><div class="inline json"><pre>{ "type": "ShapeAnd", "shapeExprs": [ <span class="comment">SE<sub>1</sub></span>, <span class="comment">SE<sub>2</sub></span> ] }</pre></div>,<br/> <span class="math">G</span>, <span class="math">m</span>)</div><div style="clear:both;"></div></div></li>
<li><div><div style="float:left;" class="code function">satisfies(</div><div style="float:left;" class="code"><span class="math">n</span>,<br/><div class="inline json"><pre>{ "type": "ShapeOr", "shapeExprs": [ <span class="comment">SE<sub>1</sub></span>, <span class="comment">SE<sub>2</sub></span>, <span class="comment">SE<sub>3</sub></span> ] }</pre></div>,<br/> <span class="math">G</span>, <span class="math">m</span>)</div><div style="clear:both;"></div></div></li>
<li><div><div style="float:left;" class="code function">notSatisfies(</div><div style="float:left;" class="code"><span class="math">n</span>,<br/><div class="inline json code"><pre>{ "type": "ShapeNot", "shapeExpr": {
{ "type": "ShapeOr", "shapeExprs": [
<span class="comment">SE<sub>1</sub></span>,
{ "type": "ShapeAnd", "shapeExprs": [ <span class="comment">SE<sub>2</sub></span>, <span class="comment">SE<sub>3</sub></span> ] }
] }
} }</pre></div>,<br/> <span class="math">G</span>, <span class="math">m</span>)</div><div style="clear:both;"></div></div></li>
</ul>
<p>
If <span class="math">Sch</span>'s <a class="param">shapes</a> maps "<code>http://schema.example/shape1</code>" to <span class="math">SE<sub>1</sub></span> then the following holds:
</p>
<ul class="codelist">
<li><div><div style="float:left;" class="code function">satisfies(</div><div style="float:left;" class="code"><span class="math">n</span>,<br/><div class="inline json"><pre>http://schema.example/shape1"</pre></div>,<br/> <span class="math">G</span>, <span class="math">m</span>)</div><div style="clear:both;"></div></div></li>
</ul>
</div>
</section>
</section>
<section id="node-constraints">
<h3>Node Constraints</h3>
<div class="shexjTable">
<table class="shexj">
<tr class="obj"><th class="obj"><dfn>NodeConstraint</dfn></th> <td>{</td><td><span class="param">id</span>:<a class="nobref">shapeExprLabel</a>? <span class="param">nodeKind</span>:(<span class="literal">"iri"</span> | <span class="literal">"bnode"</span> | <span class="literal">"nonliteral"</span> | <span class="literal">"literal"</span>)? <span class="param">datatype</span>:<a>IRI</a>? <a class="nobref">xsFacet</a>* <span class="param">values</span>:[<a class="nobref">valueSetValue</a>]? }</td></tr>
<tr class="nob"><th class="nob"><dfn>xsFacet</dfn></th> <td>=</td><td><a class="nobref">stringFacet</a> | <a class="nobref">numericFacet</a> ;</td></tr>
<tr class="nob"><th class="nob"><dfn>stringFacet</dfn></th> <td>=</td><td>(<span class="param">"length"</span>|<span class="param">"minlength"</span>|<span class="param">"maxlength"</span>):<a>INTEGER</a> | <span class="param">pattern</span>:<a>STRING</a> <span class="param">flags</span>:<a>STRING</a>? ;</td></tr>
<tr class="nob"><th class="nob"><dfn>numericFacet</dfn></th> <td>=</td><td>(<span class="param">"mininclusive"</span>|<span class="param">"minexclusive"</span>|<span class="param">"maxinclusive"</span>|<span class="param">"maxexclusive"</span>):<a class="nobref">numericLiteral</a> </td></tr>
<tr><th></th><td>|</td><td>(<span class="param">"totaldigits"</span>|<span class="param">"fractiondigits"</span>):<a>INTEGER</a> ;</td></tr>
<tr class="nob"><th class="nob"><dfn>numericLiteral</dfn></th> <td>=</td><td><a>INTEGER</a> | <a>DECIMAL</a> | <a>DOUBLE</a> ;</td></tr>
<tr class="nob"><th class="nob"><dfn>valueSetValue</dfn></th><td>=</td><td><a class="nobref">objectValue</a> | <a class="objref">IriStem</a> | <a class="objref">IriStemRange</a> | <a class="objref">LiteralStem</a> | <a class="objref">LiteralStemRange</a> | <a class="objref">Language</a> | <a class="objref">LanguageStem</a> | <a class="objref">LanguageStemRange</a> ;</td></tr>
<tr class="nob"><th class="nob"><dfn>objectValue</dfn></th><td>=</td><td><a>IRI</a> | <a class="objref">ObjectLiteral</a> ;</td></tr>
<tr class="obj"><th class="obj"><dfn>IriStem</dfn></th><td>{</td><td><span class="param">stem</span>:<a>IRI</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>IriStemRange</dfn></th><td>{</td><td><span class="param">stem</span>:(<a>IRI</a> | <a class="objref">Wildcard</a>) <span class="param">exclusions</span>:[<a class="nobref">objectValue</a>|<a class="objref">IriStem</a> +]? }</td></tr>
<tr class="obj"><th class="obj"><dfn>LiteralStem</dfn></th><td>{</td><td><span class="param">stem</span>:<a>ObjectLiteral</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>LiteralStemRange</dfn></th><td>{</td><td><span class="param">stem</span>:(<a>ObjectLiteral</a> | <a class="objref">Wildcard</a>) <span class="param">exclusions</span>:[<a class="nobref">objectValue</a>|<a class="objref">LiteralStem</a> +]? }</td></tr>
<tr class="obj"><th class="obj"><dfn>Language</dfn></th><td>{</td><td><span class="param">langTag</span>:<a>ObjectLiteral</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>LanguageStem</dfn></th><td>{</td><td><span class="param">stem</span>:<a>ObjectLiteral</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>LanguageStemRange</dfn></th><td>{</td><td><span class="param">stem</span>:(<a>ObjectLiteral</a> | <a class="objref">Wildcard</a>) <span class="param">exclusions</span>:[<a class="nobref">objectValue</a>|<a class="objref">Language</a>|<a class="objref">LanguageStem</a> +]? }</td></tr>
<tr class="obj"><th class="obj"><dfn>Wildcard</dfn></th> <td>{</td><td><span class="comment">/* empty */</span> }</td></tr>
</table>
</div>
<section id="node-constraint-semantics">
<h4>Semantics</h4>
<p id="satisfies2-NodeConstraint">
For a node <span class="param">n</span> and constraint <span class="param">nc</span>, <code class="function">satisfies2(<span class="math">n</span>, <span class="math">nc</span>)</code> if and only if for every <span class="param">nodeKind</span>, <span class="param">datatype</span>, <span class="param">xsFacet</span> and <span class="param">values</span> constraint value <span class="math">v</span> present in <span class="param">nc</span> <code class="function">nodeSatisfies(<span class="math">n</span>, <span class="math">v</span>)</code>.
The following sections define <code class="function">nodeSatisfies</code> for each of these types of constraints:
</p>
<ul>
<li><a href="#nodeKind">Node Kind Constraints</a></li>
<li><a href="#datatype">Datatype Constraints</a></li>
<li><a href="#xs-string">XML Schema String Facet Constraints</a></li>
<li><a href="#xs-numeric">XML Schema Numeric Facet Constraints</a></li>
<li><a href="#values">Values Constraints</a></li>
</ul>
</section>
<section id="nodeKind">
<h4>Node Kind Constraints</h4>
<p id="nodeSatisfies-nodeKind">
For a node <span class="math">n</span> and constraint value <span class="math">v</span>, <code class="function">nodeSatisfies(<span class="math">n</span>, <span class="math">v</span>)</code> if:
</p>
<ul>
<li><span class="math">v</span> = "iri" and <span class="math">n</span> is an <a>IRI</a>.</li>
<li><span class="math">v</span> = "bnode" and <span class="math">n</span> is a <a>blank node</a>.</li>
<li><span class="math">v</span> = "literal" and <span class="math">n</span> is a <a>Literal</a>.</li>
<li><span class="math">v</span> = "nonliteral" and <span class="math">n</span> is an <a>IRI</a> or <a>blank node</a>.</li>
</ul>
<div class="example">
<div class="example-title marker"><span>Node Kind example 1</span></div>
<p>
The following examples use a <span class="jobjref"><a>TripleConstraint</a></span> object described later in the document.
The
</p>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint", "predicate": "http://schema.example/state",
"valueExpr": { "type": "NodeConstraint", "nodeKind": "iri" } } } ] }</pre>
<pre class="shexc">
ex:IssueShape {
ex:state IRI
}
</pre>
</div>
<pre class="data">
<issue1> ex:state ex:HunkyDory .
<issue2> <span style="border-bottom: thin solid red;">ex:taste</span> ex:GoodEnough .
<span class="fail"><issue3> ex:state "just fine" .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue1></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue2></td><td><IssueShape></td><td>fail</td><td class="fail">expected 1 <code>ex:state</code> property.</td></tr>
<tr class="fail"><td><issue3></td><td><IssueShape></td><td>fail</td><td class="fail"><code>ex:state</code> expected to be an IRI, literal found.</td></tr>
</table>
<p>
Note that <issue2> <span class="fail">fails</span> not because of a nodeKind violation but instead because of a <a href="#cardinality">Cardinality</a> violation described below.
</p>
</div>
</section>
<section id="datatype">
<h4>Datatype Constraints</h4>
<p id="nodeSatisfies-datatype">
For a node <span class="math">n</span> and constraint value <span class="math">v</span>, <code class="function">nodeSatisfies(<span class="math">n</span>, <span class="math">v</span>)</code> if <span class="math">n</span> is an Literal with the datatype <span class="math">v</span> and, if <span class="math">v</span> is in the set of <a data-cite="sparql11-query#operandDataTypes">SPARQL operand data types</a>[[!sparql11-query]], an XML schema string with a value of the lexical form of <span class="math">n</span> can be cast to the target type <span class="math">v</span> per <a data-cite="xpath-functions-31#casting">XPath Functions 3.1 section 19 Casting</a>[[!xpath-functions]].
Only datatypes supported by SPARQL MUST be tested but ShEx extensions MAY add support for other datatypes.
</p>
<div class="example">
<div class="example-title marker"><span>Datatype example 1</span></div>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint", "predicate": "http://schema.example/submittedOn",
"valueExpr": {
"type": "NodeConstraint",
"datatype": "http://www.w3.org/2001/XMLSchema#date"
} } } ] }</pre>
<pre class="shexc">
ex:IssueShape {
ex:submittedOn xsd:date
}
</pre>
</div>
<pre class="data">
<issue1> ex:submittedOn "2016-07-08"^^xsd:date .
<span class="fail"><issue2> ex:submittedOn "2016-07-08T01:23:45Z"^^xsd:dateTime .</span>
<span class="fail"><issue3> ex:submittedOn "2016-07"^^xsd:date .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue1></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue2></td><td><IssueShape></td><td>fail</td><td class="fail"><code>ex:submittedOn</code> expected to be an <code>xsd:date</code>, <code>xsd:dateTime</code> found.</td></tr>
<tr class="fail"><td><issue3></td><td><IssueShape></td><td>fail</td><td class="fail"><code>2016-07</code> is not a valid <code>xsd:date</code>.</td></tr>
</table>
</div>
<div class="note">
<p>
In RDF 1.1, <dfn data-cite="rdf11-concepts#dfn-language-tagged-string" data-lt="language-tagged string">language-tagged strings</dfn>[[!rdf11-concepts]] have the datatype <code>http://www.w3.org/1999/02/22-rdf-syntax-ns#langString</code>.
</p>
<p>
RDF 1.0 included <a>RDF literals</a> with no datatype or language tag.
These are called "<a data-cite="sparql11-query#simple_literal">simple literals</a>" in SPARQL11[[!sparql11-query]].
In RDF 1.1, these literals have the datatype <code>http://www.w3.org/2001/XMLSchema#string</code>.
</p>
</div>
<div class="example">
<div class="example-title marker"><span>Datatype example 2</span></div>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://www.w3.org/2000/01/rdf-schema#label",
"valueExpr": {
"type": "NodeConstraint",
"datatype": "http://www.w3.org/1999/02/22-rdf-syntax-ns#langString"
} } } ] }</pre>
<pre class="shexc">
ex:IssueShape {
rdfs:label rdf:langString
}
</pre>
</div>
<pre class="data">
<issue3> rdfs:label "emits dense black smoke"@en .
<span class="fail"><issue4> rdfs:label "unexpected odor" .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue3></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue4></td><td><IssueShape></td><td>fail</td><td class="fail"><code>rdfs:label</code> expected to be an <code>rdf:langString</code>, <code>xsd:string</code> found.</td></tr>
</table>
</div>
</section>
<section id="xs-string">
<h4>XML Schema String Facet Constraints</h4>
<!-- ul>
<li><a href="#length">XML Schema Length Constraints</a></li>
<li><a href="#minlength">XML Schema Minlength Constraints</a></li>
<li><a href="#maxlength">XML Schema Maxlength Constraints</a></li>
<li><a href="#pattern">XML Schema Pattern Constraints</a></li>
</ul -->
<p>
String facet constraints apply to the lexical form of the <a>RDF Literals</a> and <a>IRIs</a> and <a>blank node identifiers</a> (see <a href="#blank-node-label">note below</a> regarding access to <a>blank node identifiers</a>).<br/>
Let <span class="math">lex</span> =
</p>
<ul>
<li>if the value <span class="math">n</span> is an <a>RDF Literal</a>, the <a data-cite="rdf11-concepts#dfn-lexical-form">lexical form</a> of the literal (see [[!rdf11-concepts]] <a data-cite="rdf11-concepts#section-Graph-Literal">section 3.3 Literals</a>).</li>
<li>if the value <span class="math">n</span> is an <a>IRI</a>, the <a data-cite="rdf11-concepts#dfn-iri">IRI string</a> (see [[!rdf11-concepts]] <a data-cite="rdf11-concepts#section-iris">section 3.2 IRIs</a>).</li>
<li>if the value <span class="math">n</span> is a <a>blank node</a>, the <a>blank node identifier</a> (see [[!rdf11-concepts]] <a data-cite="rdf11-concepts#section-blank-nodes">section 3.4 Blank Nodes</a>).</li>
</ul>
<p>
Let <span class="math">len</span> = the number of unicode codepoints in <span class="math">lex</span><br/>
For a node <span class="math">n</span> and constraint value <span class="math">v</span>, <code class="function">nodeSatisfies(<span class="math">n</span>, <span class="math">v</span>)</code>:
</p>
<ul>
<li id="nodeSatisfies-length">for "<code>length</code>" constraints, <span class="math">v = len</span>,</li>
<li id="nodeSatisfies-minlength">for "<code>minlength</code>" constraints, <span class="math">v >= len</span>,</li>
<li id="nodeSatisfies-maxlength">for "<code>maxlength</code>" constraints, <span class="math">v <= len</span>,</li>
<li id="nodeSatisfies-pattern">
for "<code>pattern</code>" constraints, <span class="math">v</span> is unescaped into a valid <a data-cite="xpath-functions-31#regex-syntax">XPath 3.1 regular expression</a>[[!xpath-functions-31]] <span class="math">re</span> and invoking <code class="function"><a data-cite="xpath-functions-31#func-matches">fn:matches</a>(<span class="math">lex</span>, <span class="math">re</span>)</code> returns <code>fn:true</code>.
If the <span class="param">flags</span> parameter is present, it is passed as a third argument to <code class="function">fn:matches</code>.
The pattern may have XPath 3.1 regular expression escape sequences per the modified production [10] in <a href="https://www.w3.org/TR/xpath-functions-31/#matching-start-and-end">section 5.6.1.1</a> as well as numeric escape sequences of the form 'u' HEX HEX HEX HEX or 'U' HEX HEX HEX HEX HEX HEX HEX HEX.
Unescaping replaces numeric escape sequences with the corresponding unicode codepoint.
</li>
</ul>
<div class="example">
<div class="example-title marker"><span>String Facets example 1</span></div>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://schema.example/submittedBy",
"valueExpr": { "type": "NodeConstraint", "minlength": 10 } } } ] }</pre>
<pre class="shexc">
ex:IssueShape {
ex:submittedBy MINLENGTH 10
}
</pre>
</div>
<pre class="data">
<issue1> ex:submittedBy <http://a.example/bob> . <span class="comment"># 20 characters</span>
<span class="fail"><issue2> ex:submittedBy "Bob" .</span> <span class="comment"># 3 characters</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue1></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue2></td><td><IssueShape></td><td>fail</td><td class="fail"><code>ex:submittedBy</code> expected to be >= 10 characters,<br/> 3 characters found.</td></tr>
</table>
</div>
<div class="note" id="blank-node-label">
<p>
Access to <a>blank node identifiers</a> may be impossible or unadvisable for many use cases.
For instance, the SPARQL Query and SPARQL Update languages treat blank nodes in the query, labeled or otherwise, as variables.
Lexical constraints on <a>blank node identifiers</a> can only be implemented in systems which preserve such labels on data import.
</p>
</div>
<div class="example">
<div class="example-title marker"><span>String Facets example 2</span></div>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://schema.example/submittedBy",
"valueExpr": { "type": "NodeConstraint",
"pattern": "genuser[0-9]+", "flags": "i" }
} } ] }</pre>
<pre class="shexc">
ex:IssueShape {
ex:submittedBy ~/genuser[0-9]+/i
}
</pre>
</div>
<pre class="data">
<issue6> ex:submittedBy _:genUser218 .
<span class="fail"><issue7> ex:submittedBy _:genContact817 .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue6></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue7></td><td><IssueShape></td><td>fail</td><td class="fail"><code>_:genContact817</code> expected to match <code>genuser[0-9]+</code>.</td></tr>
</table>
</div>
<p>
When expressed as JSON strings, regular expressions are subject to the JSON string escaping rules.
</p>
<div class="example">
<div class="example-title marker"><span>String Facets example 3</span></div>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/ProductShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://schema.example/trademark",
"valueExpr": { "type": "NodeConstraint",
"pattern": "^/\\t\\\\\\U0001D4B8\\?$" }
} } ] }</pre>
<pre class="shexc">
ex:ProductShape {
ex:trademark /^\/\t\\\U0001D4B8\?$/
}
</pre>
</div>
<pre class="data">
<product6> ex:trademark " \\𝒸?" .
<product7> ex:trademark "\t\\\U0001D4B8?" . <span class="comment"># Turtle literals have escape characters <a href="https://www.w3.org/TR/turtle/#grammar-production-ECHAR">[tbnrf"'\]</a>.</span>
<span class="fail"><product8> ex:trademark "\t\\\\U0001D4B8?" .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><product6></td><td><ProductShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="pass"><td><product7></td><td><ProductShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><product8></td><td><ProductShape></td><td>fail</td><td class="fail">found "<code>\U0001D4B8</code>" instead of "<code>𝒸</code>" (codepoint U+1D4B8).</td></tr>
</table>
</div>
</section>
<section id="xs-numeric">
<h4>XML Schema Numeric Facet Constraints</h4>
<!-- ul>
<li><a href="#mininclusive">XML Schema Mininclusive Constraints</a></li>
<li><a href="#minexclusive">XML Schema Minexclusive Constraints</a></li>
<li><a href="#maxinclusive">XML Schema Maxinclusive Constraints</a></li>
<li><a href="#maxexclusive">XML Schema Maxexclusive Constraints</a></li>
<li><a href="#totaldigits">XML Schema Totaldigits Constraints</a></li>
<li><a href="#fractiondigits">XML Schema Fractiondigits Constraints</a></li>
</ul -->
<p>
Numeric facet constraints apply to the numeric value of <a>RDF Literals</a> with datatypes listed in <a data-cite="sparql11-query#operandDataTypes">SPARQL 1.1 Operand Data Types</a>[[!sparql11-query]].
Numeric constraints on non-numeric values fail.
<code>totaldigits</code> and <code>fractiondigits</code> constraints on values not derived from <code>xsd:decimal</code> fail.
</p>
<p>
Let <span class="math">num</span> be the numeric value of <span class="math">n</span>.<br/>
For a node <span class="math">n</span> and constraint value <span class="math">v</span>, <code class="function">nodeSatisfies(<span class="math">n</span>, <span class="math">v</span>)</code>:
</p>
<ul>
<li id="nodeSatisfies-mininclusive">for "<code>mininclusive</code>" constraints, <span class="math">v <= num</span>,</li>
<li id="nodeSatisfies-minexclusive">for "<code>minexclusive</code>" constraints, <span class="math">v < num</span>,</li>
<li id="nodeSatisfies-maxinclusive">for "<code>maxinclusive</code>" constraints, <span class="math">v >= num</span>,</li>
<li id="nodeSatisfies-maxexclusive">for "<code>maxexclusive</code>" constraints, <span class="math">v > num</span>,</li>
<li id="nodeSatisfies-totaldigits">for "<code>totaldigits</code>" constraints, <span class="math">v</span> is less than or equals the number of digits in the <a data-cite="xmlschema-2#dt-canonical-representation">XML Schema canonical form</a>[[!xmlschema-2]] of the value of <span class="math">n</span>,</li>
<li id="nodeSatisfies-fractiondigits">for "<code>fractiondigits</code>" constraints, <span class="math">v</span> is less than or equals the number of digits to the right of the decimal place in the <a data-cite="xmlschema-2#dt-canonical-representation">XML Schema canonical form</a>[[!xmlschema-2]] of the value of <span class="math">n</span>, ignoring trailing zeros.</li>
</ul>
<p>
The operators <span class="math"><=</span>, <span class="math"><</span>, <span class="math">>=</span> and <span class="math">></span> are evaluated after performing <a data-cite="xpath20#promotion">numeric type promotion</a>[[!xpath20]].
</p>
<div class="example">
<div class="example-title marker"><span>Numeric Facets example 1</span></div>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://schema.example/confirmations",
"valueExpr": { "type": "NodeConstraint", "mininclusive": 1 } } } ] }</pre>
<pre class="shexc">
ex:IssueShape {
ex:confirmations MININCLUSIVE 1
}
</pre>
</div>
<pre class="data">
<issue1> ex:confirmations 1 .
<issue2> ex:confirmations 2^^xsd:byte .
<span class="fail"><issue3> ex:confirmations 0 .</span>
<span class="fail"><issue4> ex:confirmations "ii"^^ex:romanNumeral .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue1></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="pass"><td><issue2></td><td><IssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue3></td><td><IssueShape></td><td>fail</td><td class="fail"><code>0</code> is less than <code>1</code>.</td></tr>
<tr class="fail"><td><issue4></td><td><IssueShape></td><td>fail</td><td class="fail"><code>ex:romanNumeral</code> is not a numeric datatype.</td></tr>
</table>
</div>
</section>
<section id="values">
<h4>Values Constraint</h4>
<p>
The <code><a href="#nodeSatisfies">nodeSatisfies</a></code> semantics for <span class="jobjref"><a class="obj">NodeConstraint</a></span> <span class="param">values</span> depends on a <code>nodeIn</code> function <a href="#nodeIn">defined below</a>.
</p>
<p>
For a node <span class="math">n</span> and constraint value <span class="math">v</span>, <code class="function">nodeSatisfies(<span class="math">n</span>, <span class="math">v</span>)</code> if <span class="math">n</span> matches some <a class="nobref">valueSetValue</a> <span class="math">vsv</span> in <span class="math">v</span>.
A term matches a valueSetValue if:
</p>
<ul>
<li><span class="math" id="nodeSatisfies-objectValue">vsv</span> is an <a class="nobref">objectValue</a> and <span class="math">n = vsv</span>.</li>
<li><span class="math">vsv</span> is a <span class="jobjref"><a class="obj">Language</a></span> with <span class="param">langTag</span> <span class="math">lt</span> and <span class="math">n</span> is a <a>language-tagged string</a> with a <a>language tag</a> <span class="math">l</span> and <span class="math function" >l = lt</span>.</li>
<li><span class="math" id="nodeSatisfies-Stem">vsv</span> is a <span class="jobjref"><a class="nobref">IriStem</a></span>, <span class="jobjref"><a class="nobref">LiteralStem</a></span> or <span class="jobjref"><a class="nobref">LanguageStem</a></span> with <span class="param">stem</span> <span class="math">st</span> and <span class="math">nodeIn(n, st)</span>.</li>
<li><span class="math" id="nodeSatisfies-StemRange">vsv</span> is a <span class="jobjref"><a class="nobref">IriStemRange</a></span>, <span class="jobjref"><a class="nobref">LiteralStemRange</a></span> or <span class="jobjref"><a class="nobref">LanguageStemRange</a></span> with <span class="param">stem</span> <span class="math">st</span> and <span class="param">exclusions</span> <span class="math">excls</span> and <span class="math function" >nodeIn(n, st)</span> and there is no <span class="math">x</span> in <span class="math">excls</span> such that <span class="math function" >nodeIn(n, excl)</span>.</li>
<li><span class="math" id="nodeSatisfies-Wildcard">vsv</span> is a <span class="jobjref"><a class="nobref">Wildcard</a></span> with <span class="param">exclusions</span> <span class="math">excls</span> and there is no <span class="math">x</span> in <span class="math">excls</span> such that <span class="math function" >nodeIn(n, excl)</span>.</li>
</ul>
<p>
<span class="label" id="nodeIn">nodeIn</span>: asserts that an RDF node <span class="math">n</span> is equal to an RDF term <span class="math">s</span> or is in a set defined by a <span class="jobjref"><a class="obj">IriStem</a></span>, <span class="jobjref"><a class="obj">LiteralStem</a></span> or <span class="jobjref"><a class="obj">LanguageStem</a></span>.<br/>
The expression <code class="function">nodeIn(<span class="math">n</span>, <span class="math">s</span>)</code> is satisfied if:
</p>
<ul>
<li><span class="math">n = s</span>.</li>
<li><span class="math">s</span> is a <span class="jobjref"><a class="obj">IriStem</a></span>, <span class="jobjref"><a class="obj">LiteralStem</a></span> or <span class="jobjref"><a class="obj">LanguageStem</a></span> with <span class="param">stem</span> <span class="math">st</span> and:
<ul>
<li><span class="math">s</span> is a <span class="jobjref"><a class="obj">IriStem</a></span> and <span class="math">n</span> is an <a>IRI</a> and <span class="math function" ><a data-cite="xpath-functions-31#func-starts-with">fn:starts-with</a>(n, st)</span>.</li>
<li><span class="math">s</span> is a <span class="jobjref"><a class="obj">LiteralStem</a></span> and <span class="math">n</span> is an <a>RDF Literal</a> with a lexical value <span class="math">l</span> and <span class="math function" ><a data-cite="xpath-functions-31#func-starts-with">fn:starts-with</a>(l, st)</span>.</li>
<li><span class="math">s</span> is a <span class="jobjref"><a class="obj">LanguageStem</a></span>, <span class="math">n</span> is a <a>language-tagged string</a> with a <a>language tag</a> <span class="math">l</span>, <span class="math">st</span> is a basic language range per <a class="norm" href="http://www.ietf.org/rfc/rfc4647.txt">Matching of Language Tags</a> [[!rfc4647]] section 2.1 and <span class="math">l</span> matches <span class="math">st</span> per the basic filtering scheme defined in [[!rfc4647]] section 3.3.1.</li>
<li><span class="math">n</span> is a <a>blank node</a> with identifier <span class="math">l</span> and <span class="math function" ><a data-cite="xpath-functions-31#func-starts-with">fn:starts-with</a>(l, st)</span>.</li>
</ul></li>
</ul>
<div class="example">
<div class="example-title marker"><span>Values Constraint example 1</span></div>
<p>NoActionIssueShape requires a state of Resolved or Rejected:</p>
<div class="repchoice">
<pre class="json">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/NoActionIssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://schema.example/state",
"valueExpr": {
"type": "NodeConstraint", "values": [
"http://schema.example/Resolved",
"http://schema.example/Rejected" ] } } } ] }</pre>
<pre class="shexc">
ex:NoActionIssueShape {
ex:state [ ex:Resolved ex:Rejected ]
}
</pre>
</div>
<pre class="data">
<issue1> ex:state ex:Resolved .
<span class="fail"><issue2> ex:state ex:Unresolved .</span></pre>
<table>
<tr><th class="data">node</th><th class="schema">shape</th><th>result</th><th>reason</th></tr>
<tr class="pass"><td><issue1></td><td><NoActionIssueShape></td><td>pass</td><td class="noreason"></td></tr>
<tr class="fail"><td><issue2></td><td><NoActionIssueShape></td><td>fail</td><td class="fail"><code>ex:state</code> expected to be <code>ex:Resolved</code> or <code>ex:Rejected</code>, <code>ex:Unresolved</code> found.</td></tr>
</table>
</div>
<div class="example">
<div class="example-title marker"><span>Values Constraint example 2</span></div>
<p>An employee must have an email address that is the string "N/A" or starts with "engineering-" or "sales-" but not "sales-contacts" or "sales-interns":</p>