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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.next</title>
<!-- link rel="stylesheet" href="css/wgio.min.css"/ ask Iovka -->
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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 is an editor's draft of the Shape Expressions specification.
ShEx 2.x differs significantly from the W3C ShEx Submission.
The <a href="http://shex.io/shex-semantics-20170713/">July 2017 publication</a> included a <a href="#validation">definition of validation</a> which implied infinite recursion.
This version explicitly includes recursion checks.
No tests changed as a result of this and no implementations or applications are known to have been affected.
</p>
<p>
If you wish to make comments regarding this document, please raise them as GitHub issues.
There are separate interfaces for <a href="https://github.com/shexSpec/spec/issues">specification</a>, <a href="https://github.com/shexSpec/shex/issues">language</a> and <a href="https://github.com/shexSpec/shexTest/issues">test</a> issues.
Only send comments to <a href="mailto:public-shex@w3.org">public-shex@w3.org</a> (<a href="mailto:public-shex-request@w3.org?subject=subscribe">subscribe</a>,
<a href="https://lists.w3.org/Archives/Public/public-shex/">archives</a>) if you are unable to raise issues on GitHub. All comments are welcome.
</p>
</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 [[!rfc7159]] Syntax serves as a serializable proxy for an abstract syntax.
</p>
<p>
<a data-cite="rdf11-concepts/#dfn-rdf-term">RDF terms</a> are represented as <a data-cite="json-ld#dfn-node">JSON-LD nodes</a>.
<ul>
<li><a>IRIs</a> are represented as a <a data-cite="rfc7159#section-7">JSON string</a> consisting of the IRI string, e.g. <br/><code class="json">"http://example.org/resource"</code></li>
<li><a>Blank nodes</a> are represented as a JSON string composed of 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. <br/><code class="json">"_:blank3"</code></li>
<li><a>Literals</a> are represented as a <a>JSON object</a>s following the composition rules for <a data-cite="json-ld/#dfn-json-ld-value">JSON-LD values</a>, i.e.
<ul>
<li>literals with the datatype <code>http://www.w3.org/2001/XMLSchema#string</code> are represented with the <span class="param">value</span> property, e.g. <br/><code class="json">{ "value": "abc" }</code>.</li>
<li><a>language-tagged strings</a> are represented with an additional <span class="param">language</span> property, e.g. <br/><code class="json">{ "value": "hello world", "langague": "en-US" }</code></li>
<li>datatyped literals are represented with an additional <span class="param">datatype</span> property, e.g. <br/><code class="json">{ "value": "123", "datatype": "http://www.w3.org/2001/XMLSchema#integer" }</code></li>
</ul></li>
</ul>
</p>
<section id="json-grammar">
<h3>JSON Grammar</h3>
<p>
This specification uses a <dfn>JSON grammar</dfn> to describe the set of JSON documents that can be interpreted as a ShEx schema.
ShEx data structures are represented as <dfn data-cite="rfc7159#section-4" data-lt="json object">JSON objects</dfn> with a member with the name "<code>type</code>" (i.e. an object with a <span class="param">type</span> attribute):
</p>
<div class="json">
<pre class="json nohighlight">{ "type": "typeName", member<sub>0…n</sub> }</pre>
</div>
<p>
These are expressed in JSON grammar as <span class="shexj">typeName { member* }</span>.
<a data-cite="rfc7159#section-2">RFC7159 Section 2</a> provides syntactic constraints for JSON — the grammar constraining those to valid <a>ShExJ</a> constructs is composed of:
</p>
<ul>
<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>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>
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 four optional components called <a class="param">startActs</a>, <a class="param">start</a>, <a class="param">imports</a> and <a class="param">shapes</a>:
</p>
<ul>
<li><span class="param">startActs</span> is a list of one or more <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 one or more <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>
<section id="shex-references">
<h3>References</h3>
<p>
<a>ShExJ</a> is a dialect of JSON-LD [[!JSON-LD]] and the member <dfn class="param">id</dfn> is used as a <a data-cite="JSON-LD#node-identifiers">node identifier</a>.
An object may be represented inline or referenced by its <span class="param">id</span> 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>? <a class="param">shapeExprs</a>:[<a class="nobjref">shapeExpr</a>{2,}] }
<a class="nob">shapeExprLabel</a> = <a class="nobref">IRIREF</a> | <a class="objref">BNODE</a> ;
<a class="obj">EachOf</a> { <a class="param">id</a>:<a class="nobjref">tripleExprLabel</a>? <a class="param">expressions</a>:[<a class="nobjref">tripleExpr</a>{2,}] ... }
<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 an <span class="param">id</span>.
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 nohighlight">{ "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> nested in a schema's <a class="param">shapes</a> must have an <span class="param">id</span> and no other <a class="nobjref">shapeExpr</a> may have an <span class="param">id</span>.
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>.
This example includes a nested shape. Nested shapes are not permitted to have <span class="param">ids</span>.
</p>
<div class="json">
<pre class="json nohighlight">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/#IssueShape",
"type": "Shape", "expression": {
"type": "TripleConstraint", "predicate": "http://schema.example/#submittedBy",
"valueExpr": {
"type": "Shape", "expression": {
"type": "TripleConstraint", "predicate": "http://schema.example/#name",
"valueExpr": {
"type": "NodeConstraint", "nodeKind": "literal"
} } } } } ] }</pre>
</div>
<p class="note">
The shape expressions in a schema are expressed as a list of shape expressions with <span class="param">id</span> attributes because JSON-LD 1.0 has no provision for defining as JSON object as representing a map of URL→object.
Drafts of JSON-LD 1.1 <a href="https://www.w3.org/TR/2018/WD-json-ld11-20181011/#id-maps">include this expressivity</a> and, once JSON-LD 1.1 exits Candidate Recommendation, future versions of ShExJ will likely adopt it while requiring backard-compatibility with the list of shape expressions with <span class="param">id</span> attributes.
</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>
<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>
<!--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>" (for "conformant" status) or "<span class="fail">fail</span>" ("nonconformant" status), 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 <dfn data-cite="rdf11-concepts#dfn-iri" data-lt="iris">IRI</dfn>, <dfn data-cite="rdf11-concepts#dfn-blank-node" data-lt="bnodes|blank nodes">blank node</dfn>, <dfn data-cite="rdf11-concepts#dfn-literal" data-lt="literal|literals|RDF Literal|RDF Literals">Literal</dfn></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="data">
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 class="data">
_: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 class="data">
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 class="data">
_: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>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 incomplete">
<pre class="json nohighlight">{ "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 nohighlight">
ex:IssueShape { … }
_:UserShape { … }
ex:EmployeeShape { … }
</pre>
</div>
</section>
<section id="validation">
<h3>Validation Definition</h3>
<p>
<dfn id="isValid" label="isValid">isValid</dfn>: For a graph <span class="math">G</span>, a schema <span class="math">Sch</span> and a fixed ShapeMap <span class="math">ism</span>, <code class="function">isValid(<span class="math">G</span>, <span class="math">Sch</span>, <span class="math">ism</span>)</code> indicates that for every RDFnode/shapeLabel pair <span class="math">(n, sl)</span> in <span class="math">ism</span>, the node <span class="math">n</span> satisfies the shape expression identified by <span class="math">sl</span>.
The latter is captured by the expression <code class="function">satisfies(<span class="math">n</span>, <span class="math">s</span>, <span class="math">G</span>, <span class="math">Sch</span>, <a href="#completeTyping">completeTyping</a>(<span class="math">G</span>, <span class="math">Sch</span>))</code>.
The function <code class="function">satisfies</code> is defined for every kind of <a>shape expression</a>.
</p>
<p>
The validation of an RDF graph <span class="math">G</span> against a ShEx schema <span class="math">Sch</span> is based on the existence of <a href="#completeTyping"><code class="function">completeTyping(<span class="math">G</span>, <span class="math">Sch</span>)</code></a>.
For an RDF graph <span class="math">G</span> and a shapes schema <span class="math">Sch</span>, a <dfn>typing</dfn> is a set of pairs of the form <span class="math">(n, s)</span> where <span class="math">n</span> is a node in <span class="math">G</span> and <span class="math">s</span> is a <a>Shape</a> that appears in some shape expression in the <span class="param">shapes</span> mapping of <span class="math">Sch</span>.
A <dfn label="correct typing">correct typing</dfn> is a <span class="math">typing</span> such that for every RDFnode/shape pair <span class="math">(n,s)</span> in <span class="math">typing</span>, <a href="#satisfies-Shape"><code class="function">matchesShape(<span class="math">n</span>, <span class="math">s</span>, <span class="math">G</span>, <span class="math">Sch</span>, <span class="math">typing</span>)</code></a> holds.
<code class="function">completeTyping(<span class="math">G</span>, <span class="math">Sch</span>)</code> is a unique correct typing that exists for every graph and every ShEx schema that satisfies the <a href="#schema-requirements">schema requirements</a>.
</p>
<p>
<dfn id="completeTyping">completeTyping</dfn>: the definition of <code class="function">completeTyping(<span class="math">G</span>, <span class="math">Sch</span>)</code> is based on a <a>stratification</a> of <span class="math">Sch</span>.
The number of <dfn>strata</dfn> of <span class="math">Sch</span> is the number of maximal strongly connected components of the <a>dependency graph</a> of <span class="math">Sch</span>.
A <dfn>stratification</dfn> of a schema <span class="math">Sch</span> with <span class="math">k</span> strata is a function <code class="function">stratum</code> that associates with every <a>Shape</a> in <span class="math">Sch</span> a natural number between <span class="math">1</span> and <span class="math">k</span> such that:
</p>
<ul>
<li>
If <span class="math">s1</span> and <span class="math">s2</span> belong to the same maximal strongly connected component, then <code class="function">stratum(<span class="math">s1</span>)</code> = <code class="function">stratum(<span class="math">s2</span>)</code>.
</li>
<li>
If there is a <a>reference</a> from <span class="math">s1</span> to <span class="math">s2</span> and <span class="math">s1</span> and <span class="math">s2</span> do not belong to the same maximal strongly connected component, then <code class="function">stratum(<span class="math">s2</span>)</code> < <code class="function">stratum(<span class="math">s1</span>)</code>.
</li>
</ul>
<p>
The existence of a stratification for every schema is guaranteed by the <a href="#negation-requirement">negation requirement</a>.
</p>
<p>
Given a <a>stratification</a> <code class="function">stratum</code> of <span class="math">Sch</span> with <span class="math">k</span> strata, define inductively the series of <span class="math">k</span> typings <code class="function">completeTypingOn(<span class="math">1</span>, <span class="math">G</span>, <span class="math">Sch</span>)</code> … <code class="function">completeTypingOn(<span class="math">k</span>, <span class="math">G</span>, <span class="math">Sch</span>)</code>.
</p>
<ul>
<li>
<code class="function">completeTypingOn(<span class="math">1</span>, <span class="math">G</span>, <span class="math">Sch</span>)</code> is the union of all correct typings that contain only RDFnode/shape pairs <span class="math">(n,s)</span> with <code class="function">stratum(<span class="math">s</span>)</code> = <span class="math">1</span>;
</li>
<li>
for every <span class="math">i</span> between <span class="math">2</span> and <span class="math">k</span>, <code class="function">completeTypingOn(<span class="math">i</span>, <span class="math">G</span>, <span class="math">Sch</span>)</code> is the union of all correct typings that:
<ul>
<li> contain only RDFnode/shape pairs <span class="math">(n,s)</span> with <code class="function">stratum(<span class="math">s</span>)</code> ≤ <span class="math">i</span>
</li>
<li> are equal to <code class="function">completeTypingOn(<span class="math">i</span>-1, <span class="math">G</span>, <span class="math">Sch</span>)</code> when restricted to their RDFnode/shape pairs <span class="math">(n1,s1)</span> for which <code class="function">stratum(<span class="math">s1</span>)</code> < i.
</li>
</ul>
</li>
</ul>
<p>
Then <code class="function">completeTyping(<span class="math">G</span>, <span class="math">Sch</span>)</code> = <code class="function">completeTypingOn(<span class="math">k</span>, <span class="math">G</span>, <span class="math">Sch</span>)</code>.
</p>
<div class="note">
The definition on strogly connected component and maximal strongly connected component of a graph can be found on Wikipedia <a href="https://en.wikipedia.org/wiki/Strongly_connected_component">https://en.wikipedia.org/wiki/Strongly_connected_component</a>.
</div>
<div class="note">
<p>
The schema <span class="math">Sch</span> might have several different stratifications but <code class="function">completeTyping(<span class="math">G</span>, <span class="math">Sch</span>)</code> is the same for all these stratifications.
This property is reminiscent of the use of stratified negiation in Datalog.
</p>
<p>
In order to decide isValid(Sch, G, m), it is sufficient to compute only a portion of completeTyping using an appropriate algorithm.
</p>
</div>
<div class="note">
<p>
Popular methods for constructing the input fixed ShapeMaps can be found on <a href="https://www.w3.org/2001/sw/wiki/ShEx/ShapeMap">https://www.w3.org/2001/sw/wiki/ShEx/ShapeMap</a>.
</p>
</div>
<!--
<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>
</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>? <dfn class="param">shapeExprs</dfn>:[<a class="nobref">shapeExpr</a>{2,}] }</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>{2,}] }</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>IRIREF</a> | <a>BNODE</a> ;</td></tr>
</table>
</div>
<div class="example">
<p>
Examples of shape expressions:
</p>
<div class="repchoice incomplete">
<pre class="json nohighlight">{ "type": "Shape", <span class="comment">…</span> } </pre>
<pre class="shexc nohighlight">{ <span class="comment">…</span> } </pre>
</div>
<div style="clear:both;"> </div>
<div class="repchoice incomplete">
<pre class="json nohighlight">{ "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 nohighlight">
<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">Sch</span>, <span class="math">t</span>)</code> indicates that a node <span class="math">n</span> and a <a>graph</a> <span class="math">G</span> satisfy a <a>shape expression</a> <span class="math">se</span> with <a>typing</a> <span class="math">t</span> for schema <span class="math">Sch</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">Sch</span>, <span class="math">t</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>typing</a> <span class="math">t</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">Sch</span>, <span class="math">t</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>typing</a>.</li>
<li id="satisfies-Shape-proxy"><span class="math">se</span> is a <span class="jobjref"><a class="obj">Shape</a></span> and <span class="math">(n, se)</span> belongs to <span class="math">t</span>.
</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="math">se</span>.<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">Sch</span>, <span class="math">t</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="math">se</span>.<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">Sch</span>, <span class="math">t</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="math">se</span>.<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">Sch</span>, <span class="math">t</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 <code class="function">satisfies(<span class="math">n</span>, <span class="math">se2</span>, <span class="math">G</span>, <span class="math">Sch</span>, <span class="math">t</span>)</code> where <span class="math">se2</span> is the shape expression having <span class="math">se</span> as <span class="param">id</span>.
</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">Sch</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">Sch</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">Sch</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">Sch</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">Sch</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">Sch</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">Sch</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>IRIREF</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>IRIREF</a> | <a class="objref">ObjectLiteral</a> ;</td></tr>
<tr class="nob"><th class="nob"><dfn>ObjectLiteral</dfn></th><td>{</td><td><span class="param">value</span>:<a>STRING</a> <span class="param">language</span>:<a>STRING</a>? <span class="param">type</span>:<a>STRING</a>? }</td></tr>
<tr class="obj"><th class="obj"><dfn>IriStem</dfn></th><td>{</td><td><span class="param">stem</span>:<a>IRIREF</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>IriStemRange</dfn></th><td>{</td><td><span class="param">stem</span>:(<a>IRIREF</a> | <a class="objref">Wildcard</a>) <span class="param">exclusions</span>:[<a class="nobref">IRIREF</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>STRING</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>LiteralStemRange</dfn></th><td>{</td><td><span class="param">stem</span>:(<a class="nobref">STRING</a> | <a class="objref">Wildcard</a>) <span class="param">exclusions</span>:[<a class="nobref">STRING</a>|<a class="objref">LiteralStem</a> +] }</td></tr>
<tr class="obj"><th class="obj"><dfn>Language</dfn></th><td>{</td><td><span class="param">languageTag</span>:<a>LANGTAG</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>LanguageStem</dfn></th><td>{</td><td><span class="param">stem</span>:<a>LANGTAG</a> }</td></tr>
<tr class="obj"><th class="obj"><dfn>LanguageStemRange</dfn></th><td>{</td><td><span class="param">stem</span>:(<a>LANGTAG</a> | <a class="objref">Wildcard</a>) <span class="param">exclusions</span>:[<a class="nobref">LANGTAG</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 nohighlight">{ "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 nohighlight">
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="#matches-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]].
The lexical form and numeric value (where applicable) of all datatypes required by <a data-cite="sparql11-query#FunctionMapping">SPARQL XPath Constructor Functions</a> MUST be tested for conformance with the corresponding XML Schema form.
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 nohighlight">{ "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 nohighlight">
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 nohighlight">{ "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 nohighlight">
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 nohighlight">{ "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 nohighlight">
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 nohighlight">{ "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 nohighlight">
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 nohighlight">{ "type": "Schema", "shapes": [
{ "id": "http://schema.example/#ProductShape",
"type": "Shape", "expression": {
"type": "TripleConstraint",
"predicate": "http://schema.example/#trademark",
"valueExpr": { "type": "NodeConstraint",
"pattern": "^/\\t\\\\\uD835\uDCB8\\?$" }
} } ] }</pre>
<pre class="shexc nohighlight">
ex:ProductShape {
ex:trademark /^\/\t\\\U0001D4B8\?$/
}
</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>