diff --git a/types/n3/index.d.ts b/types/n3/index.d.ts
index cfb6149111..1b9fb95db0 100644
--- a/types/n3/index.d.ts
+++ b/types/n3/index.d.ts
@@ -21,10 +21,10 @@ export interface Prefixes<I = RDF.NamedNode> {
 export type Term = NamedNode | BlankNode | Literal | Variable | DefaultGraph;
 export type PrefixedToIri = (suffix: string) => NamedNode;
 
-export class NamedNode implements RDF.NamedNode {
+export class NamedNode<Iri extends string = string> implements RDF.NamedNode<Iri> {
     readonly termType: "NamedNode";
-    readonly value: string;
-    constructor(iri: string);
+    readonly value: Iri;
+    constructor(iri: Iri);
     readonly id: string;
     toJSON(): {};
     equals(other: RDF.Term): boolean;
@@ -83,6 +83,8 @@ export type Quad_Graph = DefaultGraph | NamedNode | BlankNode | Variable;
 
 export class BaseQuad implements RDF.BaseQuad {
     constructor(subject: Term, predicate: Term, object: Term, graph?: Term);
+    termType: 'Quad';
+    value: '';
     subject: Term;
     predicate: Term;
     object: Term;
@@ -104,7 +106,7 @@ export class Quad extends BaseQuad implements RDF.Quad {
 export class Triple extends Quad implements RDF.Quad {}
 
 export namespace DataFactory {
-    function namedNode(value: string): NamedNode;
+    function namedNode<Iri extends string = string>(value: Iri): NamedNode<Iri>;
     function blankNode(value?: string): BlankNode;
     function literal(value: string | number, languageOrDatatype?: string | RDF.NamedNode): Literal;
     function variable(value: string): Variable;
diff --git a/types/rdf-ext/lib/DataFactory.d.ts b/types/rdf-ext/lib/DataFactory.d.ts
index e9e28cade9..3a3f54c02f 100644
--- a/types/rdf-ext/lib/DataFactory.d.ts
+++ b/types/rdf-ext/lib/DataFactory.d.ts
@@ -27,7 +27,7 @@ declare class DataFactoryExt  {
     PrefixMap: typeof PrefixMap;
   };
   static factory: typeof DataFactoryExt;
-  static namedNode(value: string): NamedNodeExt;
+  static namedNode<Iri extends string = string>(value: Iri): NamedNodeExt<Iri>;
   static blankNode(value?: string): BlankNodeExt;
   static literal(value: string, languageOrDatatype?: string | NamedNode): LiteralExt;
   static variable(value: string): VariableExt;
diff --git a/types/rdf-ext/lib/NamedNode.d.ts b/types/rdf-ext/lib/NamedNode.d.ts
index f3bfd8c12c..61aa48516a 100644
--- a/types/rdf-ext/lib/NamedNode.d.ts
+++ b/types/rdf-ext/lib/NamedNode.d.ts
@@ -1,7 +1,7 @@
 import { NamedNode, Term } from "rdf-js";
 import { PropType } from './_PropType';
 
-interface NamedNodeExt extends NamedNode {
+interface NamedNodeExt<Iri extends string = string> extends NamedNode<Iri> {
   toCanonical(): string;
   toJSON(): {
     value: PropType<NamedNode, 'value'>;
diff --git a/types/rdf-ext/lib/Quad.d.ts b/types/rdf-ext/lib/Quad.d.ts
index 5319066a59..37c8de44c5 100644
--- a/types/rdf-ext/lib/Quad.d.ts
+++ b/types/rdf-ext/lib/Quad.d.ts
@@ -7,6 +7,8 @@ import VariableExt = require('./Variable');
 import DefaultGraphExt = require('./DefaultGraph');
 
 interface QuadExt extends Quad {
+  termType: 'Quad';
+  value: '';
   subject: NamedNodeExt | BlankNodeExt | VariableExt;
   predicate: NamedNodeExt | VariableExt;
   object: NamedNodeExt | LiteralExt | BlankNodeExt | VariableExt;
diff --git a/types/rdf-js/index.d.ts b/types/rdf-js/index.d.ts
index f5e027f35b..e20b9ae4f4 100644
--- a/types/rdf-js/index.d.ts
+++ b/types/rdf-js/index.d.ts
@@ -1,4 +1,4 @@
-// Type definitions for the RDFJS specification 3.0
+// Type definitions for the RDFJS specification 4.0
 // Project: https://github.com/rdfjs/representation-task-force
 // Definitions by: Ruben Taelman <https://github.com/rubensworks>
 //                 Laurens Rietveld <https://github.com/LaurensRietveld>
@@ -15,14 +15,15 @@ import { EventEmitter } from "events";
 /* https://rdf.js.org/data-model-spec/ */
 
 /**
- * Contains an Iri, RDF blank Node, RDF literal, variable name, or a default graph
+ * Contains an Iri, RDF blank Node, RDF literal, variable name, default graph, or a quad
  * @see NamedNode
  * @see BlankNode
  * @see Literal
  * @see Variable
  * @see DefaultGraph
+ * @see Quad
  */
-export type Term = NamedNode | BlankNode | Literal | Variable | DefaultGraph;
+export type Term = NamedNode | BlankNode | Literal | Variable | DefaultGraph | BaseQuad;
 
 /**
  * Contains an IRI.
@@ -145,7 +146,7 @@ export interface DefaultGraph {
  * @see BlankNode
  * @see Variable
  */
-export type Quad_Subject = NamedNode | BlankNode | Variable;
+export type Quad_Subject = NamedNode | BlankNode | Quad | Variable;
 
 /**
  * The predicate, which is a NamedNode or Variable.
@@ -161,7 +162,7 @@ export type Quad_Predicate = NamedNode | Variable;
  * @see BlankNode
  * @see Variable
  */
-export type Quad_Object = NamedNode | Literal | BlankNode | Variable;
+export type Quad_Object = NamedNode | Literal | BlankNode | Quad | Variable;
 
 /**
  * The named graph, which is a DefaultGraph, NamedNode, BlankNode or Variable.
@@ -176,6 +177,15 @@ export type Quad_Graph = DefaultGraph | NamedNode | BlankNode | Variable;
  * An RDF quad, taking any Term in its positions, containing the subject, predicate, object and graph terms.
  */
 export interface BaseQuad {
+  /**
+   * Contains the constant "Quad".
+   */
+  termType: "Quad";
+  /**
+   * Contains an empty string as constant value.
+   */
+  value: "";
+
   /**
    * The subject.
    * @see Quad_Subject
@@ -201,7 +211,7 @@ export interface BaseQuad {
    * @param other The term to compare with.
    * @return True if and only if the argument is a) of the same type b) has all components equal.
    */
-  equals(other: BaseQuad | null | undefined): boolean;
+  equals(other: Term | null | undefined): boolean;
 }
 
 /**
@@ -233,7 +243,7 @@ export interface Quad extends BaseQuad {
      * @param other The term to compare with.
      * @return True if and only if the argument is a) of the same type b) has all components equal.
      */
-    equals(other: BaseQuad | null | undefined): boolean;
+    equals(other: Term | null | undefined): boolean;
 }
 
 /**
@@ -245,10 +255,7 @@ export interface DataFactory<OutQuad extends BaseQuad = Quad, InQuad extends Bas
      * @return A new instance of NamedNode.
      * @see NamedNode
      */
-    // TODO: This could be changed into a Generic method that returns a NamedNode constained to the
-    //       given `value` - but note that that would be a breaking change. See commit
-    //       16d29e86cd6fe34e6ac6f53bba6ba1a1988d7401.
-    namedNode(value: string): NamedNode;
+    namedNode<Iri extends string = string>(value: Iri): NamedNode<Iri>;
 
     /**
      * @param value The optional blank node identifier.
diff --git a/types/rdf-js/rdf-js-tests.ts b/types/rdf-js/rdf-js-tests.ts
index eae4829551..738b9555b0 100644
--- a/types/rdf-js/rdf-js-tests.ts
+++ b/types/rdf-js/rdf-js-tests.ts
@@ -69,6 +69,11 @@ function test_datafactory() {
     const dataFactory: DataFactory = <any> {};
 
     const namedNode: NamedNode = dataFactory.namedNode('http://example.org');
+    const constantValue: 'http://example.org' = dataFactory.namedNode('http://example.org').value;
+    // $ExpectError
+    const otherConstantValue: 'http://not-example.org' = dataFactory.namedNode('http://example.org').value;
+    // $ExpectError
+    const otherConstantNamedNode: NamedNode<'http://not-example.org'> = dataFactory.namedNode('http://example.org');
 
     const blankNode1: BlankNode = dataFactory.blankNode('b1');
     const blankNode2: BlankNode = dataFactory.blankNode();
@@ -92,6 +97,54 @@ function test_datafactory() {
     const hasBnode = quad.predicate.termType === "BlankNode";
 }
 
+function test_datafactory_star() {
+    const dataFactory: DataFactory = <any> {};
+
+    // Compose the triple "<<ex:bob ex:age 23>> ex:certainty 0.9."
+    const quadBobAge: Quad = dataFactory.quad(
+        dataFactory.namedNode('ex:bob'),
+        dataFactory.namedNode('ex:age'),
+        dataFactory.literal('23'),
+    );
+    const quadBobAgeCertainty: Quad = dataFactory.quad(
+        quadBobAge,
+        dataFactory.namedNode('ex:certainty'),
+        dataFactory.literal('0.9'),
+    );
+
+    // Decompose the triple
+    if (quadBobAgeCertainty.subject.termType === 'Quad') {
+        const quadBobAge2: Quad = quadBobAgeCertainty.subject;
+
+        const equalToSelf: boolean = quadBobAge2.equals(quadBobAge);
+        const notEqualToOtherType: boolean = quadBobAge2.equals(dataFactory.namedNode('ex:something:else'));
+    }
+}
+
+function test_datafactory_star_basequad() {
+    const dataFactory: DataFactory<BaseQuad> = <any> {};
+
+    // Compose the triple "<<ex:bob ex:age 23>> ex:certainty 0.9."
+    const quadBobAge: BaseQuad = dataFactory.quad(
+        dataFactory.namedNode('ex:bob'),
+        dataFactory.namedNode('ex:age'),
+        dataFactory.literal('23'),
+    );
+    const quadBobAgeCertainty: BaseQuad = dataFactory.quad(
+        quadBobAge,
+        dataFactory.namedNode('ex:certainty'),
+        dataFactory.literal('0.9'),
+    );
+
+    // Decompose the triple
+    if (quadBobAgeCertainty.subject.termType === 'Quad') {
+        const quadBobAge2: BaseQuad = quadBobAgeCertainty.subject;
+
+        const equalToSelf: boolean = quadBobAge2.equals(quadBobAge);
+        const notEqualToOtherType: boolean = quadBobAge2.equals(dataFactory.namedNode('ex:something:else'));
+    }
+}
+
 function test_stream() {
     const stream: Stream = <any> {};
     const quad: Quad | null = stream.read();