build: fix docs not display inherited members properly

Recently due to the MDC prototypes, we have multiple layers of inheritance. Apparently
our current docs tooling sometimes does not display inherited members which are coming
from implicitly inherited class-like documents.

For example: see how the `MatTabLink` docs broke when the MDC prototype
landed: 492fdcc40

tools/dgeni/processors/docs-private-filter.ts

@@ -9,6 +9,7 @@ import {getDocsPublicTag, isPublicDoc} from '../common/private-docs';
 export class DocsPrivateFilter implements Processor {
   name = 'docs-private-filter';
   $runBefore = ['categorizer'];
+  $runAfter = ['merge-inherited-properties'];
 
   $process(docs: DocCollection) {
     return docs.filter(doc => {

tools/dgeni/processors/merge-inherited-properties.ts

@@ -1,5 +1,6 @@
 import {DocCollection, Processor} from 'dgeni';
 import {ClassExportDoc} from 'dgeni-packages/typescript/api-doc-types/ClassExportDoc';
+import {ClassLikeExportDoc} from 'dgeni-packages/typescript/api-doc-types/ClassLikeExportDoc';
 import {MemberDoc} from 'dgeni-packages/typescript/api-doc-types/MemberDoc';
 
 /**
@@ -11,18 +12,30 @@ export class MergeInheritedProperties implements Processor {
   $runBefore = ['categorizer'];
 
   $process(docs: DocCollection) {
-    return docs
-      .filter(doc => doc.docType === 'class')
-      .forEach(doc => this._addInheritedProperties(doc));
+    return docs.filter(doc => doc.docType === 'class')
+        .forEach(doc => this._addInheritedProperties(doc));
   }
 
-  private _addInheritedProperties(doc: ClassExportDoc) {
-    doc.implementsClauses.filter(clause => clause.doc).forEach(clause => {
-      clause.doc!.members.forEach(member => this._addMemberDocIfNotPresent(doc, member));
-    });
+  /** Gets all class like export documents which the given doc inherits from. */
+  private _getBaseDocuments(doc: ClassLikeExportDoc): ClassLikeExportDoc[] {
+    const directBaseDocs = [
+      ...doc.implementsClauses.filter(clause => clause.doc).map(d => d.doc!),
+      ...doc.extendsClauses.filter(clause => clause.doc).map(d => d.doc!),
+    ];
 
-    doc.extendsClauses.filter(clause => clause.doc).forEach(clause => {
-      clause.doc!.members.forEach(member => this._addMemberDocIfNotPresent(doc, member));
+    return [
+      ...directBaseDocs,
+      // recursively collect base documents of direct base documents.
+      ...directBaseDocs.reduce(
+          (res: ClassLikeExportDoc[], d) => res.concat(this._getBaseDocuments(d)), []),
+    ];
+  }
+
+  private _addInheritedProperties(doc: ClassExportDoc) {
+    // Note that we need to get check all base documents. We cannot assume
+    // that directive base documents already have merged inherited members.
+    this._getBaseDocuments(doc).forEach(d => {
+      d.members.forEach(member => this._addMemberDocIfNotPresent(doc, member));
     });
   }