CI: add check whether mdbook compiles

.github/workflows/main.yml

@@ -73,3 +73,35 @@ jobs:
       - name: Build the csharp project
         working-directory: snippets/csharp
         run: dotnet build
+  
+  build:
+    name: Build mdbook
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout repo
+        uses: actions/checkout@v3
+
+      - name: Install rust
+        run: |
+          rustup set auto-self-update disable
+          rustup toolchain install stable --profile minimal
+
+      - uses: Swatinem/rust-cache@v2
+        with:
+          workspaces: |
+            . -> target
+            snippets-processor -> snippets-processor/target
+
+      - name: Install dependencies
+        run: |
+          cargo install mdbook --vers "^0.4" --locked
+          cargo install --path ./snippets-processor
+      
+      - name: Build mdbook
+        run: mdbook build
+
+      - name: Archive book
+        uses: actions/upload-artifact@v3
+        with:
+          name: book
+          path: book