add mdbook compilation check to CI (#45)

Reasoning: till now we're only compiling it when the changes land at the
`main` branch, which allows invalid changes to the mdbook to pass the PR
check. With the update at this commit we ensure that the new PRs pass
the mdbook compilation check.

.github/workflows/mdbook-check.yml

@@ -0,0 +1,35 @@
+name: Check mdbook compilation
+
+on:
+  pull_request:
+  push:
+    branches:
+      - main
+
+jobs:
+  compile:
+    if: github.event.pull_request.draft == false
+    runs-on: ubuntu-latest
+    env:
+      MDBOOK_VERSION: 0.4.40
+      MDBOOKKATEX_VERSION: 0.7.0
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install mdBook
+        run: |
+          curl --proto '=https' --tlsv1.2 https://sh.rustup.rs -sSf -y | sh
+          rustup update
+          cargo install --version ${MDBOOK_VERSION} mdbook
+          cargo install --version ${MDBOOKKATEX_VERSION} mdbook-katex
+      - name: Build with mdBook
+        run: |
+          cd book
+          mdbook build
+      - name: Check build result
+        run: |
+          if [ -d "book/book" ]; then
+            echo "mdBook compilation success"
+          else
+            echo "mdBook compilation fail"
+            exit 1
+          fi