Add GHA workflow to resolve Manifest file

.github/workflows/resolve_manifest.yml

@@ -0,0 +1,48 @@
+# This action runs Pkg.instantiate() and Pkg.resolve() every time the master
+# branch is pushed to. If this leads to a change in the Manifest.toml file, it
+# will open a PR to update the Manifest.toml file. This ensures that the
+# contents of the Manifest in the repository are consistent with the contents
+# of the Manifest used by the CI system (i.e. during the actual docs
+# generation).
+#
+# See https://github.com/TuringLang/docs/issues/518 for motivation.
+
+name: Resolve Manifest
+on:
+  push:
+    branches:
+      - master
+  workflow_dispatch:
+
+jobs:
+  check-version:
+    runs-on: ubuntu-latest
+
+    permissions:
+      contents: write
+      pull-requests: write
+
+    env:
+      # Disable precompilation as it takes a long time and is not needed for this workflow
+      JULIA_PKG_PRECOMPILE_AUTO: 0
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Setup Julia
+        uses: julia-actions/setup-julia@v2
+
+      - name: Instantiate and resolve
+        run: |
+          julia -e 'using Pkg; Pkg.instantiate(); Pkg.resolve()'
+
+      - name: Open PR
+        id: create_pr
+        uses: peter-evans/create-pull-request@v6
+        with:
+          branch: resolve-manifest
+          add-paths: Manifest.toml
+          commit-message: "Update Manifest.toml"
+          body: "This PR is automatically generated by the `resolve_manifest.yml` GitHub Action."
+          title: "Update Manifest.toml to match CI environment"