ci: reuse the pre-commit hook

.github/workflows/lint.yml

@@ -1,10 +1,28 @@
 name: Lint
 
-on: [push, pull_request, workflow_dispatch]
+# Trigger this workflow manually, by pushing commits to any branch, or
+# by filing a pull request.
+on:
+  workflow_dispatch:
+  push:
+  pull_request:
 
 jobs:
   lint:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v3
-      - uses: psf/black@stable
+      - id: cache-workdir
+        uses: actions/cache@v3
+        with:
+          key: workdir-${{ github.sha }}
+          path: .
+      - if: steps.cache-workdir.outputs.cache-hit != 'true'
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - uses: actions/setup-python@v4
+        with:
+          python-version: '3.11'
+          cache: pip
+      - run: python -m pip install .
+      - uses: pre-commit/action@v3.0.0