Downstream test against ApproxFun (#191)

Author: jishnub

.github/workflows/downstream.yml

@@ -0,0 +1,79 @@
+name: IntegrationTest
+
+concurrency:
+  group: build-${{ github.event.pull_request.number || github.ref }}-${{ github.workflow }}
+  cancel-in-progress: true
+
+on:
+  push:
+    branches: [master]
+    tags: [v*]
+    paths-ignore:
+      - 'LICENSE.md'
+      - 'README.md'
+      - '.github/workflows/TagBot.yml'
+  pull_request:
+    paths-ignore:
+      - 'LICENSE'
+      - 'README.md'
+      - '.github/workflows/TagBot.yml'
+
+jobs:
+  pre_job:
+    # continue-on-error: true # Uncomment once integration is finished
+    runs-on: ubuntu-latest
+    # Map a step output to a job output
+    outputs:
+      should_skip: ${{ steps.skip_check.outputs.should_skip }}
+    steps:
+      - id: skip_check
+        uses: fkirc/skip-duplicate-actions@v5
+  test:
+    needs: pre_job
+    if: needs.pre_job.outputs.should_skip != 'true'
+    name: ${{ matrix.package.group }}/${{ matrix.package.repo }}/${{ matrix.julia-version }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        julia-version: ['1']
+        os: [ubuntu-latest]
+        package:
+          - {repo: ApproxFunBase.jl, group: JuliaApproximation}
+          - {repo: ApproxFun.jl, group: JuliaApproximation}
+          # - {repo: InfiniteLinearAlgebra.jl, group: JuliaLinearAlgebra}
+
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.julia-version }}
+          arch: x64
+      - uses: julia-actions/julia-buildpkg@latest
+      - name: Clone Downstream
+        uses: actions/checkout@v4
+        with:
+          repository: ${{ matrix.package.group }}/${{ matrix.package.repo }}
+          path: downstream
+      - name: Load this and run the downstream tests
+        shell: julia --color=yes --project=downstream {0}
+        run: |
+          using Pkg
+          try
+            # force it to use this PR's version of the package
+            Pkg.develop(PackageSpec(path="."))  # resolver may fail with main deps
+            Pkg.update()
+            Pkg.test(; coverage = true)  # resolver may fail with test time deps
+          catch err
+            err isa Pkg.Resolve.ResolverError || rethrow()
+            # If we can't resolve that means this is incompatible by SemVer and this is fine
+            # It means we marked this as a breaking change, so we don't need to worry about
+            # Mistakenly introducing a breaking change, as we have intentionally made one
+            @info "Not compatible with this release. No problem." exception=err
+            exit(0)  # Exit immediately, as a success
+          end
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v4
+        with:
+          token: ${{ secrets.CODECOV_TOKEN }}
+          files: lcov.info