From a3887b75a122733b43baf8e6c91fd32dace05151 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Wed, 14 Feb 2024 16:35:09 +0900
Subject: [PATCH 01/12] Version up `actions/checkout`

---
 .github/workflows/demo.yml                                  | 4 ++--
 .github/workflows/erlang.yml                                | 2 +-
 .github/workflows/run-property-based-tests-periodically.yml | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/.github/workflows/demo.yml b/.github/workflows/demo.yml
index f8c2d15..79f9882 100644
--- a/.github/workflows/demo.yml
+++ b/.github/workflows/demo.yml
@@ -22,7 +22,7 @@ jobs:
         working-directory: ./demo
 
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - name: Demonstrate with polynomial_time_without_correctness
         run: |
           mkdir _checkouts
@@ -55,7 +55,7 @@ jobs:
         working-directory: ./demo
 
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - name: Demonstrate with exp_time_with_correctness
         run: |
           mkdir _checkouts
diff --git a/.github/workflows/erlang.yml b/.github/workflows/erlang.yml
index a764ac4..adca74d 100644
--- a/.github/workflows/erlang.yml
+++ b/.github/workflows/erlang.yml
@@ -18,7 +18,7 @@ jobs:
       image: erlang:26.2.1
 
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - name: Compile
         run: rebar3 compile
       - name: Check statically
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index 158ecbb..92d7bdb 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -13,6 +13,6 @@ jobs:
       image: erlang:26.2.1
 
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From 4d23feb5c6debf0b01cb9fe2472a4088ee3cced1 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Thu, 15 Feb 2024 09:09:02 +0900
Subject: [PATCH 02/12] Rename the CI file

---
 .github/workflows/{erlang.yml => ci.yml} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename .github/workflows/{erlang.yml => ci.yml} (100%)

diff --git a/.github/workflows/erlang.yml b/.github/workflows/ci.yml
similarity index 100%
rename from .github/workflows/erlang.yml
rename to .github/workflows/ci.yml

From c26b7a0392b6e21cbf17c90c34d8f9ac1f6fdf1c Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Thu, 15 Feb 2024 09:36:57 +0900
Subject: [PATCH 03/12] Use `erlef/setup-beam@v1`

---
 .github/workflows/ci.yml                      | 39 +++++++++++++++----
 .github/workflows/demo.yml                    | 16 ++++----
 .../run-property-based-tests-periodically.yml |  7 ++--
 3 files changed, 44 insertions(+), 18 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index adca74d..a47e1de 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -10,19 +10,44 @@ permissions:
   contents: read
 
 jobs:
+  #============================================================================
+  # Build
   build:
-    # NOTE: Run on Ubuntu of Docker in my computer
     runs-on: ubuntu-22.04
 
-    container:
-      image: erlang:26.2.1
+    steps:
+      - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: 26.0
+          rebar3-version: 3.22.1
+      - run: rebar3 compile
+
+  #============================================================================
+  # Static Analysis
+  static_analysis:
+    runs-on: ubuntu-22.04
+
+    steps:
+      - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: 26.0
+          rebar3-version: 3.22.1
+      - run: rebar3 xref
+      - run: rebar3 dialyzer
+
+  #============================================================================
+  # Test
+  test:
+    runs-on: ubuntu-22.04
 
     steps:
       - uses: actions/checkout@v4
-      - name: Compile
-        run: rebar3 compile
-      - name: Check statically
-        run: rebar3 check
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: 26.0
+          rebar3-version: 3.22.1
       - name: Run sample-based-tests
         run: rebar3 do eunit, ct
       - name: Run property-based-tests
diff --git a/.github/workflows/demo.yml b/.github/workflows/demo.yml
index 79f9882..a7a78ad 100644
--- a/.github/workflows/demo.yml
+++ b/.github/workflows/demo.yml
@@ -11,18 +11,18 @@ permissions:
 
 jobs:
   demo_with_polynomial_time_without_correctness:
-    # NOTE: Run on Ubuntu of Docker in my computer
     runs-on: ubuntu-22.04
 
-    container:
-      image: erlang:26.2.1
-
     defaults:
       run:
         working-directory: ./demo
 
     steps:
       - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: 26.0
+          rebar3-version: 3.22.1
       - name: Demonstrate with polynomial_time_without_correctness
         run: |
           mkdir _checkouts
@@ -44,18 +44,18 @@ jobs:
           [ $(erl -pa _build/default/lib/demo/ebin -run run main -noshell | grep 'Result: 55' | wc -l) -eq 2 ]
 
   demo_with_exp_time_with_correctness:
-    # NOTE: Run on Ubuntu of Docker in my computer
     runs-on: ubuntu-22.04
 
-    container:
-      image: erlang:26.2.1
-
     defaults:
       run:
         working-directory: ./demo
 
     steps:
       - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: 26.0
+          rebar3-version: 3.22.1
       - name: Demonstrate with exp_time_with_correctness
         run: |
           mkdir _checkouts
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index 92d7bdb..263ccf4 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -9,10 +9,11 @@ jobs:
   test:
     runs-on: ubuntu-22.04
 
-    container:
-      image: erlang:26.2.1
-
     steps:
       - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: 26.0
+          rebar3-version: 3.22.1
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From beb5b99c24b6d96e5a8bb4d5c2be2ab4b6fe8b8c Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Thu, 15 Feb 2024 10:32:17 +0900
Subject: [PATCH 04/12] Use variables

---
 .github/workflows/ci.yml                         | 16 ++++++++++------
 .github/workflows/demo.yml                       | 12 ++++++++----
 .../run-property-based-tests-periodically.yml    |  8 ++++++--
 3 files changed, 24 insertions(+), 12 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index a47e1de..07e8f33 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -9,6 +9,10 @@ on:
 permissions:
   contents: read
 
+env:
+  otp: 26.0
+  rebar3: 3.22.1
+
 jobs:
   #============================================================================
   # Build
@@ -19,8 +23,8 @@ jobs:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
         with:
-          otp-version: 26.0
-          rebar3-version: 3.22.1
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - run: rebar3 compile
 
   #============================================================================
@@ -32,8 +36,8 @@ jobs:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
         with:
-          otp-version: 26.0
-          rebar3-version: 3.22.1
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - run: rebar3 xref
       - run: rebar3 dialyzer
 
@@ -46,8 +50,8 @@ jobs:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
         with:
-          otp-version: 26.0
-          rebar3-version: 3.22.1
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - name: Run sample-based-tests
         run: rebar3 do eunit, ct
       - name: Run property-based-tests
diff --git a/.github/workflows/demo.yml b/.github/workflows/demo.yml
index a7a78ad..03e3f33 100644
--- a/.github/workflows/demo.yml
+++ b/.github/workflows/demo.yml
@@ -9,6 +9,10 @@ on:
 permissions:
   contents: read
 
+env:
+  otp: 26.0
+  rebar3: 3.22.1
+
 jobs:
   demo_with_polynomial_time_without_correctness:
     runs-on: ubuntu-22.04
@@ -21,8 +25,8 @@ jobs:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
         with:
-          otp-version: 26.0
-          rebar3-version: 3.22.1
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - name: Demonstrate with polynomial_time_without_correctness
         run: |
           mkdir _checkouts
@@ -54,8 +58,8 @@ jobs:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
         with:
-          otp-version: 26.0
-          rebar3-version: 3.22.1
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - name: Demonstrate with exp_time_with_correctness
         run: |
           mkdir _checkouts
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index 263ccf4..3f4d32e 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -5,6 +5,10 @@ on:
     # NOTE: Every day at 00:00 (JST)
     - cron: "0 15 * * *"
 
+env:
+  otp: 26.0
+  rebar3: 3.22.1
+
 jobs:
   test:
     runs-on: ubuntu-22.04
@@ -13,7 +17,7 @@ jobs:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
         with:
-          otp-version: 26.0
-          rebar3-version: 3.22.1
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From 47778ea310d5189485c43344ec9342e191e58252 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Thu, 15 Feb 2024 11:25:21 +0900
Subject: [PATCH 05/12] Use cache

---
 .github/workflows/ci.yml                            | 13 +++++++++++++
 .github/workflows/demo.yml                          | 12 ++++++++++++
 .../run-property-based-tests-periodically.yml       |  6 ++++++
 3 files changed, 31 insertions(+)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 07e8f33..f97aed0 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -19,6 +19,7 @@ jobs:
   build:
     runs-on: ubuntu-22.04
 
+    # NOTE: To check if the first build is possible, do not use the cache.
     steps:
       - uses: actions/checkout@v4
       - uses: erlef/setup-beam@v1
@@ -38,6 +39,12 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache@v4
+        with:
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          path: |
+            ~/.cache/rebar3
+            _build
       - run: rebar3 xref
       - run: rebar3 dialyzer
 
@@ -52,6 +59,12 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache@v4
+        with:
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          path: |
+            ~/.cache/rebar3
+            _build
       - name: Run sample-based-tests
         run: rebar3 do eunit, ct
       - name: Run property-based-tests
diff --git a/.github/workflows/demo.yml b/.github/workflows/demo.yml
index 03e3f33..a8b035d 100644
--- a/.github/workflows/demo.yml
+++ b/.github/workflows/demo.yml
@@ -27,6 +27,12 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache@v4
+        with:
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          path: |
+            ~/.cache/rebar3
+            _build
       - name: Demonstrate with polynomial_time_without_correctness
         run: |
           mkdir _checkouts
@@ -60,6 +66,12 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache@v4
+        with:
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          path: |
+            ~/.cache/rebar3
+            _build
       - name: Demonstrate with exp_time_with_correctness
         run: |
           mkdir _checkouts
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index 3f4d32e..f551f2a 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -19,5 +19,11 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache@v4
+        with:
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          path: |
+            ~/.cache/rebar3
+            _build
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From 164de21540d53f3f480f862cb21b0e9dc72b5d70 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Thu, 15 Feb 2024 11:41:16 +0900
Subject: [PATCH 06/12] Fix the path of `rebar.lock`

---
 .github/workflows/ci.yml                      | 16 +++--
 .github/workflows/create-cache.yml            | 70 +++++++++++++++++++
 .github/workflows/demo.yml                    |  6 +-
 .../run-property-based-tests-periodically.yml |  7 +-
 4 files changed, 91 insertions(+), 8 deletions(-)
 create mode 100644 .github/workflows/create-cache.yml

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index f97aed0..cf9feea 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -39,12 +39,17 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache@v4
+      - uses: actions/cache/restore@v4
         with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          key: dummy-${{ github.sha }}
           path: |
             ~/.cache/rebar3
             _build
+          restore-keys: |
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+
+      - run: ls _build/default
+      - run: ls ~/.cache/rebar3
       - run: rebar3 xref
       - run: rebar3 dialyzer
 
@@ -59,12 +64,15 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache@v4
+      - uses: actions/cache/restore@v4
         with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          key: dummy-${{ github.sha }}
           path: |
             ~/.cache/rebar3
             _build
+          restore-keys: |
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+
       - name: Run sample-based-tests
         run: rebar3 do eunit, ct
       - name: Run property-based-tests
diff --git a/.github/workflows/create-cache.yml b/.github/workflows/create-cache.yml
new file mode 100644
index 0000000..5822fe7
--- /dev/null
+++ b/.github/workflows/create-cache.yml
@@ -0,0 +1,70 @@
+# NOTE:
+# Workflow for creating a cache.
+# Currently, all jobs can share the cache,
+# but the data to be cached is not necessarily created by all jobs (e.g. plt files).
+# For this reason, this workflow is used to create the cache in batches.
+# Another advantage of this method is that
+# the absence of a cache does not cause jobs to take longer to run.
+name: Create cache
+
+# dummy comment
+
+on:
+  schedule:
+    # NOTE:
+    # The validity period of the cache is virtually unlimited.
+    # Originally, a cache is valid for 7 days
+    # (c.f. https://docs.github.com/en/actions/using-workflows/caching-dependencies-to-speed-up-workflows#usage-limits-and-eviction-policy),
+    # but if a new cache is created before the cache becomes invalid,
+    # the validity period can be extended for another 7 days.
+    - cron: "0 0 */6 * *"
+
+  push:
+    branches: ["main"]
+  pull_request:
+    types: ["opened", "synchronize", "reopened"]
+  workflow_dispatch:
+
+env:
+  otp: 26.0
+  rebar3: 3.22.1
+
+jobs:
+  create-cache:
+    runs-on: ubuntu-22.04
+
+    steps:
+      - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache/restore@v4
+        id: cache-restore
+        with:
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-${{ github.run_id }}-${{ github.run_attempt }}
+          path: |
+            ~/.cache/rebar3
+            _build
+          restore-keys: |
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+
+      # NOTE:
+      # We always execute the following commands,
+      # as the presence of a cache will drastically reduce execution time.
+      # The above cache will always match the keys in `restore-keys`,
+      # so one of the outputs of the Restore action, `cache-hit`, will always be `false`,
+      # and the cost of conditional branching due to the presence of the cache will be high.
+      - name: Create cache data
+        run: |
+          rebar3 compile
+          rebar3 as test compile
+          rebar3 dialyzer
+
+      - uses: actions/cache/save@v4
+        if: always()
+        with:
+          key: ${{ steps.cache-restore.outputs.cache-primary-key }}
+          path: |
+            ~/.cache/rebar3
+            _build
diff --git a/.github/workflows/demo.yml b/.github/workflows/demo.yml
index a8b035d..1c57af1 100644
--- a/.github/workflows/demo.yml
+++ b/.github/workflows/demo.yml
@@ -29,10 +29,11 @@ jobs:
           rebar3-version: ${{ env.rebar3 }}
       - uses: actions/cache@v4
         with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('./demo/rebar.lock') }}
           path: |
             ~/.cache/rebar3
             _build
+
       - name: Demonstrate with polynomial_time_without_correctness
         run: |
           mkdir _checkouts
@@ -68,10 +69,11 @@ jobs:
           rebar3-version: ${{ env.rebar3 }}
       - uses: actions/cache@v4
         with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('./demo/rebar.lock') }}
           path: |
             ~/.cache/rebar3
             _build
+
       - name: Demonstrate with exp_time_with_correctness
         run: |
           mkdir _checkouts
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index f551f2a..e5002ae 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -19,11 +19,14 @@ jobs:
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache@v4
+      - uses: actions/cache/restore@v4
         with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+          key: dummy-${{ github.sha }}
           path: |
             ~/.cache/rebar3
             _build
+          restore-keys: |
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From 3932c9d8cc74caaa2e3a42b66aa102854f1a1a6a Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Sat, 17 Feb 2024 21:08:27 +0900
Subject: [PATCH 07/12] Split workflow by timing of cache generation

---
 .../workflows/create-cache-periodically.yml   | 50 +++++++++++++++++++
 .github/workflows/create-cache.yml            | 44 ++++------------
 2 files changed, 59 insertions(+), 35 deletions(-)
 create mode 100644 .github/workflows/create-cache-periodically.yml

diff --git a/.github/workflows/create-cache-periodically.yml b/.github/workflows/create-cache-periodically.yml
new file mode 100644
index 0000000..43dad10
--- /dev/null
+++ b/.github/workflows/create-cache-periodically.yml
@@ -0,0 +1,50 @@
+# NOTE:
+# Workflow for creating a cache.
+# Currently, all jobs can share the cache,
+# but the data to be cached is not necessarily created by all jobs (e.g. plt files).
+# For this reason, this workflow is used to create the cache in batches.
+# Another advantage of this method is that
+# the absence of a cache does not cause jobs to take longer to run.
+name: Create cache periodically
+
+on:
+  schedule:
+    # NOTE:
+    # The validity period of the cache is virtually unlimited.
+    # Originally, a cache is valid for 7 days
+    # (c.f. https://docs.github.com/en/actions/using-workflows/caching-dependencies-to-speed-up-workflows#usage-limits-and-eviction-policy),
+    # but if a new cache is created before the cache becomes invalid,
+    # the validity period can be extended for another 7 days.
+    - cron: "0 0 */6 * *"
+
+  workflow_dispatch:
+
+env:
+  otp: 26.0
+  rebar3: 3.22.1
+
+jobs:
+  create-cache:
+    runs-on: ubuntu-22.04
+
+    steps:
+      - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
+      - uses: actions/cache@v4
+        with:
+          # NOTE: No duplicate key to overwrite the cache.
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-${{ github.run_id }}-${{ github.run_attempt }}
+          path: |
+            ~/.cache/rebar3
+            _build
+          restore-keys: |
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+
+      - name: Create cache data
+        run: |
+          rebar3 compile
+          rebar3 as test compile
+          rebar3 dialyzer
diff --git a/.github/workflows/create-cache.yml b/.github/workflows/create-cache.yml
index 5822fe7..b6e34a3 100644
--- a/.github/workflows/create-cache.yml
+++ b/.github/workflows/create-cache.yml
@@ -7,23 +7,11 @@
 # the absence of a cache does not cause jobs to take longer to run.
 name: Create cache
 
-# dummy comment
-
 on:
-  schedule:
-    # NOTE:
-    # The validity period of the cache is virtually unlimited.
-    # Originally, a cache is valid for 7 days
-    # (c.f. https://docs.github.com/en/actions/using-workflows/caching-dependencies-to-speed-up-workflows#usage-limits-and-eviction-policy),
-    # but if a new cache is created before the cache becomes invalid,
-    # the validity period can be extended for another 7 days.
-    - cron: "0 0 */6 * *"
-
   push:
     branches: ["main"]
   pull_request:
     types: ["opened", "synchronize", "reopened"]
-  workflow_dispatch:
 
 env:
   otp: 26.0
@@ -35,36 +23,22 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
-        with:
-          otp-version: ${{ env.otp }}
-          rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache/restore@v4
-        id: cache-restore
+      - uses: actions/cache@v4
+        id: cache
         with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-${{ github.run_id }}-${{ github.run_attempt }}
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
           path: |
             ~/.cache/rebar3
             _build
-          restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
 
-      # NOTE:
-      # We always execute the following commands,
-      # as the presence of a cache will drastically reduce execution time.
-      # The above cache will always match the keys in `restore-keys`,
-      # so one of the outputs of the Restore action, `cache-hit`, will always be `false`,
-      # and the cost of conditional branching due to the presence of the cache will be high.
+      - uses: erlef/setup-beam@v1
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+        with:
+          otp-version: ${{ env.otp }}
+          rebar3-version: ${{ env.rebar3 }}
       - name: Create cache data
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
         run: |
           rebar3 compile
           rebar3 as test compile
           rebar3 dialyzer
-
-      - uses: actions/cache/save@v4
-        if: always()
-        with:
-          key: ${{ steps.cache-restore.outputs.cache-primary-key }}
-          path: |
-            ~/.cache/rebar3
-            _build

From 64ef6817ca546f77b738ddd53a2fc9efdcc28e11 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Sat, 17 Feb 2024 21:20:13 +0900
Subject: [PATCH 08/12] Use the new cache keys

---
 .github/workflows/ci.yml                                  | 8 ++++----
 .../workflows/run-property-based-tests-periodically.yml   | 4 ++--
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index cf9feea..0b83d09 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -41,12 +41,12 @@ jobs:
           rebar3-version: ${{ env.rebar3 }}
       - uses: actions/cache/restore@v4
         with:
-          key: dummy-${{ github.sha }}
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
           path: |
             ~/.cache/rebar3
             _build
           restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
 
       - run: ls _build/default
       - run: ls ~/.cache/rebar3
@@ -66,12 +66,12 @@ jobs:
           rebar3-version: ${{ env.rebar3 }}
       - uses: actions/cache/restore@v4
         with:
-          key: dummy-${{ github.sha }}
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
           path: |
             ~/.cache/rebar3
             _build
           restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
 
       - name: Run sample-based-tests
         run: rebar3 do eunit, ct
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index e5002ae..dc3a0e9 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -21,12 +21,12 @@ jobs:
           rebar3-version: ${{ env.rebar3 }}
       - uses: actions/cache/restore@v4
         with:
-          key: dummy-${{ github.sha }}
+          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
           path: |
             ~/.cache/rebar3
             _build
           restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
 
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From b6951a1e4f6768c5d6d7da4b1119ab97c73ace4e Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Sun, 18 Feb 2024 00:20:46 +0900
Subject: [PATCH 09/12] Add a composite action to setup beam with cache

---
 .../actions/setup-beam-with-cache/action.yml  | 55 +++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 .github/actions/setup-beam-with-cache/action.yml

diff --git a/.github/actions/setup-beam-with-cache/action.yml b/.github/actions/setup-beam-with-cache/action.yml
new file mode 100644
index 0000000..6cee60e
--- /dev/null
+++ b/.github/actions/setup-beam-with-cache/action.yml
@@ -0,0 +1,55 @@
+name: Setup beam with Rebar3 cache
+description: Action that combines `erlef/setup-beam@v1` and `action/cache@v4`
+
+inputs:
+  otp-version:
+    description: Erlang/OTP version (string)
+    required: true
+  rebar3-version:
+    description: Rebar3 version (string)
+    required: true
+  rebar-lock-path:
+    description: Path of `rebar.lock` (string)
+    required: true
+  overwrite:
+    description: Whether to overwrite the cache (bool string)
+    required: false
+    default: "false"
+
+runs:
+  using: composite
+  steps:
+    - uses: erlef/setup-beam@v1
+      with:
+        otp-version: ${{ inputs.otp-version }}
+        rebar3-version: ${{ inputs.rebar3-version }}
+
+    - uses: actions/cache@v4
+      id: cache
+      if: ${{ inputs.overwrite != 'true' }}
+      with:
+        key: ${{ runner.os }}-otp-${{ inputs.otp-version }}-rebar3-${{ inputs.rebar3-version }}-${{ hashFiles(inputs.rebar-lock-path) }}
+        path: |
+          ~/.cache/rebar3
+          _build
+        restore-keys: |
+          ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
+
+    - uses: actions/cache@v4
+      if: ${{ inputs.overwrite == 'true' }}
+      with:
+        # NOTE: No duplicate key to overwrite the cache.
+        key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-${{ github.run_id }}-${{ github.run_attempt }}
+        path: |
+          ~/.cache/rebar3
+          _build
+        restore-keys: |
+          ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
+
+    - name: Create cache data
+      shell: bash
+      if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+      run: |
+        rebar3 compile
+        rebar3 as test compile
+        rebar3 dialyzer

From 37d6b9609f702f23dfd6ea692ef9addbed8087a9 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Sun, 18 Feb 2024 00:20:59 +0900
Subject: [PATCH 10/12] Use the composite action

---
 .github/workflows/ci.yml                      | 22 ++--------
 .../workflows/create-cache-periodically.yml   | 19 ++------
 .github/workflows/create-cache.yml            | 44 -------------------
 .github/workflows/demo.yml                    | 18 ++------
 .../run-property-based-tests-periodically.yml | 11 +----
 5 files changed, 13 insertions(+), 101 deletions(-)
 delete mode 100644 .github/workflows/create-cache.yml

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 0b83d09..a08bce7 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -35,18 +35,11 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
+      - uses: ./.github/actions/setup-beam-with-cache/
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache/restore@v4
-        with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
-          path: |
-            ~/.cache/rebar3
-            _build
-          restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
+          rebar-lock-path: "./rebar.lock"
 
       - run: ls _build/default
       - run: ls ~/.cache/rebar3
@@ -60,18 +53,11 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
+      - uses: ./.github/actions/setup-beam-with-cache/
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache/restore@v4
-        with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
-          path: |
-            ~/.cache/rebar3
-            _build
-          restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
+          rebar-lock-path: "./rebar.lock"
 
       - name: Run sample-based-tests
         run: rebar3 do eunit, ct
diff --git a/.github/workflows/create-cache-periodically.yml b/.github/workflows/create-cache-periodically.yml
index 43dad10..bdf3ea6 100644
--- a/.github/workflows/create-cache-periodically.yml
+++ b/.github/workflows/create-cache-periodically.yml
@@ -29,22 +29,9 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
+      - uses: ./.github/actions/setup-beam-with-cache/
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache@v4
-        with:
-          # NOTE: No duplicate key to overwrite the cache.
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-${{ github.run_id }}-${{ github.run_attempt }}
-          path: |
-            ~/.cache/rebar3
-            _build
-          restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
-
-      - name: Create cache data
-        run: |
-          rebar3 compile
-          rebar3 as test compile
-          rebar3 dialyzer
+          rebar-lock-path: "./rebar.lock"
+          overwrite: "true"
diff --git a/.github/workflows/create-cache.yml b/.github/workflows/create-cache.yml
deleted file mode 100644
index b6e34a3..0000000
--- a/.github/workflows/create-cache.yml
+++ /dev/null
@@ -1,44 +0,0 @@
-# NOTE:
-# Workflow for creating a cache.
-# Currently, all jobs can share the cache,
-# but the data to be cached is not necessarily created by all jobs (e.g. plt files).
-# For this reason, this workflow is used to create the cache in batches.
-# Another advantage of this method is that
-# the absence of a cache does not cause jobs to take longer to run.
-name: Create cache
-
-on:
-  push:
-    branches: ["main"]
-  pull_request:
-    types: ["opened", "synchronize", "reopened"]
-
-env:
-  otp: 26.0
-  rebar3: 3.22.1
-
-jobs:
-  create-cache:
-    runs-on: ubuntu-22.04
-
-    steps:
-      - uses: actions/checkout@v4
-      - uses: actions/cache@v4
-        id: cache
-        with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
-          path: |
-            ~/.cache/rebar3
-            _build
-
-      - uses: erlef/setup-beam@v1
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        with:
-          otp-version: ${{ env.otp }}
-          rebar3-version: ${{ env.rebar3 }}
-      - name: Create cache data
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        run: |
-          rebar3 compile
-          rebar3 as test compile
-          rebar3 dialyzer
diff --git a/.github/workflows/demo.yml b/.github/workflows/demo.yml
index 1c57af1..6a96624 100644
--- a/.github/workflows/demo.yml
+++ b/.github/workflows/demo.yml
@@ -23,16 +23,11 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
+      - uses: ./.github/actions/setup-beam-with-cache/
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache@v4
-        with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('./demo/rebar.lock') }}
-          path: |
-            ~/.cache/rebar3
-            _build
+          rebar-lock-path: "./demo/rebar.lock"
 
       - name: Demonstrate with polynomial_time_without_correctness
         run: |
@@ -63,16 +58,11 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
+      - uses: ./.github/actions/setup-beam-with-cache/
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache@v4
-        with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('./demo/rebar.lock') }}
-          path: |
-            ~/.cache/rebar3
-            _build
+          rebar-lock-path: "./demo/rebar.lock"
 
       - name: Demonstrate with exp_time_with_correctness
         run: |
diff --git a/.github/workflows/run-property-based-tests-periodically.yml b/.github/workflows/run-property-based-tests-periodically.yml
index dc3a0e9..6083dbd 100644
--- a/.github/workflows/run-property-based-tests-periodically.yml
+++ b/.github/workflows/run-property-based-tests-periodically.yml
@@ -15,18 +15,11 @@ jobs:
 
     steps:
       - uses: actions/checkout@v4
-      - uses: erlef/setup-beam@v1
+      - uses: ./.github/actions/setup-beam-with-cache/
         with:
           otp-version: ${{ env.otp }}
           rebar3-version: ${{ env.rebar3 }}
-      - uses: actions/cache/restore@v4
-        with:
-          key: ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}
-          path: |
-            ~/.cache/rebar3
-            _build
-          restore-keys: |
-            ${{ runner.os }}-otp-${{ env.otp }}-rebar3-${{ env.rebar3 }}-${{ hashFiles('rebar.lock') }}-
+          rebar-lock-path: "./rebar.lock"
 
       - name: Run property-based tests
         run: rebar3 proper -n 1000

From affb6329a9768e2cb3dab045c0bd9eef857d42d0 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Sun, 18 Feb 2024 00:38:11 +0900
Subject: [PATCH 11/12] Update comments

---
 .github/workflows/create-cache-periodically.yml | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/.github/workflows/create-cache-periodically.yml b/.github/workflows/create-cache-periodically.yml
index bdf3ea6..0043a49 100644
--- a/.github/workflows/create-cache-periodically.yml
+++ b/.github/workflows/create-cache-periodically.yml
@@ -1,10 +1,7 @@
 # NOTE:
-# Workflow for creating a cache.
-# Currently, all jobs can share the cache,
-# but the data to be cached is not necessarily created by all jobs (e.g. plt files).
-# For this reason, this workflow is used to create the cache in batches.
-# Another advantage of this method is that
-# the absence of a cache does not cause jobs to take longer to run.
+# Workflow for creating a cache periodically.
+# Eliminating the period during which the cache is invalid
+# prevents the increase in execution time due to the absence of the cache.
 name: Create cache periodically
 
 on:
@@ -24,7 +21,7 @@ env:
   rebar3: 3.22.1
 
 jobs:
-  create-cache:
+  overwrite-cache:
     runs-on: ubuntu-22.04
 
     steps:

From 1f5fa263b9b4724c96c7cd26d94f263128bf5dc3 Mon Sep 17 00:00:00 2001
From: ajfAfg <56056962+ajfAfg@users.noreply.github.com>
Date: Sun, 18 Feb 2024 01:05:20 +0900
Subject: [PATCH 12/12] Update a bit

---
 .github/actions/setup-beam-with-cache/action.yml | 4 ++--
 .github/workflows/ci.yml                         | 2 --
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/.github/actions/setup-beam-with-cache/action.yml b/.github/actions/setup-beam-with-cache/action.yml
index 6cee60e..8fccf09 100644
--- a/.github/actions/setup-beam-with-cache/action.yml
+++ b/.github/actions/setup-beam-with-cache/action.yml
@@ -25,7 +25,7 @@ runs:
         rebar3-version: ${{ inputs.rebar3-version }}
 
     - uses: actions/cache@v4
-      id: cache
+      id: cache-no-overwrite
       if: ${{ inputs.overwrite != 'true' }}
       with:
         key: ${{ runner.os }}-otp-${{ inputs.otp-version }}-rebar3-${{ inputs.rebar3-version }}-${{ hashFiles(inputs.rebar-lock-path) }}
@@ -48,7 +48,7 @@ runs:
 
     - name: Create cache data
       shell: bash
-      if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+      if: ${{ steps.cache-no-overwrite.outputs.cache-hit != 'true' }}
       run: |
         rebar3 compile
         rebar3 as test compile
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index a08bce7..6ca38e6 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -41,8 +41,6 @@ jobs:
           rebar3-version: ${{ env.rebar3 }}
           rebar-lock-path: "./rebar.lock"
 
-      - run: ls _build/default
-      - run: ls ~/.cache/rebar3
       - run: rebar3 xref
       - run: rebar3 dialyzer