Revise installation guide and enhance introduction with dynamic execution details

Author: myui

docs/getting-started/hello-world.mdx

@@ -1,5 +1,5 @@
 ---
-sidebar_position: 3
+sidebar_position: 4
 ---
 
 import Tabs from '@theme/Tabs';
@@ -28,58 +28,105 @@ uv add graflow
   </TabItem>
 </Tabs>
 
-## Create a Workflow File
+## Your First Task
 
-Create a new file called `workflow.yaml`:
+Create a file called `hello.py`:
 
-```yaml
-name: hello-world
-description: My first Graflow workflow
+```python
+from graflow import task
 
-tasks:
-  - name: greet
-    script: |
-      echo "Hello, Graflow!"
-```
+@task
+def hello():
+    print("Hello, Graflow!")
+    return "success"
 
-## Run the Workflow
+if __name__ == "__main__":
+    result = hello.run()
+    print(f"Task completed with result: {result}")
+```
 
-Execute your workflow using the Graflow CLI:
+Run it:
 
 <Tabs>
   <TabItem value="pip" label="pip" default>
 
 ```bash
-graflow run workflow.yaml
+python hello.py
 ```
 
   </TabItem>
   <TabItem value="uv" label="uv">
 
 ```bash
-uv run graflow run workflow.yaml
+uv run hello.py
 ```
 
   </TabItem>
 </Tabs>
 
-You should see output similar to:
+You should see:
 
 ```
-[2025-01-01 12:00:00] Starting workflow: hello-world
-[2025-01-01 12:00:00] Running task: greet
 Hello, Graflow!
-[2025-01-01 12:00:01] Task completed: greet
-[2025-01-01 12:00:01] Workflow completed successfully
+Task completed with result: success
+```
+
+## Your First Workflow
+
+Now let's chain multiple tasks into a workflow. Create `pipeline.py`:
+
+```python
+from graflow import task, workflow
+
+with workflow("simple_pipeline") as wf:
+
+    @task
+    def start():
+        print("Starting!")
+
+    @task
+    def middle():
+        print("Middle!")
+
+    @task
+    def end():
+        print("End!")
+
+    # Define sequential pipeline: start -> middle -> end
+    start >> middle >> end
+
+    # Execute the workflow
+    wf.execute()
+```
+
+Run it:
+
+<Tabs>
+  <TabItem value="pip" label="pip" default>
+
+```bash
+python pipeline.py
 ```
 
-## Understanding the Output
+  </TabItem>
+  <TabItem value="uv" label="uv">
 
-Graflow provides detailed logging for every step:
+```bash
+uv run pipeline.py
+```
+
+  </TabItem>
+</Tabs>
+
+You should see:
+
+```
+Starting!
+Middle!
+End!
+```
 
-- **Timestamps**: When each task started and completed
-- **Task names**: Which task is currently running
-- **Output**: The actual output from your scripts
+The `>>` operator chains tasks sequentially — `middle` runs after `start`, and `end` runs after `middle`.
 
 ## Next Steps
 

docs/getting-started/installation.md

@@ -0,0 +1,84 @@
+---
+sidebar_position: 3
+---
+
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
+# Installation
+
+This guide will help you install Graflow on your system.
+
+## System Requirements
+
+- Python 3.9 or higher
+- Docker (optional, for containerized tasks)
+
+## Installation Methods
+
+<Tabs>
+  <TabItem value="pip" label="pip" default>
+
+```bash
+pip install graflow
+```
+
+  </TabItem>
+  <TabItem value="uv" label="uv">
+
+```bash
+uv add graflow
+```
+
+  </TabItem>
+</Tabs>
+
+### Install with All Extras
+
+To install Graflow with all optional dependencies:
+
+<Tabs>
+  <TabItem value="pip" label="pip" default>
+
+```bash
+pip install "graflow[all]"
+```
+
+  </TabItem>
+  <TabItem value="uv" label="uv">
+
+```bash
+uv add "graflow[all]"
+```
+
+  </TabItem>
+</Tabs>
+
+`graflow[all]` includes the following extras:
+
+| Extra | Description |
+|-------|-------------|
+| `api` | REST API server (FastAPI, Uvicorn) |
+| `visualization` | Graph visualization (Matplotlib, Graphviz) |
+| `tracing` | Observability (OpenTelemetry, Langfuse) |
+| `docker` | Docker-based task execution |
+| `redis` | Redis-backed distributed execution |
+| `adk` | Google ADK agent integration |
+| `pydantic-ai` | Pydantic AI agent integration |
+
+You can also install individual extras, e.g. `graflow[visualization]` or `graflow[tracing]`.
+
+## Verify Installation
+
+After installation, verify that Graflow is installed correctly:
+
+```python
+import graflow
+print(graflow.__version__)
+```
+
+You should see the version number printed to the console.
+
+## Next Steps
+
+Now that you have Graflow installed, let's create your first workflow in the [Hello World](./hello-world) tutorial.

docs/getting-started/installation.mdx

@@ -48,13 +48,17 @@ with workflow("etl_pipeline") as wf:
 ```
 
 :::note
-Note Graflow also provides low-level APIs to define task graphs as well. See the [Reference](/docs/reference/configuration) for details.
+Note Graflow also provides low-level APIs to define task graphs as well.
 :::
 
 ### Dynamic Transitions at Runtime
 
 Traditional DAG-based systems cannot express cycles by definition. With Graflow's **State Machine execution**, cycles and dynamic branching become natural:
 
+:::tip Defined-by-Run
+This approach is conceptually similar to the **Define-by-Run** (also known as [Dynamic Computation Graph](https://apxml.com/courses/advanced-pytorch/chapter-1-pytorch-internals-autograd/computational-graph)) paradigm found in deep learning frameworks such as PyTorch and Chainer. Instead of declaring the entire computation graph upfront (Define-and-Run), the execution graph is constructed dynamically as the code runs, enabling flexible control flow like cycles and conditional branching.
+:::
+
 ```python
 @task(inject_context=True)
 def process_data(context: TaskExecutionContext):