update flow doc

docs/flow.md

@@ -7,30 +7,30 @@ nav_order: 2
 
 # Flow
 
-A **Flow** orchestrates how Nodes connect and run, based on **Actions** returned from each Node’s `post()` method. You can chain Nodes in a sequence or create branching logic depending on the **Action** string.
+A **Flow** orchestrates a graph of Nodes. You can chain Nodes in a sequence or create branching depending on the **Actions** returned from each Node's `post()`.
 
 ## 1. Action-based Transitions
 
-Each Node's `post(shared, prep_res, exec_res)` method returns an **Action** string. By default, if `post()` doesn't explicitly return anything, we treat that as `"default"`.
+Each Node's `post()` returns an **Action** string. By default, if `post()` doesn't return anything, we treat that as `"default"`.
 
 You define transitions with the syntax:
 
-1. Basic default transition: `node_a >> node_b`
-  This means if `node_a.post()` returns `"default"` (or `None`), go to `node_b`. 
+1. **Basic default transition**: `node_a >> node_b`
+  This means if `node_a.post()` returns `"default"`, go to `node_b`. 
   (Equivalent to `node_a - "default" >> node_b`)
 
-2. Named action transition: `node_a - "action_name" >> node_b`
+2. **Named action transition**: `node_a - "action_name" >> node_b`
   This means if `node_a.post()` returns `"action_name"`, go to `node_b`.
 
-It’s possible to create loops, branching, or multi-step flows.
+It's possible to create loops, branching, or multi-step flows.
 
 ## 2. Creating a Flow
 
-A **Flow** begins with a **start** node (or flow). You call `Flow(start=some_node)` to specify the entry point. When you call `flow.run(shared)`, it executes the first node, looks at its `post()` return Action, follows the corresponding transition, and continues until there’s no next node or you explicitly stop.
+A **Flow** begins with a **start** node. You call `Flow(start=some_node)` to specify the entry point. When you call `flow.run(shared)`, it executes the start node, looks at its returned Action from `post()`, follows the transition, and continues until there's no next node.
 
 ### Example: Simple Sequence
 
-Here’s a minimal flow of two nodes in a chain:
+Here's a minimal flow of two nodes in a chain:
 
 ```python
 node_a >> node_b
@@ -41,7 +41,7 @@ flow.run(shared)
 - When you run the flow, it executes `node_a`.  
 - Suppose `node_a.post()` returns `"default"`.  
 - The flow then sees `"default"` Action is linked to `node_b` and runs `node_b`.  
-- If `node_b.post()` returns `"default"` but we didn’t define `node_b >> something_else`, the flow ends there.
+- `node_b.post()` returns `"default"` but we didn't define `node_b >> something_else`. So the flow ends there.
 
 ### Example: Branching & Looping
 
@@ -57,19 +57,19 @@ We can wire them like this:
 # Define the flow connections
 review - "approved" >> payment        # If approved, process payment
 review - "needs_revision" >> revise   # If needs changes, go to revision
-review - "rejected" >> finish           # If rejected, finish the process
+review - "rejected" >> finish         # If rejected, finish the process
 
 revise >> review   # After revision, go back for another review
-payment >> finish     # After payment, finish the process
+payment >> finish  # After payment, finish the process
 
 flow = Flow(start=review)
 ```
 
 Let's see how it flows:
 
-1. If `review.post()` returns `"approved"`, the expense moves to `payment` node
-2. If `review.post()` returns `"needs_revision"`, it goes to `revise` node, which then loops back to `review`
-3. If `review.post()` returns `"rejected"`, it moves to `finish` node and stops
+1. If `review.post()` returns `"approved"`, the expense moves to the `payment` node
+2. If `review.post()` returns `"needs_revision"`, it goes to the `revise` node, which then loops back to `review`
+3. If `review.post()` returns `"rejected"`, it moves to the `finish` node and stops
 
 ```mermaid
 flowchart TD
@@ -83,12 +83,13 @@ flowchart TD
 
 ### Running Individual Nodes vs. Running a Flow
 
-- `node.run(shared)`: Just runs that node alone (calls `prep()`, `exec()`, `post()`), returns an Action. 
-- `flow.run(shared)`: Executes from the start node, follows Actions to the next node, and so on until the flow can’t continue (no next node or no next Action).
+- `node.run(shared)`: Just runs that node alone (calls `prep->exec->post()`), returns an Action. 
+- `flow.run(shared)`: Executes from the start node, follows Actions to the next node, and so on until the flow can't continue.
 
 
-> node.run(shared) **does not** proceed automatically to the successor and may use incorrect parameters.
+> `node.run(shared)` **does not** proceed to the successor.
 > This is mainly for debugging or testing a single node.
+> 
 > Always use `flow.run(...)` in production to ensure the full pipeline runs correctly.
 {: .warning }
 
@@ -100,13 +101,6 @@ A **Flow** can act like a Node, which enables powerful composition patterns. Thi
 2. Combine multiple smaller Flows into a larger Flow for reuse.  
 3. Node `params` will be a merging of **all** parents' `params`.
 
-> While **Flow** is also a **Node**, it won't run `exec()`.
->
-> It will run `prep()` and `post()`, before and after calling the nodes within the flow.
->
-> However, `post()` always receives None for exec_res, and should instead get the flow execution results from the shared store.
-{: .warning }
-
 ### Basic Flow Nesting
 
 Here's how to connect a flow to another node:
@@ -125,7 +119,7 @@ parent_flow = Flow(start=subflow)
 
 When `parent_flow.run()` executes:
 1. It starts `subflow`
-2. `subflow` runs through its nodes (`node_a` then `node_b`)
+2. `subflow` runs through its nodes (`node_a->node_b`)
 3. After `subflow` completes, execution continues to `node_c`
 
 ### Example: Order Processing Pipeline
@@ -176,3 +170,11 @@ flowchart LR
         inventoryFlow --> shippingFlow
     end
 ```
+
+### Flow's Node Methods
+
+A **Flow** is also a **Node**, so it will run `prep()` and `post()`. However:
+
+- It **won't** run `exec()`, as its main logic is to orchestrate other nodes.
+- `post()` always receives None for exec_res and should instead get the flow execution results from the shared store.
+