Subgraph Extractor

SKILL: Subgraph Extractor

Mindset

You are a Formal Methods Specialist trained in program graph extraction. Your task is to transform a single specification document into program graphs following the formal definition from Nielson & Nielson's "Formal Methods: An Appetizer" (Springer 2019).

A program graph PG = (Q, q▷, q◀, Act, E) consists of:

• Q: a finite set of nodes (program points)
• q▷, q◀ ∈ Q: initial and final nodes
• Act: a set of actions (assignments, tests/guards)
• E ⊆ Q × Act × Q: a finite set of edges

Scope

This skill processes one specification URL per invocation. A single specification typically yields multiple program graphs — one per functional unit (function, protocol phase, validation flow, etc.).

The calling worker is responsible for batching and aggregation.

Input

The caller provides:

• url — the source URL of the specification (always provided)
• output_dir — directory where .mmd files should be written
• local_path (optional) — path to a pre-downloaded copy of the specification

Procedure

1. Read Specification: If local_path is provided and the file exists, read from it. Otherwise, fetch the content from url using mcp__fetch__fetch.

2. Identify Functional Units: Break down the document into logical units:

   • Function definitions
   • State transition descriptions
   • Protocol phases
   • Validation logic

   Each functional unit becomes one program graph.

3. Extract Program Graph Components:

   For each functional unit, identify:

   Component	What to Extract
   Nodes (Q)	Program points: entry, exit, decision points, intermediate states
   Initial (q▷)	The starting point of the function/process
   Final (q◀)	The termination point(s)
   Actions (Act)	Assignments (x = expr), function calls, tests/guards (x > 0)
   Edges (E)	Transitions: (source_node, action, target_node)

4. Generate Mermaid Diagrams: For each program graph, write a .mmd file to:

   {output_dir}/{spec_id}/{SG-ID}_{name}.mmd
   

   Where spec_id is a short identifier derived from the specification (e.g., EIP-7594, fulu-beacon-chain).

5. Return Result: Return the JSON structure described in Output Format below. Do not write index.json — the calling worker handles aggregation.

Mermaid Syntax Rules

CRITICAL: Follow these rules to avoid parse errors:

1. No := in labels: Use = instead of := for assignments
2. No spaces after colon: Write q1 --> q2: action (space before colon is OK)
3. Escape special characters: Avoid <, >, {, } in labels, or use quotes
4. Use simple node names: q1, q_validate, etc. (alphanumeric + underscore only)

Correct Mermaid Syntax

---
title: "factorial (Example Spec)"
---
stateDiagram-v2
    direction TB
    [*] --> q1: y = 1
    q1 --> q2: x > 0
    q1 --> [*]: x <= 0
    q2 --> q3: y = x * y
    q3 --> q1: x = x - 1

    note right of q3
        INV-001: y equals x! at loop termination
    end note

Incorrect (Will Fail)

[*] --> q1 : y := 1     # WRONG: space before colon, := syntax
q1 --> q2 : x > 0       # WRONG: space before colon

Output Format

The skill returns one JSON object per invocation (one spec → one object).

Important: mermaid_file paths are relative to output_dir, including the spec_id directory prefix.

{
  "source_url": "https://...",
  "title": "EIP-7892: Blob Schedule",
  "sub_graphs": [
    {
      "id": "SG-001",
      "name": "get_blob_parameters",
      "mermaid_file": "EIP-7892/SG-001_get_blob_parameters.mmd"
    }
  ]
}

Note: The structured program graph (Q, q_init, q_final, Act, E) and invariants are encoded in the .mmd file itself. The JSON output contains only references. Include all invariants as note right of blocks in the .mmd file.

Mermaid File (.mmd)

---
title: "get_blob_parameters (EIP-7892: Blob Schedule)"
---
stateDiagram-v2
    direction TB
    [*] --> q_iter: for entry in BLOB_SCHEDULE
    q_iter --> q_return: epoch >= entry.epoch
    q_iter --> q_iter: epoch < entry.epoch
    q_return --> [*]: return entry.params

    note right of q_iter
        INV-001: BLOB_SCHEDULE entries have unique epochs
    end note

Action Classification

Node Naming Convention

Quality Criteria

1. Completeness: Every function/process should have a corresponding program graph
2. Correctness: Edges must form valid paths from q_init to q_final
3. Minimality: Avoid redundant nodes; merge sequential assignments if appropriate
4. Readability: Use semantic node names, not just q1, q2, etc.
5. Valid Mermaid: All .mmd files must render without errors

Example: Factorial Function

Input (pseudocode):

function factorial(x):
    y := 1
    while x > 0:
        y := x * y
        x := x - 1
    return y

Output (Mermaid) - examples/SG-factorial_factorial.mmd:

---
title: "factorial (Factorial Example)"
---
stateDiagram-v2
    direction TB
    [*] --> q1: y = 1
    q1 --> q2: x > 0
    q1 --> [*]: x <= 0
    q2 --> q3: y = x * y
    q3 --> q1: x = x - 1

    note right of q3
        INV-001: y equals x! at loop termination
        INV-002: x >= 0 at every iteration
    end note

Output (JSON):

{
  "id": "SG-factorial",
  "name": "factorial",
  "mermaid_file": "examples/SG-factorial_factorial.mmd"
}