control-flow-abstraction-generator

Control Flow Abstraction Generator

Generate abstract Control Flow Graph representations of programs.

Overview

This skill analyzes program code and generates Control Flow Graphs (CFGs) that abstract the program's control flow structure. CFGs show how execution flows through the program via nodes (statements, conditions) and edges (control transfers), making them suitable for static analysis, formal verification, and program understanding.

How to Use

Provide:

1. Program code: Function or program to analyze
2. Analysis scope: Function-level or program-level
3. Output format (optional): Textual, DOT, JSON, or multiple

The skill will generate:

• CFG with nodes and edges
• Node types (entry, exit, statement, condition, merge)
• Edge types (sequential, true/false branches, back edges, calls)
• Optional: DOT format for visualization, JSON for tool integration

CFG Generation Workflow

Step 1: Parse Program Structure

Identify program constructs:

• Sequential statements: Assignments, expressions, declarations
• Conditional statements: if-then-else, switch-case
• Loop statements: while, for, do-while
• Function calls: Direct calls, recursive calls
• Control transfers: break, continue, return, goto
• Exception handling: try-catch-finally

Step 2: Create CFG Nodes

Generate nodes for each construct:

Entry Node: Function/program start

• Label: ENTRY or function name
• Type: entry
• Successors: First statement

Exit Node: Function/program end

• Label: EXIT or return
• Type: exit
• Predecessors: All return points

Statement Node: Regular statement

• Label: Statement text or line number
• Type: statement
• Represents: Assignment, call, expression

Condition Node: Branch decision

• Label: Boolean expression
• Type: condition
• Successors: True branch, false branch

Merge Node: Branch join point

• Label: MERGE or empty
• Type: merge
• Predecessors: Multiple branches

Step 3: Create CFG Edges

Connect nodes with appropriate edges:

Sequential Edge: Normal flow

• From: Statement/node
• To: Next statement/node
• Label: None or →

True Edge: Condition true branch

• From: Condition node
• To: True branch first statement
• Label: T or true

False Edge: Condition false branch

• From: Condition node
• To: False branch first statement
• Label: F or false

Back Edge: Loop iteration

• From: Loop body end
• To: Loop header
• Label: ↶ or back

Call Edge: Function invocation (interprocedural)

• From: Call site
• To: Called function entry
• Label: ⇒ or call

Return Edge: Function return (interprocedural)

• From: Called function exit
• To: Call site return point
• Label: ⇐ or return

Step 4: Handle Special Constructs

Loops: Create back edges from body to header

Break: Create edge from break statement to loop exit

Continue: Create back edge from continue to loop header

Return: Create edge from return to EXIT node

Exceptions: Create exception edges from try block to catch handlers

Step 5: Generate Output

Produce CFG in requested format(s):

• Textual representation
• DOT format for Graphviz
• JSON for tool integration

Example: Simple Conditional

Code:

def max_value(x, y):
    if x > y:
        result = x
    else:
        result = y
    return result

CFG (Textual):

Node 1 (ENTRY):
  Label: max_value
  Successors: [2]

Node 2 (x > y):
  Type: condition
  Predecessors: [1]
  Successors: [3 (true), 4 (false)]

Node 3 (result = x):
  Type: statement
  Predecessors: [2]
  Successors: [5]

Node 4 (result = y):
  Type: statement
  Predecessors: [2]
  Successors: [5]

Node 5 (MERGE):
  Type: merge
  Predecessors: [3, 4]
  Successors: [6]

Node 6 (return result):
  Type: statement
  Predecessors: [5]
  Successors: [7]

Node 7 (EXIT):
  Predecessors: [6]

CFG (Visual):

    ENTRY
      ↓
   [x > y]
    ↓   ↓
   T↓   ↓F
    ↓   ↓
[result=x] [result=y]
    ↓       ↓
    └→MERGE←┘
        ↓
  [return result]
        ↓
      EXIT

CFG (DOT):

digraph CFG {
  node [shape=box];

  n1 [label="ENTRY", shape=ellipse];
  n2 [label="x > y", shape=diamond];
  n3 [label="result = x"];
  n4 [label="result = y"];
  n5 [label="MERGE", shape=circle];
  n6 [label="return result"];
  n7 [label="EXIT", shape=ellipse];

  n1 -> n2;
  n2 -> n3 [label="T", color=green];
  n2 -> n4 [label="F", color=red];
  n3 -> n5;
  n4 -> n5;
  n5 -> n6;
  n6 -> n7;
}

Example: While Loop

Code:

def sum_to_n(n):
    sum = 0
    i = 0
    while i < n:
        sum += i
        i += 1
    return sum

CFG (Visual):

    ENTRY
      ↓
   [sum = 0]
      ↓
   [i = 0]
      ↓
      ┌─────────┐
      ↓         ↑
   [i < n]      ↑ (back edge)
    ↓   ↓       ↑
   T↓   ↓F      ↑
    ↓   ↓       ↑
[sum += i]      ↑
      ↓         ↑
  [i += 1]──────┘
      ↓F
[return sum]
      ↓
    EXIT

Key Features:

• Loop header: [i < n]
• Back edge: From [i += 1] to [i < n]
• Exit edge: False branch from condition to return

CFG (Textual):

Node 1 (ENTRY)
  → Node 2

Node 2 (sum = 0)
  → Node 3

Node 3 (i = 0)
  → Node 4

Node 4 (i < n) [LOOP HEADER]
  →T Node 5
  →F Node 7

Node 5 (sum += i)
  → Node 6

Node 6 (i += 1)
  → Node 4 [BACK EDGE]

Node 7 (return sum)
  → Node 8

Node 8 (EXIT)

Example: Nested Control Flow

Code:

def process(arr, threshold):
    result = []
    for item in arr:
        if item > threshold:
            result.append(item * 2)
        else:
            if item < 0:
                continue
            result.append(item)
    return result

CFG (Visual):

ENTRY
  ↓
[result = []]
  ↓
[i = 0]
  ↓
  ┌──────────────────────┐
  ↓                      ↑
[i < len(arr)]           ↑
  ↓T                     ↑
[item = arr[i]]          ↑
  ↓                      ↑
[item > threshold]       ↑
  ↓T            ↓F       ↑
[result.append  [item<0] ↑
 (item*2)]        ↓T     ↑
  ↓               └──────┘ (continue)
  ↓              ↓F
  ↓         [result.append(item)]
  ↓               ↓
  └──→MERGE←──────┘
       ↓
   [i += 1]───────┘
       ↓F
  [return result]
       ↓
     EXIT

Key Features:

• Outer loop: for loop over array
• Inner conditional: if-else with nested if
• Continue statement: back edge to loop header
• Multiple merge points

Example: Function Calls (Interprocedural)

Code:

def factorial(n):
    if n <= 1:
        return 1
    return n * factorial(n-1)

def compute(x):
    result = factorial(x)
    return result + 1

Intraprocedural CFG (factorial only):

factorial:ENTRY
      ↓
   [n <= 1]
    ↓     ↓
   T↓     ↓F
    ↓     ↓
[return 1] [call factorial(n-1)]
    ↓           ↓
    ↓      [return n * result]
    ↓           ↓
    └──→EXIT←───┘

Interprocedural CFG (with call edges):

compute:ENTRY
      ↓
[call factorial(x)] ⇒ factorial:ENTRY
      ↓                     ↓
      ↓                [n <= 1]
      ↓                  ↓   ↓
      ↓                 ...  ...
      ↓                     ↓
[result = ...] ⇐ factorial:EXIT
      ↓
[return result + 1]
      ↓
compute:EXIT

Key Features:

• Call edge: From call site to callee entry
• Return edge: From callee exit to call site
• Recursive call: Edge back to same function

Output Formats

Textual Format

Human-readable node and edge listing:

Node <id> (<label>):
  Type: <type>
  Predecessors: [<ids>]
  Successors: [<ids>]

DOT Format (Graphviz)

Graph visualization format:

digraph CFG {
  node [shape=box];
  n1 [label="...", shape=...];
  n1 -> n2 [label="...", color=...];
}

Generate PNG/SVG with: dot -Tpng cfg.dot -o cfg.png

JSON Format

Machine-readable for tool integration:

{
  "nodes": [
    {"id": 1, "label": "...", "type": "..."}
  ],
  "edges": [
    {"from": 1, "to": 2, "type": "..."}
  ]
}

Analysis Levels

Function-Level (Intraprocedural)

Scope: Single function Nodes: Statements within function Edges: Control flow within function Calls: Treated as single statement nodes

Use cases:

• Function-level analysis
• Loop detection
• Path analysis within function

Program-Level (Interprocedural)

Scope: Multiple functions Nodes: Statements across all functions Edges: Control flow + call/return edges Calls: Explicit call and return edges

Use cases:

• Whole-program analysis
• Call graph construction
• Interprocedural dataflow

CFG Properties

Dominance

Node A dominates node B if every path from ENTRY to B passes through A.

Uses: Loop header identification, optimization

Post-Dominance

Node A post-dominates node B if every path from B to EXIT passes through A.

Uses: Control dependence, merge point identification

Reachability

Node B is reachable from node A if there exists a path from A to B.

Uses: Dead code detection, path analysis

Strongly Connected Components

Maximal set of nodes where every node is reachable from every other.

Uses: Loop detection, cycle analysis

Common Patterns

Sequential Statements

Pattern: Linear flow See: [cfg_patterns.md](references/cfg_patterns.md#sequential-statements)

If-Then-Else

Pattern: Diamond shape with merge See: [cfg_patterns.md](references/cfg_patterns.md#conditional-statements)

While Loop

Pattern: Back edge from body to header See: [cfg_patterns.md](references/cfg_patterns.md#loop-statements)

Break/Continue

Pattern: Direct edges to exit/header See: [cfg_patterns.md](references/cfg_patterns.md#loop-statements)

Try-Catch

Pattern: Exception edges to handlers See: [cfg_patterns.md](references/cfg_patterns.md#exception-handling)

References

Detailed CFG construction patterns:

• [cfg_patterns.md](references/cfg_patterns.md): Comprehensive patterns for all control flow constructs with examples

Load this reference when:

• Need detailed patterns for specific constructs
• Working with complex nested structures
• Want to see all output format examples
• Need CFG property definitions

Tips

1. Start with entry/exit: Always create ENTRY and EXIT nodes first
2. Handle loops carefully: Identify loop headers and create back edges
3. Merge branches: Create explicit merge nodes after conditionals
4. Label edges clearly: Use T/F for branches, mark back edges
5. Consider scope: Choose function-level or program-level based on use case
6. Visualize complex CFGs: Use DOT format for large graphs
7. Validate structure: Check that all nodes are reachable from ENTRY
8. Document assumptions: Note how you handle language-specific constructs