abstract-state-analyzer

Abstract State Analyzer

Overview

This skill performs abstract interpretation to statically analyze source code and infer possible program states, variable ranges, and data properties. It identifies potential runtime errors without executing the program.

Analysis Workflow

Step 1: Parse and Understand Code Structure

Analyze the code to identify:

• Functions and their control flow
• Variable declarations and types
• Loops and conditionals
• Array/buffer operations
• Pointer/reference operations
• Function calls and parameter passing

Step 2: Select Abstract Domains

Choose appropriate abstract domains based on the analysis goals:

Interval Domain: Track numeric variable ranges

• Example: x ∈ [0, 100] means x is between 0 and 100
• Good for: Array bounds checking, overflow detection

Sign Domain: Track whether values are positive, negative, or zero

• Values: {+, -, 0, ⊤}
• Good for: Division by zero, sign-dependent operations

Null Domain: Track whether pointers/references can be null

• Values: {null, not-null, maybe-null, ⊤}
• Good for: Null dereference detection

Type Domain: Track possible types of variables

• Good for: Type consistency checking, dynamic language analysis

Combination: Use multiple domains together for more precise analysis

Step 3: Initialize Abstract States

Set initial abstract values for:

• Function parameters (based on preconditions or ⊤ for unknown)
• Global variables
• Constants and literals

Example:

def process(arr, index):
    # Initial state:
    # arr: not-null (assumed)
    # index: ⊤ (unknown integer)

Step 4: Perform Forward Analysis

Propagate abstract states through the program:

Assignment: Update abstract value

x = 5
# x: [5, 5]

y = x + 3
# y: [8, 8]

Conditionals: Split into branches

if x > 10:
    # Branch 1: x ∈ [11, ∞]
else:
    # Branch 2: x ∈ [-∞, 10]

Loops: Iterate until fixpoint

i = 0
while i < n:
    # Iteration 1: i ∈ [0, 0]
    # Iteration 2: i ∈ [0, 1]
    # ...
    # Fixpoint: i ∈ [0, n-1]
    i += 1