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  max_val:
            max_val = arr[i]
        i += 1
    return max_val

Analysis:

Initial State:

• arr: not-null (assumed)
• n: ⊤ (unknown integer)

**Line 2: `if n 0): n ∈ [1, ∞]

Line 3: return None (Branch 1)

• Safe return

Line 5: max_val = arr[0] (Branch 2)

• Access: arr[0]
• Check: 0 max_val`**
• Access: arr[i] where i ∈ [1, n-1]
• Check: i len(arr), out-of-bounds access
• State: maxval updated if arr[i] > maxval

Line 10: i += 1

• State: i ∈ [2, n]

Report:

POTENTIAL ERRORS FOUND:

1. Out-of-Bounds Access
   Location: line 5, arr[0]
   State: n ∈ [1, ∞], arr length unknown
   Severity: Potential
   Explanation: Array 'arr' might be empty when n > 0
   Suggestion: Add check: if len(arr) == 0 or add precondition

2. Out-of-Bounds Access
   Location: line 8, arr[i]
   State: i ∈ [1, n-1], arr length unknown
   Severity: Potential
   Explanation: If n > len(arr), accessing beyond array bounds
   Suggestion: Add precondition: n  0 and x < 10:
    # x ∈ [1, 9] (path-sensitive)
    # vs x ∈ [-∞, ∞] (path-insensitive)

References

For detailed information on abstract interpretation techniques and domains:

• references/abstract_domains.md: Detailed abstract domain definitions and operations
• references/analysis_patterns.md: Common analysis patterns for different error types
• references/language_specifics.md: Language-specific analysis considerations

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: ArabelaTso
• Source: ArabelaTso/Skills-4-SE
• License: Apache-2.0
• Homepage: https://ArabelaTso.github.io/Skills-4-SE/

Install and usage instructions live in the source repository linked above.