Symbolic Execution for Jest Test Coverage

Symbolic execution is a powerful program analysis technique that can be used to automatically generate test cases and improve test coverage. This challenge asks you to implement a simplified symbolic execution engine within the Jest testing framework to analyze a small, given function and explore its execution paths. Understanding symbolic execution can help you write more robust tests and identify potential bugs that might be missed by traditional input-based testing.

Problem Description

Your task is to create a Jest test suite that uses a basic symbolic execution engine to analyze a provided TypeScript function. The engine should be able to:

1. Track Symbolic Values: Represent inputs not as concrete values, but as symbolic variables.
2. Execute Function with Symbols: Step through the function's logic, maintaining the state of symbolic variables and applying symbolic operations.
3. Handle Branching: When the function encounters conditional statements (if/else), the engine should fork its execution path, creating separate states for each branch.
4. Identify Path Constraints: For each execution path, record the constraints (conditions that must be true) that lead to that path.
5. Generate Concrete Inputs (Optional but recommended): Based on the path constraints, attempt to derive concrete input values that would satisfy those constraints, thus executing that specific path.

The goal is to demonstrate how symbolic execution can explore different code paths within a function.

Key Requirements:

• The symbolic execution engine should be implemented in TypeScript.
• The engine should be integrated into a Jest test file.
• The engine should be able to analyze a given target function.
• The output of the symbolic execution should clearly show the different paths explored and their associated constraints.

Expected Behavior:

The Jest tests should, when run, perform symbolic execution on the target function and report on the distinct execution paths. This report should ideally include:

• A unique identifier for each path.
• The constraints that define each path.
• (If concrete input generation is implemented) A set of concrete input values that would trigger that path.

Edge Cases to Consider:

• Functions with no conditional logic.
• Functions with nested conditional logic.
• Functions with complex boolean expressions in conditions.

Examples

Let's consider a simple target function:

function conditionalAdd(a: number, b: number): number {
  if (a > 10) {
    if (b < 5) {
      return a + b + 1;
    } else {
      return a + b + 2;
    }
  } else {
    return a + b;
  }
}

Example 1: Symbolic Execution Analysis

• Target Function: conditionalAdd

• Input: a (symbolic), b (symbolic)

• Path 1:

  • Constraints: a > 10 AND b < 5
  • Symbolic Result: a + b + 1
  • Concrete Input Example: a = 11, b = 4 (which yields 11 + 4 + 1 = 16)

• Path 2:

  • Constraints: a > 10 AND b >= 5
  • Symbolic Result: a + b + 2
  • Concrete Input Example: a = 12, b = 6 (which yields 12 + 6 + 2 = 20)

• Path 3:

  • Constraints: a <= 10
  • Symbolic Result: a + b
  • Concrete Input Example: a = 5, b = 3 (which yields 5 + 3 = 8)

Example 2: Demonstrating Jest Integration

Your Jest test file might look something like this (simplified representation):

// symbolicExecutor.ts (your implementation)
// ...

describe('Symbolic Execution of conditionalAdd', () => {
  let symbolicEngine: SymbolicExecutor;

  beforeAll(() => {
    symbolicEngine = new SymbolicExecutor(conditionalAdd);
  });

  it('should explore all execution paths', () => {
    const executionPaths = symbolicEngine.execute();

    // Assertions about the number of paths, constraints, etc.
    expect(executionPaths.length).toBeGreaterThan(0); // Should find at least one path
    expect(executionPaths.length).toBe(3); // For conditionalAdd, we expect 3 paths

    // Further assertions to check specific constraints or generated inputs
  });
});

Constraints

• The target function will be a pure TypeScript function with primitive input types (e.g., number, boolean, string). No complex objects or external dependencies.
• The target function will be relatively small, focusing on basic control flow structures (if, else, potentially simple loops if your engine can handle them).
• Your symbolic execution engine should aim to identify all distinct executable paths.
• The concrete input generation (if implemented) does not need to be exhaustive but should provide one valid example for each discovered path.

Notes

• You'll need to represent symbolic variables and their associated constraints. Consider using a constraint solver library or implementing a simplified version yourself.
• Think about how to represent and manipulate symbolic expressions (e.g., a + b, a > 10).
• The core challenge is managing the state of symbolic variables and branching logic.
• This challenge focuses on the fundamental concepts of symbolic execution within a testing context. Advanced features like heap symbolic execution, complex loop handling, or full constraint satisfaction are out of scope.