Implementing Concolic Testing in Jest for Path Coverage

Concolic testing, a combination of symbolic and concrete execution, is a powerful technique for automatically generating test cases that achieve high code coverage. This challenge focuses on implementing a basic concolic testing framework within the Jest testing environment to explore different execution paths of a simple TypeScript function.

Problem Description

Your task is to create a rudimentary concolic testing engine that can be integrated with Jest to test a given TypeScript function. The engine should:

1. Symbolically Execute: Track symbolic values and constraints encountered during the execution of the target function.
2. Concretely Execute: Use concrete inputs to drive the execution.
3. Generate New Test Cases: Based on the collected constraints, systematically generate new concrete inputs that exercise previously unvisited code paths.
4. Integrate with Jest: Present the results of the concolic testing within the Jest framework, indicating which paths were covered and what inputs were used.

You will need to define a simplified symbolic execution engine that can handle basic arithmetic operations and conditional branching. The goal is to achieve path coverage for a given target function.

Key Requirements:

• Symbolic State Management: Maintain a symbolic state that includes symbolic variables and a set of collected constraints (e.g., x > 5, y === 10).
• Constraint Solver (Simplified): Implement a basic mechanism to solve simple constraints. For this challenge, you can assume a simplified solver that can handle basic comparisons and equalities, and can negate constraints to explore alternative paths.
• Path Exploration: The engine should explore different execution paths by negating constraints and attempting to find new concrete inputs.
• Jest Integration: The concolic testing process should be initiated and managed within a Jest test suite. The output should clearly show the inputs used for each covered path.
• Target Function: You will be provided with a simple TypeScript function to test.

Expected Behavior:

The concolic tester, when run with a target function, should systematically explore different execution paths. For each unique path explored, it should identify the concrete input that led to that path and report it. The process should continue until a defined coverage goal is met or no new paths can be discovered.

Important Edge Cases to Consider:

• Branching: The engine must correctly handle if, else if, and else statements.
• Looping (Optional but Recommended): If time permits, consider how to handle simple while or for loops, though this might be simplified for the core challenge.
• Function Calls: For this challenge, assume the target function does not call other functions that require symbolic execution.

Examples

Let's consider a target function:

function simpleBranching(x: number, y: number): string {
  if (x > 5) {
    if (y === 10) {
      return "Path A"; // x > 5 and y === 10
    } else {
      return "Path B"; // x > 5 and y !== 10
    }
  } else {
    return "Path C"; // x <= 5
  }
}

Example 1: Initial Execution

• Input: x = 7, y = 10
• Execution:
  • x > 5 is true.
  • y === 10 is true.
  • Returns "Path A".
• Concolic State:
  • Symbolic variables: x, y
  • Constraints: x > 5, y === 10
• Output: Path covered: "Path A" with input x=7, y=10.

Example 2: Path Exploration (Negating y === 10)

• Goal: Explore a path where x > 5 but y !== 10.
• Constraint to Negate: y === 10. The negated constraint is y !== 10.
• New Constraints for Exploration: x > 5 AND y !== 10.
• Finding a Concrete Input: The solver needs to find inputs that satisfy x > 5 and y !== 10. For example, x = 8, y = 5.
• Concrete Execution with New Input:
  • x = 8, y = 5
  • x > 5 is true.
  • y === 10 is false.
  • Returns "Path B".
• Output: Path covered: "Path B" with input x=8, y=5.

Example 3: Path Exploration (Negating x > 5)

• Goal: Explore a path where x <= 5.
• Constraint to Negate: x > 5. The negated constraint is x <= 5.
• New Constraints for Exploration: x <= 5.
• Finding a Concrete Input: The solver needs to find inputs that satisfy x <= 5. For example, x = 3, y = 7 (the value of y doesn't matter for this path).
• Concrete Execution with New Input:
  • x = 3, y = 7
  • x > 5 is false.
  • Returns "Path C".
• Output: Path covered: "Path C" with input x=3, y=7.

Constraints

• Target Function Complexity: The target function will be a simple TypeScript function with conditional logic (if/else, potentially switch statements) and basic arithmetic operations. It will not involve complex data structures, I/O, or asynchronous operations.
• Input Domain: The input values for the target function will be primitive types (numbers, strings, booleans).
• Symbolic Variable Limit: Assume a small number of symbolic variables to manage complexity.
• Constraint Solver Simplification: The constraint solver will only need to handle basic arithmetic comparisons (>, <, ===, !==, >=, <=) and logical AND (&&). You can implement a simplified solver that can derive a concrete value when a single constraint is given (e.g., if constraint is x > 5, pick x = 6) or when multiple constraints are given and are easily satisfiable.
• Jest Test Suite: The concolic testing framework must be designed to run as a Jest test suite.

Notes

• This challenge requires you to build a simplified symbolic execution engine. You'll need to instrument the target function or create a wrapper to capture symbolic states and constraints.
• Think about how to represent symbolic values and constraints. For example, a symbolic value could be an object { name: 'x', constraints: [...] }.
• The "constraint solver" is the core of the path exploration. For this exercise, a basic solver that can propose a concrete input satisfying a set of constraints will suffice. You can hardcode simple satisfying values for basic cases.
• The goal is to demonstrate the concept of concolic testing and its integration with Jest for path coverage. The solver's sophistication can be adjusted based on complexity.
• Consider how to track visited paths to avoid redundant exploration. A path can be uniquely identified by the sequence of branch decisions taken.
• The output should be clear and informative, showing the inputs used for each discovered path. You could use console.log or Jest's reporting mechanisms.