Regex Pattern Generator And Tester

**Context**: 
Regular expressions (regex) are a powerful tool used for matching patterns in strings, but creating and testing them can be challenging, especially for complex patterns. A regex pattern generator and tester is a tool that can help users create, test, and refine their regex patterns.

**Detailed Instructions**: 
Design a comprehensive regex pattern generator and tester that can perform the following functions:
1. **Pattern Generation**: Given a set of example strings (both matching and non-matching), generate a regex pattern that matches the positive examples and rejects the negative ones.
2. **Pattern Testing**: Allow users to input their own regex patterns and test them against a set of strings to see which ones match and which ones do not.
3. **Pattern Refinement**: Provide suggestions for refining the generated or user-inputted regex patterns to improve their accuracy or efficiency.
4. **Error Handling**: Identify and report any errors in the regex patterns, such as syntax errors or catastrophic backtracking.
5. **Explanation**: Offer a breakdown of how the regex pattern works, including explanations of each part of the pattern and how it contributes to the overall match.

**Output Format**: 
The output should be in a JSON format with the following keys:
- `pattern`: The generated or tested regex pattern.
- `matches`: A list of strings that match the pattern.
- `non_matches`: A list of strings that do not match the pattern.
- `errors`: A list of error messages, if any.
- `explanation`: A detailed explanation of the regex pattern.

**Examples**: 
- Input: A set of example strings, such as ["hello", "world", "hello world"] as positive examples and ["goodbye", "foo"] as negative examples.
- Output: A regex pattern that matches the positive examples, such as `hello|world|hello world`, along with explanations and test results.
- Input: A user-inputted regex pattern, such as `\d{4}-\d{2}-\d{2}`, and a set of test strings, such as ["2022-01-01", "20220101", "2022/01/01"].
- Output: The input pattern, a list of matching strings (e.g., ["2022-01-01"]), a list of non-matching strings (e.g., ["20220101", "2022/01/01"]), and an explanation of the pattern.