At least for short sequences it works, but I guess the trick is to make it work for long sequences!

Prompt and output from GPT-4:

Write a Python function to compute PARITY incrementally on a list of 0 and 1. For example, the output for [0, 1, 1] should be 0, 1, 0. Print out all the intermediate values.

Here is a Python function to compute the parity incrementally on a list of 0s and 1s. The function will print out all intermediate values as well.

    def incremental_parity(lst):
        parity = 0
        result = []

        for num in lst:
            if num not in (0, 1):
                raise ValueError("The list should contain only 0s and 1s.")
        
            parity ^= num  # XOR operation
            result.append(parity)
            print(f'Current list: {lst[:len(result)]}, Intermediate result: {result}')

        return result

    # Example usage:
    lst = [0, 1, 1]
    result = incremental_parity(lst)
    print(f'Final result: {result}')

This function computes the parity incrementally by XORing each element of the list. The intermediate and final results are printed as requested.

What is the output for this function on the list [0, 1, 1, 0, 0, 1, 0, 1, 1]

To find the output of the function on the given list, you can use the provided incremental_parity function. Here's what the output would look like:

    lst = [0, 1, 1, 0, 0, 1, 0, 1, 1]
    result = incremental_parity(lst)

Output:

    Current list: [0], Intermediate result: [0]
    Current list: [0, 1], Intermediate result: [0, 1]
    Current list: [0, 1, 1], Intermediate result: [0, 1, 0]
    Current list: [0, 1, 1, 0], Intermediate result: [0, 1, 0, 0]
    Current list: [0, 1, 1, 0, 0], Intermediate result: [0, 1, 0, 0, 0]
    Current list: [0, 1, 1, 0, 0, 1], Intermediate result: [0, 1, 0, 0, 0, 1]
    Current list: [0, 1, 1, 0, 0, 1, 0], Intermediate result: [0, 1, 0, 0, 0, 1, 1]
    Current list: [0, 1, 1, 0, 0, 1, 0, 1], Intermediate result: [0, 1, 0, 0, 0, 1, 1, 0]
    Current list: [0, 1, 1, 0, 0, 1, 0, 1, 1], Intermediate result: [0, 1, 0, 0, 0, 1, 1, 0, 1]
    Final result: [0, 1, 0, 0, 0, 1, 1, 0, 1]

The final result for the list [0, 1, 1, 0, 0, 1, 0, 1, 1] is [0, 1, 0, 0, 0, 1, 1, 0, 1].