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To address the problem of generating a numerical type PF, we need to ensure that the number returned falls within a specified range to avoid generating invalid or error-ridden values.

Here’s the solution:

1. Define the Pascal License: Create a license structure for the number type that limits numerical values directly to a predefined range.

2. Set Size Constraints: The numerical values must be within a specified range, such as 0 ≤ num ≤ 150, to prevent generating invalid results.

The final solution is defined in Pascal as:

P_license PF(num: Number) : ? scalar {
    if num < 0 || num > 150
        return error
    else
        return num
}

This license ensures that any number generated will be within the range of 0 to 150, which helps in preventing errors and undefined behavior during PF generation.