From examples to data-driven tests to properties

When I first heard about property-based tests, I had two issues. First, I thought they were meant to replace example tests—and we know now that they are not; just use the two techniques side by side. Second, I had no idea how to come up with good properties.

I had, however, a good idea on how to come with good examples and how to remove duplication between tests. We've seen a sample on how to come up with good examples for the power function; let's recap them:

• 0⁰ -> undefined (* the pow implementation in C++ returns 1 unless specific errors are enabled)
• 0^{any integer from 0 to max} -> 0
• 1^{any integer} -> 1
• (any integer except 0)⁰ -> 1
• 2² -> 4
• 2^{max int that doesn't overflow} -> value to be computed
• 10⁵ -> 100000
• 10^{max int that doesn't overflow} -> value to be computed

We've also...