There are many other kinds of proof objects https://www.philipzucker.com/proof_objects/ . A similar one that is useful is outputting a permutation from a sorting algorithm. Verifying a permutation takes O(n) but sorting under the appropriate assumptions takes O(n ln(n)), so there is a complexity gap there. https://cacm.acm.org/research/program-correctness-through-self-certification/
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Third, when I read code, I tend to start from the data: in C/C++ terms, the struct or private members of a class. Data is often more self-descriptive than operations. Once I understand the data model, the operations become transformations over that model. This is a personal bias, but it matches how I think about functional programming (FP) and data-oriented programming (DOP). It also explains why OOP doesn’t click with me as easily: it starts from behavior and encapsulation, while I prefer to anchor my understanding in data first. From this lens I could talk about side effects, mutability, and other concepts, but that would take us too far.