Sorting (TimSort) was broken for many years in Python. It was good old-fashioned logic and theorem proving, not tests or runtime assertions, that got it fixed. There is merit in proving properties of any critical implementation, no matter how difficult. However the gist you referenced looks to be someone's learning effort, so hardly a model example.
Your view on the role of types is unfortunate if you think term logic is simply mirrored at the type level (Plato's Cave). The Curry-Howard correspondence tells us to think of types as logical propositions with terms as their proofs.
Sure, you can use formal methods to prove properties that are hard to test. The point you seem to have missed is that it takes a lot of effort to do that.
The reality is that in most cases there's a cost benefit analysis regarding how much time you can spend on a particular feature and the strength of the guarantees.
>The Curry-Howard correspondence tells us to think of types as logical propositions with terms as their proofs.
Hence my point that you end up writing a metaprogram that emits the logic. Ensuring that the metaprogram is correct is a manual process. The more complex the proof, the harder it becomes to understand.
Consider Fermat's conjecture. It's trivial to state it, it's trivial to test it to be correct for a given set of inputs. However, proving it for the general case is quite difficult, and only a handful of people in the world can follow that proof.
> onsider Fermat's conjecture. It's trivial to state it, it's trivial to test it to be correct for a given set of inputs. However, proving it for the general case is quite difficult, and only a handful of people in the world can follow that proof.
This is a strawman, conventional static type system can't prove all general cases either and no body is saying that they do that. Yet, they being a superset of dynamic typing, they allow to have the same expesiveness as such by providing a bypass like 'Object' or 'any'.
Your view on the role of types is unfortunate if you think term logic is simply mirrored at the type level (Plato's Cave). The Curry-Howard correspondence tells us to think of types as logical propositions with terms as their proofs.