Comment by kccqzy

I think the explosion in the popularity of Lean probably means that tactic-based proofs have won. I wrote many proofs in college and on mere aesthetic grounds I avoided the use of theorem provers with tactics. Invoking a tactic is like calling a function without writing down what the arguments to the function are and what the result of the function is. As a reader you gain little knowledge about the proof unless you run it interactively and observe the goals at each step. In contrast languages like Idris do not use tactics and require explicit manipulation of proof objects; it’s a lot less automated and verbose. Using the function call analogy, it’s like having to write down every argument passed to a function call and name every return value. It’s more tedious to write but both the writer and the reader gain more by the explicitness. But in the age of AI, the tedium to write proofs without tactics really shouldn’t have mattered.