[ryjo]

Very cool. Neat how you managed to get logical symbols in to the language itself! When might someone use preconditions in Lean theorems?

This article caught my eye because it's focused on imperative programming, and I've been very focused on declarative vs imperative programming over the last few years. I implemented a version of your function in CLIPS, a Rules-based language that takes a declarative approach to code:

(defrule sum-is-0 (list $? ?first $? ?second $?) (test (= 0 (+ ?first ?second))) => (println TRUE))

(defrule sum-is-not-0 (not (and (list $? ?first $? ?second $?) (test (= 0 (+ ?first ?second))))) => (println FALSE))

(assert (list 1 0 2 -1)) (run) (exit)

The theorem you write in Lean to prove the function kind-of exists in CLIPS Rules; you define the conditions that must occur in order to execute the Right Hand Side of the Rule. Note that the above simply prints `TRUE` or `FALSE`; it is possible to write imperative `deffunction`s that return values in CLIPS, but I wanted to see if I could draw parallels for myself between Lean code and theorems. Here's a gist with the simple version and a slightly more robust version that describes the index at which the matching numbers appear: https://gist.github.com/mrryanjohnston/680deaee87533dfedc74b...

Thank you for writing this and for your work on Lean! This is a concept that's been circling in my head for a minute now, and I feel like this article has unlocked some level of understanding I was missing before.