From Logic to Code: Understanding the Curry–Howard Correspondence in Lean

For many programmers, precise mathematical logic and general programming feel like different worlds. Logic is about proving theorems. Programming is about making systems behave correctly. Proofs belong to mathematicians. Functions belong to engineers. But in systems like Lean, those boundaries start collapsing. One of the deepest ideas behind this is the Curry–Howard correspondence -- the observation that: logical propositions correspond to types proofs correspond to programs proof checking corr