[James_K]

  import Mathlib
  def Goldbach := ∀ x : ℕ, Even x → x > 2 → ∃ (y z: ℕ), Nat.Prime y ∧ Nat.Prime z ∧ x = y + z

A short specification for the proof of the Goldbach conjecture in Lean. Much harder to implement though. Implementation details are always hidden by the interface, which makes it easier to specify than produce. The Curry-Howard correspondence means that Joel's position here is that any question is as hard to ask as answer, and any statement as hard to formulate as it is to prove, which is really just saying that all describable statements are true.

[xigoi]

This argument is based on the notion of proof irrelevance – if a theorem is true, any proof is as good as any other. This is not the case for computer programs – two programs that implement the same specification may be very different in terms of performance, size, UI/UX, code maintainability, etc.

[James_K]

Performance and size can easily be added to any specification, maintainability is not a problem if you never have to maintain it, UI/UX are design issues not code issues. If you specify a UI, it will have the UX you want. We can already do UI creation with visual editors.

[antonvs]

    theorem goldbach : Goldbach := *message truncated*