alt Hacker NewsThat's not true. Non-constructive logics are extensions of constructive logics. You can express any algorithm in TLA+, and much more than algorithms.
You are right that when using non constructive logics, it's not guaranteed that the proof is executable as a program, but that's not a downside. Having the proof be a program in some sense is interesting, but it's not particularly useful.
How do you express computational content in non-constructive logic while both making it usable from proofs (e.g. if I have some algorithm that turns A's into B's, I want that to be directly referenceable in a proof - if A's have been posited, I must be able to turn them into B's) and keeping its character as specifically computational? Expressing algorithms in a totally separate way from proofs is arguably not much of a solution.