If Idris thinks that things can be total, that is not, can Idris be used for evidence?

Question

http://docs.idris-lang.org/en/v0.99/tutorial/theorems.html#totality-checking-issues states that:

Secondly, the current implementation currently has limited efforts, so there may be times when she believes that the function is common, but it is not. Do not rely on this for your evidence yet!

Does this mean that Idris should not rely on evidence, or is there a way to create evidence that does not need to be checked for integrity?

Answer 1

All bug fixes are at risk of implementation errors (or even hardware errors!) That can lead to system inconsistencies and allow users to prove something. This risk can never be zero. Even if we prove the correctness of the implementation of the proof assistant, this proof must also be proved in some other formal or informal system, taking into account the same risks.

Therefore, what we should expect from a proof assistant is not an infallible truth, but simply a convincing proof of reality. How strong this evidence is depends on our preliminary information on the reliability of the system and on the extent to which we can look at a particular evidence and determine whether it uses inconsistencies.

So this is not a clear example of how convincingly the evidence of Idris is proven. I would say that they are quite strong compared to unofficial evidence. In addition, Idris’s evidence is not yet scaled until evidence of Agda or especially Coq is proven, so it can probably be verified by a human inspection for “exploits.”