  In this paper, we present a novel framework for studying the syntactic
completeness of computational effects and we apply it to the exception effect.
When applied to the states effect, our framework can be seen as a
generalization of Pretnar's work on this subject. We first introduce a relative
notion of Hilbert-Post completeness, well-suited to the composition of effects.
Then we prove that the exception effect is relatively Hilbert-Post complete, as
well as the "core" language which may be used for implementing it; these proofs
have been formalized and checked with the proof assistant Coq.
