In the first part of this paper, we define two resource aware typing systems for the {\lambda}{\mu}-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments-based on decreasing measures of type derivations-to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the lengths of the head reduction and the maximal reduction sequences to normal-form. In the second part of this paper, the {\lambda}{\mu}-calculus is refined to a small-step calculus called {\lambda}{\mu}s, which is inspired by the substitution at a distance paradigm. The {\lambda}{\mu}s-calculus turns out to be compatible with a natural extensionof the non-idempotent interpretations of {\lambda}{\mu}, i.e., {\lambda}{\mu}s-reduction preserves and decreases typing derivations in an extended appropriate typing system. We thus derive a simple arithmetical characterization of strongly {\lambda}{\mu}s-normalizing terms by means of typing.

@article{KesnerV19,
  title = {Non-idempotent types for classical calculi in natural deduction style},
  author = {Delia Kesner and Pierre Vial},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 16, Issue 1},
  year = {2020},
  doi = {10.23638/lmcs-16(1:3)2020}
}