Normalization for fitch-style modal calculi

@article{Valliappan2022NormalizationFF,
  title={Normalization for fitch-style modal calculi},
  author={Nachiappan Valliappan and Fabian Ruch and Carlos Tom{\'e} Corti{\~n}as},
  journal={Proceedings of the ACM on Programming Languages},
  year={2022},
  volume={6},
  pages={772 - 798}
}
Fitch-style modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by鈥β

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