Using Zippers for Nested Sequents with Focus
Shing Yau Simon Chiu

Abstract:
Nested sequent calculus augments the formalism of standard Gentzen-style sequents by allowing nesting of sequents, giving them a tree-like structure. In the classical modal setting, the resulting calculus is invertible, enabling terminating root-first proof search without backtracking. While provers based on nested sequents exist, they involve additional structure and heuristics not formally part of the proof system, indicating a gap between theory and implementation. Here, we augment nested sequents by adding a current focus, internalising the heuristics of proof search into the calculus. We implement this using the zipper data structure in Haskell, and test it on various examples to ensure correctness.