We present a sound and complete focusing calculus for the core of the logic
behind the proof assistant Beluga as well as an overview of its implementation
as a tactic in Beluga's interactive proof environment Harpoon. The focusing
calculus is designed to construct uniform proofs over contextual LF and its
meta-logic in Beluga: a dependently-typed first-order logic with recursive
definitions. The implemented tactic is intended to complete straightforward
sub-cases in proofs allowing users to focus only on the interesting aspects of
their proofs, leaving tedious simple cases to Beluga's theorem prover. We
demonstrate the effectiveness of our work by using the tactic to simplify
proving weak-head normalization for the simply-typed lambda-calculus.Comment: In Proceedings LFMTP 2023, arXiv:2311.0991