Detection and analysis of some redundancies in linear logic sequent proofs

Proof search in inference systems such as the sequent calculus is a process of discovery. Once a proof is found, there is often information in the proof which is redundant. In this article we show how to detect and eliminate certain kinds of redundant formulae from a given proof, and in particular in a way which does not require further proof search or any rearrangement of the proof found. Our technique involves adding constraints to the inference rules, which are used once the proof is complete to determine redundant formulae and how they may be eliminated. We show how this technique can be applied to propositional linear logic, and prove its correctness for this logic. We also discuss how our approach can be extended to other logics without much change.