A Deep Inference System for Differential Linear Logic

Abstract

Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system every provable formula admits a derivation in normal form, via a normalization procedure that commutes with the translation from sequent calculus to deep inference.

In Proceedings Linearity&TLLA 2020, arXiv:2112.14305