A Linear-Time Abstract Machine for Cut Elimination in Intuitionistic Multiplicative Exponential Linear Logic

The authors design an environment-based abstract machine that implements a good cut elimination strategy for the Exponential Substitution Calculus (ESC), which is an untyped calculus of proof terms for Intuitionistic Multiplicative Exponential Linear Logic (IMELL). They prove that the machine has a bi-linear overhead, providing the first linear-time cost model for an expressive fragment of linear logic.