Operational Interpretations of Linear Logic

Two diierent operational interpretations of intuitionistic linear logic have been proposed in the literature. The simplest interpretation recomputes non-linear values every time they are required. It has good memory-management properties , but is often dismissed as being too ineecient. Alternatively , one can memoize the results of evaluating non-linear values. This avoids any recomputation, but has weaker memory-management properties. Using a novel combination of type-theoretic and operational techniques we give a concise formal comparison of the two interpretations. Moreover , we show that there is a subset of linear logic where the two operational interpretations coincide. In this subset , which is suuciently expressive to encode call-by-value lambda-calculus, we can have the best of both worlds: a simple and eecient implementation, and good memory-management properties.