Proving Memory Management Invariants for a Language Based on Linear Logic

We develop a tool for the rigorous formulation and proof of properties of runtime memory management for a sample programming language based on a linear type system. Two semantics are described, one at a level of observable results of computations and one that describes linear connectives in terms of memory-management primitives. The two semantics are proven equivalent and the memory-management model is proven to satisfy fundamental correctness criteria for reference counts.