Weak updates and separation logic

Separation logic provides a simple but powerful technique for reasoning about low-level imperative programs that use shared data structures. Unfortunately, separation logic supports only "strong updates," in which mutation to a heap location is safe only if a unique reference is owned. This limits the applicability of separation logic when reasoning about the interaction between many high-level languages (e.g., ML, Java, C#) and low-level ones since the high-level languages do not support strong updates. Instead, they adopt the discipline of "weak updates," in which there is a global "heap type" to enforce the invariant of type-preserving heap updates. We present SL ^w, a logic that extends separation logic with reference types and elegantly reasons about the interaction between strong and weak updates. We describe a semantic framework for reference types, which is used to prove the soundness of SL ^w. Finally, we show how to extend SL ^w with concurrency.