32 research outputs found
Two for the Price of One: Lifting Separation Logic Assertions
Recently, data abstraction has been studied in the context of separation
logic, with noticeable practical successes: the developed logics have enabled
clean proofs of tricky challenging programs, such as subject-observer patterns,
and they have become the basis of efficient verification tools for Java
(jStar), C (VeriFast) and Hoare Type Theory (Ynot). In this paper, we give a
new semantic analysis of such logic-based approaches using Reynolds's
relational parametricity. The core of the analysis is our lifting theorems,
which give a sound and complete condition for when a true implication between
assertions in the standard interpretation entails that the same implication
holds in a relational interpretation. Using these theorems, we provide an
algorithm for identifying abstraction-respecting client-side proofs; the proofs
ensure that clients cannot distinguish two appropriately-related module
implementations
A Concurrent Logical Relation
Abstract—We present a logical relation for showing the correctness of program transformations based on a new type-and-effect system for a concurrent extension of an ML-like language with higher-order functions, higher-order store and dynamic memory allocation. We show how to use our model to verify a number of interesting program transformations that rely on effect annotations. In particular, we prove a Parallelization Theorem, which expresses when it is sound to run two expressions in parallel instead of sequentially. The conditions are expressed solely in terms of the types and effects of the expressions. To the best of our knowledge, this is the first such result for a concurrent higher-order language with higher-order store and dynamic memory allocation. I