Constraint Semantics for Abstract Read Permissions

Abstract

The concept of controlling access to mutable shared data via permissions is at the heart of permission logics such as separation logic and implicit dynamic frames, and is also used in type systems, for instance, to give a semantics to "read-only" annotations. Existing permission models have different strengths in terms of expressiveness. Fractional permissions, for example, enable unbounded (recursive) splitting, whereas counting permissions enable unbounded subtraction of the same permission amount. Combining these strengths in a single permission model appeared to increase the complexity for the user and tools. In this paper we extend our previous work on abstract read permissions by providing them with a novel constraint semantics, which retains the use of the domain of rational numbers but enables unbounded subtraction of identical amounts. Thus we can keep an intuitive model conducive to SMT solvers while enabling "counting."