Modeling Reachability Types with Logical Relations

Reachability types are a recent proposal to bring Rust-style reasoning about memory properties to higher-level languages. While key type soundness results for reachability types have been established using syntactic techniques in prior work, stronger metatheoretic properties have so far been unexplored. This paper presents an alternative semantic model of reachability types using logical relations, providing a framework in which to study key properties of interest such as (1) semantic type soundness, including of not syntactically well-typed code fragments, (2) termination, especially in the presence of higher-order state, and (3) program equivalence, especially reordering of non-interfering expressions for parallelization or compiler optimization.