Refinement types for precisely named cache locations
  Many programming language techniques for incremental computation employ programmer-specified names for cached information. At runtime, each name identifies a "cache location" for a dynamic data value or a sub-computation; in sum, these cache location choices guide change propagation and incremental (re)execution.   We call a cache location name precise when it identifies at most one value or subcomputation; we call all other names imprecise, or ambiguous. At a minimum, cache location names must be precise to ensure that change propagation works correctly; yet, reasoning statically about names in incremental programs remains an open problem.   As a first step, this paper defines and solves the precise name problem, where we verify that incremental programs with explicit names use them precisely. To do so, we give a refinement type and effect system, and prove it sound (every well-typed program uses names precisely). We also demonstrate that this type system is expressive by verifying example programs that compute over efficient representations of incremental sequences and sets. Beyond verifying these programs, our type system also describes their dynamic naming strategies, e.g., for library documentation purposes. 
Matthew A. Hammer, Jana Dunfield, Dimitrios J. Economou and Monal   Narasimhamurthy
cs.PL