We present a lightweight approach to Hoare-style specifications for
fine-grained concurrency, based on a notion of time-stamped histories that
abstractly capture atomic changes in the program state. Our key observation is
that histories form a partial commutative monoid, a structure fundamental for
representation of concurrent resources. This insight provides us with a
unifying mechanism that allows us to treat histories just like heaps in
separation logic. For example, both are subject to the same assertion logic and
inference rules (e.g., the frame rule). Moreover, the notion of ownership
transfer, which usually applies to heaps, has an equivalent in histories. It
can be used to formally represent helping---an important design pattern for
concurrent algorithms whereby one thread can execute code on behalf of another.
Specifications in terms of histories naturally abstract granularity, in the
sense that sophisticated fine-grained algorithms can be given the same
specifications as their simplified coarse-grained counterparts, making them
equally convenient for client-side reasoning. We illustrate our approach on a
number of examples and validate all of them in Coq.Comment: 17 page
