Operational semantics of proto

The Proto spatial computing language in Beal and Bachrach (2006) [1] simplifies the creation of scalable, robust, distributed programs by abstracting a network of locally communicating devices as a continuous geometric manifold. However, Proto's successful application in a number of domains is challenging its coherence across different platforms and distributions. We thus present a complete operational semantics for the Proto language, as executed asynchronously on a network of fast message-passing devices. This semantics covers all of the operations of the three space-time operator families unique to Proto-restriction, feedback, and neighborhood-as well as the current pointwise operations that it shares with most other languages. This formalization will provide a reference to aid implementers in preserving language coherence across platforms, domains, and distributions. The formalization process has also advanced the Proto language in several ways, which we explain in detail.