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The Proto spatial computing language 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 becoming a challenge to its coherence across different platforms and distributions. We thus present an operational semantics for a core subset of the Proto language. This semantics covers all the key operations of the three space-time operator families unique to Proto-restriction, feedback, and neighborhood-as well as a few of the pointwise operations that it shares with most other languages. Because Proto programs are distributed, we also present an operational semantics for their asynchronous execution across a network. This formalization will provide a reference to aid implementers in preserving language coherence across platforms, domains, and distributions.
