A formal library of set relations and its application to synchronous languages

Set relations are particularly suitable for specifying the small-step operational semantics of synchronous languages. In this paper, a formal library of set relations for the definition, verification of properties, and execution of binary set relations is presented. The formal library consists of a set of theories written in the Prototype Verification System (PVS) that contains definitions and proofs of properties, such as determinism and compositionality, for synchronous relations. The paper also proposes a serialization procedure that enables the simulation of synchronous set relations via set rewriting systems. The library and the serialization procedure are illustrated with the rewriting logic semantics of the Plan Execution Interchange Language (PLEXIL), a rich synchronous plan execution language developed by NASA to support autonomous spacecraft operations.