Concurrent ML (CML) is an extension of Standard ML of New Jersey with concurrent features similar to those of process algebra. In this paper, we build upon John Reppy's reduction semantics for CML by constructing a compositional operational semantics for a fragment of CML, based on higher-order process algebra. Using the operational semantics we generalise the notion of weak bisimulation equivalence to build a semantic theory of CML. We give some small examples of proofs about CML expressions, and show that our semantics corresponds to Reppy's up to weak first-order bisimulation.
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