AbstractCircus specifications define both data and behavioural aspects of systems using a combination of Z and CSP. Previously, a denotational semantics has been given to Circus; however, as a shallow embedding of Circus in Z, it was not possible to use it to prove properties like the refinement laws that justify the distinguishing development technique associated with Circus. This work presents a final reference for the Circus denotational semantics based on Hoare and He's Unifying Theories of Programming (UTP). Finally, it discusses the library of theorems on the UTP that was created and used in the proofs of the refinement laws.