Understanding and implementing Reo has been challenging due to interaction of the 'channel metaphor', which is an inherently local notion, and the non-local nature of constraint propagation imposed by composition. In this work, the channel metaphor takes a back seat, and we focus on the behavioural constraints imposed by the composition of primitives, and phrase the semantics of Reo as a constraint satisfaction problem. Not only does this provide a clear intensional description of the behaviour of Reo connectors in terms of synchronisation and data flow constraints, it also paves the way for new implementation techniques based on constraint propagation and satisfaction. In fact, decomposing Reo into constraints provides a new computational model for connectors, which we extend to model interaction with an unknown external world beyond what is currently possible in Reo.