More and more personal information is exchanged on-line using communication protocols. This makes it increasingly important that such protocols satisfy privacy by data minimisation. Formal methods have been used to verify privacy properties of protocols; but so far, mostly in an ad-hoc way. In previous work, we provided general definitions for the fundamental privacy concepts of linkability and detectability. However, this approach is only able to verify privacy properties for given protocol instances. In this work, by generalising the approach, we formally analyse privacy of communication protocols independently from any instance. We implement the model; identify its assumptions by relating it to the instantiated model; and show how to visualise results. To demonstrate our approach, we analyse privacy in Identity Mixer.