Typing Asymmetric Client-Server Interaction

We investigate client-server interaction where duties and rights of the parties are asymmetric, in the sense that the client is allowed to abort any session before the server has completed, but not vice versa. This implies that the client can interact with any server offering at least what she is looking for, but possibly more. We formalize such asymmetry in the setting of session types via a form of subtyping in depth, which we call prefix relation. This is apparently conflicting with the rigid duality imposed by session types; nonetheless the resulting system retains all basic correctness properties. Moreover, the system we propose highlights interesting aspects concerning the flow of communication inside a session. In particular it reveals that usual subtyping theories cannot be extended by means of prefix, which turns out to be a different concept.