The design of the future Internet is facing real challenges on network architecture. Attempts to resolve the issues related to naming/addressing, middle boxes, QoS-Security-Mobility interactions, cross-layer and inter-domain usually lead to endless debates. This is because the structure of the Internet has become too complex and has evolved with new functions added which are not always compatible with the existing functions. In order to analyze the architecture of the Internet in a strict manner, it is necessary to understand in depth the composition of functionalities within a protocol or between protocols. This paper presents a study on the composition of network functionalities and highlights future directions towards a theory for network architectures which includes the principles that network architectures should follow to ensure the normal operation of the member functions, detect all possible conflicts between them as well as figure out impossibilities.