Formal correctness of complex multi-party network protocols can be difficult to verify. While models of specific fixed compositions of agents can be checked against design constraints, protocols which lend themselves to arbitrarily many compositions of agents--such as the chaining of proxies or the peering of routers--are more difficult to verify because they represent potentially infinite state spaces and may exhibit emergent behaviors that may not materialize under particular fixed compositions. We address this challenge by developing an algebraic approach that enables us to reduce arbitrary compositions of network agents into a behaviorally-equivalent (with respect to some correctness property) compact, canonical representation, which is amenable to mechanical verification. Our approach consists of an algebra and a set of property-preserving rewrite rules for the Canonical Homomorphic Abstraction of Infinite Network protocol compositions (CHAIN). Using CHAIN, an expression over our algebra (i.e., a set of configurations of network protocol agents) could be reduced to another behaviorally-equivalent expression (i.e., a smaller set of configurations). Repeated applications of such rewrite rules produces a canonical expression which can be checked mechanically. I will demonstrate the CHAIN approach as applied to standardized and experimental internet protocols, and discuss how it may be applied to a broad class of applications.