An implementation model for a retrieval and inference system based on the theory of conceptual graphs is presented. Several hard issues related to the full implementation of the theory are taken up and solutions presented. The solutions attempt to exploit existing but not fully recognized symmetries in CG theory. These symmetries include those between formation and inference rules, AND and OR, positive and negative, copy and restrict, general and specific, etc. Topics taken up include the implementation of Sowa's formation rules, the storage of a conceptual graph hierarchy involving contexts and negation as a conjunctive normal form (CNF) lattice, the extension of existing retrieval algorithms, such as Levinson's Method III and UDS, to handle complex referents and nested contexts, the checking of consistency, and the definition of Peirce's inference rules in terms of formation rules. A distinction is made between syntactic implication and semantic implication.