The paper addresses problems in conceptual graph implementation: subsumption and classification in a taxonomy. Conceptual graphs are typically stored using a directed acyclic graph data structure based on the partial order over conceptual graphs. We give an improved algorithm for classifying conceptual graphs into this hierarchy. It prunes the search space in the database using the information gathered while searching. We show how conceptual graphs in this hierarchy can be compiled into instructions which represent specialized cases of the canonical formation rules. This compiles subsumption of conceptual graphs and compresses knowledge in a knowledge base. Conceptual graphs are compiled as differences between adjacent graphs in the hierarchy. The differences represent the rules used in deriving the graph from the adjacent graphs. We illustrate how the method compresses knowledge bases in some experiments. Compilation is effected in three ways: removal of redundant data, use of simple instructions which ignore redundant checks when performing matching, and by sharing common processing between graphs.>