In many creative design processes, cross-domain knowledge is required to inspire the new design result. Thus, in knowledge-based design, how we represent the cross-domain knowledge becomes a key issue. In this paper, we present a formalism for design knowledge representation. By analyzing function representation in different design domains, from graphic design and industrial design to architectural and engineering device designs, we find that although the focus of each kind of design is different, the function representation can be generalized into a small number of categories. This formalism can be used in an explorative model of design by analogy, where designs from different design domains are sources to help produce a new design.