The design of effective operators is a matter of some interest in the evolutionary computing community, and Radcliffe’s forma analysis is one notable approach to formally incorporate domain knowledge in operator design by manipulating the formal descriptions of problem domain. Since formal description is the key issue that affects the effectiveness of derived operator, this paper examines the concepts of Dedekind Cut and Isodedekind Cut introduced by Surry. Though they serve as very useful descriptions of the continuous domain, they have not been fully formalised. Some new concepts are developed or updated based on the original work and some ambiguous points (e.g. the derivation of operators with these formal descriptions) are also made clearer. A case study is also presented to illustrate the formal derivation of concrete operators with some predefined operator templates.