HOS (higher order software) methodology is very useful in the development of reliable software. However, for lack of an explicit and formal functional specification facility, HOS methodology, by its very nature, can only make the interface of HOS specification consistent and does not support any form of semantic verification. In this article, the formal functional specification mechanism based on the first-order prediate calculus is introduced, and semantic synthesis rules concerning HOS's primitive control structures OR, INCLUDE, and JOIN and cocontrol structures COOR, COJOIN, and COINCLUDE are given. Based on these semanic rules, a bottom-up hierarchical understanding method for HOS specification is presented, and its application to the verification of HOS specification is also discussed.