Algorithm Refinement with Read and Write Frames

The read and write frames of reference variables used in the VDM style of operation decomposition serve two purposes. Syntactically, they bind the variables that occur in the predicates of the operation speciication; and semantically, they record what access to the state an implementation can be allowed to make. This paper examines the use of frames in these two roles, in particular considering the case when there is an invariant on the state. It argues that the two roles can be usefully distinguished. A model for operation speciication and reenement is developed where full account is taken of both syntactic and semantic roles of the frames. Consideration of their syntactic role gives rise to the idea that a part of the state can be independent of the rest with respect to the invariant that is in force: a deenition of independence is given together with a syntactic suucient-condition for it. The semantic role of the frames is examined in connection with notions of satissability and satisfaction. Satissability is modiied to capture the restricted possible interdependen-cies between read and write variables and the rules for satisfaction are given that restrict the usual relation in order to respect the constraints on implementations imposed by the frames.