A Structural Approach to Prophecy Variables

Verifying the implementation of concurrent objects essentially proves the fine-grained implementation of object methods refines the corresponding abstract atomic operations. To simplify the specifications and proofs, we usually need auxiliary history and prophecy variables to record events occur historically and to predict the occurrence of certain events, respectively. Although the meaning of history variables is obvious, the semantics of prophecy variables and the corresponding auxiliary code is tricky and has never been clearly spelled out operationally. In this paper, we propose a new language construct, future blocks, that allows structural use of prophecy variables to refer to events in the future. The semantics of the construct is simple and easy to understand, without using any form of oracle or backward reasoning. Our language also separates auxiliary states from physical program states. With careful syntactic constraints, it ensures the use of history and prophecy variables would not affect the behaviors of the original program, which justifies the verification method depending on auxiliary variables.