WP Semantics and Behavioral Subtyping

For the object oriented (OO) world, developing formal semantics for theoretical study and practical use is still an important topic despite of a decade's efforts. In this paper, for a sufficiently large subset of sequential Java with a pure reference semantics model, we define a Weakest Precondition (WP) semantics, and prove its soundness and completeness. Based on thisWP semantics, we study specifications of methods and the refinement relationship between specifications, and we propose new definitions for object invariants and behavioral subtyping notation for general OO programs.

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