An Extension of Dynamic Logic for Modelling OCL's @pre Operator

We consider first-order Dynamic Logic (DL) with non-rigid functions, which can be used to model certain features of programming languages such as array variables and object attributes. We extend this logic by introducing, for each non-rigid function symbol f, a new function symbol f@pre that after program execution refers to the old value of f before program execution. We show that DL formulas with @pre can be transformed into equivalent formulas without @pre. We briefly describe the motivation for this extension coming from a related concept in the Object Constraint Language (OCL).