Evaluation of Underdetermined Explicit Deenitions ?

The speciication language VDM-SL is used in the model-oriented formal method known as the Vienna Development Method. There have been a number of diierent dialects of this language, but a standard for the language has now been deened. The draft standard includes a dynamic semantics which, in general, is not executable. A given speciication denotes a (possibly innnite) set of models according to the dynamic semantics. This paper illustrates how all the valid results from evaluating a given expression in all the diierent models can be collected. It is important to be able to do this in order to investigate the amount of looseness which is present in the given speciication, such that correctness properties of the expression as a whole can be derived. We present a speciication of such a loose evaluation for an executable subset of VDM-SL. The subset is interesting because it also illustrates how underdeterminedness is combined with recursion in VDM-SL.