Modeling Partiality by Nondeterminism { from Abstract Speciications to Exible Error Handling

The paper presents a new way to model partial operations by use of nondeterminism: a partial operation is modeled as a nondeterministic operation returning, possibly, any value of the carrier. We introduce an institution of multialgebras MA (modelling nondeterministic operations by set-valued functions) and illustrate the exibility of our approach by examples showing uniform treatment of strictness, non-strictness and various error handling. We present a methodology for speciication development from an abstract speciication to low level error handling. We also study the conditions for MA speciications to ensure the existence of initial models. Finally we relate MA to other institutions, in particular, we show embedding of partial algebras and membership algebras into MA. Applying institution transformation instead of embedding leads to the possibility of resuing partial algebra speciications in the proposed framework { a partial algebra speciication can be conservatively (preserving the models) imported to MA while the extension of the model class allows for furhter development towrds explicit error treatement.