Modeling partiality by nondeterminism - from abstract specifications to flexible error handling
Reports in Informatics No. 178, August 1999, Department of
Informatics, University of Bergen, Norway.
Abstract
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 $\inst{MA}$ (modelling
nondeterministic operations by set-valued functions) and illustrate
the flexibility of our approach by examples showing uniform treatment
of strictness, non-strictness and various error handling. We present a
methodology for specification development from an abstract
specification to low level error handling. We also study the
conditions for $\inst{MA}$ specifications to ensure the existence of
initial models. Finally we relate $\inst{MA}$ to other institutions,
in particular, we show embedding of partial algebras and membership
algebras into $\inst{MA}$. Applying institution transformation instead
of embedding leads to the possibility of resuing partial algebra
specifications in the proposed framework -- a partial algebra
specification can be conservatively (preserving the models) imported
to $\inst{MA}$ while the extension of the model class allows for
furhter development towrds explicit error treatement.
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