DISI Dipartimento di Informatica e Scienze dell'Informazione

Non-strict don't care Algebras and Specifications

E. Astesiano and M. Cerioli .

Mathematical Structures in Computer Science, 6(1):85--125, 1996.

Non-strict don't care functions, whose foremost representative is the ubiquitous if_then_else, play an essential role in computer science.
As for what concerns semantics, they can be modelled by their totalizations with the appropriate use of elements representing undefinedness, as D. Scott has shown in his denotational approach. The situation is not so straightforward when we consider non-strict functions in the context of an algebraic framework; this point is discussed in the last section, where we explore the relationship between non-strict don't care and total algebras.
The central part of this paper, after presenting the basic properties of the category of non-strict algebras, is an investigation of conditional algebraic specifications. It is shown that non-strict conditional specifications are equivalent to disjunctive specifications and necessary and sufficient conditions for the existence of initial models are given. Since non-strict don't care specifications generalize both the total and the partial case, it is shown how the results about initiality can be obtained as specializations.
This is an extended version of a paper with the same title presented at TAPSOFT91 .

The compressed postscript version of this paper is available through anonymous ftp at ftp.disi.unige.it, in /person/CerioliM/mscs96.ps.gz (131268 Kb)