Dipartimento di Informatica e Scienze dell'Informazione
Non-strict don't care
Algebras and Specifications
E. Astesiano and M. Cerioli .
In S. Abramsky and T.S.E. Maibaum, editors, Proceedings of
TAPSOFT'91, number 493 in Lecture Notes in Computer Science, pages 121--142,
Berlin, 1992. Springer Verlag.
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.
In this paper, after presenting the basic properties of the category of non-strict
algebras, we explore the relationship between non-strict don't care and total algebras.
Then the conditional algebraic specifications are investigated; 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.
The compressed postscript version of this paper is available through anonymous ftp
at ftp.disi.unige.it, in