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Dipartimento di Informatica e Scienze dell'Informazione

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Non-strict don't care
Algebras and Specifications

E. Astesiano and M. Cerioli .
* Mathematical Structures in Computer Science*, 6(1):85--125, 1996.

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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)