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P9602b  J.A. Bergstra & M.P.A. Sellink
        "Sequential data algebra primitives" (revised version of P9602)


The purpose of this paper is to develop a family of data type
specifications and a particular method for writing such specifications based
on the four valued logic of Bergstra, Bethke and Rodenburg. 
The method is an informal one cast in a number of design rules for
specifications of data algebras. The phrase data algebra is used rather
than abstract data type in order to emphasise that the data types are first
order many sorted algebras that comply a number of requirements
(design rules).

The four valued (McCarthyan) logic, the new notations for list operators,
the omnipresent divergent and meaningless objects, and the very hierarchy of
modules below can be viewed as primitives for data algebra. Because all
operations including the logical connectives are sequential in the sense
that they inspect their arguments in some definite order this style of data
algebra is called sequential data algebra.

Evidently what we propose is only a choice from an infinite number of
different options. So what is being developed below is in fact a set of
primitives for a style of sequential data algebra. Modules written in that
style indicate so by having a name ending with DA.  

Some style of data algebra is needed in order to avoid endless duplication
and reinvention in the practice of algebraic specification. The mere
presence of module libraries will not suffice to reduce the frequency of
these improductive events. More importantly far more standardisation will
be needed to obtain a body of algebraic specifications with high
credibility. Again libraries as such will not generate confidence. In order
to achieve standardisation explicit specification styles are needed. The
style of sequential data algebra that we use is characterized by a number
of rather restrictive design rules, that simultaneously constitute its
rationale. The structuring mechanisms as well as the approach to syntax
definition and prettyprinting are based on ASF+SDF.
It follows that our style of sequential data algebra is geared towards and
biased by ASF+SDF. This, however, has had no significant impact on the
semantics of the descriptions or on the choice of operators and equations.