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Dipartimento di Informatica e Scienze dell'Informazione

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Algebraic oriented Institutions

M. Cerioli and G. Reggio .

In T. Rus M. Nivat, C. Rattray and G. Scollo, editors, * Algebraic
Methodology and Software Technology (AMAST'93)*, Workshops in Computing,
pages 103--210. Springer Verlag, 1994.
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In many recent applications of the algebraic paradigm to formal specification
methodologies, basic frameworks are endowed with new features,
tailored for special purposes, that mostly are ``orthogonal'' to
the underlying algebraic framework, in the sense that they are instances
of a parametric constructions.
This lack of generality is conflicting with the ability of changing the basic
formalism, and hence with the reuse of methodologies, seen as high-level
theoretical tools for the software development.

In any real application two steps can be distinguished in the process of
getting the most suitable algebraic formalism:
the choice of the most appropriate basic algebraic formalism (i.e. sufficiently
powerful for the problem, but non-overcomplex) and the addition of the features
needed in the particular case (e.g. entities for structured parallelism or
higher-order functions for functional programming).
Thus here we propose a modular
construction of algebraic frameworks, formalized by means of operations on
institutions, used as a synonym for logical formalism, in order to build
richer institutions by adding one feature at a time.

Many constructions used in the practice have meaning only for those institutions
that represent ``algebraic formalisms''.
In order to give sound foundations for the treatment of such operations, a
preliminary step is the formal definition of which institutions correspond to
algebraic frameworks.
Here we propose a first attempt at the definition of algebraic-oriented
institutions, that includes all interesting cases.
Then, using this definition, we formally define
some operations adding features to basic algebraic frameworks and show that
the result of such operations applied to any algebraic-oriented institution is
an algebraic-oriented institution, too; so that the result can be used as input
for other operations, modularly building a formalism as rich as needed
by the application.

Technically algebraic-oriented institutions are described by (standard) algebraic
specifications,
so that both theoretical and software tools are at hand to help in the
building process; moreover algebraic specification users already have the
know-how to understand and manipulate metaoperations building algebraic
formalisms.
The compressed postscript version of this paper is available through anonymous ftp
at ftp.disi.unige.it, in
/person/CerioliM/AMAST93.ps.z
(43873 Kb).