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Object oriented institutions to specify symbolic computationsystems

Published online by Cambridge University Press:  18 July 2007

César Domínguez ,
Laureano Lambán  and
Julio Rubio
César Domínguez
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n, E-26004 Logroño, La Rioja, Spain [email protected]; [email protected]; [email protected]
Laureano Lambán
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n, E-26004 Logroño, La Rioja, Spain [email protected]; [email protected]; [email protected]
Julio Rubio
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n, E-26004 Logroño, La Rioja, Spain [email protected]; [email protected]; [email protected]
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Abstract

The specification of the data structures used in EAT, a software system for symbolic computation in algebraic topology, is based on an operation that defines a link among different specification frameworks like hidden algebras and coalgebras. In this paper, this operation is extended using the notion of institution, giving rise to three institution encodings. These morphisms define a commutative diagram which shows three possible views of the same construction, placing it in an equational algebraic institution, in a hidden institution or in a coalgebraic institution. Moreover, these morphisms can be used to obtain a new description of the final objects of the categories of algebras in these frameworks, which are suitable abstract models for the EAT data structures. Thus, our main contribution is a formalization allowing us to encode a family of data structures by means of a single algebra (which can be described as a coproduct on the image of the institution morphisms). With this aim, new particular definitions of hidden and coalgebraic institutions are presented.

Keywords

Institutionsymbolic computationspecificationobject orientation
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 2 , April 2007 , pp. 191 - 214
Copyright
© EDP Sciences, 2007

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References

M. Barr and Ch. Wells, Category Theory for Computer Science. Prentice Hall International (1995).
M. Bidoit and R. Hennicker, Constructor-based observational logic. Technical Report LSV-03-9, Lab. Specification et Verification, ENS de Cachan, Cachan, France (2003).
R.M. Burstall, R. Diaconescu, Hiding and behaviour: an institutional approach, in A Classical Mind: Essays in Honour of C.A.R. Hoare, edited by A. William Roscoe. Prentice-Hall, Englewood Cliffs, NJ (1994) 75–92.
Calmet, J. and Tjandra, I.A., A unified-algebra-based specification language for symbolic computing, in Design and Implementation of Symbolic Computation Systems (DISCO'93), edited by A. Miola, Springer, Berlin. Lect. Notes Comput. Sci. 722 (1993) 122–133. CrossRef
Calmet, J., Homann, K. and Tjandra, I.A., Unified domains and abstract computational structures, in Artificial Intelligence and Symbolic Mathematical Computation (AISMC'92), edited by J. Calmet and J.A. Campbell, Springer, Berlin. Lect. Notes Comput. Sci. 737 (1993) 166–177. CrossRef
Cîrstea, C., Coalgebra semantics for hidden algebra: parameterised objects and inheritance, in Recent Trends in Algebraic Development Techniques, edited by F. Parisi-Presicce, Springer, Berlin. Lect. Notes Comput. Sci. 1376 (1998) 174–189. CrossRef
Cîrstea, C., A coalgebraic equational approach to specifying observational structures. Theoret. Comput. Sci. 280 (2002) 35–68. CrossRef
Corradini, A., A completeness result for equational deduction in coalgebraic specification, in Recent Trends in Algebraic Development Techniques, edited by F. Parisi-Presicce, Springer, Berlin. Lect. Notes Comput. Sci. 1376 (1998) 190–205. CrossRef
C. Domínguez, J. Rubio, Modeling inheritance as coercion in a symbolic computation system, in International Symposium on Symbolic and Algebraic Computation (ISSAC'2001), edited by B. Mourrain, ACM Press (2001) 107–115.
Domínguez, C., Lambán, L., Pascual, V. and Rubio, J., Hidden specification of a functional system, in Computer Aided Systems Theory (EUROCAST'2001), edited by R. Moreno-Díaz, B. Buchberger, J.L. Freire, Springer, Berlin. Lect. Notes Comput. Sci. 2178 (2001) 555–569. CrossRef
X. Dousson, F. Sergeraert and Y. Siret, The Kenzo program, Institut Fourier, Grenoble, (1999), Available at http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo
Duval, D., Diagrammatic Specifications. Math. Structures Comput. Sci. 13 (2003) 857–890. CrossRef
Goguen, J.A. and Burstall, R.M., Institutions: Abstract model theory for specification and programming. J. ACM 39 (1992) 95–146. CrossRef
Goguen, J.A. and Diaconescu, R., Towards an algebraic semantics for the object paradigm, in Recent Trends in Data Type Specification, edited by H. Ehrig and F. Orejas Springer, Berlin. Lect. Notes Comput. Sci. 785 (1994) 1–29. CrossRef
Goguen, J.A. and Malcolm, G., A hidden agenda. Theoret. Comput. Sci. 245 (2000) 55–101. CrossRef
J.A. Goguen, G. Roşu, Hiding more of hidden algebra, in Formal Methods (FM'99), edited by J.M. Wing, J. Woodcook, J. Davies, Springer, Berlin. Lect. Notes Comput. Sci. 1709, (1999) 1704–1719.
Goguen, J.A. and Roşu, G., Institution morphisms. Form. Asp. Comput. 13 (2002) 274–307. CrossRef
Goguen, J.A., Malcolm, G. and Kemp, T., A hidden herbrand theorem: combining the object and logic paradigms. J. Log. Algebr. Program. 51 (2002) 1–41. CrossRef
Hennicker, R. and Bidoit, M., Observational logic, in Algebraic Methodology and Software Technology (AMAST'98), edited by A.M. Haeberer, Springer, Berlin. Lect. Notes Comput. Sci. 1584 (1999) 263–277.
Kurz, A. and Hennicker, R., On institutions for modular coalgebraic specifications. Theoret. Comput. Sci. 280 (2002) 69–103. CrossRef
L. Lambán, V. Pascual and J. Rubio, Specifying implementations, in International Symposium on Symbolic and Algebraic Computation (ISSAC'99), edited by S. Dooley. ACM Press, (1999) 245–251.
L. Lambán, V. Pascual and J. Rubio, An object-oriented interpretation of the EAT system, Applicable Algebra in Engineering, Comm. Comput. 14 (2003) 187–215.
J. Loeckx, H.D. Ehrich and M. Wolf, Specification of Abstract Data Types. Wiley and Teubner, New York (1996).
Rubio, J., Sergeraert, F., Constructive algebraic topology. Bull. Sci. Math. 126 (2002) 389–412. CrossRef
J. Rubio, F. Sergeraert and Y. Siret, EAT: Symbolic Software for Effective Homology Computation, Institut Fourier, Grenoble, 1997. Available at ftp://fourier.ujf-grenoble.fr/pub/EAT
Rubio, J., Sergeraert, F. and Siret, Y., Overview of EAT, a System for Effective Homology Computation. The SAC Newsletter 3 (1998) 69–79.
J.J.M.M. Rutten, Universal coalgebra: a theory of systems, Theoret. Comput. Sci. 249 (2000) 3–80. CrossRef
Tarlecki, A., Towards heterogeneous specifications, in Frontiers of Combinig Systems (FroCos'98), Research Studies Press/Wiley, edited by D.M. Gabbay, M. de Rijke. Stud. Logic Comput. 7 (2000) 337–360.