Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-08T21:08:20.155Z Has data issue: false hasContentIssue false
  • English
  • Français

Sketches and computation – II: dynamic evaluation and applications

Published online by Cambridge University Press:  04 March 2009

Dominique Duval  and
Jean-Claude Reynaud
Dominique Duval
Affiliation:
Laboratoire d'Arithmétique, Calcul formel et Optimisation 123 Avenue Albert Thomas, 87060 LIMOGES cedex (France)
Jean-Claude Reynaud
Affiliation:
LGI-IMAG-CNRS, B.P.53, 38041 GRENOBLE cedex 9 (France)
Get access Rights & Permissions [Opens in a new window]

Abstract

In the first part of this paper (Duval and Reynaud 1994), we defined a categorical framework, based on the notion of sketch, for specification and evaluation in the senses of algebraic specifications and algebraic programming. Static evaluation in quasi-projective sketches was defined in Part I; in this paper, dynamic evaluation is introduced. It deals with more general structures, which may have no initial model. Until now, this process has not been used in algebraic specification systems, but computer algebra systems are beginning to use it as a basic tool. Finally, we give some applications of dynamic evaluation to computation in field extensions.

Information

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 4 , Issue 2 , June 1994 , pp. 239 - 271
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Barkatou, M. A. (1989) Contribution à l‘étude des équations différentielles et aux différences dans lechamp complexe, Thése, Institut National Polytechnique de Grenoble.Google Scholar
Della Dora, J., Dicrescenzo, C. and Duval, D. (1985) About a new method for computing in algebraic number fields. Proceedings Eurocal‘85. Springer-Verlag Lecture Notes in Computer Science 204 289–290.CrossRefGoogle Scholar
Dicrescenzo, C. and Duval, D. (1985) Algebraic computation on algebraic numbers. Computers and computing, Wiley-Masson 54–61.Google Scholar
Dicrescenzo, C. and Duval, D. (1989) Algebraic extensions and algebraic closure in Scratchpad. Symbolic and algebraic computation (ISSAC‘88). Springer-Verlag Lecture Notes in Computer Science 358 440–446.Google Scholar
Diers, Y. (1977) Catégories localisables, Thése de doctorat d’état, Université de Paris 6.Google Scholar
Duval, D. (1989) Simultaneous computations in fields of arbitrary characteristic. In: Kaltofen, E. and Watt, S. M. (eds.) Computers and Mathematics, Springer 321–326.CrossRefGoogle Scholar
Duval, D. and Gonzalez-Vega, L. (1993) Dynamic evaluation and real closure. Proceedings of IMACS’93.Google Scholar
Duval, D. and Reynaud, J.-C. (1989,1990) Esquisses et Calcul. In: Dehornoy, P. (ed.) Annales Université de Caen VII 15–83.Google Scholar
Duval, D. and Reynaud, J.-C. (1991) Sketches and computation. Rapport de recherche RR871-I-IMAG-123-LIFIA, Institut National Polytechnique de Grenoble.Google Scholar
Duval, D. and Reynaud, J.-C. (1994) Sketches and computation - Part I: basic definitions and staticevaluation. MSCS 4 185–238.Google Scholar
Duval, D. and Sénéchaud, P. (1991) Sketches and parametrization. Theoretical Computer Science. (To appear)Google Scholar
Futamura, Y. (1988) Program evaluation and generalized partial computation. Proceedings of the international conference on fifth generation computer systems, ICOT 685–692.Google Scholar
Gomez-Diaz, T. (1993) Examples of using dynamic constructible closure. Proceedings of IMACS’93.Google Scholar
Gonzàlez, L., Lombardi, H., Recio, T. and Roy, M.-F. (1989) Sturm-Habicht sequence. Proceedings ISSAC’89, ACM 136–146.CrossRefGoogle Scholar
Guitart, R. and Lair, C. (1980) Calcul syntaxique des modéles et calcul des formules internes. Diagrammes 4, Paris.Google Scholar
Jenks, R. D. and Sutor, R. S. (1992) Axiom. The Scientific Computation System. NAG, Springer Verlag.Google Scholar
Lair, C. (1983) Diagrammes localement libres, extensions de corps et théorie de Galois. Diagrammes 10, Paris.Google Scholar
Mac Lane, S. (1971) Categories for the working mathematician. Springer.CrossRefGoogle Scholar
Rioboo, R. (1992) Real algebraic closure of an ordered field, Implementation in Axiom. Proceedings ISSAC’92, ACM 206–215.CrossRefGoogle Scholar
Roch, J.-L. (1986) Calcul avec des nombres algébriques sous Reduce. Rapport de projet, ENSIMAG, Grenoble.Google Scholar
Rybowicz, M. (1990) Sur le calcul des places et des anneaux d’entiers d’un corps de functions algébriques, Thése, Université de Limoges.Google Scholar
Sestoft, P. and Søndergaard, H. (1987) A bibliography on partial evaluation. SIGPLAN notices 23.219–27CrossRefGoogle Scholar