Abstract
This article presents the definition and some basic properties of the Deva meta-calculus, a generic logical framework whose design was driven by the needs arising from the instantiation to software development methods. As a result, Deva contains structures that do not occur in comparable logical frameworks. There now exist a number of case studies about the formalization of software development methods in Deva. In this article, a structured definition of Deva is presented and basic parts of its language theory, viz Church-Rosser, closure, and strong normalization, are summarized.
Similar content being viewed by others
References
de Bruijn, N. G.:Lambda calculus notation with nameless dummies, Indagationes Mathematicae, 34:381–392, 1972.
de Bruijn, N.G.:A Survey of the Project AUTOMATH. In: J.P.Seldin and J.R.Hindley (eds),To H.B.Curry: Essays in Combinatory Logic, Lambda Calculus, and Formalism, pp.589–606, Academic Press, 1980.
Bert, D. and Sebbar, S.:Synthesizing Abstract Data Type Representation in the DEVA Meta-Calculus, Proceedings of the IFIP TC2 Working Conference on Constructing Programs from Specifications, Pacific Grove, Ca., 1991.
Coquand, I. and Huet, G.:Constructions: A Higher Order Proof System for Mechanizing Mathematics. InProceedings of EUROCAL 85, Linz, Austria, 1985.
van Daalen, D.T.:The Language Theory of AUTOMATH, PhD thesis, Technische Hogeschool Eindhoven, 1980.
Gabriel, R.: (ed.),ESPRIT Project ToolUse, Final Report of the Deva Support Task: Retrospective and Manuals, Arbeitspapiere der GMD, no.425, GMD Karlsruhe, 1990.
Gabriel, R.:Program Transformation Expressed in the DEVA Meta-Calculus, Proceedings of the IFIP TC2 Working Conference on Constructing Programs from Specifications, Pacific Grove, Ca., 1991.
Gordon, M.J.C.:HOL: A Proof Generating System for Higher Order Logic, in G.Birtwhistle and P.A.Subrahmanyam, editors, VLSI pecification, Verification and Synthesis, Kluwer, 1987.
de Groote, Ph.:Définition et Properiéetés d'un métacalcul de répresentation de théories, Thése d'Etat, Unité d'Informatique, Université Catholique de Louvain, Belgium, 1990.
Harper, R., Honsell, F.A. and Plotkin, G.:A Framework for Defining Logics. Proceedings of the 2nd Symposium on Logic in Computer Science, pp. 194–204, IEEE, 1986.
Hindley, J.R. and Seidin, J.P.:Introduction to Combinators and λ-Calculus, Cambridge University Press, 1986.
Jones, C.B., Jones, K.D., Lindsay, P.A. and Moore, R.:Mural: A Formal Development Support System. Springer, 1991.
Lafontaine, C:Formalization of the VDM Reification in the DEVA Meta Calculus. The Human-Leucocyte-Antigen case study. In: M. Broy and C.B. Jones (editors),Programming Concepts and Methods, pp.333–368, North-Holland, 1990.
Nederpelt, R.P.:An Approach to Theorem Proving on the Basis of a Typed Lambda Calculus, LNCS 87, pp.181–190, Springer, 1980.
Paulson, L.;Logic and Computation, Cambridge University Press, 1987
Sintzoff, M.:Understanding and Expressing Software Construction, In P.Pepper, editor,Program Transformations and Programming Environments, pages 169–180, Springer Verlag, 1980.
Sintzoff, M., Weber, M., de Groote, Ph. and Cazin, J.:Definition 1.1 of the Generic Development Language Deva. ToolUse-project, Research report, Unité d'Informatique, Université Catholique de Louvain, Belgium (also available at the author's adress), 1989.
Weber, M.:Formalization of the Bird-Meertens Algorithmic Calculus in the Deva Meta-Calculus, In: M. Broy and C.B. Jones (editors),Programming Concepts and Methods, pp. 201–232, North-Holland, 1990.
Weber, M.:A Meta-Calculus for Formal System Development, GMD-Bericht Nr. 195, Oldenburg Verlag, München/Wien, 1991.
Weber, M.:Deriving Transitivity of VDM-reification in Deva, Proceedings of the VDM'91 conference, LNCS 551, Springer Verlag, 1991.
Weber, M.:Calculating explicit proofs from implicit proofs, internal manuscript, Technical University of Berlin, 1992.
Weber, M., Simons, M. and Lafontaine, C.:The Generic Development Language Deva: Presentation and Case Studies, to be published as an LNCS volume.
Author information
Authors and Affiliations
Corresponding author
Additional information
Major parts of the work reported here were carried out while the author was under contract at the German National Research Centre (GMD) in Karlsruhe and at the University of Karlsruhe
Rights and permissions
About this article
Cite this article
Weber, M. Definition and basic properties of the deva meta-calculus. Formal Aspects of Computing 5, 391–431 (1993). https://doi.org/10.1007/BF01212485
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01212485