Abstract
A Typed Equational Logic (TEL) has been recently proposed as an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type assignment, polymorphism and dependent types. In this paper the pragmatic motivations for this logic are recalled, as they arise from specification of abstract data types. An overview of TEL is then presented, and its usage illustrated by simple examples where the aforementioned phenomena occur.
Preview
Unable to display preview. Download preview PDF.
References
H. Andreka, P. Burmeister and I. Nemeti, Quasivarieties of partial algebras — a unifying approach towards a two-valued model theory for partial algebras, Preprint Nr. 557, FB Mathematik und Informatik, TH Darmstadt, 1980.
H. Brinksma, On the Design of Extended LOTOS: A Specification Language for Open Distributed Systems, Thesis Doct. Phil., Univ. Twente, November 1988.
J.A. Bergstra and J.W. Klop, Conditional rewrife rules: confluence and termination, J. Comput. Sys. Sci. 32, 3 (1986) 323–362.
H. Ehrig, B. Mahr, Fundamentals of Algebraic Specification 1, Springer-Verlag, Berlin, 1985.
P.H.J. van Eijk, C.A. Vissers, M. Diaz (Eds.), The Formal Description Technique LOTOS, Results of the ESPRIT/SEDOS project, North-Holland, Amsterdam, 1988.
K. Futatsugi, J.A. Goguen, J.-P. Jouannaud, and J. Meseguer, Principles of OBJ2, Proc. Principles of Programming Languages, ACM, 1985.
H. Ganzinger, Completion with hystory-dependent complexities for generated equations, in: D. Sannella, A. Tarlecki (Eds.), Recent Trends in Data Type Specification, Springer-Verlag LNCS 332 (1988) 73–91.
M. Gerritsen, Type Assignment Functions, Thesis Doct. Phil., Univ. Twente, June 1988.
J.A. Goguen, Order Sorted Algebra, Semantics and Theory of Computation Report 14, UCLA Computer Science Dept., 1978.
J.A. Goguen, J.W. Thatcher, E.G. Wagner, An Initial Algebra Approach to the Specification, Correctness, and Implementation of Abstract Data Types, in: R. Yeh (Ed.), Current Trends in Programming Methodology IV, Prentice-Hall (1978) 80–149.
ISO — Information processing system — Open systems interconnection — LOTOS — A Formal Description Technique Based on the Temporal Ordering of Observational Behaviour, DIS 8807 (Final Text), 1988.
P.D. Mosses, Unified Algebras and Modules, DAIMI PB-266, Univ. Aarhus, Computer Science Dept., October 1988; to appear in Proc. ACM POPL '89.
P.D. Mosses, Unified Algebras and Institutions, DAIMI IR-83, Univ. Aarhus, Computer Science Dept., February 1989; to appear in Proc. LICS '89.
V. Manca and A. Salibra, On the power of equational logic: applications and extensions, Univ. Pisa, Dip. Informatica, TR-19/88; presented at Int.1 Conf. on Algebraic Logic, Budapest, August 8–14, 1988.
V. Manca, A. Salibra and G. Scollo, On the nature of TELLUS, Univ. Twente, Memorandum INF-88-57, December 1988.
V. Manca, A. Salibra and G. Scollo, DELTA: a Deduction system integrating Equational Logic and Type Assignment, AMAST '89, Int.1 Conf. on Algebraic Methodology And Software Technology, Iowa City, Iowa, USA, May 22–24, 1989.
V. Manca, A. Salibra and G. Scollo, Equational Type Logic, Univ. Pisa & Univ. Twente, Draft (in preparation).
M.J. O'Donnell, Computing in Systems Described by Equations, Springer-Verlag LNCS 58, 1977.
A. Poigné, Partial Algebras, Subsorting and Dependent Types: Prerequisites of Error Handling in Algebraic Specification, in: D. Sannella, A. Tarlecki (Eds.), Recent Trends in Data Type Specification, Springer-Verlag LNCS 332 (1988) 208–234.
H. Reichel, Initial Computability, Algebraic Specifications, and Partial Algebras, Oxford University Press, 1987.
M. Rycko, Partial Partial Evaluators: What They Can Do, Metasoft Project, Polish Academy of Sciences, Institute of Computer Science, Warsaw, Poland, October 1988, submitted for publication.
G. Scollo, Some facilities for concise data type definitions in LOTOS, ESPRIT/SEDOS/C1/WP/13/T, Univ. of Twente, March 1986, also in: Potential Enhancements to LOTOS, ISO/TC 97/SC 21 N 2015.
G. Smolka, Type Logic, 6th ADT Workshop, Berlin, FRG, Aug.29–Sept.2, 1988 (Abstract).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Manca, V., Salibra, A., Scollo, G. (1989). On the nature of TELLUS. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_81
Download citation
DOI: https://doi.org/10.1007/3-540-51486-4_81
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51486-2
Online ISBN: 978-3-540-48176-8
eBook Packages: Springer Book Archive