Abstract
The semantic and logical treatment of recursion and of recursive definitions in computer science, in particular in requirements specification, in programming languages and related formalisms such as λ-calculus or recursively defined functions is one of the key issues of the semantic theory of programming and programming languages. As it has been recognised already in the early days of the theory of programming there are several options to formalise and give a theory of the semantics of recursive function declarations. In different branches of computer science, logics, and mathematics various techniques for dealing with the semantics of recursion have been developed and established. We outline, compare, and shortly discuss advantages and disadvantages of these different possibilities, illustrate them by a simple running example, and relate these approaches.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Broy, M.: Partial interpretations of higher order algebraic types. In: Wiedermann, J., Gruska, J., Rovan, B. (eds.) MFCS 1986. LNCS, vol. 233, pp. 29–43. Springer, Heidelberg (1986)
Wirsing, M., Broy, M.: Abstract data types as lattices of finitely generated models. In: Dembinski, P. (ed.) MFCS 1980. LNCS, vol. 88, pp. 673–685. Springer, Heidelberg (1980)
Broy, M., Wirsing, M.: Initial versus terminal algebra semantics for partially defined abstract types. Technische Universität München, Institut für Informatik, TUM-I8018 (December 1981), Revidierte Fassung: Partial Abstract Types, Acta Informatica 18, 47–64 (1982)
Broy, M., Pepper, M., Wirsing, M.: On the algebraic definition of programming languages. Technische Universität München, Institut für Informatik, TUM-I8204 (1982), Revised version in TOPLAS 9(1) 54–99 (1987)
de Bakker, J.W., Zucker, J.I.: Processes and the denotational semantics of concurrency. Information and Control 54(1/2), 70–120 (1984)
Hehner, E.C.R.: Predicative Programming. Comm. ACM 27(2), 134–151 (1984)
Tarski, A.: A lattice-theoretical fixpoint theorem and its application. Pacific Journal of Mathematics 5, 285–309 (1955)
Guttag, J.V., Horning, J.J., Garland, S.J., Jones, K.D., Modet, A., Wing, J.M.: Larch: Languages and Tools for Formal Specification. Texts and Monographs in Computer Science. Springer, Heidelberg (1993)
Barendregt, H.P.: The Lambda Calculus: Its Syntax and Semantics. North-Holland, Amsterdam (1981)
Hitchcock, P., Park, D.: Induction rules and termination proofs. In: Nivat, M. (ed.) Proc. Ist ICALP, p. 73. North Holland, Amsterdam (1973)
Milner, R.: Communication and mobile systems: the π-calculus. Cambridge University Press, Cambridge (1999)
Lloyd, J.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)
Owre, S., Rushby, J.M., Shankar, N.: PVS: A Prototype Verification System. In: Kapur, D. (ed.) 11th Conference on Automated Deduction, Saratoga, NY (June 1992)
Schieder, B., Broy, M.: Adapting Calculational Logic to the Undefined. The Computer Journal 42(2) (1999)
Sintzoff, M.: Expressing program developments in a design calculus. In: Broy, M. (ed.) Logic of programming and calculi of discrete design. NATO ASI Series, Series F:Computer and System Sciences, vol. 36, pp. 343–365. Springer, Heidelberg (1987)
Scott, D.: Lectures on a mathematical theory of computation. In: Broy, M., Schmidt, G. (eds.) Theoretical Foundations of Programming Methodology, pp. 145–292. D. Reidel Publishing Company, Dordrechtz (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Broy, M. (2006). From Chaos to Undefinedness. In: Futatsugi, K., Jouannaud, JP., Meseguer, J. (eds) Algebra, Meaning, and Computation. Lecture Notes in Computer Science, vol 4060. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780274_25
Download citation
DOI: https://doi.org/10.1007/11780274_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35462-8
Online ISBN: 978-3-540-35464-2
eBook Packages: Computer ScienceComputer Science (R0)