Abstract
The standard denotational semantics of a programming language, being based on Tarski’s Theorem, is often not capable of expressing program properties. Annotated semantic domains and corresponding semantic functions capacitate us to express the properties, but the resulting structures may no longer be partially ordered sets. Instead we obtain quasi ordered sets, which lack the antisymmetry of partially ordered sets. To cater with these structures, we introduce a new kind of structure called metrified quasi ordered sets and develop a generalisation of Tarski’s Theorem for these structures.
We demonstrate the techniques for a simple lazy functional language F by modelling the escape behaviour of F programs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
K. R. Apt and G. D. Plotkin. Countable Nondeterminism and Random Assignment. JACM, 33 (4): 724–767, October 1986.
C. Baier and M. E. Majster-Cederbaum. Denotational semantics in the cpo and metric approach. Theoretical Computer Science, 135(2):171-220, December 1994.
J. W. de Bakker and J. I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54 (1 2): 70–120, July 1982.
F. Henglein and D. Sands. A Semantic Model of Binding Times for Safe Partial Evaluation. In Hermenegildo and Swierstra [HS95b].
M. Hermenegildo and S. Doaitse Swierstra, editors. Proceedings of PULP ‘85, number 982 in Lecture Notes in Computer Science. Springer, 1995.
S. Hughes. Compile-time Garbage Collection for Higher-Order Functional Languages. Journal of Logic and Computation, 2 (4): 483–509, 1992.
K. Inoue, H. Seki, and H. Yagi. Analysis of Functional Programs to Detect Run-Time Garbage Cells. TOPLAS, 10 (4): 555–578, October 1988.
M. Mohnen. Efficient Compile-Time Garbage Collection for Arbitrary Data Structures. In Hermenegildo and Swierstra [HS95b], pages 241–258.
M. Mohnen. Optimising the Memory Management of Higher—Order Functional Programs. Technical Report AIB-97–13, RWTH Aachen, 1997. PhD Thesis.
P.D. Mosses. Denotational Semantics. In J. van Leeuwen, editor, Handbook of TCS,Volume B: Formal Models and Semantics, chapter 11. Elsevier, 1990.
A. Mycroft. The Theory and Practice of Transforming CBN into CBV. In Proc. of the In’tl Sym. on Programming, number 83 in LNCS. Springer, 1980.
Y. G. Park and B. Goldberg. Escape Analysis on Lists. In Proceedings of PLDI’92, SIGPLAN Notices 27(7), pages 116–127. ACM, June 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mohnen, M. (1999). Fixed Points in Metrified Quasi Ordered Sets: Modelling Escaping in Functional Programs. In: Beiersdörfer, K., Engels, G., Schäfer, W. (eds) Informatik’99. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01069-3_55
Download citation
DOI: https://doi.org/10.1007/978-3-662-01069-3_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66450-5
Online ISBN: 978-3-662-01069-3
eBook Packages: Springer Book Archive