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A deterministic rewrite system for the probabilistic λ-calculus

Published online by Cambridge University Press:  06 June 2019

Thomas Leventis
Thomas Leventis*
Affiliation:
Institut de Mathématiques de Marseille (I2M), Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France and Institut de Recherche en Informatique Fondamentale (IRIF), Université Paris Diderot, Paris, France
*
*Corresponding author. Email: [email protected]
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Abstract

In this paper we present an operational semantics for the ‘call-by-name’ probabilistic λ-calculus, whose main feature is to use only deterministic relations and to have no constraint on the reduction strategy. The calculus enjoys similar properties to the usual λ-calculus. In particular we prove it to be confluent, and we prove a standardisation theorem.

Keywords

Lambda-calculusprobabilistic lambda-calculusoperational semanticsequational theoriesstandardisation
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 10 , November 2019 , pp. 1479 - 1512
Copyright
© Cambridge University Press 2019 

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References

Alberti, M. (2014). On operational properties of quantitative extensions of λ-calculus. Phd thesis, Aix Marseille Université, Università di Bologna, https://hal.inria.fr/tel-01096067.Google Scholar
Barendregt, H. P. (1981). The Lambda Calculus, Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics, vol. 103, Amsterdam – New York – Oxford, North-Holland Publishing Company, XIV, 615 p. $ 109.75; Dfl. 225.00.Google Scholar
Bezem, M., Klop, J. W., de Vrijer, R. and Terese, (2003). Term Rewriting Systems. Cambridge University Press.Google Scholar
Dal Lago, U. and Zorzi, M. (2012). Probabilistic operational semantics for the lambda calculus. RAIRO – Theoretical Informatics and Applications 46 (3) 413–450. http://dx.doi.org/10.1051/ita/2012012.CrossRefGoogle Scholar
De’Liguoro, U. and Piperno, A. (1995). Nondeterministic extensions of untyped λ-calculus. Information and Computation 122 149–177.CrossRefGoogle Scholar
Ehrhard, T. and Danos, V. (2011). Probabilistic coherence spaces as a model of higher-order probabilistic computation. Information and Computation 152 (1) 111–137.CrossRefGoogle Scholar
Ehrhard, T., Pagani, M. and Tasson, C. (2011). The computational meaning of probabilistic coherence spaces. In: Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011, June 21–24, 2011, Toronto, Ontario, Canada, IEEE Computer Society, 87–96. isbn: 978-0-7695-4412-0, http://dx.doi.org/10.1109/LICS.2011.29.Google Scholar
Leventis, T. (2016). Probabilistic Lambda-theories. Theses, Aix-Marseille Universitè, https://tel.archives-ouvertes.fr/tel-01427279.Google Scholar
Stone, M. H. (1949). Postulates for the barycentric calculus. Annali di Matematica Pura ed Applicata 29 (1) 25–30.CrossRefGoogle Scholar
Takahashi, M. (1995). Parallel reductions in λ-calculus. Information and Computation 118 (1) 120–127.CrossRefGoogle Scholar
Vaux, L. (2009). The algebraic lambda calculus. Mathematical Structures in Computer Science 19 (5) 1029–1059.CrossRefGoogle Scholar