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Probabilistic operational semanticsfor the lambda calculus

Published online by Cambridge University Press:  22 June 2012

Ugo Dal Lago  and
Margherita Zorzi
Ugo Dal Lago
Affiliation:
Universitàdi Bologna & EPI FOCUS, Dipartimento di Scienze dell’Informazione Mura Anteo Zamboni, 7, 40127 Bologna, Italy. dallago@cs.unibo.it
Margherita Zorzi
Affiliation:
Laboratoire d’Informatique L.I.P.N., Université Paris-Nord, supported by ANR Complice Project, France; margherita.zorzi@univr.it
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Abstract

Probabilistic operational semantics for a nondeterministic extension of pure λ-calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics, inductively and coinductively defined, are given. Moreover, small-step and big-step semantics are shown to produce identical outcomes, both in call-by-value and in call-by-name. Plotkin’s CPS translation is extended to accommodate the choice operator and shown correct with respect to the operational semantics. Finally, the expressive power of the obtained system is studied: the calculus is shown to be sound and complete with respect to computable probability distributions.

Keywords

Lambda calculusprobabilistic computaionoperational semantics

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 3 , July 2012 , pp. 413 - 450
Copyright
© EDP Sciences 2012

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