Probabilistic operational semantics for the lambda calculus

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-...

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Published inRAIRO. Informatique théorique et applications Vol. 46; no. 3; pp. 413 - 450
Main Authors Lago, Ugo Dal, Zorzi, Margherita
Format Journal Article
LanguageEnglish
Published Paris EDP Sciences 01.07.2012
Subjects
03B70
68Q55
Cognitive science
Computer science
Lambda calculus
operational semantics
probabilistic computaion
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ISSN0988-3754
1290-385X
DOI10.1051/ita/2012012

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Summary: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.
Bibliography:dallago@cs.unibo.it
istex:E0901AD41435895B6BDCA43069F61B738E088C0E
PII:S0988375412000124
publisher-ID:ita110023
ark:/67375/80W-HRH95SPG-4
ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0988-3754
1290-385X
DOI:10.1051/ita/2012012