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
Online AccessGet full text
ISSN0988-3754
1290-385X
DOI10.1051/ita/2012012

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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.
AbstractList Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics are both inductively and coinductively defined. 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.
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.
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. [PUBLICATION ABSTRACT]
Author Lago, Ugo Dal
Zorzi, Margherita
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10.1145/565816.503288
10.1093/logcom/exi008
10.1007/11783596_6
10.1145/357766.351262
10.1016/0890-5401(91)90052-4
10.1109/LICS.1996.561453
10.1017/S0960129500001535
10.1109/LICS.1989.39155
10.1017/CBO9780511809088
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Snippet Probabilistic operational semantics for a nondeterministic extension of pure λ-calculus is studied. In this semantics, a term evaluates to a (finite or...
Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or...
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SubjectTerms 03B70
68Q55
Cognitive science
Computer science
Lambda calculus
operational semantics
probabilistic computaion
Title Probabilistic operational semantics for the lambda calculus
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