# Probabilistic operational semantics for the lambda calculus

Ugo Dal Lago; Margherita Zorzi

RAIRO - Theoretical Informatics and Applications (2012)

- Volume: 46, Issue: 3, page 413-450
- ISSN: 0988-3754

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topLago, Ugo Dal, and Zorzi, Margherita. "Probabilistic operational semantics for the lambda calculus." RAIRO - Theoretical Informatics and Applications 46.3 (2012): 413-450. <http://eudml.org/doc/277837>.

@article{Lago2012,

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.},

author = {Lago, Ugo Dal, Zorzi, Margherita},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Lambda calculus; probabilistic computaion; operational semantics; lambda calculus},

language = {eng},

month = {8},

number = {3},

pages = {413-450},

publisher = {EDP Sciences},

title = {Probabilistic operational semantics for the lambda calculus},

url = {http://eudml.org/doc/277837},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Lago, Ugo Dal

AU - Zorzi, Margherita

TI - Probabilistic operational semantics for the lambda calculus

JO - RAIRO - Theoretical Informatics and Applications

DA - 2012/8//

PB - EDP Sciences

VL - 46

IS - 3

SP - 413

EP - 450

AB - 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.

LA - eng

KW - Lambda calculus; probabilistic computaion; operational semantics; lambda calculus

UR - http://eudml.org/doc/277837

ER -

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