Probabilistic Coherence Spaces As a Model of Higher-order Probabilistic Computation

Vincent Danos; Thomas Ehrhard

doi:10.1016/j.ic.2011.02.001

Probabilistic Coherence Spaces As a Model of Higher-order Probabilistic Computation

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Abstract

We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.

Original language	English
Pages (from-to)	966-991
Number of pages	26
Journal	Information and Computation
Volume	209
Issue number	6
DOIs	https://doi.org/10.1016/j.ic.2011.02.001
Publication status	Published - 1 Jun 2011

Keywords / Materials (for Non-textual outputs)

Denotational semantics
Lambda-calculus
Linear logic
PCF
Probabilistic models

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10.1016/j.ic.2011.02.001

http://dx.doi.org/10.1016/j.ic.2011.02.001

Cite this

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title = "Probabilistic Coherence Spaces As a Model of Higher-order Probabilistic Computation",

abstract = "We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.",

keywords = "Denotational semantics, Lambda-calculus, Linear logic, PCF, Probabilistic models",

author = "Vincent Danos and Thomas Ehrhard",

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AU - Ehrhard, Thomas

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N2 - We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.

AB - We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.

KW - Denotational semantics

KW - Lambda-calculus

KW - Linear logic

KW - PCF

KW - Probabilistic models

U2 - 10.1016/j.ic.2011.02.001

DO - 10.1016/j.ic.2011.02.001

M3 - Article

SN - 0890-5401

VL - 209

SP - 966

EP - 991

JO - Information and Computation

JF - Information and Computation

IS - 6

ER -

Probabilistic Coherence Spaces As a Model of Higher-order Probabilistic Computation

Abstract

Keywords / Materials (for Non-textual outputs)

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