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The Benefit of Being Non-Lazy in Probabilistic λ-calculus
[article]

2020
*
arXiv
*
pre-print

*In*particular, PAB has been proven to

*be*fully abstract with respect to

*the*contextual equivalence

*in*cbv but not

*in*

*lazy*cbn. ... We consider

*the*

*probabilistic*applicative bisimilarity (PAB), a coinductive relation comparing

*the*applicative behaviour

*of*

*probabilistic*untyped lambda terms according to a specific operational semantics ... This material is based upon work supported by

*the*French ANR : "Agence National de Recherche" under Grant "PPS:

*Probabilistic*Program Semantics", No. ANR-19-CE48-0014. ...

##
###
The Benefit of Being Non-Lazy in Probabilistic λ-calculus

2020
*
Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
*

*In*particular, PAB has been proven to

*be*fully abstract with respect to

*the*contextual equivalence

*in*cbv [6] but not

*in*

*lazy*cbn [16] . ... We consider

*the*

*probabilistic*applicative bisimilarity (PAB)a coinductive relation comparing

*the*applicative behaviour

*of*

*probabilistic*untyped

*λ*-terms according to a specific operational semantics. ... This material is based upon work supported by

*the*French ANR : "Agence National de Recherche" under Grant "PPS:

*Probabilistic*Program Semantics", No. ANR-19-CE48-0014. ...

##
###
The Discriminating Power of the Let-In Operator in the Lazy Call-by-Name Probabilistic lambda-Calculus

2019
*
International Conference on Rewriting Techniques and Applications
*

We consider

doi:10.4230/lipics.fscd.2019.26
dblp:conf/rta/KasterovicP19
fatcat:gzzuue5k4neeppbfl3tood7vs4
*the*notion*of**probabilistic*applicative bisimilarity (PAB), recently introduced as a behavioural equivalence over a*probabilistic*extension*of**the*untyped*λ*-*calculus*. ... We prove that extending this*calculus*with a let-*in*operator allows for achieving*the*full abstraction. ... Acknowledgements We wish to thank*the*anonymous reviewers for their valuable suggestions, helping us to improve*the*paper. ...##
###
Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus
[chapter]

2018
*
Lecture Notes in Computer Science
*

We extend

doi:10.1007/978-3-319-89884-1_8
fatcat:dq4oqbtembbmloqadvtwexdx7q
*the*simply-typed guarded*λ*-*calculus*with discrete probabilities and endow it with a program logic for reasoning about relational properties*of*guarded*probabilistic*computations. ... We demonstrate*the*logic sound by interpreting its judgements*in**the*topos*of*trees and by using*probabilistic*couplings for*the*semantics*of*relational assertions over distributions on discrete types. ... This research was supported*in*part by*the*ModuRes Sapere Aude Advanced Grant from*The*Danish Council for Independent Research for*the*Natural Sciences (FNU), by a research grant (12386, Guarded Homotopy ...##
###
Reasoning Algebraically About Probabilistic Loops
[chapter]

2006
*
Lecture Notes in Computer Science
*

Back and von Wright have developed algebraic laws for reasoning about loops

doi:10.1007/11901433_21
fatcat:xend4bqv4zaz7mcdyutokrh3ka
*in**the*refinement*calculus*. ... We extend their work to reasoning about*probabilistic*loops*in**the**probabilistic*refinement*calculus*. We apply our algebraic reasoning to derive transformation rules for*probabilistic*action systems. ...*The**probabilistic*refinement*calculus*[11] is an extension*of**the*refinement*calculus*,*in*which programs may also include discrete*probabilistic*choice. ...##
###
Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus
[article]

2018
*
arXiv
*
pre-print

We extend

arXiv:1802.09787v1
fatcat:67ysfpksobfulpi7ie3ox2lxpm
*the*simply-typed guarded*λ*-*calculus*with discrete probabilities and endow it with a program logic for reasoning about relational properties*of*guarded*probabilistic*computations. ... We demonstrate*the*logic sound by interpreting its judgements*in**the*topos*of*trees and by using*probabilistic*couplings for*the*semantics*of*relational assertions over distributions on discrete types. ... This research was supported*in*part by*the*Mod-uRes Sapere Aude Advanced Grant from*The*Danish Council for Independent Research for*the*Natural Sciences (FNU), by a research grant (12386, Guarded Homotopy ...##
###
Linear Additives
[article]

2021
*
arXiv
*
pre-print

𝖫𝖠𝖬 is presented as

arXiv:2104.13739v1
fatcat:uash2cplnveehdgkseulbrvdtm
*the*type assignment system for a*calculus*endowed with copy constructors, which deal with substitution*in*a linear fashion. ... As opposed to*the*standard additive rules,*the*linear additive rules do not affect*the*complexity*of*term reduction: typable terms*of*𝖫𝖠𝖬 enjoy linear strong normalization. ... Roversi for*the*precious discussions about*the*topic, and*the*anonymous reviewers for useful comments and suggestions. ...##
###
Stochastic lambda calculus and monads of probability distributions

2002
*
Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '02
*

But

doi:10.1145/503272.503288
dblp:conf/popl/RamseyP02
fatcat:6x3eju4puvexzjxtlhw6maacva
*the*monadic implementation*of**the*expectation query can*be*much less efficient than current best practices*in**probabilistic*modeling. ... Probability distributions are useful for expressing*the*meanings*of**probabilistic*languages, which support formal modeling*of*and reasoning about uncertainty. ... Acknowledgments Simon Peyton Jones helped unstick our discussions*of*measure terms and variable elimination. Bob Muller helped us work out lift and guided us through*the*thickets*of*domain theory. ...##
###
Factorize Factorization
[article]

2020
*
arXiv
*
pre-print

Concretely, we apply our technique to diverse extensions

arXiv:2005.01808v2
fatcat:udda4mn64bbqnldb4oipsivb6a
*of**the*lambda-*calculus*, among which de' Liguoro and Piperno's*non*-deterministic lambda-*calculus*and -- for call-by-value -- Carraro and Guerrieri's ... We then closely analyze some common factorization schemas for*the*lambda-*calculus*. ... ( 5*The**Non*-Deterministic*λ*-*Calculus**Λ*⊕ De' Liguoro and Piperno's*non*-deterministic*λ*-*calculus**Λ*⊕ is defined*in*[14] by extending*the**λ*-*calculus*with a new operator ⊕ whose rule models*non*-deterministic ...##
###
Stochastic lambda calculus and monads of probability distributions

2002
*
SIGPLAN notices
*

But

doi:10.1145/565816.503288
fatcat:2aoiduubsfcw7mnxp2rag3ciem
*the*monadic implementation*of**the*expectation query can*be*much less efficient than current best practices*in**probabilistic*modeling. ... Probability distributions are useful for expressing*the*meanings*of**probabilistic*languages, which support formal modeling*of*and reasoning about uncertainty. ... Acknowledgments Simon Peyton Jones helped unstick our discussions*of*measure terms and variable elimination. Bob Muller helped us work out lift and guided us through*the*thickets*of*domain theory. ...##
###
Functional Tensors for Probabilistic Programming
[article]

2020
*
arXiv
*
pre-print

-- that captures many

arXiv:1910.10775v2
fatcat:lotryn2vtzcyzg45derogdr4b4
*of**the**benefits**of*tensors, while also*being*able to describe continuous probability distributions. ... Noting that*the*versatility*of*modern automatic differentiation frameworks is based*in*large part on*the*unifying concept*of*tensors, we describe a software abstraction for integration --functional tensors ... to allow free variables*of**non*-integer types that appear*in**probabilistic*models, such as real number, real-valued vector, or real-valued matrix. ...##
###
Expressing contract monitors as patterns of communication

2015
*
SIGPLAN notices
*

*be*expressed

*in*a single language built on well-understood constructs. ... A straightforward implementation

*in*Racket demonstrates

*the*practicality

*of*our approach which not only enriches existing Racket monitoring strategies, but also support a new style

*of*monitoring

*in*which ... We thank

*the*anonymous reviewers

*of*ICFP 2015 for their detailed reviews, which helped to improve

*the*presentation and technical content

*of*

*the*paper. ...

##
###
Expressing contract monitors as patterns of communication

2015
*
Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming - ICFP 2015
*

*be*expressed

*in*a single language built on well-understood constructs. ... A straightforward implementation

*in*Racket demonstrates

*the*practicality

*of*our approach which not only enriches existing Racket monitoring strategies, but also support a new style

*of*monitoring

*in*which ... We thank

*the*anonymous reviewers

*of*ICFP 2015 for their detailed reviews, which helped to improve

*the*presentation and technical content

*of*

*the*paper. ...

##
###
Differential privacy with information flow control

2011
*
Proceedings of the ACM SIGPLAN 6th Workshop on Programming Languages and Analysis for Security - PLAS '11
*

We investigate

doi:10.1145/2166956.2166958
dblp:conf/pldi/BirgissonMA11
fatcat:hxtvbaxfsbfz3dfcr5bdti62h4
*the*integration*of*two approaches to information security: information flow analysis,*in*which*the*dependence between secret inputs and public outputs is tracked through a program, and differential ... Differential privacy's strong guarantees allow for efficient and accurate dynamic tracking*of*information flow, allowing*the*use*of*existing technology to extend and improve*the*state*of**the*art for*the*...*In*other words, we partly lose*the**benefits**of**lazy*evaluation. ...##
###
A Lambda-Calculus Foundation for Universal Probabilistic Programming
[article]

2017
*
arXiv
*
pre-print

We develop

arXiv:1512.08990v5
fatcat:dqjdmgd5cfamphojimuky5bk4q
*the*operational semantics*of*an untyped*probabilistic*lambda-*calculus*with continuous distributions, as a foundation for universal*probabilistic*programming languages such as Church, Anglican ... Our second contribution is to formalize*the*implementation technique*of*trace Markov chain Monte Carlo (MCMC) for our*calculus*and to show its correctness. ...*In*recent work for a*non*-recursive*λ*-*calculus*with score, Staton et al. [35] note that unbounded scores introduce*the*possibility*of*"infinite model evidence errors". ...
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