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

Gianluca Curzi, Michele Pagani
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.  ... 
arXiv:2004.12891v1 fatcat:6tllct7raffijat2rkstqro63a

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

Gianluca Curzi, Michele Pagani
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.  ... 
doi:10.1145/3373718.3394806 dblp:conf/lics/CurziP20 fatcat:yqh36hhfubfmxo5rmwzijj5bxu

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

Simona Kasterovic, Michele Pagani, Michael Wagner
2019 International Conference on Rewriting Techniques and Applications  
We consider 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.  ... 
doi:10.4230/lipics.fscd.2019.26 dblp:conf/rta/KasterovicP19 fatcat:gzzuue5k4neeppbfl3tood7vs4

Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus [chapter]

Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Aleš Bizjak, Marco Gaboardi, Deepak Garg
2018 Lecture Notes in Computer Science  
We extend 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  ... 
doi:10.1007/978-3-319-89884-1_8 fatcat:dq4oqbtembbmloqadvtwexdx7q

Reasoning Algebraically About Probabilistic Loops [chapter]

Larissa Meinicke, Ian J. Hayes
2006 Lecture Notes in Computer Science  
Back and von Wright have developed algebraic laws for reasoning about loops 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.  ... 
doi:10.1007/11901433_21 fatcat:xend4bqv4zaz7mcdyutokrh3ka

Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus [article]

Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Aleš Bizjak, Marco Gaboardi, Deepak Garg
2018 arXiv   pre-print
We extend 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  ... 
arXiv:1802.09787v1 fatcat:67ysfpksobfulpi7ie3ox2lxpm

Linear Additives [article]

Gianluca Curzi
2021 arXiv   pre-print
𝖫𝖠𝖬 is presented as 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.  ... 
arXiv:2104.13739v1 fatcat:uash2cplnveehdgkseulbrvdtm

Stochastic lambda calculus and monads of probability distributions

Norman Ramsey, Avi Pfeffer
2002 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '02  
But 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.  ... 
doi:10.1145/503272.503288 dblp:conf/popl/RamseyP02 fatcat:6x3eju4puvexzjxtlhw6maacva

Factorize Factorization [article]

Beniamino Accattoli, Claudia Faggian, Giulio Guerrieri
2020 arXiv   pre-print
Concretely, we apply our technique to diverse extensions 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  ... 
arXiv:2005.01808v2 fatcat:udda4mn64bbqnldb4oipsivb6a

Stochastic lambda calculus and monads of probability distributions

Norman Ramsey, Avi Pfeffer
2002 SIGPLAN notices  
But 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.  ... 
doi:10.1145/565816.503288 fatcat:2aoiduubsfcw7mnxp2rag3ciem

Functional Tensors for Probabilistic Programming [article]

Fritz Obermeyer, Eli Bingham, Martin Jankowiak, Du Phan, Jonathan P. Chen
2020 arXiv   pre-print
-- that captures many 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.  ... 
arXiv:1910.10775v2 fatcat:lotryn2vtzcyzg45derogdr4b4

Expressing contract monitors as patterns of communication

Cameron Swords, Amr Sabry, Sam Tobin-Hochstadt
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.  ... 
doi:10.1145/2858949.2784742 fatcat:vyo37wxy7fg3fkhvqpqaboqqiq

Expressing contract monitors as patterns of communication

Cameron Swords, Amr Sabry, Sam Tobin-Hochstadt
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.  ... 
doi:10.1145/2784731.2784742 dblp:conf/icfp/SwordsST15 fatcat:qbt346ttvzh63hd4eqdxhdt3ni

Differential privacy with information flow control

Arnar Birgisson, Frank McSherry, Martín Abadi
2011 Proceedings of the ACM SIGPLAN 6th Workshop on Programming Languages and Analysis for Security - PLAS '11  
We investigate 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.  ... 
doi:10.1145/2166956.2166958 dblp:conf/pldi/BirgissonMA11 fatcat:hxtvbaxfsbfz3dfcr5bdti62h4

A Lambda-Calculus Foundation for Universal Probabilistic Programming [article]

Johannes Borgström and Ugo Dal Lago and Andrew D. Gordon and Marcin Szymczak
2017 arXiv   pre-print
We develop 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".  ... 
arXiv:1512.08990v5 fatcat:dqjdmgd5cfamphojimuky5bk4q
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