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Towards Denotational Semantics of AD for Higher-Order, Recursive, Probabilistic Languages [article]

Alexander K. Lew, Mathieu Huot, Vikash K. Mansinghka
2021 arXiv   pre-print
We study an expressive differentiable programming language, with piecewise-analytic primitives, higher-order functions, and general recursion.  ...  Our main result is that even in this general setting, a version of Lee et al. [2020]'s correctness theorem (originally proven for a first-order language without partiality or recursion) holds: all programs  ...  Towards Denotational Semantics of AD for Higher-Order, Recursive, Probabilistic Languages  ... 
arXiv:2111.15456v2 fatcat:3nhzpfr5u5cstonw7slwrz7co4

The Functional Perspective on Advanced Logic Programming

Alexander Vandenbroucke, Marc Herbstritt
2016 International Conference on Logic Programming  
The basics of logic programming, as embodied by Prolog, are generally well-known in the programming language community.  ...  However, more advanced techniques, such as tabling, answer subsumption and probabilistic logic programming fail to attract the attention of a larger audience.  ...  I would like to thank the reviewers for taking the time to provide insightful comments and in-depth remarks.  ... 
doi:10.4230/oasics.iclp.2016.20 dblp:conf/iclp/Vandenbroucke16 fatcat:ljbcyks7tne63kbjlbgvyf37va

On continuation-passing transformations and expected cost analysis

Martin Avanzini, Gilles Barthe, Ugo Dal Lago
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
We define a continuation-passing style (CPS) translation for a typed λ-calculus with probabilistic choice, unbounded recursion, and a tick operator — for modeling cost.  ...  We also introduce a formal system for higher-order logic, called EHOL, prove it sound, and show it can derive tight upper bounds on the expected cost of classic examples, including Coupon Collector and  ...  served as a motivation for the study of higher-order probabilistic programming languages.  ... 
doi:10.1145/3473592 fatcat:cpjwu2jc5nd53hcfpepztqscku

Running Probabilistic Programs Backwards [article]

Neil Toronto and Jay McCarthy and David Van Horn
2015 arXiv   pre-print
We develop a measure-theoretic semantics for a first-order probabilistic language with recursion, which interprets programs as functions that compute preimages.  ...  Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference.  ...  Special thanks to Mitchell Wand for careful review and helpful feedback.  ... 
arXiv:1412.4053v2 fatcat:ewitbymf4nfq7p2pgztehrjkli

Classical Control and Quantum Circuits in Enriched Category Theory

Mathys Rennela, Sam Staton
2018 Electronical Notes in Theoretical Computer Science  
Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads.  ...  ., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language.  ...  first author at Tulane University during the elaboration of this work, and Jennifer Paykin for introducing us to the subtle aspects of QWire.  ... 
doi:10.1016/j.entcs.2018.03.027 fatcat:lknzyacpbzbwtdjhkj34ypaade

Quantum Domain Theory - Definitions and Applications [article]

Elham Kashefi
2003 arXiv   pre-print
Classically domain theory is a rigourous mathematical structure to describe denotational semantics for programming languages and to study the computability of partial functions.  ...  Recently, the application of domain theory has also been extended to the quantum setting. In this note we review these results and we present some new thoughts in this field.  ...  Sanders, Vlatko Vedral and Herbert Wiklicky for useful comments and discussions on this topic.  ... 
arXiv:quant-ph/0306077v1 fatcat:pco75c4fkja2vlm5kn6dgdxgz4

Two Recursively Inseparable Problems for Probabilistic Automata [chapter]

Nathanaël Fijalkow, Hugo Gimbert, Florian Horn, Youssouf Oualhadj
2014 Lecture Notes in Computer Science  
This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact  ...  We show that the two following properties of numberless probabilistic automata are recursively inseparable: • all instances of the numberless automaton have value 1, • no instance of the numberless automaton  ...  Acknowledgments We would like to thank the referees for their helpful comments.  ... 
doi:10.1007/978-3-662-44522-8_23 fatcat:reosrjzp3bdxrdup2kqugk5oli

Two Recursively Inseparable Problems for Probabilistic Automata [article]

Nathanaël Fijalkow and Hugo Gimbert and Florian Horn and Youssouf Oualhadj
2017 arXiv   pre-print
This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact  ...  We show that the two following properties of numberless probabilistic automata are recursively inseparable: - all instances of the numberless automaton have value 1, - no instance of the numberless automaton  ...  Acknowledgments We would like to thank the referees for their helpful comments.  ... 
arXiv:1709.03122v1 fatcat:iipv4kpdvrahxmkukd2dpjwzby

Fine-Grained Semantics for Probabilistic Programs [chapter]

Benjamin Bichsel, Timon Gehr, Martin Vechev
2018 Lecture Notes in Computer Science  
In this paper, we provide an expressive probabilistic programming language together with a fine-grained measure-theoretic denotational semantics that handles and distinguishes non-termination, observation  ...  Probabilistic programming is an emerging technique for modeling processes involving uncertainty.  ...  Higher-Order Functions Our language cannot express higher-order functions.  ... 
doi:10.1007/978-3-319-89884-1_6 fatcat:otlzuyzl2zgzda6immmaee4dru

Probabilistic Linda-Based Coordination Languages [chapter]

Alessandra Di Pierro, Chris Hankin, Herbert Wiklicky
2005 Lecture Notes in Computer Science  
The main objective of such a study is to develop a semantic basis for a quantitative analysis of systems of interconnected or interacting components, which allows us to address not only the functional  ...  We review various approaches to introducing probabilistic or stochastic features in coordination languages.  ...  in t (x).P, TS ] This raises an issue about the choice of a value for p. This could be avoided by adding named processes and recursion rather than replication.  ... 
doi:10.1007/11561163_6 fatcat:paq4lukxxrchhjwyqxa62pe7e4

Probabilistic communicating processes

Karen Seidel
1995 Theoretical Computer Science  
We explore the suitability of two semantic spaces as a basis for a probabilistic variant of the language of Communicating Sequential Processes (UP), so as to provide a formalism for the specification and  ...  The advantage of this semantics is that it is simple and good for reasoning about probabilistic properties such as self-stabilisation or fairness of random algorithms.  ...  For the semantics of the recursion operator we define an ordering on the space PM by saying that a process P is below a process Q if the probability of Q performing any visible event is always higher than  ... 
doi:10.1016/0304-3975(94)00286-0 fatcat:ehyvqekycvcpfihyqb3gj27pzi

An Application of Computable Distributions to the Semantics of Probabilistic Programs [article]

Daniel Huang, Greg Morrisett, Bas Spitters
2019 arXiv   pre-print
Towards this end, we sketch an encoding of computable distributions in a fragment of Haskell and show how topological domains can be used to model the resulting PCF-like language.  ...  We also examine the implications that a (Type-2) computable semantics has for implementing conditioning.  ...  Borgström et al. (2011) also interpret a type as a measurable space and use it to give denotational semantics to a first-order language without recursion based on measure transformers.  ... 
arXiv:1806.07966v2 fatcat:csz7pdbd45fsvoy4oac23eixie

Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory [article]

Mathys Rennela, Sam Staton
2020 arXiv   pre-print
Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads.  ...  ., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language.  ...  , and Vladimir Zamdzhiev for hosting the first author at Tulane University during the early stage of the elaboration of this work, and Jennifer Paykin and Robert Rand for introducing us to the subtle aspects  ... 
arXiv:1711.05159v5 fatcat:ogtw3asicvazhcak25bvxth2re

Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory

Mathys Rennela, Sam Staton
2017 Logical Methods in Computer Science  
Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads.  ...  ., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language.  ...  , and Vladimir Zamdzhiev for hosting the first author at Tulane University during the early stage of the elaboration of this work, and Jennifer Paykin and Robert Rand for introducing us to the subtle aspects  ... 
doi:10.23638/lmcs-16(1:30)2020 fatcat:mzdtexumm5ayvjdk3vkxrx25k4

PhD Abstracts

GRAHAM HUTTON
2018 Journal of functional programming  
As a service to the community, the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.  ...  In this work, we show that GdTT is a natural setting to give denotational semantics of typed functional programming languages with recursion and recursive types.  ...  Finally, this work builds the foundations for doing denotational semantics of languages with much more challenging features, e.g. general references, for which denotational techniques were previously beyond  ... 
doi:10.1017/s0956796818000175 fatcat:lt6u6vlagfe7jgo73cm3nax4aq
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