@inproceedings{dal_lago_geometry_2019,
title = {The {Geometry} of {Bayesian} {Programming}},
doi = {10/ggdk85},
author = {Dal Lago, Ugo and Hoshino, Naohiko},
month = jun,
year = {2019},
note = {ZSCC: 0000000},
keywords = {Bayesian inference, Denotational semantics, Linear logic, Probabilistic programming, Programming language theory, Rewriting theory, Transition systems},
pages = {1--13}
}
@article{ehrhard_differentials_2019,
title = {Differentials and distances in probabilistic coherence spaces},
url = {http://arxiv.org/abs/1902.04836},
abstract = {In probabilistic coherence spaces, a denotational model of probabilistic functional languages, mor-phisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to compute the expectation of execution time in the weak head reduction of probabilistic PCF (pPCF). Next we apply a general notion of "local" differential of morphisms to the proof of a Lipschitz property of these morphisms allowing in turn to relate the observational distance on pPCF terms to a distance the model is naturally equipped with. This suggests that extending probabilistic programming languages with derivatives, in the spirit of the differential lambda-calculus, could be quite meaningful.},
urldate = {2019-11-28},
journal = {arXiv:1902.04836 [cs]},
author = {Ehrhard, Thomas},
month = feb,
year = {2019},
note = {ZSCC: 0000000
arXiv: 1902.04836},
keywords = {Coherence spaces, Denotational semantics, Differential Linear Logic, Differentiation, Linear logic, Probabilistic programming, Programming language theory}
}
@inproceedings{kerjean_higher-order_2019,
address = {Cham},
series = {Lecture {Notes} in {Computer} {Science}},
title = {Higher-{Order} {Distributions} for {Differential} {Linear} {Logic}},
isbn = {978-3-030-17127-8},
doi = {10/ggdmrj},
abstract = {Linear Logic was introduced as the computational counterpart of the algebraic notion of linearity. Differential Linear Logic refines Linear Logic with a proof-theoretical interpretation of the geometrical process of differentiation. In this article, we construct a polarized model of Differential Linear Logic satisfying computational constraints such as an interpretation for higher-order functions, as well as constraints inherited from physics such as a continuous interpretation for spaces. This extends what was done previously by Kerjean for first order Differential Linear Logic without promotion. Concretely, we follow the previous idea of interpreting the exponential of Differential Linear Logic as a space of higher-order distributions with compact-support, which is constructed as an inductive limit of spaces of distributions on Euclidean spaces. We prove that this exponential is endowed with a co-monadic like structure, with the notable exception that it is functorial only on isomorphisms. Interestingly, as previously argued by Ehrhard, this still allows the interpretation of differential linear logic without promotion.},
language = {en},
booktitle = {Foundations of {Software} {Science} and {Computation} {Structures}},
publisher = {Springer International Publishing},
author = {Kerjean, Marie and Pacaud Lemay, Jean-Simon},
editor = {Bojańczyk, Mikołaj and Simpson, Alex},
year = {2019},
note = {ZSCC: NoCitationData[s1]},
keywords = {Denotational semantics, Differential Linear Logic, Differentiation, Linear logic},
pages = {330--347}
}
@misc{murfet_dmurfet/deeplinearlogic_2018,
title = {dmurfet/deeplinearlogic},
url = {https://github.com/dmurfet/deeplinearlogic},
abstract = {Deep learning and linear logic. Contribute to dmurfet/deeplinearlogic development by creating an account on GitHub.},
urldate = {2019-11-22},
author = {Murfet, Daniel},
month = jul,
year = {2018},
note = {ZSCC: NoCitationData[s0]
original-date: 2016-11-05T09:17:10Z},
keywords = {Categorical ML, Implementation, Linear logic, Machine learning, Semantics}
}
@misc{murfet_dmurfet/polysemantics_2018,
title = {dmurfet/polysemantics},
url = {https://github.com/dmurfet/polysemantics},
abstract = {Polynomial semantics of linear logic. Contribute to dmurfet/polysemantics development by creating an account on GitHub.},
urldate = {2019-11-22},
author = {Murfet, Daniel},
month = apr,
year = {2018},
note = {ZSCC: NoCitationData[s0]
original-date: 2016-02-23T03:29:42Z},
keywords = {Categorical ML, Implementation, Linear logic, Machine learning, Semantics}
}
@article{ehrhard_probabilistic_2018,
title = {Probabilistic call by push value},
url = {http://arxiv.org/abs/1607.04690},
doi = {10/ggdk8z},
abstract = {We introduce a probabilistic extension of Levy's Call-By-Push-Value. This extension consists simply in adding a " flipping coin " boolean closed atomic expression. This language can be understood as a major generalization of Scott's PCF encompassing both call-by-name and call-by-value and featuring recursive (possibly lazy) data types. We interpret the language in the previously introduced denotational model of probabilistic coherence spaces, a categorical model of full classical Linear Logic, interpreting data types as coalgebras for the resource comonad. We prove adequacy and full abstraction, generalizing earlier results to a much more realistic and powerful programming language.},
urldate = {2019-11-27},
journal = {arXiv:1607.04690 [cs]},
author = {Ehrhard, Thomas and Tasson, Christine},
year = {2018},
note = {ZSCC: 0000013[s0]
arXiv: 1607.04690},
keywords = {Denotational semantics, Linear logic, Probabilistic programming, Programming language theory}
}
@article{ehrhard_introduction_2016,
title = {An introduction to {Differential} {Linear} {Logic}: proof-nets, models and antiderivatives},
shorttitle = {An introduction to {Differential} {Linear} {Logic}},
url = {http://arxiv.org/abs/1606.01642},
abstract = {Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic and a categorical axiomatization of its denotational models. We also introduce a simple categorical condition on these models under which a general antiderivative operation becomes available. Last we briefly describe the model of sets and relations and give a more detailed account of the model of finiteness spaces and linear and continuous functions.},
urldate = {2019-11-28},
journal = {arXiv:1606.01642 [cs]},
author = {Ehrhard, Thomas},
month = jun,
year = {2016},
note = {ZSCC: 0000002
arXiv: 1606.01642},
keywords = {Denotational semantics, Differential Linear Logic, Differentiation, Linear logic}
}
@inproceedings{ehrhard_probabilistic_2014,
address = {San Diego, California, USA},
title = {Probabilistic coherence spaces are fully abstract for probabilistic {PCF}},
isbn = {978-1-4503-2544-8},
url = {http://dl.acm.org/citation.cfm?doid=2535838.2535865},
doi = {10/ggdf9x},
abstract = {Probabilistic coherence spaces (PCoh) yield a semantics of higherorder probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in PCoh characterizes the operational indistinguishability of programs in PCF with a random primitive.},
language = {en},
urldate = {2019-11-22},
booktitle = {Proceedings of the 41st {ACM} {SIGPLAN}-{SIGACT} {Symposium} on {Principles} of {Programming} {Languages} - {POPL} '14},
publisher = {ACM Press},
author = {Ehrhard, Thomas and Tasson, Christine and Pagani, Michele},
year = {2014},
note = {ZSCC: 0000060},
keywords = {Coherence spaces, Probabilistic programming, Programming language theory, Semantics},
pages = {309--320}
}
@article{ehrhard_probabilistic_2011,
title = {Probabilistic coherence spaces as a model of higher-order probabilistic computation},
volume = {209},
issn = {0890-5401},
url = {http://www.sciencedirect.com/science/article/pii/S0890540111000411},
doi = {10/ctfch6},
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.},
language = {en},
number = {6},
urldate = {2019-11-22},
journal = {Information and Computation},
author = {Ehrhard, Thomas and Danos, Vincent},
month = jun,
year = {2011},
note = {ZSCC: 0000065},
keywords = {Coherence spaces, Probabilistic programming, Programming language theory, Semantics},
pages = {966--991}
}
@inproceedings{ehrhard_computational_2011,
address = {Toronto, ON, Canada},
title = {The {Computational} {Meaning} of {Probabilistic} {Coherence} {Spaces}},
isbn = {978-1-4577-0451-2},
url = {http://ieeexplore.ieee.org/document/5970206/},
doi = {10/cpv52n},
abstract = {We study the probabilistic coherent spaces — a denotational semantics interpreting programs by power series with non negative real coefﬁcients. We prove that this semantics is adequate for a probabilistic extension of the untyped λ-calculus: the probability that a term reduces to a head normal form is equal to its denotation computed on a suitable set of values. The result gives, in a probabilistic setting, a quantitative reﬁnement to the adequacy of Scott’s model for untyped λ-calculus.},
language = {en},
urldate = {2019-11-26},
booktitle = {2011 {IEEE} 26th {Annual} {Symposium} on {Logic} in {Computer} {Science}},
publisher = {IEEE},
author = {Ehrhard, Thomas and Pagani, Michele and Tasson, Christine},
month = jun,
year = {2011},
note = {ZSCC: 0000036},
keywords = {Coherence spaces, Denotational semantics, Probabilistic programming, Programming language theory},
pages = {87--96}
}
@article{fiore_cartesian_2008,
title = {The cartesian closed bicategory of generalised species of structures},
volume = {77},
issn = {00246107},
url = {http://doi.wiley.com/10.1112/jlms/jdm096},
doi = {10/bd2mr9},
abstract = {The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These deﬁnitions encompass most notions of combinatorial species considered in the literature—including of course Joyal’s original notion—together with their associated substitution operation. Our ﬁrst main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our second main result establishes that the bicategory of generalised species of structures is cartesian closed.},
language = {en},
number = {1},
urldate = {2019-11-28},
journal = {Journal of the London Mathematical Society},
author = {Fiore, M. and Gambino, N. and Hyland, M. and Winskel, G.},
month = feb,
year = {2008},
note = {ZSCC: 0000067},
keywords = {Denotational semantics, Differential Linear Logic, Differentiation, Linear logic},
pages = {203--220}
}
@article{ehrhard_differential_2003,
title = {The differential lambda-calculus},
volume = {309},
issn = {0304-3975},
url = {http://www.sciencedirect.com/science/article/pii/S030439750300392X},
doi = {10/bf3b8v},
abstract = {We present an extension of the lambda-calculus with differential constructions. We state and prove some basic results (confluence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambda-calculus.},
language = {en},
number = {1},
urldate = {2019-11-24},
journal = {Theoretical Computer Science},
author = {Ehrhard, Thomas and Regnier, Laurent},
month = dec,
year = {2003},
note = {ZSCC: 0000307},
keywords = {Differentiation, Linear logic, Programming language theory},
pages = {1--41}
}
@article{girard_linear_1987,
title = {Linear logic},
volume = {50},
issn = {0304-3975},
url = {http://www.sciencedirect.com/science/article/pii/0304397587900454},
doi = {10/cmv5mj},
abstract = {The familiar connective of negation is broken into two operations: linear negation which is the purely negative part of negation and the modality “of course” which has the meaning of a reaffirmation. Following this basic discovery, a completely new approach to the whole area between constructive logics and programmation is initiated.},
language = {en},
number = {1},
urldate = {2019-11-26},
journal = {Theoretical Computer Science},
author = {Girard, Jean-Yves},
month = jan,
year = {1987},
note = {ZSCC: 0005505},
keywords = {Denotational semantics, Linear logic, Type theory},
pages = {1--101}
}
@misc{murfet_linear_nodate,
title = {Linear logic and deep learning},
language = {en},
author = {Murfet, Daniel and Hu, Huiyi},
note = {ZSCC: NoCitationData[s0]},
keywords = {Categorical ML, Linear logic, Machine learning, Semantics}
}