@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}
}
@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}
}
@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}
}
@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}
}