@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{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}
}