@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}
}
@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}
}