Differentials and distances in probabilistic coherence spaces

Resource type
Author/contributor
Title
Differentials and distances in probabilistic coherence spaces
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.
Publication
arXiv:1902.04836 [cs]
Date
2019-02-13
Accessed
2019-11-28T11:57:10Z
Library Catalog
Extra
ZSCC: 0000000 arXiv: 1902.04836
Citation
Ehrhard, T. (2019). Differentials and distances in probabilistic coherence spaces. ArXiv:1902.04836 [Cs]. Retrieved from http://arxiv.org/abs/1902.04836
DIFFERENTIAL CALCULUS
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