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## Differentials and distances in probabilistic coherence spaces

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Author/contributor

- Ehrhard, Thomas (Author)

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

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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
CATEGORICAL LOGIC

DIFFERENTIAL CALCULUS

PROGRAMMING LANGUAGES

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