TY - JOUR
TI - Differentials and distances in probabilistic coherence spaces
AU - Ehrhard, Thomas
T2 - arXiv:1902.04836 [cs]
AB - 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.
DA - 2019/02/13/
PY - 2019
DP - arXiv.org
UR - http://arxiv.org/abs/1902.04836
Y2 - 2019/11/28/11:57:10
KW - Coherence spaces
KW - Denotational semantics
KW - Differential Linear Logic
KW - Differentiation
KW - Linear logic
KW - Probabilistic programming
KW - Programming language theory
ER -