TY - JOUR
TI - Continuous Probability Distributions in Concurrent Games
AU - Paquet, Hugo
AU - Winskel, Glynn
T2 - Electronic Notes in Theoretical Computer Science
T3 - Proceedings of the Thirty-Fourth Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXIV)
AB - We present a model of concurrent games in which strategies are probabilistic and support both discrete and continuous distributions. This is a generalisation of the probabilistic concurrent strategies of Winskel, based on event structures. We first introduce measurable event structures, discrete fibrations of event structures in which each fibre is turned into a measurable space. We then construct a bicategory of measurable games and measurable strategies based on measurable event structures, and add probability to measurable strategies using standard techniques of measure theory. We illustrate the model by giving semantics to an affine, higher-order, probabilistic language with a type of real numbers and continuous distributions.
DA - 2018/12/01/
PY - 2018
DO - 10/ggdmwv
DP - ScienceDirect
VL - 341
SP - 321
EP - 344
J2 - Electronic Notes in Theoretical Computer Science
LA - en
SN - 1571-0661
UR - http://www.sciencedirect.com/science/article/pii/S1571066118300975
Y2 - 2019/11/28/15:35:23
KW - Game semantics
KW - Interactive semantics
KW - Probabilistic programming
KW - Programming language theory
ER -
TY - CONF
TI - The concurrent game semantics of Probabilistic PCF
AU - Castellan, Simon
AU - Clairambault, Pierre
AU - Paquet, Hugo
AU - Winskel, Glynn
T2 - the 33rd Annual ACM/IEEE Symposium
AB - We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with symmetry, recently introduced by Castellan et al, with probability. This model supports two interpretations of PPCF, one sequential and one parallel. We make the case for this model by exploiting the causal structure of probabilistic concurrent strategies. First, we show that the strategies obtained from PPCF programs have a deadlock-free interaction, and therefore deduce that there is an interpretation-preserving functor from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract. Finally, we propose a definition of probabilistic innocence and prove a finite definability result, leading to a second (independent) proof of full abstraction.
C1 - Oxford, United Kingdom
C3 - Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18
DA - 2018///
PY - 2018
DO - 10/ggdjfz
DP - Crossref
SP - 215
EP - 224
LA - en
PB - ACM Press
SN - 978-1-4503-5583-4
UR - http://dl.acm.org/citation.cfm?doid=3209108.3209187
Y2 - 2019/11/26/16:57:36
KW - Denotational semantics
KW - Game semantics
KW - Interactive semantics
KW - Probabilistic programming
KW - Programming language theory
ER -