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The Concurrent Game Semantics of Probabilistic PCF

Simon CASTELLAN, Pierre CLAIRAMBAULT, Hugo PAQUET, Glynn WINKSEL

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.

@inproceedings{CCPW2018,
  author = {Simon Castellan and Pierre Clairambault and Hugo Paquet and Glynn Winksel},
  title = {{The Concurrent Game Semantics of Probabilistic PCF}},
  booktitle = {Thirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science},
  pages = {215--224},
  publisher = {ACM},
  year = 2018
}

@inproceedings{CCPW2018,
  author = {Simon Castellan and Pierre Clairambault and Hugo Paquet and Glynn Winksel},
  title = {{The Concurrent Game Semantics of Probabilistic PCF}},
  booktitle = {Thirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science},
  pages = {215--224},
  publisher = {ACM},
  doi = "10.1145/3209108.3209187",
  year = 2018
}