Fully Abstract Models of the Probabilistic λ-calculus

Abstract : We compare three models of the probabilistic λ-calculus: the probabilistic Böhm trees of Leventis, the probabilistic concurrent games of Winskel et al., and the weighted relational model of Ehrhard et al. Probabilistic Böhm trees and probabilistic strategies are shown to be related by a precise correspondence theorem, in the spirit of existing work for the pure λ-calculus. Using Leventis' theorem (probabilistic Böhm trees characterise observational equivalence), we derive a full abstraction result for the games model. Then, we relate probabilistic strategies to the weighted relational model, using an interpretation-preserving functor from the former to the latter. We obtain that the relational model is also fully abstract.
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Pierre Clairambault, Hugo Paquet. Fully Abstract Models of the Probabilistic λ-calculus. 27th EACSL Annual Conference on Computer Science Logic (CSL 2018), Sep 2018, Birmingham, United Kingdom. ⟨10.4230/LIPIcs.CSL.2018.16⟩. ⟨hal-01886956⟩

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