The Discriminating Power of the Let-In Operator in the Lazy Call-by-Name Probabilistic lambda-Calculus

Authors Simona Kašterović, Michele Pagani

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Simona Kašterović
  • Faculty of Technical Sciences, University of Novi Sad , Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Michele Pagani
  • IRIF, University Paris Diderot - Paris 7, France


We wish to thank the anonymous reviewers for their valuable suggestions, helping us to improve the paper.

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Simona Kašterović and Michele Pagani. The Discriminating Power of the Let-In Operator in the Lazy Call-by-Name Probabilistic lambda-Calculus. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We consider the notion of probabilistic applicative bisimilarity (PAB), recently introduced as a behavioural equivalence over a probabilistic extension of the untyped lambda-calculus. Alberti, Dal Lago and Sangiorgi have shown that PAB is not fully abstract with respect to the context equivalence induced by the lazy call-by-name evaluation strategy. We prove that extending this calculus with a let-in operator allows for achieving the full abstraction. In particular, we recall Larsen and Skou’s testing language, which is known to correspond with PAB, and we prove that every test is representable by a context of our calculus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
  • probabilistic lambda calculus
  • bisimulation
  • Howe’s technique
  • context equivalence
  • testing


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