University of Birmingham > Talks@bham > Theoretical computer science seminar > On program equivalence in the probabilistic lambda calculus

On program equivalence in the probabilistic lambda calculus

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If you have a question about this talk, please contact Anupam Das.

We consider probabilistic applicative bisimilarity (PAB), a coinductive relation comparing the applicative behaviour of probabilistic untyped lambda terms according to a specific operational semantics. This notion has been studied with respect to the two standard parameter passing policies, call-by-value (cbv) and call-by-name (cbn), using a lazy reduction strategy not reducing within the body of a function. In particular, PAB has been proven fully abstract with respect to the contextual equivalence in cbv but not in lazy cbn. We overcome this issue of cbn by relaxing the laziness constraint: we prove that PAB is fully abstract with respect to the standard head reduction contextual equivalence. The proof is based on the Leventis Separation Theorem, using probabilistic Nakajima trees as a tree-like representation of the contextual equivalence classes. Finally, we prove also that the inequality full abstraction fails, showing that the probabilistic applicative similarity is strictly contained in the contextual preorder.

This talk is part of the Theoretical computer science seminar series.

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