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Probabilistic functions and cryptographic oracles in higher order logic. (English) Zbl 1335.68033

Thiemann, Peter (ed.), Programming languages and systems. 25th European symposium on programming, ESOP 2016, held as part of the European joint conferences on theory and practice of software, ETAPS 2016, Eindhoven, The Netherlands, April 2–8, 2016. Proceedings. Berlin: Springer (ISBN 978-3-662-49497-4/pbk; 978-3-662-49498-1/ebook). Lecture Notes in Computer Science 9632, 503-531 (2016).
Summary: This paper presents a shallow embedding of a probabilistic functional programming language in higher order logic. The language features monadic sequencing, recursion, random sampling, failures and failure handling, and black-box access to oracles. Oracles are probabilistic functions which maintain hidden state between different invocations. To that end, we propose generative probabilistic systems as the semantic domain in which the operators of the language are defined. We prove that these operators are parametric and derive a relational program logic for reasoning about programs from parametricity. Several examples demonstrate that our language is suitable for conducting cryptographic proofs.
For the entire collection see [Zbl 1333.68019].

MSC:

68N18 Functional programming and lambda calculus
94A60 Cryptography
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