License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2018.4
URN: urn:nbn:de:0030-drops-91749
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9174/
Go to the corresponding LIPIcs Volume Portal

Vignudelli, Valeria

Proof Techniques for Program Equivalence in Probabilistic Higher-Order Languages (Invited Talk)

pdf-format:
LIPIcs-FSCD-2018-4.pdf (0.2 MB)

Abstract

While the theory of functional higher-order languages, starting from lambda-calculi, is a well-established research field, it is only in recent years that the operational semantics of higher-order languages with probabilistic operators has started to be extensively studied. A fundamental notion in the semantics of programming languages is that of program equivalence. In higher-order languages, program equivalence is generally formalized as a contextual equivalence [Morris, 1968], which can be hard to prove directly. This has motivated the study of proof techniques for contextual equivalence, from inductive ones, such as logical relations [Andrew Pitts, 2005], to coinductive ones, mainly in the form of bisimulations [Abramsky, 1990]. In this talk I will discuss proof techniques for program equivalence in languages combining higher-order and probabilistic features. Several operational methods, traditionally developed in a deterministic setting, have been adapted to probabilistic higher-order languages [Ales Bizjak and Lars Birkedal, 2015; Dal Lago et al., 2014; Raphaëlle Crubillé and Ugo Dal Lago, 2014]. I will discuss these proof methods and focus on bisimulation-based techniques, showing how probabilities, combined with different language features, force a number of modifications to the definition of bisimulation [Crubillé et al., 2015; Sangiorgi and Vignudelli, 2016].

BibTeX - Entry

@InProceedings{vignudelli:LIPIcs:2018:9174,
  author =	{Valeria Vignudelli},
  title =	{{Proof Techniques for Program Equivalence in Probabilistic Higher-Order Languages (Invited Talk)}},
  booktitle =	{3rd International Conference on Formal Structures for  Computation and Deduction (FSCD 2018)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{H{\'e}l{\`e}ne Kirchner},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9174},
  URN =		{urn:nbn:de:0030-drops-91749},
  doi =		{10.4230/LIPIcs.FSCD.2018.4},
  annote =	{Keywords: Lambda Calculus, Contextual Equivalence, Bisimulation, Probabilistic Programming Languages}
}

Keywords: Lambda Calculus, Contextual Equivalence, Bisimulation, Probabilistic Programming Languages
Collection: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)
Issue Date: 2018
Date of publication: 04.07.2018

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI