On Applicative Similarity, Sequentiality, and Full Abstraction

• Published in: Correct System Design pp. 65 - 82
• Main Authors: Crubillé, Raphaëlle, Dal Lago, Ugo, Sangiorgi, Davide, Vignudelli, Valeria
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Bisimulation; Coinduction; Probabilistic lambda calculus; Sequentiality
• ISBN: 9783319235059; 3319235052
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-23506-6_7

We study how applicative bisimilarity behaves when instantiated on a call-by-value probabilistic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-calculus, endowed with Plotkin’s parallel disjunction operator. We prove that congruence and coincidence with the corresponding context relation hold for both bisimilarity and similarity, the latter known to be impossible in sequential languages.