Applicative Bisimulations for Delimited-Control Operators

TL;DR

This paper develops a behavioral theory for a lambda calculus with delimited-control operators, introducing applicative bisimilarity to characterize contextual equivalence and comparing it with CPS equivalence.

Contribution

It introduces an applicative bisimilarity framework for delimited-control operators and compares it with CPS equivalence, aiding in proving term equivalence.

Findings

Applicative bisimilarity characterizes contextual equivalence.

Comparison between bisimilarity and CPS equivalence.

Bisimilarity aids in proving equivalence of control-effect terms.

Abstract

We develop a behavioral theory for the untyped call-by-value lambda calculus extended with the delimited-control operators shift and reset. For this calculus, we discuss the possible observable behaviors and we define an applicative bisimilarity that characterizes contextual equivalence. We then compare the applicative bisimilarity and the CPS equivalence, a relation on terms often used in studies of control operators. In the process, we illustrate how bisimilarity can be used to prove equivalence of terms with delimited-control effects.