Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation
Abstract
We present sound and complete environmental bisimilarities for a variant of
Dybvig et al.’s calculus of multi-prompted delimited-control operators with dynamic prompt
generation. The reasoning principles that we obtain generalize and advance the existing
techniques for establishing program equivalence in calculi with single-prompted delimited
control.
The basic theory that we develop is presented using Madiot et al.’s framework that
allows for smooth integration and composition of up-to techniques facilitating bisimulation
proofs. We also generalize the framework in order to express environmental bisimulations
that support equivalence proofs of evaluation contexts representing continuations. This
change leads to a novel and powerful up-to technique enhancing bisimulation proofs in the
presence of control operators.