Summary: A Type­Theoretic Foundation of
Delimited Continuations +
Zena M. Ariola #
University of Oregon
Hugo Herbelin
INRIA­Futurs
Amr Sabry §
Indiana University
Abstract. There is a correspondence between classical logic and programming lan­
guage calculi with first­class continuations. With the addition of control delimiters,
the continuations become composable and the calculi are believed to become more
expressive. We formalise that the addition of control delimiters corresponds to the
addition of a single dynamically­scoped variable modelling the special top­level con­
tinuation. From a type perspective, the dynamically­scoped variable requires e#ect
annotations. From a logic perspective, the e#ect annotations can be understood in
a standard logic extended with the dual of implication, namely subtraction.
Keywords: callcc, monad, prompt, reset, shift, subcontinuation, subtraction
1. Introduction
Programming practice suggests that control operators add expressive
power to purely functional languages. For example, control operators

Source: Ariola, Zena M. - Department of Computer and Information Science, University of Oregon

Collections: Computer Technologies and Information Sciences