Continuations, particularly delimited continuations, enable manipulation of control flow and are thus useful for implementing new control structures. Even though continuations have been studied for a long time, and teaching them as an advanced topic for CS majors is becoming increasingly relevant, little research exists on teaching (delimited) continuations. This paper aims to start filling this gap by investigating students' understanding of continuations using thematic analysis and identifying mistakes students tend to make when tracing programs that use continuations. The findings consist of categories that describe common views of continuations, as well as different sets of mistakes that correspond to different misinterpretations of continuations or the underlying computational model. These early results are useful for informing future teaching of continuations and guide development of teaching tools, and furthermore, they provide a starting point for research into more formal misconceptions and development of concept inventories.

Algebraic effect handlers and delimited control operators are language facilities for expressing computational effects. Their labeled variations can express multiple kinds of exceptions, multiple states, and so on. We prove that labeled effect handlers and labeled control operators have equal expressive power. To show this, we develop a type-sound calculus for each facility and define macro translations between the typed calculi. The established equivalence can be used to understand and implement one facility in terms of the other.

Algebraic effects and handlers are a promising technique for incorporating composable computational effects into functional programming languages. Effect handlers enable concisely programming with different effects, but they do not offer a convenient way to program with different instances of the same effect. As a solution to this inconvenience, previous studies have introduced _named effect handlers_, which allow the programmer to distinguish among different effect instances. However, existing formalizations of named handlers are both involved and restrictive, as they employ non-standard mechanisms to prevent the escaping of handler names. In this paper, we propose a simple and flexible design of named handlers. Specifically, we treat handler names as first-class values, and prevent their escaping while staying within the ordinary λ-calculus. Such a design is enabled by combining named handlers with _scoped effects_, a novel variation of effects that maintain a scope via rank-2 polymorphism. We formalize two combinations of named handlers and scoped effects, and implement them in the Koka programming language. We also present practical applications of named handlers, including a neural network and a unification algorithm.