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.

A type-preserving compiler converts a well-typed input program into a well-typed output program. Previous studies have developed type-preserving compilers for various source languages, including the simply-typed lambda calculus and calculi with control constructs. Our goal is to realize type-preserving compilation of languages that have facilities for manipulating first-class continuations. In this paper, we focus on algebraic effects and handlers, a generalization of exceptions and their handlers with resumable continuations. Specifically, we choose an effect handler calculus and a typed stack-machine-based assembly language as the source and the target languages, respectively, and formalize the target language and a type preserving compiler. The main challenge posed by first-class continuation is how to ensure safety of continuation capture and resumption, which involves concatenation of unknown stacks. We solve this challenge by incorporating stack polymorphism, a technique that has been used for compilation from a language without first-class continuations to a stack-based assembly language. To prove that our compiler is type preserving, we implemented the compiler in Agda as a function between intrinsically typed ASTs. We believe that our contributions could lead to correct and efficient compilation of continuation-manipulating facilities in general.

Novice learners of programming tend to neglect error messages, even though the messages have a lot of useful information for solving problems. While there exists research that aims to user-friendly error messages by changing the wording and by adding visual assistance, most of them do not focus on drawing learners' attention to error messages. We propose the enbugging quiz, a novel quiz format that requests the learner to craft a program that produces a specified error. This paper reports our design of enbugging quizzes and reports the results of our initial experiment, where we observed positive effects on the learners' attitudes towards error messages.

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.

In their paper "A Functional Abstraction of Typed Contexts", Danvy and Filinski show how to derive a monomorphic type system of the shift and reset operators from a CPS semantics. In this paper, we show how this method scales to Felleisen's control and prompt operators. Compared to shift and reset, control and prompt exhibit a more dynamic behavior, in that they can manipulate a trail of contexts surrounding the invocation of previously captured continuations. Our key observation is that, by adopting a functional representation of trails in the CPS semantics, we can derive a type system that encodes all and only constraints imposed by the CPS semantics.

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.

What makes a good compiler IR? In the context of functional languages, there has been an extensive debate on the advantages and disadvantages of continuation-passing-style (CPS). The consensus seems to be that some form of explicit continuations is necessary to model jumps in a functional style, but that they should have a 2nd-class status, separate from regular functions, to ensure efficient code generation. Building on this observation, a recent study from PLDI 2017 proposed a direct-style IR with explicit join points, which essentially represent local continuations, i.e., functions that do not return or escape. While this IR can work well in practice, as evidenced by the implementation of join points in the Glasgow Haskell Compiler (GHC), there still seems to be room for improvement, especially with regard to the way continuations are handled in the course of optimization. In this paper, we contribute to the CPS debate by developing a novel IR with the following features. First, we integrate a control operator that resembles Felleisen’s C , eliminating certain redundant rewrites observed in the previous study. Second, we treat the non-returning and non-escaping aspects of continuations separately, allowing efficient compilation of well-behaved functions defined by the user. Third, we define a selective CPS translation of our IR, which erases control operators while preserving the meaning and typing of programs. These features enable optimizations in both direct style and full CPS, as well as in any intermediate style with selectively exposed continuations. Thus, we change the spectrum of available options from “CPS yes or no” to “as much or as little CPS as you want, when you want it”.

Dependently typed languages such as Coq are used to specify and prove functional correctness of source programs, but what we ultimately need are guarantees about correctness of compiled code. By preserving dependent types through each compiler pass, we could preserve source-level specifications and correctness proofs into the generated target-language programs. Unfortunately, type-preserving compilation of dependent types is hard. In 2002, Barthe and Uustalu showed that type-preserving CPS is not possible for languages such as Coq. Specifically, they showed that for strong dependent pairs (Σ types), the standard typed call-by-name CPS is not type preserving . They further proved that for dependent case analysis on sums, a class of typed CPS translations—including the standard translation—is not possible . In 2016, Morrisett noticed a similar problem with the standard call-by-value CPS translation for dependent functions (Π types). In essence, the problem is that the standard typed CPS translation by double-negation, in which computations are assigned types of the form ( A → ⊥) → ⊥, disrupts the term/type equivalence that is used during type checking in a dependently typed language. In this paper, we prove that type-preserving CPS translation for dependently typed languages is not not possible. We develop both call-by-name and call-by-value CPS translations from the Calculus of Constructions with both Π and Σ types (CC) to a dependently typed target language, and prove type preservation and compiler correctness of each translation. Our target language is CC extended with an additional equivalence rule and an additional typing rule, which we prove consistent by giving a model in the extensional Calculus of Constructions. Our key observation is that we can use a CPS translation that employs answer-type polymorphism , where CPS-translated computations have type ∀ α. ( A → α) → α. This type justifies, by a free theorem , the new equality rule in our target language and allows us to recover the term/type equivalences that CPS translation disrupts. Finally, we conjecture that our translation extends to dependent case analysis on sums, despite the impossibility result, and provide a proof sketch.

Dependent types are a powerful tool for maintaining program invariants. To take advantage of this aspect in real-world programming, efforts have been put into enriching dependently typed languages with missing constructs, most notably, effects. This paper presents a language that has two practically interesting ingredients: dependent inductive types, and the delimited control constructs shift and reset. When integrating delimited control into a dependently typed language, however, two challenges arise. First, the dynamic nature of control operators, which is the source of their expressiveness, can break fundamental language properties such as logical consistency and subject reduction. Second, CPS translations, which we often use to define the semantics of control operators, do not scale straightforwardly to dependently typed languages. We solve the former issue by restricting dependency of types, and the latter using answer-type polymorphism of pure terms. The main contribution of this paper is to give a sound type system of our language, as well as a type-preserving CPS translation. We also discuss various extensions, which would make our language more like a full-spectrum proof assistant but pose non-trivial issues.