In ML-style module type theory, sealing often leads to situations in which type variables must leave scope, and this creates a need for signatures that avoid such variables. Unfortunately, in general, there is no best signature that avoids a variable, so modules do not always enjoy principal signatures. This observation is called the avoidance problem. In the past, the problem has been circumvented

The three-continuation approach to coroutine pipelines efficiently represents a large number of connected components. Previous work in this area introduces this alternative encoding but does not shed much light on the underlying principles for deriving this encoding from its specification. This paper gives this missing insight by deriving the three-continuation encoding based on eliminating the mutual

Algebraic effects and handlers are a convenient method for structuring monadic effects with primitive effectful operations and separating the syntax from the interpretation of these operations. However, the scope of conventional handlers is limited as not all side effects are monadic in nature. This paper generalizes the notion of algebraic effects and handlers from monads to generalized monoids, which

Many students complete PhDs in functional programming each year. As a service to the community, twice per year the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.

Consider two widely used definitions of equality. That of Leibniz: one value equals another if any predicate that holds of the first holds of the second. And that of Martin-Löf: the type identifying one value with another is occupied if the two values are identical. The former dates back several centuries, while the latter is widely used in proof systems such as Agda and Coq. Here we show that the

As popularity of algebraic effects and handlers increases, so does a demand for their efficient execution. Eff, an ML-like language with native support for handlers, has a subtyping-based effect system on which an effect-aware optimising compiler could be built. Unfortunately, in our experience, implementing optimisations for Eff is overly error-prone because its core language is implicitly typed,

Multi types – aka non-idempotent intersection types – have been used. to obtain quantitative bounds on higher-order programs, as pioneered by de Carvalho. Notably, they bound at the same time the number of evaluation steps and the size of the result. Recent results show that the number of steps can be taken as a reasonable time complexity measure. At the same time, however, these results suggest that

Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory, sacrificing both reasoning power and safety. We present an alternative approach where the type system tracks equations that are observed in subparts of the program, yielding

Highly critical application domains, like medicine and aerospace, require the use of strict design, implementation, and validation techniques. Functional languages have been used in these domains to develop synchronous dataflow programming languages for reactive systems. Causal stream functions and functional reactive programming (FRP) capture the essence of those languages in a way that is both elegant

Build systems are awesome, terrifying – and unloved. They are used by every developer around the world, but are rarely the object of study. In this paper, we offer a systematic, and executable, framework for developing and comparing build systems, viewing them as related points in a landscape rather than as isolated phenomena. By teasing apart existing build systems, we can recombine their components

Effect handlers are a promising way to structure effectful programs in a modular way. We present the Scala library Effekt, which is centered around capability passing and implemented in terms of a monad for multi-prompt delimited continuations. Effekt is the first library implementation of effect handlers that supports effect safety and effect polymorphism without resorting to type-level programming

We explore the design and implementation of Frank, a strict functional programming language with a bidirectional effect type system designed from the ground up around a novel variant of Plotkin and Pretnar’s effect handler abstraction. Effect handlers provide an abstraction for modular effectful programming: a handler acts as an interpreter for a collection of commands whose interfaces are statically

From the outset, lambda calculus represented natural numbers through iterated application. The successor hence adds one more application, and the predecessor removes. In effect, the predecessor un-applies a term—which seemed impossible, even to Church. It took Kleene a rather oblique glance to sight a related representation of numbers, with an easier predecessor. Let us see what we can do if we look

Plotkin and Pretnar’s effect handlers offer a versatile abstraction for modular programming with user-defined effects. This paper focuses on foundations for implementing effect handlers, for the three different kinds of effect handlers that have been proposed in the literature: deep, shallow, and parameterised. Traditional deep handlers are defined by folds over computation trees and are the original

In a dependently typed language, we can guarantee correctness of our programmes by providing formal proofs. To check them, the typechecker elaborates these programs and proofs into a low-level core language. However, this core language is by nature hard to understand by mere humans, so how can we know we proved the right thing? This question occurs in particular for dependent copattern matching, a