Plotkin and Pretnar's handlers for algebraic effects occupy a sweet spot in the design space of abstractions for effectful computation. By separating effect signatures from their implementation, algebraic effects provide a high degree of modularity, allowing programmers to express effectful programs independently of the concrete interpretation of their effects. A handler is an interpretation of the effects of an algebraic computation. The handler abstraction adapts well to multiple settings: pure or impure, strict or lazy, static types or dynamic types. This is a position paper whose main aim is to popularise the handler abstraction. We give a gentle introduction to its use, a collection of illustrative examples, and a straightforward operational semantics. We describe our Haskell implementation of handlers in detail, outline the ideas behind our OCaml, SML, and Racket implementations, and present experimental results comparing handlers with existing code.

International audienceType Classes have met a large success in Haskell and Isabelle, as a solution for sharing notations by overloading and for specifying with abstract structures by quantification on contexts. However, both systems are limited by second-class implementations of these con- structs, and these limitations are only overcomed by ad-hoc extensions to the respective systems. We propose an embedding of type classes into a dependent type theory that is first-class and supports some of the most popular extensions right away. The implementation is correspondingly cheap, general and integrates well inside the system, as we have experimented in Coq. We show how it can be used to help structured programming and proving by way of examples

This paper exhibits the power of programming with dependent types by dint of embedding three domain-specific languages: Cryptol, a language for cryptographic protocols; a small data description language; and relational algebra. Each example demonstrates particular design patterns inherent to dependently-typed programming. Documenting these techniques paves the way for further research in domain-specific embedded type systems.

Abstract. The recent success of languages like Agda and Coq demonstrates the potential of using dependent types for programming. These systems rely on many high-level features like datatype definitions, pattern matching and implicit arguments to facilitate the use of the languages. However, these features complicate the metatheoretical study and are a potential source of bugs. To address these issues we introduce ΠΣ, a dependently typed core language. It is small enough for metatheoretical study and the type checker is small enough to be formally verified. In this language there is only one mechanism for recursion-used for types, functions and infinite objectsand an explicit mechanism to control unfolding, based on lifted types. Furthermore structural equality is used consistently for values and types; this is achieved by a new notion of α-equality for recursive definitions. We show, by translating several high-level constructions, that ΠΣ is suitable as a core language for dependently typed programming.

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