Algebraic Effects and Effect Handlers for Idioms and Arrows

Plotkin and Power’s algebraic effects combined with Plotkin and Pretnar’s effect handlers provide a foundation for modular pro-gramming with effects. We present a generalisation of algebraic effects and effect handlers to support other kinds of effectful com-putations corresponding to McBride and Paterson’s idioms and Hughes ’ arrows

Doo bee doo bee doo

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 tracked by the type system. However, Frank eliminates the need for an additional effect handling construct by generalising the basic mechanism of functional abstraction itself. A function is but the special case of a Frank operator that interprets no commands. Moreover, Frank's operators can be multihandlers which simultaneously interpret commands from several sources at once, without disturbing the direct style of functional programming with values. Effect typing in Frank employs a novel form of effect polymorphism which avoids mentioning effect variables in source code. This is achieved by propagating an ambient ability inwards, rather than accumulating unions of potential effects outwards. With the ambient ability describing the effects that are available at a certain point in the code, it can become necessary to reconfigure access to the ambient ability. A primary goal is to be able to encapsulate internal effects, eliminating a phenomenon we call effect pollution. Moreover, it is sometimes desirable to rewire the effect flow between effectful library components. We propose adaptors as a means for supporting both effect encapsulation and more general rewiring. Programming with effects and handlers is in its infancy. We contribute an exploration of future possibilities, particularly in combination with other forms of rich type systems

Versatile event correlation with algebraic effects

We present the first language design to uniformly express variants of n -way joins over asynchronous event streams from different domains, e.g., stream-relational algebra, event processing, reactive and concurrent programming. We model asynchronous reactive programs and joins in direct style, on top of algebraic effects and handlers. Effect handlers act as modular interpreters of event notifications, enabling fine-grained control abstractions and customizable event matching. Join variants can be considered as cartesian product computations with ”degenerate” control flow, such that unnecessary tuples are not materialized a priori. Based on this computational interpretation, we decompose joins into a generic, naive enumeration procedure of the cartesian product, plus variant-specific extensions, represented in terms of user-supplied effect handlers. Our microbenchmarks validate that this extensible design avoids needless materialization. Alongside a formal semantics for joining and prototypes in Koka and multicore OCaml, we contribute a systematic comparison of the covered domains and features. ERC, Advanced Grant No. 321217 ERC, Consolidator Grant No. 617805 DFG, SFB 1053 DFG, SA 2918/2-

Lewis meets Brouwer: constructive strict implication

C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than the box and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the "strength" axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction and the strong constructive strict implication itself has been also discovered by the functional programming community in their study of "arrows" as contrasted with "idioms". Our particular focus is on arithmetical interpretations of the intuitionistic strict implication in terms of preservativity in extensions of Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years later

Introducing ⦇ λ ⦈, a λ-calculus for effectful computation

International audienceWe present λ , a calculus with special constructions for dealing with effects and handlers. This is an extension of the simply-typed λ-calculus (STLC). We enrich STLC with a type for representing effectful computations alongside with operations to create and process values of this type. The calculus is motivated by natural language modelling, and especially semantic representation. Traditionally, the meaning of a sentence is calculated using λ-terms, but some semantic phenomena need more flexibility. In this article we introduce the calculus and show that the calculus respects the laws of algebraic structures and it enjoys strong normalisation. To do so, confluence is proven using the Combinatory Reduction Systems (CRSs) of Klop and termination using the Inductive Data Type Systems (IDTSs) of Blanqui

A Direct-Style Effect Notation for Sequential and Parallel Programs

Modeling sequential and parallel composition of effectful computations has been investigated in a variety of languages for a long time. In particular, the popular do-notation provides a lightweight effect embedding for any instance of a monad. Idiom bracket notation, on the other hand, provides an embedding for applicatives. First, while monads force effects to be executed sequentially, ignoring potential for parallelism, applicatives do not support sequential effects. Composing sequential with parallel effects remains an open problem. This is even more of an issue as real programs consist of a combination of both sequential and parallel segments. Second, common notations do not support invoking effects in direct-style, instead forcing a rigid structure upon the code. In this paper, we propose a mixed applicative/monadic notation that retains parallelism where possible, but allows sequentiality where necessary. We leverage a direct-style notation where sequentiality or parallelism is derived from the structure of the code. We provide a mechanisation of our effectful language in Coq and prove that our compilation approach retains the parallelism of the source program

Modular interpreters with implicit context propagation

Modular interpreters are a crucial first step towards component-based language development: instead of writing language interpreters from scratch, they can be assembled from reusable, semantic building blocks. Unfortunately, traditional language interpreters can be hard to extend because different language constructs may require different interpreter signatures. For instance, arithmetic interpreters produce a value without any context information, whereas binding constructs require an additional environment.In this paper, we present a practical solution to this problem based on implicit context propagation. By structuring denotational-style interpreters as Object Algebras, base interpreters can be retroactively lifted into new interpreters that have an extended signature. The additional parameters are implicitly propagated behind the scenes, through the evaluation of the base interpreter.Interpreter lifting enables a flexible style of modular and extensible language development. The technique works in mainstream object-oriented languages, does not sacrifice type safety or separate compilation, and can be easily automated, for instance using macros in Scala or dynamic proxies in Java. We illustrate implicit context propagation using a modular definition of Featherweight Java and its extension to support side-effects, and an extensible domain-specific language for state machines. We finally investigate the performance overhead of lifting by running the DeltaBlue benchmark program in Javascript on top of a modular implementation of LambdaJS and a dedicated micro-benchmark. The results show that lifting makes interpreters roughly twice as slow because of additional call overhead. Further research is needed to eliminate this performance penalty