The Essence of Nested Composition

Calculi with disjoint intersection types support an introduction form for intersections called the merge operator, while retaining a coherent semantics. Disjoint intersections types have great potential to serve as a foundation for powerful, flexible and yet type-safe and easy to reason OO languages. This paper shows how to significantly increase the expressive power of disjoint intersection types by adding support for nested subtyping and composition, which enables simple forms of family polymorphism to be expressed in the calculus. The extension with nested subtyping and composition is challenging, for two different reasons. Firstly, the subtyping relation that supports these features is non-trivial, especially when it comes to obtaining an algorithmic version. Secondly, the syntactic method used to prove coherence for previous calculi with disjoint intersection types is too inflexible, making it hard to extend those calculi with new features (such as nested subtyping). We show how to address the first problem by adapting and extending the Barendregt, Coppo and Dezani (BCD) subtyping rules for intersections with records and coercions. A sound and complete algorithmic system is obtained by using an approach inspired by Pierce\u27s work. To address the second problem we replace the syntactic method to prove coherence, by a semantic proof method based on logical relations. Our work has been fully formalized in Coq, and we have an implementation of our calculus

Dependent Merges and First-Class Environments

In most programming languages a (runtime) environment stores all the definitions that are available to programmers. Typically, environments are a meta-level notion, used only conceptually or internally in the implementation of programming languages. Only a few programming languages allow environments to be first-class values, which can be manipulated directly in programs. Although there is some research on calculi with first-class environments for statically typed programming languages, these calculi typically have significant restrictions. In this paper we propose a statically typed calculus, called ?_i, with first-class environments. The main novelty of the ?_i calculus is its support for first-class environments, together with an expressive set of operators that manipulate them. Such operators include: reification of the current environment, environment concatenation, environment restriction, and reflection mechanisms for running computations under a given environment. In ?_i any type can act as a context (i.e. an environment type) and contexts are simply types. Furthermore, because ?_i supports subtyping, there is a natural notion of context subtyping. There are two important ideas in ?_i that generalize and are inspired by existing notions in the literature. The ?_i calculus borrows disjoint intersection types and a merge operator, used in ?_i to model contexts and environments, from the ?_i calculus. However, unlike the merges in ?_i, the merges in ?_i can depend on previous components of a merge. From implicit calculi, the ?_i calculus borrows the notion of a query, which allows type-based lookups on environments. In particular, queries are key to the ability of ?_i to reify the current environment, or some parts of it. We prove the determinism and type soundness of ?_i, and show that ?_i can encode all well-typed ?_i programs

A new modular implementation for Stateful Traits

International audienceThe term traits is overloaded in the literature. In this work we refer to traits as the stateless model and implementation described in Schaerli et al. articles. Traits provide a flexible way to support multiple inheritance code reuse in the context of a single inheritance language. The Pharo programming language includes the second implementation of stateless traits based on the original version of Schaerli's one. Even if it is the second iteration of such an implementation, it presents several limitations. First, it does not support state in traits. Second, its implementation is monolithic i.e., it is deeply coupled with the rest of the language kernel: it cannot be loaded nor unloaded. Furthermore, trait support impacts all classes, even classes not using traits. In addition, while the development tools include full support to work with classes, trait support is more limited because classes and traits do not present the same Metaobject Protocol (MOP). Finally, being monolithic and integrated in the language kernel, it is difficult to extend this current implementation. This article describes a new modular and extensible implementation of traits: it is easily loadable and unloadable as any other package. In addition, classes not using traits are not impacted. Finally, this new implementation includes a new and carefully designed Metaobject Protocol (MOP) that is compatible with both classes and traits. This allows one to reuse existing tools as they do not require special support for traits. Then, following the semantics proposed for stateful traits in [BDNW07], we present a new implementation of stateful traits. This implementation is an extension of our new modular implementation. We implemented modular traits using specialized metaclasses as our main language extension mechanism. By replacing the implementation we reduced the Pharo Language Kernel size by 15%. This model and implementation are used in production since Pharo7.0 (January 2019)

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019

Typed First-Class Traits

Many dynamically-typed languages (including JavaScript, Ruby, Python or Racket) support first-class classes, or related concepts such as first-class traits and/or mixins. In those languages classes are first-class values and, like any other values, they can be passed as an argument, or returned from a function. Furthermore first-class classes support dynamic inheritance: i.e. they can inherit from other classes at runtime, enabling programmers to abstract over the inheritance hierarchy. In contrast, type system limitations prevent most statically-typed languages from having first-class classes and dynamic inheritance. This paper shows the design of SEDEL: a polymorphic statically-typed language with first-class traits, supporting dynamic inheritance as well as conventional OO features such as dynamic dispatching and abstract methods. To address the challenges of type-checking first-class traits, SEDEL employs a type system based on the recent work on disjoint intersection types and disjoint polymorphism. The novelty of SEDEL over core disjoint intersection calculi are source level features for practical OO programming, including first-class traits with dynamic inheritance, dynamic dispatching and abstract methods. Inspired by Cook and Palsberg\u27s work on the denotational semantics for inheritance, we show how to design a source language that can be elaborated into Alpuim et al.\u27s F_{i} (a core polymorphic calculus with records supporting disjoint polymorphism). We illustrate the applicability of SEDEL with several example uses for first-class traits, and a case study that modularizes programming language interpreters using a highly modular form of visitors

Typed First-Class Traits (Artifact)

This artifact contains the prototype Haskell implementation of SEDEL, with support for first-class traits, as described in the companion paper. This artifact also contains the source code of the case study on "Anatomy of Programming Languages", illustrating how effective SEDEL is in terms of modularizing programming language features. For comparison, it also includes a vanilla Haskell implementation of the case study without any code reuse