Andreas Rossberg

Generativity and dynamic opacity for abstract types

The standard formalism for explaining abstract types is existential quantification. While it provides a sufficient model for type abstraction in entirely statically typed languages, it proves to be too weak for languages enriched with forms of dynamic typing, where parametricity is violated. As an alternative approach to type abstraction that addresses this shortcoming we present a calculus for dynamic type generation. It features an explicit construct for generating new type names and relies on coercions for managing abstraction boundaries between generated types and their designated representation. Sealing is represented as a generalized form of these coercions. The calculus maintains abstractions dynamically without restricting type analysis.

F-ing Modules

ML modules are a powerful language mechanism for decomposing programs into reusable components. Unfortunately, they also have a reputation for being “complex” and requiring fancy type theory that is mostly opaque to non-experts. While this reputation is certainly understandable, given the many non-standard methodologies that have been developed in the process of studying modules, we aim here to demonstrate that it is undeserved. To do so, we present a novel formalization of ML modules, which defines their semantics directly by a compositional “elaboration” translation into plain System F ω (the higher-order polymorphic λ-calculus). To demonstrate the scalability of our “F-ing” semantics, we use it to define a representative, higher-order ML-style module language, encompassing all the major features of existing ML module dialects (except for recursive modules). We thereby show that ML modules are merely a particular mode of use of System F ω . To streamline the exposition, we present the semantics of our module language in stages. We begin by defining a subset of the language supporting a Standard ML-like language with second-class modules and generative functors. We then extend this sublanguage with the ability to package modules as first-class values (a very simple extension, as it turns out) and OCaml-style applicative functors (somewhat harder). Unlike previous work combining both generative and applicative functors, we do not require two distinct forms of functor or signature sealing. Instead, whether a functor is applicative or not depends only on the computational purity of its body. In fact, we argue that applicative/generative is rather incidental terminology for pure versus impure functors. This approach results in a semantics that we feel is simpler and more natural than previous accounts, and moreover prohibits breaches of abstraction safety that were possible under them.

The missing link: dynamic components for ML

Despite its powerful module system, ML has not yet evolved for the modern world of dynamic and open modular programming, to which more primitive languages have adapted better so far. We present the design and semantics of a simple yet expressive firstclass component system for ML. It provides dynamic linking in a type-safe and type-flexible manner, and allows selective execution in sandboxes. The system is defined solely by reduction to higherorder modules plus an extension with simple module-level dynamics, which we call packages. To represent components outside processes we employ generic pickling. We give a module calculus formalising the semantics of packages and pickling.

Dynamic Translucency with Abstraction Kinds and Higher-Order Coercions

When a module language is combined with forms of non-parametric type analysis, abstract types require an opaque dynamic representation in order to maintain abstraction safety. As an idealisation of such a module language, we present a foundational calculus that combines higher-order type generation, modelling type abstraction, with singleton kinds, modelling translucency. In this calculus, type analysis can dynamically exploit translucency, without breaking abstraction. Abstract types are classified by a novel notion of abstraction kinds. These are analogous to singletons, but instead of inducing equivalence they induce an isomorphism that is witnessed by explicit type coercions on the term level. To encompass higher-order forms of translucent abstraction, we give an account for higher-order coercions in a rich type system with higher-order polymorphism and dependent kinds. The latter necessitate the introduction of an analogous notion of kind coercions on the type level. Finally, we give an abstraction-safe encoding of ML-style module sealing in terms of higher-kinded type generation and higher-order coercion.

Status report: hot pickles, and how to serve them

The need for flexible forms of serialisation arises under many circumstances, e.g. for doing high-level inter-process communication or to achieve persistence. Many languages, including variants of ML, thus offer pickling as a system service, but usually in a both unsafe and inexpressive manner, so that its use is discouraged.In contrast, safe generic pickling plays a central role in the design and implementation of Alice ML: components are defined as pickles, and modules can be exchanged between processes using pickling. For that purpose, pickling has to be higher-order and typed (HOT), i.e. embrace code mobility and involve runtime type checks for safety. We show how HOT pickling can be realised with a modular architecture consisting of multiple abstraction layers for separating concerns, and how both language and implementation benefit from a design consistently based on pickling.

Generativity and dynamic opacity for abstract types (extended version)

The standard formalism for explaining abstract types is existential quantification. While it provides a sufficient model for type abstraction in entirely statically typed languages, it proves to be too weak for languages enriched with forms of dynamic typing, where parametricity is violated. As an alternative approach to type abstraction that addresses this shortcoming we present a calculus for dynamic type generation. It features an explicit construct for generating new type names and relies on coercions for managing abstraction boundaries between generated types and their designated representation. Sealing is represented as a generalized form of these coercions. The calculus maintains abstractions dynamically without restricting type analysis.

Dynamic opacity for abstract types

Existential types are the standard formalisation of abstract types. While this formulation is sufficient in entirely statically typed languages, it proves to be too weak for languages enriched with forms of dynamic typing: in the presence of operations performing type analysis, the abstraction barrier erected by the static typing rules for existential types is no longer impassable, because parametricity is violated. We present a light-weight calculus for polymorphic languages with abstract types that addresses this shortcoming. It features a variation of existential types that retains most of the simplicity of standard existentials. It relies on modified scoping rules and explicit coercions between the quantified variable and its witness type.