We present an internal language with equivalent expressive power to Standard ML, and discuss its formalization in LF and the machine-checked verification of its type safety in Twelf. The internal language is intended to serve as the target of elaboration in an elaborative semantics for Standard ML in the style of Harper and Stone. Therefore, it includes all the programming mechanisms necessary to implement Standard ML, including translucent modules, abstraction, polymorphism, higher kinds, references, exceptions, recursive types, and recursive functions. Our successful formalization of the proof involved a careful interplay between the precise formulations of the various mechanisms, and required the invention of new representation and proof techniques of general interest.

The programming language Standard ML is an amalgam of two, largely orthogonal, languages. The Core language expresses details of algorithms and data structures. The Modules language expresses the modular architecture of a software system. Both languages are statically typed, with their static and dynamic semantics specified by a formal definition.

Massive amounts of useful data are stored and processed in ad hoc formats for which common tools like parsers, printers, query engines and format converters are not readily available. In this paper, we explain the design and implementation of PADS/ML, a new language and system that facilitates the generation of data processing tools for ad hoc formats. The PADS/ML design includes features such as dependent, polymorphic and recursive datatypes, which allow programmers to describe the syntax and semantics of ad hoc data in a concise, easy-to-read notation. The PADS/ML implementation compiles these descriptions into ML structures and functors that include types for parsed data, functions for parsing and printing, and auxiliary support for user-specified, format-dependent and format-independent tool generation.

ML modules and Haskell type classes have proven to be highly effective tools for program structuring. Modules emphasize explicit configuration of program components and the use of data abstraction. Type classes emphasize implicit program construction and ad hoc polymorphism. In this paper, we show how the implicitlytyped style of type class programming may be supported within the framework of an explicitly-typed module language by viewing type classes as a particular mode of use of modules. This view offers a harmonious integration of modules and type classes, where type class features, such as class hierarchies and associated types, arise naturally as uses of existing module-language constructs, such as module hierarchies and type components. In addition, programmers have explicit control over which type class instances are available for use by type inference in a given scope. We formalize our approach as a Harper-Stone-style elaboration relation, and provide a sound type inference algorithm as a guide to implementation.

In this dissertation I argue that modal type systems provide an elegant and practical means for controlling local resources in spatially distributed computer programs. A distributed program is one that executes in multiple physical or logical places. It usually does so because those places have local resources that can only be used in those locations. Such resources can include processing power, proximity to data, hardware, or the physical presence of a user. Programmers that write distributed applications therefore need to be able to reason about the places in which their programs will execute. This work provides an elegant and practical way to think about such programs in the form of a type system derived from modal logic. Modal logic allows for reasoning about truth from multiple simultaneous perspectives. These perspectives, called "worlds," are identified with the locations in the distributed program. This enables the programming language to be simultaneously aware of the various hosts involved in a program, their

The ML module system is useful for building large-scale programs. The programmer can factor programs into nested and parameterized modules, and can control abstraction with signatures. Yet ML prohibits recursion between modules. As a result of this constraint, the programmer may have to consolidate conceptually separate components into a single module, intruding on modular programming. Introducing recursive modules is a natural way out of this predicament. Existing proposals, however, vary in expressiveness and verbosity. In this paper, we propose a type system for recursive modules, which can infer their signatures. Opaque signatures can also be given explicitly, to provide type abstraction either inside or outside the recursion. The type system is provably decidable, and is sound for a call-by-value semantics. We also gives a solution to the expression problem, in support of our design choices. 1 1

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.

There has been much work in recent years on extending ML with recursive modules. One of the most difficult problems in the development of such an extension is the double vision problem, which concerns the interaction of recursion and data abstraction. In previous work, I defined a type system called RTG, which solves the double vision problem at the level of a System-F-style core calculus. In this paper, I scale the ideas and techniques of RTG to the level of a recursive ML-style module calculus called RMC, thus establishing that no tradeoff between data abstraction and recursive modules is necessary. First, I describe RMC’s typing rules for recursive modules informally and discuss some of the design questions that arose in developing them. Then, I present the formal semantics of RMC, which is interesting in its own right. The formalization synthesizes aspects of both the Definition and the Harper-Stone interpretation of Standard ML, and includes a novel two-pass algorithm for recursive module typechecking in which the coherence of the two passes is emphasized by their representation in terms of the same set of inference rules.

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.

Developing a general component system for a statically typed, object-oriented language is a challenging design problem for two reasons. First, mutually recursive references across components are common in object-oriented programs—an issue that has proven troublesome in the context of component systems for functional and procedural languages. Second, inheritance across component boundaries can cause accidental method overrides. Our recent research shows that a component framework can be constructed for a nominally typed object-oriented language supporting first-class 1 generic types simply by adding appropriate annotations, syntactic sugar, and component-level type-checking. The fundamental semantic building blocks for constructing, type-checking and manipulating components