We present a type theory for higher-order modules that accounts for many central issues in module system design, including translucency, applicativity, generativity, and modules as first-class values. Our type system harmonizes design elements from previous work, resulting in a simple, economical account of modular programming. The main unifying principle is the treatment of abstraction mechanisms as computational effects. Our language is the first to provide a complete and practical formalization of all of these critical issues in module system design.

A hierarchical module system is an effective tool for structuring large programs. Strictly hierarchical module systems impose an acyclic ordering on import dependencies among program units. This can impede modular programming by forcing mutually-dependent components to be consolidated into a single module. Recently there have been several proposals for module systems that admit cyclic dependencies, but it is not clear how these proposals relate to one another, nor how one might integrate them into an expressive module system such as that of ML.To address this question we provide a type-theoretic analysis of the notion of a recursive module in the context of a "phase-distinction" formalism for higher-order module systems. We extend this calculus with a recursive module mechanism and a new form of signature, called a recursively dependent signature , to support the definition of recursive modules. These extensions are justified by an interpretation in terms of more primitive language constructs. This interpretation may also serve as a guide for implementation.

This paper presents two techniques for improving garbage collection performance: generational stack collection and profile-driven pretenuring. The first is applicable to stack-based implementations of functional languages while the second is useful for any generational collector. We have implemented both techniques in a generational collector used by the TIL compiler (Tarditi, Morrisett, Cheng, Stone, Harper, and Lee 1996), and have observed decreases in garbage collection times of as much as 70% and 30%, respectively.Functional languages encourage the use of recursion which can lead to a long chain of activation records. When a collection occurs, these activation records must be scanned for roots. We show that scanning many activation records can take so long as to become the dominant cost of garbage collection. However, most deep stacks unwind very infrequently, so most of the root information obtained from the stack remains unchanged across successive garbage collections. Generational stack collection greatly reduces the stack scan cost by reusing information from previous scans.Generational techniques have been successful in reducing the cost of garbage collection (Ungar 1984). Various complex heap arrangements and tenuring policies have been proposed to increase the effectiveness of generational techniques by reducing the cost and frequency of scanning and copying. In contrast, we show that by using profile information to make lifetime predictions, pretenuring can avoid copying data altogether. In essence, this technique uses a refinement of the generational hypothesis (most data die young) with a locality principle concerning the age of data: most allocations sites produce data that immediately dies, while a few allocation sites consistently produce data that survives many collections.

Ordered type theory is an extension of linear type theory in which variables in the context may be neither dropped nor re-ordered. This restriction gives rise to a natural notion of adjacency. We show that a language based on ordered types can use this property to give an exact account of the layout of data in memory. The fuse constructor from ordered logic describes adjacency of values in memory, and the mobility modal describes pointers into the heap. We choose a particular allocation model based on a common implementation scheme for copying garbage collection and show how this permits us to separate out the allocation and initialization of memory locations in such a way as to account for optimizations such as the coalescing of multiple calls to the allocator.

Formal constructive type theory has proved to be an effective language for mechanized proof. By avoiding non-constructive principles, such as the law of the excluded middle, type theory admits sharper proofs and broader interpretations of results. From a computer science perspective, interest in type theory arises from its applications to programming languages. Standard constructive type theories used in mechanization admit computational interpretations based on meta-mathematical normalization theorems. These proofs are notoriously brittle; any change to the theory potentially invalidates its computational meaning. As a case in point, Voevodsky's univalence axiom raises questions about the computational meaning of proofs. We consider the question: Can higher-dimensional type theory be construed as a programming language? We answer this question affirmatively by providing a direct, deterministic operational interpretation for a representative higher-dimensional dependent type theory with higher inductive types and an instance of univalence. Rather than being a formal type theory defined by rules, it is instead a computational type theory in the sense of Martin-Löf's meaning explanations and of the NuPRL semantics. The definition of the type theory starts with programs; types are specifications of program behavior. The main result is a canonicity theorem stating that closed programs of boolean type evaluate to true or false.