program accesses resources in a valid manner. For example, a memory region that has been allocated should be eventually deallocated, and after the deallocation, the region should no longer be accessed. A file that has been opened should be eventually closed. So far, most of the methods to analyze this kind of property have been proposed in rather specific contexts (like studies of memory management and verification of usage of lock primitives), and it was not so clear what is the essence of those methods or how methods proposed for individual problems are related. To remedy this situation, we formalize a general problem of analyzing resource usage as a resource usage analysis problem, and propose a type-based method as a solution to the problem.

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.

E#cient low-level systems need more control over memory than safe high-level languages usually provide. As a result, run-time systems are typically written in unsafe languages such as C. This paper extends previous work on linear types, alias types, regions, and typed garbage collection to give type-safe code more control over memory. The approach is truly low-level: memory consists of a single linear array of words, with load and store operations but no built-in notion of an object. The paper constructs lists and arrays out of the basic linear memory primitives, and then introduces type sequences for building regions of nonlinear data. It then describes a Cheney queue typed garbage collector, implemented safely over regions.

We present a type system that can effectively facilitate the use of types in capturing invariants in stateful programs that may involve (sophisticated) pointer manipulation. With its root in a recently developed framework Applied Type System (ATS), the type system imposes a level of abstraction on program states by introducing a novel notion of recursive stateful views and then relies on a form of linear logic to reason about such views. We consider the design and then the formalization of the type system to constitute the primary contribution of the paper. In addition, we mention a prototype implementation of the type system and then give a variety of examples that attest to the practicality of programming with recursive stateful views.

In this day and age of multicore architectures, programming language support is in urgent need for constructing programs that can take great advantage of machines with multiple cores. We present in this paper an approach to safe multicore programming in ATS, a recently developed functional programming language that supports both linear and dependent types. In particular, we formalize a type system capable of guaranteeing safe manipulation of resources on multicore machines and establish its soundness. We also provide concrete examples as well as experimental results in support of the practicality of the presented approach to multicore programming.

The potential of linear logic in facilitating reasoning on resource usage has long been recognized. However, convincing uses of linear types in practical programming are still rather rare. In this paper, we present a general design to effectively support practical programming with linear types. In particular, we introduce and then formalize a modality, which we refer to as the sharing modality, in support of sharing of linear resources (with no use of locks). We develop the underlying type theory for the sharing modality and establish its soundness based on a notion of types with effects. We also point out an intimate relation between this modality and the issue of code reentrancy. In addition, we present realistic examples to illustrate the use of sharing modality, which are verified in the programming language ATS and thus provide a solid proof of concept.

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.