Abstract not found

We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the Curry-Howard isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cut-elimination.

The syntactic theories of control and state are conservative extensions of the v -calculus for equational reasoning about imperative programming facilities in higher-order languages. Unlike the simple v -calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higher-order programming languages. The new theories subsume the original calculi of control and state and satisfy the usual Church-Rosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs. 1 The syntactic theories of control and state Most -calculus-based programming languages provide imperative programming facilities such as assignment statements, exceptions, and continuations. Typical examples are ML [16], Schem...

Introduction The commonly accepted basis for functional programming is the -calculus; and it is folklore that the -calculus is the prototypical functional language in puri ed form. But what is the -calculus? The syntax is simple and classical; variables, abstraction and application in the pure calculus, with applied calculi obtained by adding constants. The further elaboration of the theory, covering conversion, reduction, theories and models, is laid out in Barendregt's already classical treatise [Bar84]. It is instructive to recall the following crux, which occurs rather early in that work (p. 39): Meaning of -terms: rst attempt The meaning of a -term is its normal form (if it exists). All terms without normal forms are identi ed. This proposal incorporates such a simple and natural interpretation of the -calculus as

The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with first-class labels and jumps. We show that the well-known formulae-astypes correspondence, which relates a constructive proof of a formula ff to a program of type ff, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting "classical programs" --- programs of type ff, where ff holds classically, but not constructively --- is illustrated by the definition of conjunctive, disjunctive, and existential types using standard classical definitions. We also prove that all evaluations of typed terms in Idealized Scheme are finite.

We present an actor language which is an extension of a simple functional language, and provide a precise operational semantics for this extension. Actor configurations represent open distributed systems, by which we mean that the specification of an actor system explicitly takes into account the interface with external components. We study the composability of such systems. We define and study various notions of testing equivalence on actor expressions and configurations. The model we develop provides fairness. An important result is that the three forms of equivalence, namely, convex, must, and may equivalences, collapse to two in the presence of fairness. We further develop methods for proving laws of equivalence and provide example proofs to illustrate our methodology.

The Standard ML of New Jersey compiler has been under development for five years now. We have developed a robust and complete environment for Standard ML that supports the implementation of large software systems and generates efficient code. The compiler has also served as a laboratory for developing novel implementation techniques for a sophisticated type and module system, continuation based code generation, efficient pattern matching, and concurrent programming features.

The views and conclusions contained in this document are those of the authors and should not be interpreted as representing o cial policies, either expressed or implied, of the Advanced Research Projects Agency or the U.S. Government. Any opinions, ndings, and conclusions or recommendations expressed in this material are those of the We study the typing properties of closure conversion for simply-typed and polymorphic-calculi. Unlike most accounts of closure conversion, which only treat the untyped-calculus, we translate well-typed source programs to well-typed target programs. This allows later compiler phases to take advantage of types for representation analysis and tag-free garbage collection, and it facilitates correctness proofs. Our account of closure conversion for the simply-typed language takes advantage of a simple model of objects by mapping closures to existentials. Closure conversion for the polymorphic language requires additional type machinery, namely translucency in the style of Harper and Lillibridge's module calculus, to express the type of a closure.

Today's type-safe low-level languages rely on garbage collection to recycle heap-allocated objects safely. We present LTAL, a safe, low-level, yet simple language that "stands on its own": it guarantees safe execution within a fixed memory space, without relying on external run-time support. We demonstrate the expressiveness of LTAL by giving a type-preserving compiler for the functional core of ML. But this independence comes at a steep price: LTAL's type system imposes a draconian discipline of linearity that ensures that memory can be reused safely, but prohibits any useful kind of sharing. We present the results of experiments with a prototype LTAL system that show just how high the price of linearity can be.

This paper describes the principles underlying an efficient implementation of a lazy functional language, compiling to code for ordinary computers. It is based on combinator-like graph reduction: the user defined functions are used as rewrite rules in the graph. Each function is compiled into an instruction sequence for an abstract graph reduction machine, called the G-machine, the code reduces a function application graph to its value. The G-machine instructions are then translated into target code. Speed improvements by almost two orders of magnitude over previous lazy evaluators have been measured; we provide some performance figures.