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.

It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation,...

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 Spineless Tagless G-machine is an abstract machine designed to support nonstrict higher-order functional languages. This presentation of the machine falls into three parts. Firstly, we give a general discussion of the design issues involved in implementing non-strict functional languages. Next, we present the STG language, an austere but recognisably-functional language, which as well as a denotational meaning has a well-defined operational semantics. The STG language is the "abstract machine code" for the Spineless Tagless G-machine. Lastly, we discuss the mapping of the STG language onto stock hardware. The success of an abstract machine model depends largely on how efficient this mapping can be made, though this topic is often relegated to a short section. Instead, we give a detailed discussion of the design issues and the choices we have made. Our principal target is the C language, treating the C compiler as a portable assembler. Version 2.5 of this paper (minus appendix) appe...

Abstract. We establish new upperbounds on the complexity ofmultidimensional 3earching. Our results include, in particular, linear-size data structures for range and rectangle counting in two dimensions with logarithmic query time. More generally, we give improved data structures for rectangle problems in any dimension, in a static as well as a dynamic setting. Several ofthe algorithms we give are simple to implement and might be the solutions of choice in practice. Central to this paper is the nonstandard approach followed to achieve these results. At its rootwe find a redefinition ofdata structures interms offunctional specifications.

We present a functional language with a type system such that well typed programs run within stated space-bounds. The language is a strict, first-order variant of ML with constructs for explicit storage management. The type system is a variant of Tofte and Talpin's region inference system to which the notion of sized types, of Hughes, Pareto and Sabry, has been added.

Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper,

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: We develop tools for the rigorous formulation and proof of properties of runtime memory management for a sample programming language based on a linear type system. Two semantics are described, one at a level of observable results of computations and one describing linear connectives in terms of memory-management primitives. The two semantics are proven equivalent and the memory-management model is proven to satisfy fundamental correctness criteria for reference counts. 1 Introduction Although much literature on optimization of programs discusses the interaction of program execution and memory management, one does not often find formal statements and proofs regarding this interaction. For instance, a compiler for a functional language may generate code that updates an array in-place instead of copying the entire array, even though this optimization is not always safe. The compiler writer probably does not prove the optimization is safe: the size and complexity of real compilers is on...

Derivation and verification represent alternate approaches to design. Derivation aims at deriving a "correct by construction" design while verification aims at constructing a post factum "proof of correctness" for a design. However, as researchers and engineers gain design experience in a formal framework, both approaches are emerging as interdependent facets of design. The thesis of this work is that alternate forms of formal reasoning must be integrated if formal methods are to support the natural analytical and generative reasoning that takes place in engineering practice. As a vehicle for this research, the DDD digital design derivation system was implemented to study formal hardware design in an algebraic framework. DDD is a first-order transformation system which mechanizes a basic design algebra for synthesizing digital circuit descriptions from high-level functional specifications. The system is a collection of correctness preserving transformations that promote a topdown desig...