Contexts have been proposed as a means of performing strictness analysis on non-flat domains. Roughly speaking, a context describes how much a sub-expression will be evaluated by the surrounding program. This paper shows how contexts can be represented using the notion of projection from domain theory. This is clearer than the previous explanation of contexts in terms of continuations. In addition, this paper describes finite domains of contexts over the non-flat list domain. This means that recursive context equations can be solved using standard fixpoint techniques, instead of the algebraic manipulation previously used. Praises of lazy functional languages have been widely sung, and so have some curses. One reason for praise is that laziness supports programming styles that are inconvenient or impossible otherwise [Joh87, Hug84, Wad85a]. One reason for cursing is that laziness hinders efficient implementation. Still, acceptable efficiency for lazy languages is at last being achieved...

Interpretation of Reference Counting The semantics presented thus far is exact, and thus evaluating a particular reference count may not terminate, any more than a program in the standard semantics would. For use by a compiler we must choose a suitable abstraction (i.e., approximation) that will guarantee termination yet still provide useful information about the true reference counts. For us a suitable abstraction is one in which the inferred reference count is at least as great as the true one; i.e., we wish to err on the side of thinking there are more pointers to an object than there actually are. In this section we methodically develop such an abstraction in which: (1) the base domains are abstracted to powersets of finite approximations, (2) the primitive functions are abstracted similarly, (3) an abstract interpretation is thus induced on R p and R, and finally (4) a collecting interpretation of expressions is developed. 4.1 Preliminaries To set up things to come, we first gi...

We propose a theoretical framework for adding assignments and dynamic data to functional languages without violating their semantic properties. This differs from semi-functional languages like Scheme and ML in that values of expressions remain static and side-effect-free. A new form of abstraction called observer is designed to encapsulate state-oriented computation from the remaining purely applicative computation. The type system ensures that observers are combined linearly, allowing an implementation in terms of a global store. The utility of this extension is in manipulating shared dynamic data embedded in data structures. Evaluation of well-typed programs is Church-Rosser. Thus, programs produce the same results whether an eager or lazy evaluation order is used (assuming termination). A simple, sound logic permits reasoning about well-typed programs. The benefits of this work include greater expressive power and efficiency (compared to applicative languages), while retaining simplicity of reasoning.

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DATA TYPES A. Comparing Type Objects There has been as much confusion over type identity as there has been over object identity, although the type identity problem is usually referred to as the type equivalence problem [Aho86,s.6.3] [Wegbreit74] [Welsh77]. The type identity problem is to determine when two types are equal, so that type checking can be done in a programming language. 22 Algol-68 takes the point of view of "structural" equivalence, in which nonrecursive types that are built up from primitive types using the same type constructors in the same order should compare equal, while Ada takes the point of view of "name" equivalence, in which types are equivalent if and only if they have the same name. We will ignore the software engineering issues of which kind of type equivalence makes for better-engineered programs, and focus on the basic issue of type equivalence itself. We note that if a type system offers the type TYPE---i.e., it offers first-class representations of typ...

Copy elimination is an important optimization for compiling functional languages. Copies arise because these languages lack the concepts of state and variable; hence updating an object involves a copy in a naive implementation. Copies are also possible if proper targeting has not been carried out inside functions and across function calls. Targeting is the proper selection of a storage area for evaluating an expression. By abstracting a collection of functions by a target operator, we compute targets of function bodies that can then be used to define an optimized interpreter to eliminate copies due to updates and copies across function calls. The language we consider is typed lambda calculus with higherorder functions and special constructs for array operations. Our approach can eliminate copies in divide and conquer problems like quicksort and bitonic sort that previous approaches could not handle. We also present some results of implementing a compiler for a single assignment language called SAL on some small but tough programs. Our results indicate that it is possible to approach a performance comparable to imperative languages like Pascal. 1

Existing techniques for garbage collection and machine code optimizations can interfere with each other. The inability to fully optimize code in a garbage-collected system is a hidden cost of garbage collection. One solution to this problem is proposed; an inexpensive protocol that permits most optimizations and garbage collection to coexist. A second approach to this problem and a separate problem in its own right is to reduce the need for garbage collection. This requires analysis of storage lifetime. Inferring storage lifetime is di#cult in a language with nested and recursive data structures, but it is precisely these languages in which garbage collection is most useful. An improved analysis for "storage containment" is described. Containment information can be represented in a directed graph. The derivation of this graph falls into a monotone data-flow analysis framework; in addition, the derivation has the Church-Rosser property. The graphs produced in the analysis of a value-a...

this paper is the first to make the connection with the literature on variable-binding environments.

This paper proposes a new solution, which is a variant on the "monolothic" approach to array operations. The new solution is also not completely satisfactory, but does have advantages complementary to other proposals. It makes a class of programs easy to express, notably those involving the construction of histograms. It also allows for parallel implementations without the need to introduce non-determinism. The work reported here was motivated by discussions at the Workshop on Graph Reduction, of which this is the proceedings. In particular, it was motivated by the contributions of Arvind and Paul Hudak (see this volume), and especially Arvind's observation that the histogram problem is difficult to solve in a satisfactory way. After the first draft of this paper was written, I discovered that Simon Peyton Jones independently suggested the same idea, also prompted by one of Arvind's talks. After the second draft was written, I discovered that Guy Steele and Daniel Hillis use a very similar notion in Connection Machine Lisp [SH86]. Apparently the simple innovation described in this paper is an idea whose time has come. This paper is organized as follows. Section 1 briefly surveys previously proposed array operations. Section 2 introduces the new operation. Section 3 gives a small example of its use. Section 4 discusses two variations on the array operation. Section 5 concludes. 1 Background