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.

In this paper we introduce a variable typed logic of effects inspired by the variable type systems of Feferman for purely functional languages. VTLoE (Variable Typed Logic of Effects) is introduced in two stages. The first stage is the first-order theory of individuals built on assertions of equality (operational equivalence `a la Plotkin), and contextual assertions. The second stage extends the logic to include classes and class membership. The logic we present provides an expressive language for defining and studying properties of programs including program equivalences, in a uniform framework. The logic combines the features and benefits of equational calculi as well as program and specification logics. In addition to the usual first-order formula constructions, we add contextual assertions. Contextual assertions generalize Hoare's triples in that they can be nested, used as assumptions, and their free variables may be quantified. They are similar in spirit to program modalities in ...

this paper we study the constrained equivalence of programs with effects. In particular, we present a formal system for deriving such equivalences. Constrained equivalence is defined via a model theoretic characterization of operational, or observational, equivalence called strong isomorphism. Operational equivalence, as introduced by Morris [23] and Plotkin [27], treats programs as black boxes. Two expressions are operationally equivalent if they are indistinguishable in all program contexts. This equivalence is the basis for soundness results for program calculi and program transformation theories. Strong isomorphism, as introduced by Mason [14], also treats programs as black boxes. Two expressions are strongly isomorphic if in all memory states they return the same value, and have the same effect on memory (modulo the production of garbage). Strong isomorphism implies operational equivalence. The converse is true for first-order languages; it is false for full higher-order languages. However, even in the higher-order case, it remains an useful tool for establishing equivalence. Since strong isomorphism is defined by quantifying over memory states, rather than program contexts, it is a simple matter to restrict this equivalence to those memory states which satisfy a set of constraints. It is for this reason that strong isomorphism is a useful relation, even in the higher-order case. The formal system we present defines a single-conclusion consequence relation \Sigma ` \Phi where \Sigma is a finite set of constraints and \Phi is an assertion. The semantics of the formal system is given by a semantic consequence relation, \Sigma j= \Phi, defined in terms of a class of memory models for assertions and constraints. The assertions we consider are of the following two forms...

objects Abstract objects exhibit the non-inheritance aspects of object-oriented programming. An abstract object is a function with local store. Abstract objects provide a means of encapsulating features of a structure and controlling access to that structure. The idea is that the local store can only be changed by sending a message to the object. The operations on the encapsulated structure are determined by the messages accepted by the object. We illustrate these ideas for the special case of accumulators. An accumulator object accumulates a sequence of the things sent to it (via a !put; x? message) and responds to a !get? message by returning the sequence collected. If mkac(y) creates an accumulator object with initial contents the elements of y, then it mus satisfy the following three laws: Specification (Accumulator behavior): (put) letfa := mkac(y)gseq(a(!put; x?); e) 12 ' letfa := mkac(append (y; cons (x; Nil)))ge (get) letfa := mkac(y)gletfz := a(!get?)ge ' letfa := mkac(...

In this paper we report progress in the development of methods for reasoning about the equivalence of objects with memory, and the use of these methods to describe sound operations on objects in terms of formal program transformations. We also formalize three different aspects of objects: their specification, their behavior, and their canonical representation. Formal connections among these aspects provide methods for optimization and reasoning about systems of objects. To illustrate these ideas we give a formal derivation of an optimized specialized window editor from generic specifications of its components. A new result in this paper enables one to make use of symbolic evaluation (with respect to a set of constraints) to establish the equivalence of objects. This form of evaluation is not only mechanizable, it is also generalizes the conditions under which partial evaluation usually takes place. 1 Overview In [19] a general challenge for partial evaluation technology was presented ...