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Reviewer: Robert D. Tennent

From the Introduction: Higher order languages present difficult challenges for any style of semantics, be it axiomatic, denotational, or operationsl. For example, an axiomatic semantics of higher order procedures which is sound, expressive and usable has proved elusive. Another well-known example is the difficulty of finding mathematical structures which yield denotational semantics that are both compositional and agree with the observable behaviour of programs. The challenge of higher order languages for operational semantics is somewhat different. In contrast to the axiomatic and denotational approaches, it is relatively easy to give inductively defined, structural operational semantics. What is not so easy is to develop the mathematical properties and applications of such operational definitions. The articles in this book discuss various techniques for achieving such a development. This collection of articles gives a good picture of the current state of the art of using operational semantics to reason about programs. The techniques discussed include extensionality principles, bisimulations and other relational approaches, a method for proving congruences due to Howe [1], analogues of denotational-semantic techniques, such as logical relations and fixed-point induction, and methods adapted from lambda calculi. [1] Howe, D. J. Proving congruence of bisimulation in functional programming languages. Information and Computation, vol. 124(2), 103--112 (1966).

Reviewer: Gudula Rünger

According to the preface, this book “is a collection of articles about recent developments in operational semantics for higher order programming languages, by some of the leading researchers in the field. The idea for the book arose at the workshop on Higher Order Operational Techniques in Semantics (HOOTS) that took place in October 1995.…The nine contributions to the volume are original articles which develop in depth many of the themes introduced at the workshop.” After the preface and an introduction by the editors, there are nine chapters, one for each of the research papers: “Operational Equivalences for Untyped and Polymorphic Object Calculi,” by A. G. Gordon; “Semantics for Core Concurrent ML Using Computation Types,” by A. Jeffrey; “Relational Reasoning about Contexts,” by S. B. Lassen; “Labelling Techniques and Typed Fixed-Point Operators,” by J. C. Mitchell, M. Hoang, and B. T. Howard; “Semantics of Memory Management for Polymorphic Languages,” by G. Morrisett and R. Harper; “Operational Reasoning for Functions with Local States,” by A. M. Pitts and I. D. B. Stark; “Improvement Theory and Its Applications,” by D. Sands; “The Coverage of Operational Semantics,” by S. F. Smith; and “Reasoning about Functions with Effects,” by C. Talcott. The introduction gives a brief overview of recent contributions to operational semantics; higher-order languages; and aims, methods, and techniques in this area. The topics of the papers are set in a wider context, and their aims and methods are given. The papers by Gordon, Jeffrey, Lassen, Pitts and Stark, and Talcott are aimed at proving properties of programs. Correctness of interpreters and compilers is addressed in the papers by Jeffrey, Morrisett and Harper, and Smith. Both the Morrisett and Harper paper and that of Sands consider questions of efficiency. Context lemmas and extensionality principles are used by Talcott and by Pitts and Stark. Bisimulation is used by Pitts and Stark and by Gordon. Both Gordon's and Jeffrey's papers use Howe's method for proving congruence. Relational proof techniques are used in the chapters by Lassen and Sands. Lassen, Pitts and Stark, and Smith use analogs of domain-theoretic methods. Methods from the lambda calculus are applied by Mitchell, Hoang, and Howard. The introduction is written for nonexperts, but the research papers are intended primarily for researchers or people who want to begin research in the field. There is no in dex, and each chapter contains its own references.