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 expository article discusses recent progress on the problem of giving sufficiently abstract semantics to local-variable declarations in Algol-like languages, especially work using categorical methods.

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Many object-oriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and classes. An important idea that comes to light is that classes are abstract data types, whose theory corresponds to that of existential types. Equational and Hoare-like reasoning methods, and relational parametricity provide powerful formal tools for reasoning about Algol-like object-oriented programs. 1

We present a new semantics for Algol-like languages that combines methods from two prior lines of development: ffl the object-based approach of [21,22], where the meaning of an imperative program is described in terms of sequences of observable actions, and ffl the functor-category approach initiated by Reynolds [24], where the varying nature of the run-time stack is explained using functors from a category of store shapes to a category of cpos. The semantics

Abstract. In this paper, we present a new model of class-based Algollike programming languages inspired by automata-theoretic concepts. The model may be seen as a variant of the ”object-based ” model previously proposed by Reddy, where objects are described by their observable behaviour in terms of events. At the same time, it also reflects the intuitions behind state-based models studied by Reynolds, Oles, Tennent and O’Hearn where the effect of commands is described by state transformations. The idea is to view stores as automata, capturing not only their states but also the allowed state transformations. In this fashion, we are able to combine both the state-based and event-based views of objects. We illustrate the efficacy of the model by proving several test equivalences and discuss its connections to the previous models. 1