This paper is a tutorial introduction to the theory of programming language semantics developed by D. Scott and C. Strachey. The application of the theory to formal language specification is demonstrated and other applications are surveyed. The first language considered, LOOP, is very elementary and its definition merely introduces the notation and methodology of the approach. Then the semantic concepts of environments, stores, and continuations are introduced to model classes of programming language features and the underlying mathematical theory of computation due to Scott is motivated and outlined. Finally, the paper presents a formal definition of the language GEDANKEN.

We propose that the phenomenon of local state may be understood in terms of Strachey's concept of parametric (i.e., uniform) polymorphism. The intuitive basis for our proposal is the following analogy: a non-local procedure is independent of locally-declared variables in the same way that a parametrically polymorphic function is independent of types to which it is instantiated.A connection between parametricity and representational abstraction was rst suggested by J.C. Reynolds. Reynolds used logical relations to formalize this connection in languages with type variables and user-de ned types. We use relational parametricity to construct a model for an Algol-like language in which interactions between local and non-local entities satisfy certain relational criteria. Reasoning about local variables essentially involves proving properties of polymorphic functions. The new model supports straightforward validations of all the test equivalences that have been proposed in the literature for local-variable semantics, and encompasses standard methods of reasoning about data representations. It is not known whether our techniques yield fully abstract semantics. A model based on partial equivalence relations on the natural numbers is also brie y examined.

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