Action semantics

Action semantics is a framework for the formal specification of semantics of programming languages invented by David Watt and Peter D. Mosses in the 1990s. It is a mixture of denotational, operational and algebraic semantics.

Action Semantics aims to be pragmatic. Action-Semantic Descriptions (ASDs) are designed to scale up to handle realistic programming languages. This is aided by the extensibility and modifiability of ASDs. This helps to ensure that extensions and changes do not require too many changes in the description. This is in contrast to the typical case when extending denotational or operational semantics, which may require reformulation of the entire description.

The Action Semantics framework was originally developed at the University of Aarhus and the University of Glasgow. Groups and individuals around the world have since contributed further to the approach.

An important part of action semantics that gives it a modularity not seen in previous programming language semantics is the use of first-order semantic entities. First-order refers to how, unlike in denotational semantics, where a semantic function can be applied to another semantic function, in action semantics, a semantic entity cannot be applied to another semantic entity of its kind. Furthermore, the semantic entities utilized by action semantics broaden the framework’s ability to describe a programming language’s constructs by serving to denote both program behavior that is independent of any particular implementation and the way in which parts of a program influence the overall performance of the whole. The appropriately named action notation is employed to express the three types of semantic entities found in action semantics: actions, data, and yielders. The central semantic entity in this framework is actions, with data and yielders occupying supplementary roles. More specifically, actions are the mechanisms through which yielders and data are processed. An action, which can occur within another action, is a step-by-step representation of program behavior, where each step accesses current information, changes current information, or does both. Yielders appear within actions and only access current information. A yielder entity is capable of being evaluated, and when it is, the product is a datum entity.

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