Category-sorted algebra-based action semantics

Abstract

In a series of papers, Mosses and Watt define action semantics, a metalanguage for high level, domain-independent formulation of denotational semantics definitions. Action semantics hides details about domain structure (e.g., direct semantics domains vs. continuation semantics domains vs. resumption semantics domains) and coercions (e.g., integers into reals, injections of summands into sum domains) to encourage readability and modifiability. Action semantics notation is of interest as a programming language of itself, for its components (called actions) are polymorphic operators that can be composed in several fundamental ways. We formulate a model for action semantics based on Reynolds' category-sorted algebra. In the model, actions are natural transformations, and the composition operators are compositions in a “category of actions.” We use the model to prove semantic soundness and completeness of a unification-based, decidable type inference algorithm for action semantics expressions.