Structural Operational Semantics for Computational Effects

Abstract:

In seeking a unified study of computational effects, a fundamental task is to give a unified structural operational semantics, together with an adequate denotational semantics for it, in such a way that, for the leading examples of computational effects, the general definitions are consistent with the usual operational semantics for the relevant effects. One can readily produce a unified operational semantics that works fine for examples that include various forms of nondeterminism and probabilistic nondeterminism. But that simple semantics fails to yield a sensible result in the vitally important case of state or variants of state. The problem is that one must take serious account of coalgebraic structure. I shall not formally enunciate a general operational semantics and adequacy theorem in this talk, but I shall explain the category theory that supports such a semantics and theorem. I shall investigate, describe, and characterise a kind of tensor of a model and a comodel of a countable Lawvere theory, calculating it in leading examples, primarily involving state. Ultimately, this research supports a distinction between what one might call coalgebraic effects, such as state, and algebraic effects, such as nondeterminism