Abstract

I shall demonstrate how we can transfer established notions from algebra (e.g. centralisers and stabilisers in group theory) to programming languages with effects (like store, exceptions, and continuations).

Establishing connections with Moggi's "notions of computation", I shall relate these algebraic notions with properties of strong monads (like commutativity, affineness, and relevance).

Using generalised Honda/Yoshida Games as an example, I shall a present a newly-born project that applies these algebraic notions to fully abstract models of first-class continuations and higher-order store.