Stores as Homomorphisms and Their Transformations: A Uniform Approach to Structured Types in Imperative Languages

We address the problem of giving a clean and uniform mathematical model for handling user deened data types in imperative languages, contrary to the ad-hoc treatment usual in classical denotational semantics. The problem is solved by deen-ing the store as a homomorphic mapping of an algebraic structure of left values modelling containers into another one of right values modelling contents. Consequently store transformations can be deened uniformly on the principle that they are minimal variations of the store embedding some basic intended eeects and compatible with the homomorphic structure of the store.