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-defined data types in imperative languages, contrary to the ad hoc treatment usual in classical denotational semantics. The problem is solved by defining 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 defined uniformly on the principle that they are minimal variations of the store embedding some basic intended effects and compatible with the homomorphic structure of the store.