Stores as homomorphisms and their transformations: A uniform approach to structured types in imperative languages

摘要

We address the problem of giving a clean and uniform mathematical model for handling user- defined data mapes 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 structrure of left values modelling containers into another one of right values modelling contents. Consequently, store transformations can be defined uniformly on the prin- ciple that they are minimal variations of the store embedding some basic intended effects and compatible with the homomorphic structure of the store.