Structure-Preserving Binary Relations for Program Abstraction

An abstraction is a property-preserving contraction of a program’s model into a smaller one that is suitable for automated analysis. An abstraction must be sound, and ideally, complete. Soundness and completeness arguments are intimately connected to the abstraction process, and approaches based on homomorphisms and Galois connections are commonly employed to define abstractions and prove their soundness and completeness. This paper develops Mycroft and Jones’s proprosal that an abstraction should be stated as a form of structure-preserving binary relation. Mycroft-Jones-style relations are defined, developed, and employed in characterizations of the homomorphism and Galois-connection approaches to abstraction.