Modular Bialgebraic Semantics and Algebraic Laws

The ability to independently describe operational rules is indispensable for a modular description of programming languages. This paper introduces a format for open-ended rules and proves that conservatively adding new rules results in well-behaved translations between the models of the operational semantics. Silent transitions in our operational model are truly unobservable, which enables one to prove the validity of algebraic laws between programs. We also show that algebraic laws are preserved by extensions of the language and that they are substitutive. The work presented in this paper is developed within the framework of bialgebraic semantics.