Modular Bialgebraic Semantics and Algebraic Laws

Abstract

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.

Combining Bialgebraic Semantics and Equations

“…Further, in [10] each operator is either specified by an equation or by operational rules, disallowing a specification such as that of the parallel operator in (2). The recent [15] applies the theory of [10] to add silent transitions to their concept of open GSOS laws. This is then used to show that equations are preserved by conservative extensions.…”