Rule formats for determinism and idempotence

Determinism is a semantic property of (a fragment of) a language that specifies that a program cannot evolve operationally in several different ways. Idempotence is a property of binary composition operators requiring that the composition of two identical specifications or programs will result in a piece of specification or program that is equivalent to the original components. In this paper, we propose (related) meta-theorems for guaranteeing the determinism and idempotence of binary operators. These meta-theorems are formulated in terms of syntactic templates for operational semantics, called rule formats. In order to obtain a powerful rule format for idempotence, we make use of the determinism of certain transition relations in the definition of the format for idempotence. We show the applicability of our formats by applying them to various operational semantics from the literature.