A Rule Format for Unit Elements

Abstract

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Well-Typed Languages are Sound

“…These results offer templates and restrictions to operational semantics specifications that can guarantee that some property holds. Typical work from this line of research have been used for establishing various results for process algebras and mostly in the context of equations modulo bisimilarity and congruence [3,7,13,1]. This paper shares the same strive to ensure properties by design for languages given as input.…”

“…The symbolic type environment contains the typing formulae of the premises of the two rules combined. The symbolic assigned type is that of (1).…”

Proving the validity of equations in GSOS languages using rule-matching bisimilarity

“…A related line of work has been pursued in, for example, Aceto et al (2010), Aceto et al (2010b), Cranen et al (2008) and , which present rule formats that guarantee the soundness of certain algebraic laws over a process language 'by design', provided the SOS rules giving the semantics of certain operators fit that format. This is an orthogonal line of investigation to the one reported in the current paper.…”

Rule formats for determinism and idempotence

“…The meta-theory of SOS provides powerful tools for proving semantic properties for programming and specification languages without investing too much time on the actual proofs; it offers syntactic templates for SOS rules, called rule formats, which guarantee semantic properties once the SOS rules conform to the templates (see, e.g., the references [3,23] for surveys on the meta-theory of SOS). There are various rule formats in the literature for many different semantic properties, ranging from basic properties such as commutativity [21] and associativity [10] of operators, the existence of unit elements [4] and congruence of behavioral equivalences (see, e.g., [15,30]) to more technical and involved ones such as (semi-)stochasticity [18] and non-interference [26]. In this paper, we propose rule formats for two (related) properties, namely determinism and idempotence.…”

“…This paper is part of our ongoing line of research on capturing basic properties of composition operators in terms of syntactic rule formats, exemplified by rule formats for commutativity [21], associativity [10], and left and right unit elements [4].…”