Term Charters

Abstract

Expressions in specification and programming languages often extend algebraic terms by additional term formation rules and enlarged evaluation domains. For use in different contexts, the semantics of these expressions must allow for interface modification, that is, evaluation must be compatible with signature translation and with variable renaming. This work introduces term charters as an abstract framework for terms and expressions following the slogan "evaluation is invariant under change of notation". Several examples illustrate the use of term charters. Different term charter representations are discussed and morphisms between term charters are defined. Finally, the relation of term charters with institutions in general and with context institutions in particular is demonstrated.

2-Term Charters.

“…The OCL is a syntactically and semantically heterogeneous language that involves different algebraic and non-algebraic expression constructs as well as different semantic domains for partiality, non-determinism, and non-termination. Although all features can be faithfully captured by term charter domains and term charters as well as put into relation by term charter (domain) morphisms (Knapp & Cengarle 2018), a general procedure for constructively combining different syntactic constructs over different semantic domains is still missing.…”

“…Having illustrated what is needed to formalise the semantics of OCL types and expressions to be evaluated over a single system state, we now provide a rather abstract account of all the ingredients used. On the one hand, the proposed framework (Knapp & Cengarle 2018) of term charter domains and term charters aims at making transparent and precise the required interactions of the various parts of signatures and translations, (algebraic) structures, variables and renamings, values, and evaluation. On the other hand, the abstract formulation offers means to combine different instantiations of the framework for modular language engineering (Knapp & Cengarle 2015).…”

“…In our framework of term charter domains and term charters (Knapp & Cengarle 2018), the domain of evaluation describes values and variables, structures, and the underlying values of structures, all indexed over signatures. A term charter consists of a term constructor, a variable embedding, and evaluation maps for terms over a signature and variables; the interaction of these ingredients is regulated by three axioms for variable evaluation, variable renaming, and signature translations.…”

“…Moreover, term charters give rise to institutions and thus a formulation of OCL by means of term charters makes it possible to integrate also this language into an institution-based modularisation of the UML as a heterogeneous language (Cengarle et al 2008). Furthermore, for modular language design, term charter domains and term charters can be combined systematically keeping up the invariance of evaluation under change of notation (Knapp & Cengarle 2015, 2018.…”