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\(\hbox {OCL}_\textsf {FO}\): first-order expressive OCL constraints for efficient integrity checking


OCL is the standard language for defining constraints in UML class diagrams. Unfortunately, as we show in this paper, full OCL is so expressive that it is not possible to check general OCL constraints efficiently. In particular, we show that checking general OCL constraints is not only not polynomial, but not even semidecidable. To overcome this situation, we identify \(\hbox {OCL}_\textsf {FO}\), a fragment of OCL which is expressively equivalent to relational algebra (RA). By equivalent we mean that any \(\hbox {OCL}_\textsf {FO}\) constraint can be checked through a RA query (which guarantees that \(\hbox {OCL}_\textsf {FO}\) checking is efficient, i.e., polynomial), and any RA query encoding some constraint can be written as an \(\hbox {OCL}_\textsf {FO}\) constraint (which guarantees expressiveness of \(\hbox {OCL}_\textsf {FO}\)). In this paper we define the syntax of \(\hbox {OCL}_\textsf {FO}\), we concisely determine its semantics through set theory, and we prove its equivalence to RA. Additionally, we identify the core of this language, i.e., a minimal subset of \(\hbox {OCL}_\textsf {FO}\) equivalent to RA.

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    FO stands for first order, since relational algebra is, essentially, first-order logics.


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This work has been partially supported by the Ministerio de Economía y Competitividad, under Project TIN2017-87610-R, and by the Secreteria d’Universitats i Recerca de la Generalitat de Catalunya under 2017 SGR 1749.

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Correspondence to Xavier Oriol.

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Communicated by Dr Manuel Wimmer.

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Franconi, E., Mosca, A., Oriol, X. et al. \(\hbox {OCL}_\textsf {FO}\): first-order expressive OCL constraints for efficient integrity checking. Softw Syst Model 18, 2655–2678 (2019).

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  • OCL
  • Relational algebra
  • Integrity checking