### Institutions: abstract model theory for specification and programmingInstitutions: abstract model theory for specification and programming

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 Author Goguen, Joseph A. ♦ Burstall, Rod M. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1992 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract There is a population explosion among the logical systems used in computing science. Examples include first-order logic, equational logic, Horn-clause logic, higher-order logic, infinitary logic, dynamic logic, intuitionistic logic, order-sorted logic, and temporal logic; moreover, there is a tendency for each theorem prover to have its own idiosyncratic logical system. The concept of $\textit{institution}$ is introduced to formalize the informal notion of “logical system.” The major requirement is that there is a satisfaction relation between models and sentences that is consistent under change of notation. Institutions enable abstracting away from syntactic and semantic detail when working on language structure “in-the-large”; for example, we can define language features for building large logical system. This applies to both specification languages and programming languages. Institutions also have applications to such areas as database theory and the semantics of artificial and natural languages. A first main result of this paper says that any institution such that signatures (which define notation) can be glued together, also allows gluing together theories (which are just collections of sentences over a fixed signature). A second main result considers when theory structuring is preserved by institution morphisms. A third main result gives conditions under which it is sound to use a theorem prover for one institution on theories from another. A fourth main result shows how to extend institutions so that their theories may include, in addition to the original sentences, various kinds of constraint that are useful for defining abstract data types, including both “data” and “hierarchy” constraints. Further results show how to define institutions that allow sentences and constraints from two or more institutions. All our general results apply to such “duplex” and “multiplex” institutions. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1992-01-02 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 39 Issue Number 1 Page Count 52 Starting Page 95 Ending Page 146

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Source: ACM Digital Library