Date: | 2016, November 15 |
Author: | Mossakowski, Till |
Title: | Institutional Monads |
After last week's talk, this one presents another institution-independent notion that can be used for giving a semantics to queries and answer substitutions.
The notion of signature morphism is basic to the theory of institutions. It provides a powerful primitive for the study of specifications, their modularity and their relations in an abstract setting. The notion of derived signature morphism generalises signature morphisms to more complex constructions, where symbols may be mapped not only to symbols, but to arbitrary terms. The purpose of this work is to study derived signature morphisms in an institution-independent way. We will therefore introduce the notion of an institutional monad. Monads are a category-theoretic generalisation of the notion of term with variables and of substitution.
The motivation is to give an independent semantics to the notion of derived signature morphism, query and substitution in the context of the Distributed Ontology, Model and Specification Language DOL.