Mal'cev algebras for universal algebra terms
We discuss formal treatments of composition and terms in universal algebra, propositional logics etc. which may serve as an indispensable base for computer programs capable of term building and term comparison, an important problem in theoretical computer science. After a survey we discuss various Mal'cev algebras introduced for this purpose: preiterative, preiterative with identity, iterative and postiterative. These algebras seem to be simple to implement. We then show how these algebras allow to bring certain universal algebra concepts (as varieties and subvarieties, interpretation and hyperidentities) one conceptual level down. We conclude with a list of properties of preiterative algebras.
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