Algebraic Theories over Nominal Sets

Details Algebraic Theories over Nominal Sets Algebraic Theories over Nominal Sets

2010-06-15

arxiv.org/abs/1006.3027v1

Computer Science

Logic in Computer Science

16 pages

Scientific paper

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.

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