Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
On universal algebra over nominal sets
Mathematical Structures in Computer Science
Equational presentations of functors and monads
Mathematical Structures in Computer Science
Stone duality for nominal Boolean algebras with И
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Permissive-nominal logic: First-order logic over nominal terms and sets
ACM Transactions on Computational Logic (TOCL)
| Hi-index | 0.00 |
Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work, it has been shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as first-order logic, the λ-calculus or process calculi. Nominal algebra has a semantics in nominal sets (sets with a finitely supported permutation action); previous work proved soundness and completeness. The HSP theorem characterizes the class of models of an algebraic theory as a class closed under homomorphic images, subalgebras and products, and is a fundamental result of universal algebra. It is not obvious that nominal algebra should satisfy the HSP theorem: nominal algebra axioms are subject to so-called freshness conditions which give them some flavour of implication; nominal sets have significantly richer structure than the sets semantics traditionally used in universal algebra. The usual method of proof for the HSP theorem does not obviously transfer to the nominal algebra setting. In this article, we give the constructions which show that, after all, a ‘nominal’ version of the HSP theorem holds for nominal algebra; it corresponds to closure under homomorphic images, subalgebras, products and an atoms-abstraction construction specific to nominal-style semantics.