Nominal rewriting with name generation: abstraction vs. locality

Nominal rewriting extends first-order rewriting with Gabbay-Pitts abstractors: bound entities are named, matching respects α-conversion and can be directly implemented thanks to the use of freshness constraints. In this paper we study two extensions to nominal rewriting. First we introduce a NEW quantifier for modelling name generation and restriction. This allows us to model higher-order functions involving local state, and has also applications in concurrency theory. The second extension introduces new constraints in freshness contexts. This allows us to express strategies of reduction and has applications in programming language design and implementation. Finally, we study confluence properties of nominal rewriting and its extensions.

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