Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
The lambda-context calculus (extended version)
Information and Computation
Principal types for nominal theories
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
PNL to HOL: From the logic of nominal sets to the logic of higher-order functions
Theoretical Computer Science
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The lambda calculus is fundamental in computer science. It resists an algebraic treatment because of capture-avoidance sideconditions. Nominal algebra is a logic of equality designed for specifications involving binding. We axiomatize the lambda calculus using nominal algebra, demonstrate how proofs with these axioms reflect the informal arguments on syntax and we prove the axioms to be sound and complete. We consider both non-extensional and extensional versions (alpha-beta and alpha-beta-eta equivalence). This connects the nominal approach to names and binding with the view of variables as a syntactic convenience for describing functions. The axiomatization is finite, close to informal practice and it fits into a context of other research such as nominal rewriting and nominal sets.