On the undecidability of second-order unification
Information and Computation - Special issue on RTA-98
Nominal Logic: A First Order Theory of Names and Binding
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Decidable and Undecidable Second-Order Unification Problems
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Higher-order unification and matching
Handbook of automated reasoning
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Theoretical Computer Science
Nominal rewriting with name generation: abstraction vs. locality
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Electronic Notes in Theoretical Computer Science (ENTCS)
Information and Computation
Implementing Nominal Unification
Electronic Notes in Theoretical Computer Science (ENTCS)
A polynomial nominal unification algorithm
Theoretical Computer Science
Nominal Unification from a Higher-Order Perspective
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Journal of Logic and Computation
Simplifying the signature in second-order unification
Applicable Algebra in Engineering, Communication and Computing
A formal calculus for informal equality with binding
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Avoiding equivariance in alpha-prolog
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
PNL to HOL: From the logic of nominal sets to the logic of higher-order functions
Theoretical Computer Science
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Nominal logic is an extension of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to lambda-terms, in nominal terms, bindable names, called atoms, and instantiable variables are considered as distinct entities. Moreover, atoms are capturable by instantiations, breaking a fundamental principle of the lambda-calculus. Despite these differences, nominal unification can be seen from a higher-order perspective. From this view, we show that nominal unification can be quadratically reduced to a particular fragment of higher-order unification problems: higher-order pattern unification. We also prove that the translation preserves most generality of unifiers.