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Nominal Unification
 Theoretical Computer Science
, 2003
"... We present a generalisation of firstorder unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #equivalent, i.e. equal up to renaming bound names. For the a ..."
Abstract

Cited by 52 (20 self)
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We present a generalisation of firstorder unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #equivalent, i.e. equal up to renaming bound names. For the applications we have in mind, we must consider the simple, textual form of substitution in which names occurring in terms may be captured within the scope of binders upon substitution. We are able to take a `nominal' approach to binding in which bound entities are explicitly named (rather than using nameless, de Bruijnstyle representations) and yet get a version of this form of substitution that respects #equivalence and possesses good algorithmic properties. We achieve this by adapting an existing idea and introducing a key new idea. The existing idea is terms involving explicit substitutions of names for names, except that here we only use explicit permutations (bijective substitutions). The key new idea is that the unification algorithm should solve not only equational problems, but also problems about the freshness of names for terms. There is a simple generalisation of the classical firstorder unification algorithm to this setting which retains the latter's pleasant properties: unification problems involving #equivalence and freshness are decidable; and solvable problems possess most general solutions.
Complexity and Implementation of Nominal Algorithms
"... 1 I would like to dedicate this thesis to my loving grandparents and the teachers who believed in me...Acknowledgements I want to express the deepest gratitude to my supervisor, Maribel Fernández, for all the support, the constant help and the dedication she put into teaching me how to be a good res ..."
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1 I would like to dedicate this thesis to my loving grandparents and the teachers who believed in me...Acknowledgements I want to express the deepest gratitude to my supervisor, Maribel Fernández, for all the support, the constant help and the dedication she put into teaching me how to be a good researcher. I wish to be one day, for my students, as nice as she has been for me. I wish to thank particularly Olivier Danvy for having invited me at BRICS in Aarhus. It was a wonderful and very rewarding experience, as much on the research level as the personal level. Without him the part of this thesis about continuations would have been much lighter. I thank Mathieu Boesp ug and Zoé Drey for the great time it was searching and living with them in Aarhus. I wish the stay could have continued more, but reaching the end of the PhD, time was delimited.