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Published in:
2006 | OriginalPaper | Chapter
Capture-Avoiding Substitution as a Nominal Algebra
Authors : Murdoch J. Gabbay, Aad Mathijssen
Published in: Theoretical Aspects of Computing - ICTAC 2006
Publisher: Springer Berlin Heidelberg
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Substitution is fundamental to computer science, underlying for example quantifiers in predicate logic and beta-reduction in the lambda-calculus. So is substitution something we define on syntax on a case-by-case basis, or can we turn the idea of ‘substitution’ into a mathematical object?
We exploit the new framework of Nominal Algebra to axiomatise substitution. We prove our axioms sound and complete with respect to a canonical model; this turns out to be quite hard, involving subtle use of results of rewriting and algebra.