Abstract
Placing our result in a web of related mechanised results, we give a direct proof that the de Bruijn λ-calculus (à la Huet, Nipkow and Shankar) is isomorphic to an α-quotiented λ-calculus. In order to establish the link, we introduce an “index-carrying” abstraction mechanism over de Bruijn terms, and consider it alongside a simplified substitution mechanism. Relating the new notions to those of the α-quotiented and the proper de Bruijn formalisms draws on techniques from the theory of nominal sets.
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Norrish, M., Vestergaard, R. (2007). Proof Pearl: De Bruijn Terms Really Do Work. In: Schneider, K., Brandt, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74591-4_16
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DOI: https://doi.org/10.1007/978-3-540-74591-4_16
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