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Encoding Abstract Syntax Without Fresh Names

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Abstract

This paper introduces a variant of nominal abstract syntax in which bindable names are represented by normal meta-variables as opposed to a separate class of globally fresh names. Distinct meta-variables can be instantiated with the same concrete name, which we call aliasing. The possible aliasing patterns are controlled by explicit constraints on the distinctness (freshness) of names. This approach has already been used in the nominal meta-programming language αML. We recap that language and develop a theory of contextual equivalence for it. The central result of the paper is that abstract syntax trees (ASTs) involving binders can be encoded into αML in such a way that α-equivalence of ASTs corresponds with contextual equivalence of their encodings. This is novel because the encoding does not rely on the existence of globally fresh names and fresh name generation, which are fundamental to the correctness of the pre-existing encoding of abstract syntax into FreshML.

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  1. Matthew R. Lakin

    Present address: Microsoft Research, Cambridge, UK

Authors and Affiliations

  1. University of Cambridge Computer Laboratory, Cambridge, UK

    Matthew R. Lakin & Andrew M. Pitts

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  1. Matthew R. Lakin
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  2. Andrew M. Pitts
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Correspondence to Matthew R. Lakin.

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Research supported by UK EPSRC grant EP/D000459/1.

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Lakin, M.R., Pitts, A.M. Encoding Abstract Syntax Without Fresh Names. J Autom Reasoning 49, 115–140 (2012). https://doi.org/10.1007/s10817-011-9220-7

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  • DOI: https://doi.org/10.1007/s10817-011-9220-7

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