Nominal logic, a first order theory of names and binding

  • Authors:

  • Andrew M. Pitts

  • Affiliations:

  • University of Cambridge Computer Laboratory, William Gates Building, J.J. Thomson Avenue, Cambridge CB3 0FD, UK

  • Venue:
  • Information and Computation - TACS 2001
  • Year:
  • 2003

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Abstract

This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving lexically scoped binding constructs. It introduces Nominal Logic, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping, for freshness of names, and for name-binding. Its axioms express properties of these constructs satisfied by the FM-sets model of syntax involving binding, which was recently introduced by the author and M.J. Gabbay and makes use of the Fraenkel-Mostowski permutation model of set theory. Nominal Logic serves as a vehicle for making two general points. First, name-swapping has much nicer logical properties than more general, non-bijective forms of renaming while at the same time providing a sufficient foundation for a theory of structural induction/recursion for syntax modulo α-equivalence. Secondly, it is useful for the practice of operational semantics to make explicit the equivariance property of assertions about syntax - namely that their validity is invariant under name-swapping.