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Structural recursion with locally scoped names

  • ANDREW M. PITTS (a1)

This paper introduces a new recursion principle for inductively defined data modulo α-equivalence of bound names that makes use of Odersky-style local names when recursing over bound names. It is formulated in simply typed λ-calculus extended with names that can be restricted to a lexical scope, tested for equality, explicitly swapped and abstracted. The new recursion principle is motivated by the nominal sets notion of ‘α-structural recursion’, whose use of names and associated freshness side-conditions in recursive definitions formalizes common practice with binders. The new calculus has a simple interpretation in nominal sets equipped with name-restriction operations. It is shown to adequately represent α-structural recursion while avoiding the need to verify freshness side-conditions in definitions and computations. The paper is a revised and expanded version of Pitts (Nominal System T. In Proceedings of the 37th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL 2010 (Madrid, Spain). ACM Press, pp. 159–170, 2010).

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A. M. Pitts & I. D. B. Stark (1993) Observable properties of higher order functions that dynamically create local names, or: What's new? In Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science (Gdańsk, 1993), Lecture Notes in Computer Science, vol. 711. Springer-Verlag, Berlin, pp. 122141.

E. Westbrook , A. Stump & E. Austin (2009) The calculus of nominal inductive constructions: An intensional approach to encoding name-bindings. In Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, LFMTP 2009 (Montreal, Canada), ACM International Conference Proceeding Series. ACM Press, pp. 7483.

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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
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