A Proof Theory for Generic Judgments: An extended abstract

  • Authors:
  • Dale Miller;Alwen Tiu

  • Affiliations:
  • -;-

  • Venue:
  • LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
  • Year:
  • 2003

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Abstract

A powerful and declarative means of specifying computationscontaining abstractions involves meta-level, universallyquantified generic judgments. We present a prooftheory for such judgments in which signatures are associatedto each sequent (used to account for eigenvariables ofthe sequent) and to each formula in the sequent (used toaccount for generic variables locally scoped over the formula).A new quantifier, \bigtriangledown, is introduced to explicitly manipulatethe local signature. Intuitionistic logic extendedwith \bigtriangledown satisfies cut-elimination even when the logic is additionallystrengthened with a proof theoretic notion of definitions.The resulting logic can be used to encode naturallya number of examples involving name abstractions, and weillustrate using the \pi-calculus and the encoding of object-levelprovability.