ACM/IEEE Symposium on Logic in Computer Science

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Twenty-Third Annual IEEE Symposium on

Logic in Computer Science (LICS 2008)

Paper: Combining Generic Judgments with Recursive Definitions (at LICS 2008)

Authors: Andrew Gacek Dale A. Miller Gopalan Nadathur


Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that allow direct, logic-based reasoning about such descriptions: the treatment of atomic judgments as fixed points (recursive definitions) and an encoding of binding constructs via generic judgments. However, the logics encompassing these two features have thus far treated them orthogonally: that is, they do not provide the ability to define object-logic properties that themselves depend on an intrinsic treatment of binding. We propose a new and simple integration of these features within an intuitionistic logic enhanced with induction over natural numbers and we show that the resulting logic is consistent. The pivotal benefit of the integration is that it allows recursive definitions to not just encode simple, traditional forms of atomic judgments but also to capture generic properties pertaining to such judgments. The usefulness of this logic is illustrated by showing how it can provide elegant treatments of object-logic contexts that appear in proofs involving typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.


    author = 	 {Andrew Gacek and Dale A. Miller and Gopalan Nadathur},
    title = 	 {Combining Generic Judgments with Recursive Definitions},
    booktitle =  {Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008)},
    year =	 {2008},
    month =	 {June}, 
    pages =      {33--44},
    location =   {Pittsburgh, PA, USA}, 
    publisher =	 {IEEE Computer Society Press}

Last modified: 2022-10-3113:49
Sam Staton