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Combining Typing and Size Constraints for Checking the Termination of Higher-Order Conditional Rewrite Systems

  • Frédéric Blanqui (INRIA)
  • Colin Riba (INPL)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)

Abstract

In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like programs. Here, we go one step further by considering conditional rewriting and explicit quantifications and constraints on size annotations. This allows to describe more precisely how the size of the output of a function depends on the size of its inputs. Hence, we can check the termination of more functions. We first give a general type-checking algorithm based on constraint solving. Then, we give a termination criterion with constraints in Presburger arithmetic. To our knowledge, this is the first termination criterion for higher-order conditional rewriting taking into account the conditions in termination.

Keywords

Induction Hypothesis Termination Criterion Function Symbol Recursive Call Proof Assistant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Frédéric Blanqui (INRIA)
    • 1
  • Colin Riba (INPL)
    • 1
  1. 1.LORIACampus ScientifiqueVandoeuvre-lès-NancyFrance

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