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On the Relation between Sized-Types Based Termination and Semantic Labelling

  • Frédéric Blanqui
  • Cody Roux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5771)

Abstract

We investigate the relationship between two independently developed termination techniques. On the one hand, sized-types based termination (SBT) uses types annotated with size expressions and Girard’s reducibility candidates, and applies on systems using constructor matching only. On the other hand, semantic labelling transforms a rewrite system by annotating each function symbol with the semantics of its arguments, and applies to any rewrite system.

First, we introduce a simplified version of SBT for the simply-typed lambda-calculus. Then, we give new proofs of the correctness of SBT using semantic labelling, both in the first and in the higher-order case. As a consequence, we show that SBT can be extended to systems using matching on defined symbols (e.g. associative functions).

Keywords

Base Type Function Symbol Recursive Call Semantic Labelling Rich Type 
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 2009

Authors and Affiliations

  • Frédéric Blanqui
    • 1
  • Cody Roux
    • 2
  1. 1.FIT 3-604Tsinghua University, Haidian DistrictBeijingChina
  2. 2.LORIA, Pareo team, Campus ScientifiqueVandoeuvre-lès-Nancy, CedexFrance

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