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)


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).


Base Type Function Symbol Recursive Call Semantic Labelling Rich Type 
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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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