On the relation between sized-types based termination and semantic labelling

Frédéric Blanqui (1) , Cody Roux (2)

1 FORMES - Formal Methods for Embedded Systems
2 PAREO - Formal islands: foundations and applications

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).

Mots clés: rewriting; termination; lambda-calculus; typing; size; semantic labelling; high-order

Domaines: Logique en informatique [cs.LO]

Frédéric Blanqui, Cody Roux. On the relation between sized-types based termination and semantic labelling. 18th EACSL Annual Conference on Computer Science Logic - CSL 09, Sep 2009, Coimbra, Portugal. ⟨inria-00397689⟩