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## Section: New Results

### Termination

F. Blanqui revised his paper on “size-based termination of higher-order rewrite systems” submitted to the Journal of Functional Programming [23]. This paper is concerned with the termination, in Church’ simply-typed λ-calculus, of the combination of β-reduction and arbitrary user-defined rewrite rules fired using matching modulo α-congruence only. Several authors have devised termination criteria for fixpoint-based function definitions using deduction rules for bounding the size of terms inhabiting inductively defined types, where the size of a term is (roughly speaking) the set-theoretical height of the tree representation of its normal form. In the present paper, we extend this approach to rewriting-based function definitions and more general notions of size.

G. Dowek has finished writing a paper on the notion of model and its application to termination proofs for the $\lambda \Pi$-calculus modulo theory. This paper is submitted for publication.