A domain model characterising strong normalisation

Building on previous work by Coquand and Spiwack [T. Coquand, A. Spiwack, A proof of strong normalisation using domain theory, in: Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science, LICS’06, IEEE Computer Society Press, 2006, pp. 307–316] we construct a strict domain-theoretic model for the untyped λ-calculus with pattern matching and term rewriting which has the property that a term is strongly normalising if its value is not ⊥. There are no disjointness or confluence conditions imposed on the rewrite rules, and under a mild but necessary condition completeness of the method is proven. As an application, we prove strong normalisation for barrecursion in higher types combined with polymorphism and non-deterministic choice.