The first-order theory of subtyping constraints

Authors:
Zhendong Su;Alexander Aiken;Joachim Niehren;Tim Priesnitz;Ralf Treinen
Affiliations:
University of California, Berkeley, CA;University of California, Berkeley, CA;Universität des Saarlandes, Saarbrücken, Germany;Universität des Saarlandes, Saarbrücken, Germany;Université Paris-Sud, F91405 Orsay cedex, France
Venue:
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Year:
2002

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Abstract

We investigate the first-order of subtyping constraints. We show that the first-order theory of non-structural subtyping is undecidable, and we show that in the case where all constructors are either unary or nullary, the first-order theory is decidable for both structural and non-structural subtyping. The decidability results are shown by reduction to a decision problem on tree automata. This work is a step towards resolving long-standing open problems of the decidability of entailment for non-structural subtyping.