Publication details

Saarland University Computer Science

First-Order Theory of Subtyping Constraints

Zhendong Su, Alexander Aiken, Joachim Niehren, Tim Priesnitz, Ralf Treinen

ACM Transactions on Programming Languages and Systems, 2006

We investigate the first-order theory 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. Our results hold for both simple and recursive types. The undecidability result is shown by a reduction from the Post's Correspondence Problem, and the decidability results are shown by a reduction to a decision problem on tree automata. In addition, we introduce the notion of a constrained tree automaton to express non-structural subtype entailment. This work is a step towards resolving long-standing open problems of the decidability of entailment for non-structural subtyping.

Entended Version of POPL 2002

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