<title>First-Order Theory of Subtyping Constraints</title>

<author>Zhendong Su</author>

<author>Alexander Aiken</author>

<author>Joachim Niehren</author>

<author>Tim Priesnitz</author>

<author>Ralf Treinen</author>

<comment>TOPLAS. Extended Version of ACM POPL 2002.</comment>

<abstract><p>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.</p></abstract>

<title>First-Order Theory of Subtyping Constraints</title>

<author>Zhendong Su</author>

<author>Alexander Aiken</author>

<author>Joachim Niehren</author>

<author>Tim Priesnitz</author>

<author>Ralf Treinen</author>

<comment>TOPLAS. Extended Version of ACM POPL 2002.</comment>

<abstract><p>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.</p></abstract>