The First-Order Theory of Subtype Constraints
نویسندگان
چکیده
We investigate the first-order theory of subtype 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 result is 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.
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