Non-structural subtype entailment in automata theory

Decidability of non-structural subtype entailment is a long standing open problem in programming language theory. In this paper, we apply automata theoretic methods to characterize the problem equivalently by using regular expressions and word equations. This characterization induces new results on nonstructural subtype entailment, constitutes a promising starting point for further investigations on decidability, and explains for the first time why the problem is so difficult. The difficulty is caused by implicit word equations that we make explicit.

[1]  François Pottier,et al.  Simplifying subtyping constraints , 1996, ICFP '96.

[2]  Jens Palsberg,et al.  A type system equivalent to flow analysis , 1995, TOPL.

[3]  Fritz Henglein,et al.  Constraint Automata and the Complexity of Recursive Subtype Entailment , 1998, ICALP.

[4]  Prateek Mishra,et al.  Type Inference with Subtypes , 1990, Theor. Comput. Sci..

[5]  John C. Mitchell,et al.  Type inference with simple subtypes , 1991, Journal of Functional Programming.

[6]  Jens Palsberg,et al.  Efficient recursive subtyping , 1992, POPL '93.

[7]  Ralf Treinen,et al.  Predicate Logic and Tree Automata with Tests , 2000, FoSSaCS.

[8]  Joachim Niehren,et al.  The first-order theory of ordering constraints over feature trees , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[9]  Ju M Važenin,et al.  Decidability of the Positive Theory of a Free Countably Generated Semigroup , 1983 .

[10]  Scott F. Smith,et al.  Sound polymorphic type inference for objects , 1995, OOPSLA.

[11]  Jens Palsberg,et al.  Efficient inference of partial types , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[12]  G. Makanin.  The Problem of Solvability of Equations in a Free Semigroup , 1977 .

[13]  François Pottier,et al.  A framework for type inference with subtyping , 1998, ICFP '98.

[14]  Klaus U. Schulz,et al.  Makanin's Algorithm for Word Equations - Two Improvements and a Generalization , 1990, IWWERT.

[15]  Jakob Rehof,et al.  The complexity of simple subtyping systems , 1998, Technical report / University of Copenhagen / Datalogisk institut.

[16]  Joachim Niehren,et al.  The first-order theory of subtyping constraints , 2002, POPL '02.

[17]  Scott F. Smith,et al.  Type inference for recursively constrained types and its application to OOP , 1995, MFPS.

[18]  Jakob Rehof.  Minimal typings in atomic subtyping , 1997, POPL '97.

[19]  Joachim Niehren,et al.  Entailment of atomic set constraints is PSPACE-complete , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[20]  François Pottier,et al.  Type Inference in the Presence of Subtyping: from Theory to Practice , 1998 .

[21]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[22]  Joachim Niehren,et al.  Entailment of Non-structural Subtype Constraints , 1999, ASIAN.

[23]  Joachim Niehren,et al.  Non-structural subtype entailment in automata theory , 2003, Inf. Comput..

[24]  Wojciech Plandowski,et al.  Satisfiability of word equations with constants is in PSPACE , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[25]  Luca Cardelli,et al.  Subtyping recursive types , 1991, POPL '91.

[26]  Fritz Henglein,et al.  The complexity of subtype entailment for simple types , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[27]  Franz Baader,et al.  Unification in the Union of Disjoint Equational Theories: Combining Decision Procedures , 1992, CADE.