Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation
Type systems for distributed data structures
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The first-order theory of subtyping constraints
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Entailment with Conditional Equality Constraints
ESOP '01 Proceedings of the 10th European Symposium on Programming Languages and Systems
Non-structural Subtype Entailment in Automata Theory
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Entailment of Non-structural Subtype Constraints
ASIAN '99 Proceedings of the 5th Asian Computing Science Conference on Advances in Computing Science
Atomic Set Constraints with Projection
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
An extension of HM(X) with bounded existential and universal data-types
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Non-structural subtype entailment in automata theory
Information and Computation - TACS 2001
A flow-based approach for variant parametric types
Proceedings of the 21st annual ACM SIGPLAN conference on Object-oriented programming systems, languages, and applications
Type inference and informative error reporting for secure information flow
Proceedings of the 44th annual Southeast regional conference
Detecting format string vulnerabilities with type qualifiers
SSYM'01 Proceedings of the 10th conference on USENIX Security Symposium - Volume 10
Detecting format string vulnerabilities with type qualifiers
SSYM'01 Proceedings of the 10th conference on USENIX Security Symposium - Volume 10
Type systems for distributed data sharing
SAS'03 Proceedings of the 10th international conference on Static analysis
Type inference and strong static type checking for Promela
Science of Computer Programming
Complexity of subtype satisfiability over posets
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
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A subtyping /spl tau//spl les//spl tau/' is entailed by a set of subtyping constraints C, written C |=/spl tau//spl les//spl tau/', if every valuation (mapping of type variables to ground types) that satisfies C also satisfies /spl tau//spl les//spl tau/'. We study the complexity of subtype entailment for simple types over lattices of base types. We show that: deciding C |=/spl tau//spl les//spl tau/' is coNP-complete; deciding C |=/spl alpha//spl les//spl beta/ for consistent, atomic C and /spl alpha/, /spl beta/ atomic can be done in linear time. The structural lower (coNP-hardness) and upper (membership in coNP) bounds as well as the optimal algorithm for atomic entailment are new. The coNP-hardness result indicates that entailment is strictly harder than satisfiability, which is known to be in PTIME for lattices of base types. The proof of coNP-completeness gives an improved algorithm for deciding entailment and puts a precise complexity-theoretic marker on the intuitive "exponential explosion" in the algorithm. Central to our results is a novel characterization of C |=/spl alpha//spl les//spl beta/ for atomic, consistent C. This is the basis for correctness of the linear-time algorithm as well as a complete axiomatization of C |=/spl alpha//spl les//spl beta/ for atomic C by extending the usual proof rules for subtype inference. It also incorporates the fundamental insight for understanding the structural complexity bounds in the general case.