Conditional rewrite rules: Confluence and termination
Journal of Computer and System Sciences
Proofs and types
Structural subtyping and the notion of power type
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence by decreasing diagrams
Theoretical Computer Science
Bounded quantification is undecidable
Information and Computation
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Parallel reductions in &lgr;-calculus
Information and Computation
Types and programming languages
Types and programming languages
Subtyping Calculus of Construction (Extended Abstract)
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Subtyping with Singleton Types
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Singleton kinds and singleton types
Singleton kinds and singleton types
Typed operational semantics for higher-order subtyping
Information and Computation
Typed $\lambda$-calculi with one binder
Journal of Functional Programming
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Eliminating distinctions of class: using prototypes to model virtual classes
Proceedings of the 21st annual ACM SIGPLAN conference on Object-oriented programming systems, languages, and applications
Mixin' up the ML module system
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
A calculus for uniform feature composition
ACM Transactions on Programming Languages and Systems (TOPLAS)
Hi-index | 0.00 |
This paper introduces a new approach to type theory called pure subtype systems . Pure subtype systems differ from traditional approaches to type theory (such as pure type systems) because the theory is based on subtyping, rather than typing. Proper types and typing are completely absent from the theory; the subtype relation is defined directly over objects. The traditional typing relation is shown to be a special case of subtyping, so the loss of types comes without any loss of generality. Pure subtype systems provide a uniform framework which seamlessly integrates subtyping with dependent and singleton types. The framework was designed as a theoretical foundation for several problems of practical interest, including mixin modules, virtual classes, and feature-oriented programming. The cost of using pure subtype systems is the complexity of the meta-theory. We formulate the subtype relation as an abstract reduction system, and show that the theory is sound if the underlying reductions commute. We are able to show that the reductions commute locally, but have thus far been unable to show that they commute globally. Although the proof is incomplete, it is ``close enough'' to rule out obvious counter-examples. We present it as an open problem in type theory.