Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
An ideal model for recursive polymorphic types
Information and Control
Typing and computational properties of lambda expressions
Theoretical Computer Science
Polymorphic type inference and containment
Information and Computation - Semantics of Data Types
F-semantics for type assignment systems
Theoretical Computer Science
Intersection and union types: syntax and semantics
Information and Computation
The simple semantics for Coppe-Dezani-Sallé types
Proceedings of the 5th Colloquium on International Symposium on Programming
Completeness of Type Assignment Systems with Intersection, Union, and Type Quantifiers
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
A cut-free sequent calculus for pure type systems verifying the structural rules of Gentzen/Kleene
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Strictness analysis algorithms based on an inequality system for lazy types
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
| Hi-index | 0.00 |
This paper develops type assignment systems with intersection and union types, and type quantifiers. We show that the known system for these types is not semantically complete. However, the following two hold for a certain class of typing statements, called stable statements, which include all statements without type quantifier: (1) the validity of stable statements for Kripke models is equivalent to that for standard models, (2) if we add two axioms expressing the distributive laws of intersection over union and existential-type quantifier, then the resulting system is complete for Kripke models. As a consequence, the known system with the axioms for distributive laws is complete for standard models if we restrict statements to stable ones. All the results are obtained in a systematic way with sequent-style formulations of type assignment and the cut-elimination property for them.