An ideal model for recursive polymorphic types
Information and Control
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Polymorphic type inference and containment
Information and Computation - Semantics of Data Types
COLOG-88 Proceedings of the international conference on Computer logic
Type inference with recursive types: syntax and semantics
Information and Computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Basic proof theory
Information and Computation
Coinductive axiomatization of recursive type equality and subtyping
Fundamenta Informaticae - Special issue: typed lambda-calculi and applications, selected papers
A sequent calculus for subtyping polymorphic types
Information and Computation - Special issue on FLOC '96
Recursive Types Are not Conservative over F
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Reasoning in Interval Temporal Logic
Proceedings of the Carnegie Mellon Workshop on Logic of Programs
Recursive Definitions in Type Theory
Proceedings of the Conference on Logic of Programs
The Subtyping Problem for Second-Order Types is Undecidable
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Subtyping Recursive Types in Kernel Fun - Abstract
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Prolegomena to Dynamic Epistemic Preference Logic
New Frontiers in Artificial Intelligence
Measurement-theoretic foundation of preference-based dyadic deontic logic
LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
Hi-index | 0.00 |
We introduce new modal logical calculi that describe subtyping properties of Cartesian product and disjoint union type constructors as well as mutually recursive types defined using those type constructors.Basic logic of subtyping S extends classical propositional logic by two new binary modalities ⊗ and ⊕. An interpretation of S is a function that maps standard connectives into set-theoretical operations (intersection, union, and complement) and modalities into Cartesian product and disjoint union type constructors. This allows S to capture many subtyping properties of the above type constructors. We also consider logics Sρ and Sρω that incorporate into S mutually recursive types over arbitrary and well-founded universes correspondingly.The main results are completeness of the above three logics with respect to appropriate type universes. In addition, we prove Cut elimination theorem for S and establish decidability of S and Sρω.