On understanding types, data abstraction, and polymorphism
ACM Computing Surveys (CSUR) - The MIT Press scientific computation series
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Theoretical aspects of object-oriented programming: types, semantics, and language design
Theoretical aspects of object-oriented programming: types, semantics, and language design
An algorithm for type-checking dependent types
Science of Computer Programming - Special issue on mathematics of program construction
Pragmatic subtyping in polymorphic languages
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
ESOP '99 Proceedings of the 8th European Symposium on Programming Languages and Systems
Subtyping Calculus of Construction (Extended Abstract)
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Eta-Expansions in Dependent Type Theory - The Calculus of Constructions
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Pure Type Systems with Subtyping
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A short and flexible proof of Strong Normalization for the Calculus of Constructions
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Implicit Coercions in Type Systems
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
STACS '87 Proceedings of the 4th Annual Symposium on Theoretical Aspects of Computer Science
FoSSaCS '99 Proceedings of the Second International Conference on Foundations of Software Science and Computation Structure, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
| Hi-index | 0.00 |
The Calculus of Inductive Constructions (CIC) is a powerful type system, featuring dependent types and inductive definitions, that forms the basis of proof-assistant systems such as Coq and Lego. We extend CIC with constructor subtyping, a basic form of subtyping in which an inductive type σ is viewed as a subtype of another inductive type Τ if Τ has more elements than σ. It is shown that the calculus is well-behaved and provides a suitable basis for formalizing natural semantics in proof-development systems.