Dependent Intersection: A New Way of Defining Records in Type Theory
by Alexei Kopylov
Proceedings of 18th Annual IEEE Symposium on Logic in Computer Science.
Records and dependent records are a powerful tool for programming, representing mathematical concepts, and program verification. In the last decade several type systems with records as primitive types were proposed. The question is arisen: whether it is possible to define record type in existent type theories using standard types without introducing new primitives.
It was known that independent records can be defined in type theories with dependent functions or intersection. On the other hand dependent records cannot be formed using standard types. Hickey introduced a complex notion of very dependent functions to represent dependent records. In the current paper we introduce a simpler type constructor dependent intersection, i.e., the intersection of two types, where the second type may depend on elements of the first one (do not confuse it with the intersection of a family of types). This new type constructor allows us to define dependent records in a very simple way and also inherently interesting on its own.
bibTex ref: Kop03