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Dependent Intersection: A New Way of Defining Records in Type Theory

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by Alexei Kopylov
Citations:17 - 2 self
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@MISC{Kopylov_dependentintersection:,
    author = {Alexei Kopylov},
    title = { Dependent Intersection: A New Way of Defining Records in Type Theory},
    year = {}
}

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Abstract

Record types are an important tool for programming and are essential in objectoriented calculi. Dependent record types are proven to be very useful for program specification and verification. Unfortunately, all known embedding of the dependent record type in the type theory had some imperfections. In this paper we present a new 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.

Citations

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31 The MetaPRL Logical Programming Environment - Hickey - 2001
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13 Types in logic, mathematics and programming - Constable - 1997
10 Aleksey Nogin, Alexei Kopylov, et al. MetaPRL home - Hickey
8 Predicate transformers for infinite-state automata in Nuprl type theory. Irish formal methods workshop - Bickford, Hickey - 1999
7 Markov’s principle for propositional type theory - Kopylov, Nogin - 2001
6 Quotient types: A modular approach - Nogin - 2002
5 A Non-type-theoretic De of Martin-Lof's Types - Allen - 1987
4 Preliminary investigation of a calculus with intersection and union types. Unpublished manuscript - Pierce - 1990
3 Objects and theories as very dependent types - Hickey - 1996
2 Betarte and Alvaro Tasistro. Extension of Martin-Löf’s type theory with record types and subtyping - Gustavo - 1998
1 Predicate transformers for in automata in NuPRL type theory - Bickford, Hickey - 1999
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