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  Dependently Typed Records for Representing Mathematical Structure (2000) [12 citations — 0 self]

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by Robert Pollack
Theorem Proving in Higher Order Logics, TPHOLs 2000
http://www.dcs.ed.ac.uk/~rap/export/records.ps
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Abstract:

Consider a statement about groups "For G a group,... ". A naive approach to formalize this is to unfold the meaning of group, so that every statement about groups begins with

Citations

263 A type-theoretic approach to higher-order modules with sharing – Harper, Lillibridge - 1994
209 Manifest types, modules, and separate compilation – Leroy - 1994
125 Using dependent types to express modular structure – MacQueen - 1986
48 A syntactic theory of type generativity and sharing – Leroy - 1996
30 Coercive subtyping – Luo - 1999
27 The Machine-checked Literate Formalisation of Algebra in Type Theory – Bailey - 1999
27 a Kernel Language for Modules and Abstract Data Types – Lampson, Burstall
27 Typing algorithm in type theory with inheritance – Saïbi - 1997
25 A Module Calculus for Pure Type Systems – Courant - 1997
18 Extension of Martin-Löf’s type theory with record types and subtyping – Betarte, Tasistro - 1998
17 Intuitionistic Type Theory, volume 1 – Martin-Löf - 1984
10 Universes and a general notion of simultaneous inductive-recursive definition in type theory – Dybjer - 1992
10 Record Types and Subtyping in Type Theory, with Applications to the Theory of Programming – Substitution - 1997
8 Dependent Record Types and Formal Abstract Reasoning – Betarte - 1998
7 de Bruijn. Telescopic mappings in typed lambda calculus – G - 1991
6 Dependent coercions – Luo, Soloviev - 1999
5 Modular Structures as Dependent Types in Isabelle – Kammuller - 1999
3 Simple overloading for type theories. Privately circulated notes – Aczel - 1994
2 Algebra with Coq. See User contributions in Coq release [5 – Pottier - 1999