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Typing Algorithm in Type Theory with Inheritance
 Proc of POPL'97
, 1997
"... We propose and study a new typing algorithm for dependent type theory. This new algorithm typechecks more terms by using inheritance between classes. This inheritance mechanism turns out to be powerful: it supports multiple inheritance, classes with parameters and uses new abstract classes FUNCLASS ..."
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Cited by 42 (0 self)
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We propose and study a new typing algorithm for dependent type theory. This new algorithm typechecks more terms by using inheritance between classes. This inheritance mechanism turns out to be powerful: it supports multiple inheritance, classes with parameters and uses new abstract classes FUNCLASS and SORTCLASS (respectively classes of functions and sorts). We also defines classes as records, particularily suitable for the formal development of mathematical theories. This mechanism, implemented in the proof checker Coq, can be adapted to all typed calculus. 1 Introduction In the last years, proof checkers based on type theory appeared as convincing systems to formalize mathematics (especially constructive mathematics) and to prove correctness of software and hardware. In a proof checker, one can interactively build definitions, statements and proofs. The system is then able to check automatically whether the definitions are wellformed and the proofs are correct. Modern systems ar...
Dependently Typed Records for Representing Mathematical Structure
 Theorem Proving in Higher Order Logics, TPHOLs 2000
, 2000
"... this paper appears in Theorem Proving in Higher Order Logics, TPHOLs 2000, c ..."
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Cited by 14 (0 self)
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this paper appears in Theorem Proving in Higher Order Logics, TPHOLs 2000, c