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Inductive Definitions in the System Coq Rules and Properties
, 1992
"... In the pure Calculus of Constructions, it is possible to represent data structures and predicates using higherorder quantification. However, this representation is not satisfactory, from the point of view of both the efficiency of the underlying programs and the power of the logical system. For ..."
Abstract

Cited by 162 (1 self)
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In the pure Calculus of Constructions, it is possible to represent data structures and predicates using higherorder quantification. However, this representation is not satisfactory, from the point of view of both the efficiency of the underlying programs and the power of the logical system. For these reasons, the calculus was extended with a primitive notion of inductive definitions [8]. This paper describes the rules for inductive definitions in the system Coq. They are general enough to be seen as one formulation of adding inductive definitions to a typed lambdacalculus. We prove strong normalization for a subsystem of Coq corresponding to the pure Calculus of Constructions plus Inductive Definitions with only weak nondependent eliminations.
Typechecking in Pure Type Systems
 Informal proceedings of Logical Frameworks'92
, 1992
"... Introduction This work is motivated by two related problems. The first is to find reasonable algorithms for typechecking Pure Type Systems [Bar91] (PTS); the second is a technical question about PTS, the so called Expansion Postponment property (EP), which is tantalizingly simple but remains unsolv ..."
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Cited by 5 (2 self)
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Introduction This work is motivated by two related problems. The first is to find reasonable algorithms for typechecking Pure Type Systems [Bar91] (PTS); the second is a technical question about PTS, the so called Expansion Postponment property (EP), which is tantalizingly simple but remains unsolved. There are several implementations of formal systems that are either PTS or closely related to PTS. For example, LEGO [LP92] implements the Pure Calculus of Constructions [CH88] (PCC), the Extended Calculus of Constructions [Luo90] and the Edinburgh Logical Framework [HHP87]. ELF [Pfe89] implements LF; CONSTRUCTOR [Hel91] implements arbitrary PTS with finite set of sorts. Are these implementations actually correct? It is not difficult to find a natural efficient algorithm that is provably sound (Section 3), but completeness is more difficult. In fact Jutting has shown typechecking is decidable for all normalizing PTS with a finite set of sorts [vBJ92], but his algorithm, which com