Judical Courant. A Module Calculus for Pure Type Systems. In Typed Lambda Calculi and Applications 97, Lecture Notes in Computer Science, pages 112  128. SpringerVerlag, 1997. 17  Home/Search   Document Details and Download   Summary   Related Articles   Check

....responsible for user interface, interactive proof development, etc. Fil00] We discuss implementation choices and important modi cations in Coq mechanisms. From the theoretical point of view, a version of ML style module system suitable for type theory has been proposed by Judical Courant in [Cou97, Cou98]. In his work, an arbitrary pure type system is extended with a calculus of anonymous modules. Courant shows the conservativity of the resulting system over the base PTS and termination and con uence of module reductions. Unfortunately his calculus is too complicated for direct implementation in ....

....modules. The complete set of rules may be found in [Chr03] The basic module expressions are structures, which represent sequences of toplevel Coq entries. For the sake of brevity of module typing rules, we ignore inductive de nitions in this presentation and adopt the convention from [Cou97, Cou98] to represent the toplevel entries as triples: a name, a speci cation and an implementation. The speci cation is used for typing subsequent entries, and the implementation is provided only as a witness of the validity of the speci cation. According to this convention Definition v 1 :e 1 : e 1 ....

Judical Courant. A Module Calculus for Pure Type Systems. In Typed Lambda Calculi and Applications 97, Lecture Notes in Computer Science, pages 112  128. Springer-Verlag, 1997. 26

....this approach blurs the phase distinction between compile time and run time, Courant carefully avoids using equational reasoning on core terms, preserving the decidability of type checking. Courant has managed to adapt his ideas to more general core languages including dependently typed logics[13]. However, the need to perform even limited compile time equational reasoning on module terms is a distinct departure from the rigid phase distinction enjoyed by Standard ML. 56 2.3.4 Miscellaneous Related Work The second part of Tofte s thesis [55] investigates a skeletal, first order modules ....

Judicael Courant. A Module Calculus for Pure Type Systems. In TLCA'97, LNCS, pages 112 --- 128. Springer-Verlag, 1997.

....following [12] we plan to try the use of the j rule as an expansion, instead of as a reduction. In this context, it would also be interesting to see to which extent the works by Nipkow [20] and Klop [19] on higher order rewriting systems could be integrated in our framework. Fourthly, following [13], we also want to introduce modules in our calculus to be able to develop libraries of reusable parameterized proofs. Acknowledgements: We want to thank Maribel Fern andez for her careful reading, and the useful remarks by the anonymous referees. ....

J. Courant. A module calculus for Pure Type Systems. TLCA'97.

....is well de ned. Then, we de ne the measure of a judgment i 1 n i 2 as (i 1 ) i 2 ) For each rule given in gure 4, the premises are clearly smaller than the conclusion. 5 Implementation We extended uf, our prototype implementation of a module calculus over the Calculus of Constructions [Cou97,Cou01] with the constructs and rules of EPECC. This prototype is written in Objective Caml with the help of a homemade tool compiling typing rules into Objective Caml code. uf with polymorphic universes weights about 2800 lines of code. Adding polymorphic universes to uf was quite simple: we added or ....

Judical Courant. A Module Calculus for Pure Type Systems. In Typed Lambda Calculi and Applications 97, Lecture Notes in Computer Science, pages 112  128. Springer-Verlag, 1997.

....the phase distinction [HMM90] hence equality of code has to be tested by the proof checker. Of course, this test is undecidable in usual programming languages. On the contrary, its adaptation to proof systems seems really interesting, as shown in this paper and for an early version of MC 2 [Cou97b] Although MC 2 has much more satisfying metatheoretical properties with respect to reduction, the complexity of its rules is quite similar to the systems of Leroy and Harper and Lillibridge. Harper and Stone recently studied languages with singleton kinds [SH00] Singleton kinds are intended ....

Judicael Courant. A Module Calculus for Pure Type Systems. In Typed Lambda Calculi and Applications 97, Lecture Notes in Computer Science, pages 112 - 128. Springer-Verlag, 1997.

....basis for its use in proofs systems. In this respect, we are currently working on its adaptation to the Calculus of Constructions [CH88] which is quite easy, in spite of the interaction of fi reduction with typing, in order to have a modular proof language well suited to proving modular programs [Cou97]. Since the Calculus of Construction is both a programming language and a proof language, this have the advantage to provide a unified framework, simpler than the Extended ML approach [San90] because of the inherent complexity of the semantics of the SML module system. We also believe our system ....

Judicael Courant. A module calculus for pure type systems. In Typed Lambda Calculi and Applications 97, LNCS. Springer-Verlag, 1997.

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Judical Courant. A Module Calculus for Pure Type Systems. In Typed Lambda Calculi and Applications 97, Lecture Notes in Computer Science, pages 112  128. SpringerVerlag, 1997. 17

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J. Courant. C: A module calculus for Pure Type Systems. Technical Report 1217, CNRS Universite Paris Sud 8623: LRI, June 1999.

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