Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference 38 April 1999. Springer-Verlag LNCS 1581.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....LLF avoids the conversion problem by restricting the syntax to long terms [Cer96] The equality of the framework is still de ned in terms of reduction. This is possible because the reducts of long terms are long. Goguen proposes an elegant theory based on a typed notion of reduction [Gog94, Gog99]. An operational semantics based on this typed reduction is then shown to be decidable, and 5 CONCLUSION 31 equivalent to a (not manifestly decidable) axiomatization of equality from rst principles such as extensionality. However, being based on reduction, this approach does not decide equality ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177{ 197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....called commuting conversions recover the subformula property for terms in normal form in a system with sum types and a case construct. Diculties arise Based on a draft version of the present article, an extension to a logical framework using dependent types has been carried out by Goguen [Gog99] whose typed operational semantics [Gog95] has been found independently of [vRS95] Interestingly, the initial motivation for the work reported here was a kind of reverse engineering of Goguen s thesis [Gog94] for systems without dependent types. vR96] stated and proved this characterization ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Typed Lambda Calculi and Applications, 4th International Conference, TLCA'99, L'Aquila, Italy, April 7-9, 1999, Proceedings, volume 1581 of Lecture Notes in Computer Science, pages 177-197. Springer Verlag, 1999.

....LLF avoids the # conversion problem by restricting the syntax to # long terms [Cer96] The equality of the framework is still defined in terms of # reduction. This is possible because the # reducts of # long terms are # long. Goguen proposes an elegant theory based on a typed notion of reduction [Gog94, Gog99]. An operational semantics based on this typed reduction is then shown to be decidable, and 5 CONCLUSION 31 equivalent to a (not manifestly decidable) axiomatization of equality from first principles such as extensionality. However, being based on # reduction, this approach does not decide ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177-- 197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....## reduction is confluent only for well typed terms, and subject reduction depends on strengthening, which is di#cult to prove directly. These technical problems with ## reduction have been addressed in work by Salvesen [Sal90] Geuvers [Geu92] and later with a di#erent method by Goguen [Gog99], but nevertheless several problems remain. First, canonical forms are not ## normal forms and so conversion to canonical form must be handled separately. The work by Dowek et al. DHW93] shows how to do this for the Calculus of Constructions, but it is not clear that their approach would scale to ....

....second logical relations argument. We suspect that this may be extended to the case of predicative universes, but the impredicative case is likely to require completely new ideas as discussed in the conclusion. Our approach is similar to the technique of typed operational semantics of Goguen [Gog94, Gog99] in that both take advantage of types during reduction. However, as pointed out by Goguen [Gog99] the development of the complete meta theory of the LF requires the use of an untyped reduction relation. Our techniques avoid this entirely, fulfilling Goguen s conjecture that a complete development ....

[Article contains additional citation context not shown here]

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....In particular, fij reduction is confluent only for well typed terms, and subject reduction depends on strengthening, which is difficult to prove directly. These technical problems with fij reduction have been solved by Salvesen [Sal90] Geuvers [Geu92] and later with a different method by Goguen [Gog99], but nevertheless several problems remain. First, canonical forms are not fij normal forms and so conversion to canonical form must be handled separately. Second, the algorithms implicit in the reduction based accounts are not practical; if two terms are not definitionally equal, we can hope to ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....fij reduction is confluent only for well typed terms, and subject reduction depends on strengthening, which is difficult to prove directly. These technical problems with fij reduction have been addressed in work by Salvesen [Sal90] Geuvers [Geu92] and later with a different method by Goguen [Gog99], but nevertheless several problems remain. First, canonical forms are not fij normal forms and so conversion to canonical form must be handled separately. Second, the algorithms implicit in the reduction based accounts are not practical; if two terms are not definitionally equal, we can hope to ....

....factors. The reason is the flexibility of type directed equality in the simply typed case and the harmony between the definition of the logical relation and the algorithm, both of which are based on the erased types. Our approach is similar to the technique of typed operational semantics of Goguen [Gog94, Gog99] in that both take advantage of types during reduction. However, as pointed out by Goguen [Gog99] the development of the complete metatheory of the LF requires the use of an untyped reduction relation. Our techniques avoid this entirely, fulfilling Goguen s conjecture that a complete development ....

[Article contains additional citation context not shown here]

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....fij reduction is confluent only for well typed terms, and subject reduction depends on strengthening, which is difficult to prove directly. These technical problems with fij reduction have been addressed in work by Salvesen [Sal90] Geuvers [Geu92] and later with a different method by Goguen [Gog99], but nevertheless several problems remain. First, canonical forms are not fij normal forms and so conversion to canonical form must be handled separately. Second, the algorithms implicit in the reduction based accounts are not practical; if two terms are not definitionally equal, we can hope to ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....fij reduction is confluent only for well typed terms, and subject reduction depends on strengthening, which is difficult to prove directly. These technical problems with fij reduction have been addressed in work by Salvesen [Sal90] Geuvers [Geu92] and later with a different method by Goguen [Gog99], but nevertheless several problems remain. First, canonical forms are not fij normal forms and so conversion to canonical form must be handled separately. Second, the algorithms implicit in the reduction based accounts are not practical; if two terms are not definitionally equal, we can hope to ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

....In particular, fij reduction is confluent only for well typed terms, and subject reduction depends on strengthening, which is difficult to prove directly. These technical problems with fij reduction have been solved by Salvesen [Sal90] Geuvers [Geu92] and later with a different method by Goguen [Gog99], but nevertheless several problems remain. First, canonical forms are not fij normal forms and so conversion to canonical form must be handled separately. Second, the algorithms implicit in the reduction based accounts are not practical; if two terms are not definitionally equal, we can hope to ....

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

No context found.

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference 38 April 1999. Springer-Verlag LNCS 1581.

No context found.

Healfdene Goguen. Soundness of the logical framework for its typed operational semantics. In Jean-Yves Girard, editor, Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), pages 177--197, L'Aquila, Italy, April 1999. Springer-Verlag LNCS 1581.

No context found.

Goguen, H. 1999. Soundness of the logical framework for its typed operational semantics. In Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99), J.-Y. Girard, Ed. Springer-Verlag LNCS 1581, L'Aquila, Italy, 177--197.

No context found.

Goguen, Healfdene. (1999). Soundness of the logical framework for its typed operational semantics. International Conference on Typed Lambda Calculi and Applications. L'Aquila, Italy: Springer-Verlag LNCS 1581.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC