Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, TLCA'95, volume 902 of LNCS, pages 186--200, Berlin, 1995. Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....likewise for an extension of the system of generalized applications by a rule of immediate simpli cation . By introducing an in nitely branching inductive rule the method even extends to G odel s T. Introduction Normalization proofs for the simply typed calculus enjoy continuous interest [Gog95, vRS95, vRSSX99] in the literature although the main results of weak and strong normalization have been established quite early by Turing (around 1941, published in [Gan80] and Sanchis [San67] This article employs a proof method that allows to show strong normalization for all typed terms without recourse to ....

....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 correct for pure untyped calculus. ....

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Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer Verlag, 1995.

....likewise for an extension of the system of generalized applications by a rule of immediate simpli cation . By introducing an in nitely branching inductive rule the method even extends to G odel s T. Introduction Normalization proofs for the simply typed calculus enjoy continuous interest [Gog95, vRS95, vRSSX99] in the literature although the main results of weak and strong normalization have been established quite early by Turing (around 1941, published in [Gan80] and Sanchis [San67] This paper employs a proof method that allows to show strong normalization for all typed terms without recourse to ....

....In fact, the lemma is an instance of the following proposition, the generality of which will pay o in section 5. Proposition. Let be a binary relation on the set WF . with 8r 8r :r . r r ) 9r (commutation) Then WF WF . Goguen s typed operational semantics [Gog95], which inspired our work, can be understood as a combination of SN; NF and the normal form function # into one inductive de nition. This argument is crucial to the proof of strong normalization and to our knowledge it is an unavoidable part of any strong normalization proof amenable to a ....

Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer Verlag, 1995.

....cation of modal logics) in the presentation by Frank Pfenning and Hao Chi Wong [PW95] We have chosen this variant because the terms generated by the syntax are simpler than those of [BdP96] PW95] or [DP96] since we have no let construction. The proof follows Healfdene Goguen s method [Gog94, Gog95] of typed operational semantics. It appears to be surprisingly dicult to extend the method to the modal case, because the type system we choose uses context 1 stacks. In particular, we have to extend the notion of typed substitution, which is central to the method, in a nontrivial way. As a ....

....: A, then there is a P such that M , P and N , P . 7 Conclusion We have presented in this paper the proofs of strong normalization, subject reduction, and Church Rosser theorems for a modal calculus S4 [PW95] The proof followed the typed operational semantics method introduced by Goguen [Gog94, Gog95] for the simply typed calculus. We have succeeded in adapting his method despite the fact that our typing rules are not syntaxdriven and we had to deal with context stacks instead of simple contexts. In the course of the proof, we have extracted an interesting notion of typed 29 substitution ....

Healfdene Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer-Verlag, 1995.

....classication of modal logics) in the presentation by Frank Pfenning and Hao Chi Wong [PW95] We have chosen this variant because the terms generated by the syntax are simpler than those of [BdP96] PW95] or [DP96] since we have no let construction. The proof follows Healfdene Goguen s method [Gog94, Gog95], called Typed Operational Semantics . It appeared to be surprisingly diOEcult to apply the method to the modal case, because the type system we chose uses context stacks. In particular, we had to extend the notion of typed substitution, which is central to the method, in a non trivial way. As a ....

....there is a P such that M , P and N , P . 7 Conclusion We have presented in this paper the proofs of Strong Normalization, Subject Reduction, and Church Rosser theorems for a modal calculus S4 [PW95] The proof followed the Typed Operational Semantics method introduced by Healfdene Goguen [Gog94, Gog95] for the simply typed calculus. We have succeeded in adapting his method although our typing rules are not syntaxdriven and we had to deal with context stacks instead of simple contexts. In the course of the proof, we have extracted an interesting notion of typed substitution for our modal ....

Healfdene Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186200. SpringerVerlag, 1995.

....in Informatics t[z : r[x : s] S 2 SN r; s 2 SN (b) lxr) s;z:t) S 2 SN It is shown in [5] that SN exactly captures the strongly normalizing terms of LJ. 1 This will be heavily used throughout this article, and it is motivated by a similar characterization for usual l calculus in [4, 11]. The above mentioned embedding of LJ into l calculus justifies another rule: r(s;z:t) k t if z = 2FV(t) Let us extend appropriately. It is shown in [5] that SN also characterizes the strongly normalizing terms w. r. t. this extended reduction relation. In the following we assume that ....

GOGUEN, H. Typed operational semantics. In Proceedings of TLCA '95, Edinburgh (1995), M. Dezani-Ciancaglini and G. Plotkin, Eds., vol. 902 of Lecture Notes in Computer Science, Springer Verlag, pp. 186--200.

....and likewise for an extension of the system of generalized applications by a rule of immediate simpli cation . By introducing an in nitely branching inductive rule the method even extends to G odel s T. Introduction Normalization proofs for the simply typed calculus enjoy continuous interest [Gog95, vRS95, vRSSX99] in the literature although the main results of weak and strong normalization have been established quite early by Turing (around 1941, published in [Gan80] and Sanchis [San67] This paper employs a proof method that allows to show strong normalization for all typed terms without recourse to ....

....instance of the following proposition, the generality of which will pay o in section 5. Proposition. Let be a binary relation on the set WF . with 8r 8r 0 8r 00 :r . r 0 r 00 ) 9r 000 :r r 000 . r 00 (commutation) Then WF WF . 19 Goguen s typed operational semantics [Gog95], which inspired our work, can be understood as a combination of SN; NF and the normal form function # into one inductive de nition. 20 This argument is crucial to the proof of strong normalization and to our knowledge it is an unavoidable part of any strong normalization proof amenable to a ....

Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer Verlag, 1995.

....computability candidate style a la Tait and Girard this proof can be formalized in primitive recursive arithmetic. By introducing an infinitely branching inductive rule the method extends to Godel s T. Introduction Normalization proofs for the simply typed calculus enjoy continuous interest [Gog95, vRS95, vRSSX] in the literature although the main results of weak and strong normalization have been established quite early by Turing (around 1941, published in [Gan80] and Sanchis [San67] This paper employs a proof method that allows to show strong normalization for all typed terms without recourse to ....

.... that underlies the definition of WN actually is the standard reduction strategy guaranteed to exist by the standardization theorem (see, e.g. Dav95] for a short exposition or [JM98] for remarks on the relationship between WN, NF and standardization) 19 Goguen s typed operational semantics [Gog95], which inspired our work, can be understood as a combination of SN; NF and the normal form function # into one inductive definition. 20 This argument is crucial to the proof of strong normalization and to our knowledge it is an unavoidable part of any strong normalization proof amenable to a ....

Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186--200. Springer Verlag, 1995.

.... , rules for the traditional presentation of F , and rules for the typed operational semantics. Typed Operational Semantics Our proof of anti symmetry of higher order subtyping relies on our understanding of subtyping built up using typed operational semantics. Typed operational semantics [22] gives an alternative induction principle for type theories, by presenting type theory operationally rather than declaratively. The typed operational semantics for F has judgements for reduction to weak head and normal form for types, and for subtyping comparison between types in weak head ....

H. Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer{Verlag, Apr. 1995.

....a proof. In particular, Kripke models might only need to vary with respect to the metatheoretic context, avoiding the complex Kripke interpretation of functional types. This would lead to a proof that is simpler in some aspects than proofs of strong normalization for traditional lambda calculi [10, 11], especially when considered for systems of dependent types [4] Although the form of our judgements and rules is intuitively similar to the sequent calculus, the actual rules are different, instead resembling the rules for the combinators S and K. A calculus following the sequent calculus more ....

H. Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186--200. Springer--Verlag, 1995.

....two steps of the model construction and the typed operational semantics in more detail, and mention which metatheoretic results follow from each step, with particular attention to the treatment of the subtyping judgement. We refer the reader to the original papers on typed operational semantics [24, 25, 26] for a more complete description of this technique. 1.3 The Typed Operational Semantics The intermediate system in our proof, the typed operational semantics, offers an alternative induction principle to prove syntactic properties of type theories. We can use this system 1 INTRODUCTION 5 to ....

H. Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186--200. Springer--Verlag, 1995.

....can be extended successfully to type theories with subtyping. We give here a brief introduction to typed operational semantics, including the aspects of particular interest in the development of the metatheory of subtyping. We refer the reader to the original papers on typed operational semantics [28, 29, 30] for a complete description of this technique. Typed operational semantics gives a clarification of proofs of strong normalization. The traditional proof of strong normalization for type theories builds a model where types are interpreted as sets of strongly normalizing terms. In this proof, ....

H. Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186--200. Springer--Verlag, Apr. 1995.

.... that it can be considerably simplified; at least the fact that substitution in SKIn and SKInT is essentially first order substitution (recall that S 0 ( x]M; N) M [x N ] should simplify the models for proofs of strong normalization, compared to traditional calculi (Girard et al. 1989; Goguen, 1995). The form of our judgments and rules is intuitively similar to the sequent calculus, but the actual rules are different, instead resembling the rules for the combinators S and K. Following the sequent calculus more closely is a natural continuation of this work. This also leads to the study of ....

Goguen, H. (1995). Typed operational semantics. In Proceedings of the 2nd International Conference on Typed Lambda-Calculi and Applications (TLCA'95), pages 186--200. SpringerVerlag LNCS 902.

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Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, TLCA'95, volume 902 of LNCS, pages 186--200, Berlin, 1995. Springer-Verlag.

No context found.

Healfdene Goguen. Typed operational semantics. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer-Verlag, 1995.

No context found.

H. Goguen. Typed operational semantics. In M. Dezani-Ciancaglini and G. Plotkin, eds., Proc. of TLCA '95 , vol. 902 of LNCS , pp. 186-200. 1995.

No context found.

Healfdene Goguen. Typed operational semantics. In Mariangiola Dezani-Ciancaglini and Gordon Plotkin, editors, TLCA'95, volume 902 of LNCS, pages 186--200, Berlin, 1995. Springer-Verlag.

No context found.

Healfdene Goguen. Typed operational semantics. In M. Deziani-Ciancaglini and G. D. Plotkin, editors, Typed Lambda Calculi and Applications (TLCA 1995), Proceedings, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer, 1995.

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