H. Xi. On weak and strong normalisations. Manuscript announced on the types mailing list, February, 1996. 45  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... too numerous to be listed exhaustively here, include compilation, transformation, and analysis of typed languages [1, 13, 36, 64, 76, 77, 82] embedding of classical logics in intuitionistic logics [44, 59] techniques to infer strong normalization from weak normalization in typed calculi [85, 91], and the construction of looping combinators in inconsistent logical pure type systems [16] The range of these applications have been confined thus far by the fact that CPS translations are known only for non dependent type systems. Indeed, the most general class of systems with known CPS ....

....de Groote [26] and Kfoury and Wells [53] have invented techniques to infer strong normalization from weak normalization. However, these techniques all infer strong normalization of one notion of reduction from weak normalization of a more complicated notion of reduction. S rensen [85] and Xi [91] recently developed techniques which infer strong normalization of some notion of reduction in a typed calculus from weak normalization of the same notion of reduction. These techniques provide some hope for a positive answer to a conjecture, presented by Barendregt at Typed Lambda Calculus and ....

H. Xi. On weak and strong normalisations. Manuscript announced on the types mailing list, February, 1996. 4-31

....typed calculus and in certain systems with subtypes and recursive types. For a domain free [5] version of higher order typed calculus he also shows that strong normalization of all legal objects follows from weak normalization of all legal objects, but states nothing about constructors. Xi [23] independently uses the same technique to reduce strong normalization of simply and second order typed calculus to weak normalization of the same systems extended with certain pairing operators and type constants. Each of the systems mentioned above are known to be strongly normalizing. Thus, for ....

....puts all the pieces together. 5.1. Preservation of infinite reductions In this subsection we show that, for every M 2 Term s Gamma , M ] s Gamma 2 SN fi ) M 2 SN fi when S is generalized non dependent, weakly normalizing and clean, and s is negatable. The proof technique, due to Xi [23], uses a variant of Plotkin s [20] colon translation. Other proofs are discussed by Srensen [21] 5.1. Definition. Let S be generalized non dependent, weakly normalizing, and clean, and s 2 S be negatable. For K 2 E and M 2 Term s Gamma , define M : s Gamma K 2 E and M ; s Gamma 2 E as ....

H. Xi. On weak and strong normalisations. Manuscript announced on the types mailing list, February, 1996. 45

.... too numerous to be listed exhaustively here, include compilation, transformation, and analysis of typed languages [1, 5, 9, 15, 16, 17, 19] embedding of classical logics in intuitionistic logics [11, 14] techniques to infer strong normalization from weak normalization in pure type systems [20, 22], and the construction of looping combinators in inconsistent logical pure type systems [6] The range of these applications have been confined thus far by the fact that CPS translations are known only for non dependent type systems. Indeed, the most general class of systems with known CPS ....

H. Xi. On weak and strong normalisations. Manuscript announced on the types mailing list, February, 1996.

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