Handbook of logic in computer science (vol. 2)
Strong normalization from weak normalization in typed &lgr;-calculi
Information and Computation
Perpetual reductions in &lgr;-calculus
Information and Computation
The Conservation Theorem revisited
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Perpetuality and Strong Normalization in Orthogonal Term Rewriting Systems
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
"Delayability" in Proofs of Strong Normalizability in the Typed Lambda Calculus
CAAP '85 Proceedings of the International Joint Conference on Theory and Practice of Software Development (TAPSOFT), Volume 1: Colloquium on Trees in Algebra and Programming: Mathematical Foundations of Software Development
Weak and Strong Beta Normalisations in Typed Lambda-Calculi
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Addendum to ``New Notions of Reduction and Non-Semantic Proofs of Beta Strong Normalization in Typed Lambda Calculi''''
Journal of Functional Programming
Strong normalization proofs by CPS-translations
Information Processing Letters
Hi-index | 0.00 |
This paper offers a systematic account of techniques to infer strong normalization from weak normalization that make use of syntactic translations from λ-terms to λI-terms. We present variants of such techniques due to Klop, Sørensen, Xi, Gandy, and Loader.We show that all the translations, in some cases via adjustments, are special cases of a generic scheme of translations, known as permutative inner interpretations. Having established this, which is easy, the fact that all the translations can be used to reduce strong normalization to weak normalization can be obtained from a single, general result concerning permutative inner interpretations.Furthermore, we show that each of the translations can be obtained as the composition of Klop's well-known ι-translation and some other translation of independent interest. For instance, in the case of Xi's translation, this other translation is a thunkification translation.Finally we compare the above techniques in some detail to the intimately related techniques by de Vrijer and Girard.A main contribution of the paper is to compare the techniques of Gandy, Klop, and Girard in detail. For instance, we prove the main property of Gandy's translation without reference to functionals using instead ideas from Klop's translation.