Abstract
We prove a general strong normalization theorem for higher type rewrite systems based on Tait’s strong computability predicates and a strictly continuous domain-theoretic semantics. The theorem applies to extensions of Gödel’s system T but also to various forms of bar recursion for which strong normalization was hitherto unknown.
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References
Barendregt, H.: Lambda calculi with types. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 2, pp. 117–309. Clarendon Press, Oxford (1992)
Berardi, S., Bezem, M., Coquand, T.: On the computational content of the axiom of choice. Journal of Symbolic Logic 63(2), 600–622 (1998)
Berger, U.: A computational interpretation of open induction. In: Titsworth, F. (ed.) Proceedings of the Ninetenth Annual IEEE Symposium on Logic in Computer Science, pp. 326–334. IEEE Computer Society, Los Alamitos (2004)
Berger, U., Oliva, P.: Modified bar recursion and classical dependent choice. In: Logic Colloquium 2001. Springer, Heidelberg (2001) (to appear)
Bezem, M.: Strong normalization of barrecursive terms without using infinite terms. Archive for Mathematical Logic 25, 175–181 (1985)
Blanqui, F., Jouannaud, J.-P., Okada, M.: The calculus of algebraic constructions. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 301–316. Springer, Heidelberg (1999)
Coquand, T.: Une théorie des constructions. PhD thesis, Université Paris VII (1985)
Geuvers, H., Nederhof, M.J.: A modular proof of strong normalization for the calculus of constructions. Journal of Functional Programming 1(2), 155–189 (1991)
Girard, J.-Y.: Une extension de l’interprétation de Gödel à l’analyse, et son application à l’élimination des coupures dans l’analyse et la théorie des types. In: Fenstad, J.E. (ed.) Proceedings of the Second Scandinavian Logic Symposium, North–Holland, Amsterdam, pp. 63–92 (1971)
Luckhardt, H.: Extensional Gödel Functional Interpretation – A Consistency Proof of Classical Analysis. Lecture Notes in Mathematics, vol. 306. Springer, Heidelberg (1973)
Matthes, R.: Monotone inductive and coinductive constructors of rank 2. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 600–615. Springer, Heidelberg (2001)
Plotkin, G.D.: LCF considered as a programming language. Theoretical Computer Science 5, 223–255 (1977)
Spector, C.: Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles in current intuitionistic mathematics. In: Dekker, F.D.E. (ed.) Recursive Function Theory: Proc. Symposia in Pure Mathematics, vol. 5, pp. 1–27. American Mathematical Society, Providence (1962)
Tait, W.W.: Normal form theorem for barrecursive functions of finite type. In: Fenstad, J.E. (ed.) Proceedings of the Second Scandinavian Logic Symposium, North–Holland, Amsterdam, pp. 353–367 (1971)
Troelstra, A.S.: Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Lecture Notes in Mathematics, vol. 344. Springer, Heidelberg (1973)
van de Pol, J., Schwichtenberg, H.: Strict functionals for termination proofs. In: Dezani-Ciancaglini, M., Plotkin, G. (eds.) TLCA 1995. LNCS, vol. 902, pp. 350–364. Springer, Heidelberg (1995)
Vogel, H.: Ein starker Normalisationssatz für die barrekursiven Funktionale. Archive for Mathematical Logic 18, 81–84 (1985)
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Berger, U. (2005). Continuous Semantics for Strong Normalization. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_4
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DOI: https://doi.org/10.1007/11494645_4
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