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Abstract: First we give a grammatical (or equational) description of the set fM normal form j 0 ` M : Ag for a given basis 0 and a given type A in the simple type system, and give some applications of the description. Then we extend the idea to systems in -cube and more generally to normalizing pure type systems. The attempt resulted in derived (or `macro') rules the totality of which is complete for normal derivations in each of the systems. The derived rules reflect the syntactic structure of legal... (Update)
Context of citations to this paper: More
...a measure on the structure of a term in normal form. Finally, Ben Yelles de ned in [2] a Search Algorithm (others are in [6] 7] and [5]) that given a type and any integer d 0 can be used to compute all (a nite number) long normal inhabitants of a type with depth...
...chapter we review some basic notion and theorems on Natural Deduction system and an typed calculus. Most of them are found in [4, 5, 6, 10, 14, 15]. We include them in this chapter so that the thesis is self contained. 2.1 Natural deduction system For the simplicity of the...
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BibTeX entry: (Update)
M. Takahashi, Y. Akama, and S. Hirokawa. Normal proofs and their grammar. In M. Hagiya and J. Mitchell, editors, Theoretical Aspects of Computer Software (TACS'94), volume 789 of LNCS, pages 465-493. Springer Verlag, 1994. http://citeseer.ist.psu.edu/article/takahashi94normal.html More
@incollection{ takahashi96normal,
author = "Masako Takahashi and Yohji Akama and Sachio Hirokawa",
title = "Normal Proofs and Their Grammar",
booktitle = "Proceedings 2nd Int.\ Symp.\ on Theoretical Aspects of Computer Software, {TACS}'94, Sendai, Japan, 19--22 Apr 1994",
volume = "789",
publisher = "Springer-Verlag",
address = "Berlin",
editor = "M. Hagiya and J. C. Mitchell",
pages = "465--493",
year = "1996",
url = "citeseer.ist.psu.edu/article/takahashi94normal.html" }
Citations (may not include all citations):1911 Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
382 Lambda calculi with types - Barendregt - 1992
41 Information and Computation (context) - Jutting, pure et al. - 1993
25 Modular proof of strong normalisation for the calculus of co.. (context) - Geuvers, Nederhof - 1991
14 Almqvist and Wiksell (context) - Prawitz - 1965
4 Word operation definable in the typed -calculus (context) - Zaionc - 1987
4 Annals of Pure and Applied Logic (context) - Zaionc, free - 1991
3 Type-assignment in the Lambda-calculus (context) - Ben-Yelles - 1979
3 Embedding first order predicate logic in fragments of intuit.. (context) - Lob - 1976
2 Conservativity between logics and typed calculi (context) - Geuvers - 1993
2 The Simple Theory of Type Assignment (context) - Hindley
2 Number of proofs and tree automaton (context) - Akama - 1991
2 The number of proofs for implicational formulas (context) - Hirokawa - 1992
2 Personal communication (context) - Berardi - 1993
1 Personal communication (context) - Geuvers - 1994
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