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References
H. P. Barendregt, The lambda calculus (North-Holland, Amsterdam, 1981).
Th. Coquand and G. Huet, Calculus of constructions, Information and Computation 76 (1988), 95–120.
J-Y. Girard, P. Taylor and Y. Lafont, Proofs and types (Cambridge University Press, Cambridge, 1989).
W. A. Howard and G. Kreisel, Transfinite induction and bar induction of types zero and one, and the role of continuity in intuitionistic analysis, J. Symbolic Logic 31 (1966), 325–358.
J. Lambek and P. J. Scott, Introduction to higher order categorical logic (Cambridge University Press, Cambridge, 1984).
Z. Luo, An extended calculus of constructions (Department of Computer Science, University of Edinburgh, 1990).
G. Takeuti and M. Yasugi, The ordinals of the systems of second order arithmetic with the provably Δ 1 2-comprehension axiom and with the Δ 1 2-comprehension axiom respectively, Japanese J. Math. 41 (1973), 1–67.
M. Yasugi, Construction principle and transfinite induction up to ε 0, J. Austral. Math. Soc. 32 (1982), 24–47.
M. Yasugi, Hyper-principle and the functional structure of ordinal diagrams, Comment. Math. Univ. St. Pauli 34 (1985), 227–263 (the opening part); 35 (1986), 1–37 (the concluding part).
M. Yasugi and S. Hayashi, Interpretations of transfinite recursion and parametric abstraction in types, Words, Languages and Combinatorics IIedited by M. Ito and H. Jurgensen (World Scientific Publ., Singapore), to appear.
J. I. Zucker, Iterated inductive definitions, trees and ordinals, Metamathematical investigations of intuitionistic arithmetic and analysis, ed. by A. S. Troelstra, Lecture Notes in Math. 344 (Springer-Verlag, Berlin 1973), 392–453.
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Yasugi, M., Hayashi, S. (1994). A functional system with transfinitely defined types. In: Jones, N.D., Hagiya, M., Sato, M. (eds) Logic, Language and Computation. Lecture Notes in Computer Science, vol 792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032393
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DOI: https://doi.org/10.1007/BFb0032393
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